From 6e5d388a7b4b54b41fb1127d69eb35e7d7ac89b5 Mon Sep 17 00:00:00 2001 From: Giacomo Fiorin Date: Tue, 28 Nov 2023 14:40:15 -0500 Subject: [PATCH] Update GROMACS 2024 doc --- gromacs-2024/colvars-refman-gromacs.css | 45 +- gromacs-2024/colvars-refman-gromacs.html | 4062 +++++++++++----------- gromacs-2024/colvars-refman-gromacs.pdf | Bin 1590068 -> 1595498 bytes 3 files changed, 2090 insertions(+), 2017 deletions(-) diff --git a/gromacs-2024/colvars-refman-gromacs.css b/gromacs-2024/colvars-refman-gromacs.css index 4b9adaa0d..379ce3992 100644 --- a/gromacs-2024/colvars-refman-gromacs.css +++ b/gromacs-2024/colvars-refman-gromacs.css @@ -220,21 +220,22 @@ span#colorbox1{background-color:rgb(214,214,214);} #mdframed-2{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox2{background-color:#F2CCF2;} #mdframed-3{border:2.0pt solid #FF991A; background-color: #FFF5E5; color:#000000;} -#mdframed-4{border:2.0pt solid #FF991A; background-color: #FFF5E5; color:#000000;} span#colorbox3{background-color:#F2CCF2;} span#colorbox4{background-color:#F2CCF2;} span#colorbox5{background-color:#F2CCF2;} +#mdframed-4{border:2.0pt solid #FF991A; background-color: #FFF5E5; color:#000000;} +#mdframed-5{border:2.0pt solid #FF991A; background-color: #FFF5E5; color:#000000;} span#colorbox6{background-color:#F2CCF2;} -#mdframed-5{border:2.0pt solid #0D3300; background-color: #F2FFCC; color:#000000;} -#mdframed-6{border:2.0pt solid #FF991A; background-color: #FFF5E5; color:#000000;} -#mdframed-7{border:2.0pt solid #0D3300; background-color: #F2FFCC; color:#000000;} -#mdframed-8{border:2.0pt solid #0D3300; background-color: #F2FFCC; color:#000000;} -#mdframed-9{border:2.0pt solid #FF991A; background-color: #FFF5E5; color:#000000;} -#mdframed-10{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox7{background-color:#F2CCF2;} span#colorbox8{background-color:#F2CCF2;} span#colorbox9{background-color:#F2CCF2;} span#colorbox10{background-color:#F2CCF2;} +#mdframed-6{border:2.0pt solid #0D3300; background-color: #F2FFCC; color:#000000;} +#mdframed-7{border:2.0pt solid #FF991A; background-color: #FFF5E5; color:#000000;} +#mdframed-8{border:2.0pt solid #0D3300; background-color: #F2FFCC; color:#000000;} +#mdframed-9{border:2.0pt solid #0D3300; background-color: #F2FFCC; color:#000000;} +#mdframed-10{border:2.0pt solid #FF991A; background-color: #FFF5E5; color:#000000;} +#mdframed-11{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox11{background-color:#F2CCF2;} span#colorbox12{background-color:#F2CCF2;} span#colorbox13{background-color:#F2CCF2;} @@ -353,7 +354,6 @@ span#colorbox125{background-color:#F2CCF2;} span#colorbox126{background-color:#F2CCF2;} span#colorbox127{background-color:#F2CCF2;} span#colorbox128{background-color:#F2CCF2;} -#mdframed-11{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox129{background-color:#F2CCF2;} span#colorbox130{background-color:#F2CCF2;} span#colorbox131{background-color:#F2CCF2;} @@ -362,8 +362,8 @@ span#colorbox132{background-color:#F2CCF2;} span#colorbox133{background-color:#F2CCF2;} span#colorbox134{background-color:#F2CCF2;} span#colorbox135{background-color:#F2CCF2;} -#mdframed-13{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox136{background-color:#F2CCF2;} +#mdframed-13{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox137{background-color:#F2CCF2;} span#colorbox138{background-color:#F2CCF2;} span#colorbox139{background-color:#F2CCF2;} @@ -372,6 +372,7 @@ span#colorbox140{background-color:#F2CCF2;} span#colorbox141{background-color:#F2CCF2;} span#colorbox142{background-color:#F2CCF2;} span#colorbox143{background-color:#F2CCF2;} +#mdframed-15{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox144{background-color:#F2CCF2;} span#colorbox145{background-color:#F2CCF2;} span#colorbox146{background-color:#F2CCF2;} @@ -381,11 +382,11 @@ span#colorbox149{background-color:#F2CCF2;} span#colorbox150{background-color:#F2CCF2;} span#colorbox151{background-color:#F2CCF2;} span#colorbox152{background-color:#F2CCF2;} -#mdframed-15{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox153{background-color:#F2CCF2;} span#colorbox154{background-color:#F2CCF2;} span#colorbox155{background-color:#F2CCF2;} span#colorbox156{background-color:#F2CCF2;} +#mdframed-16{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox157{background-color:#F2CCF2;} span#colorbox158{background-color:#F2CCF2;} span#colorbox159{background-color:#F2CCF2;} @@ -415,11 +416,11 @@ span#colorbox182{background-color:#F2CCF2;} span#colorbox183{background-color:#F2CCF2;} span#colorbox184{background-color:#F2CCF2;} span#colorbox185{background-color:#F2CCF2;} -#mdframed-16{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox186{background-color:#F2CCF2;} span#colorbox187{background-color:#F2CCF2;} span#colorbox188{background-color:#F2CCF2;} span#colorbox189{background-color:#F2CCF2;} +#mdframed-17{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox190{background-color:#F2CCF2;} span#colorbox191{background-color:#F2CCF2;} span#colorbox192{background-color:#F2CCF2;} @@ -428,11 +429,11 @@ span#colorbox194{background-color:#F2CCF2;} span#colorbox195{background-color:#F2CCF2;} span#colorbox196{background-color:#F2CCF2;} span#colorbox197{background-color:#F2CCF2;} -#mdframed-17{border:2.0pt solid #800080; 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background-color: #FFF2FF; color:#000000;} span#colorbox311{background-color:#F2CCF2;} span#colorbox312{background-color:#F2CCF2;} span#colorbox313{background-color:#F2CCF2;} span#colorbox314{background-color:#F2CCF2;} +#mdframed-25{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} +#mdframed-26{border:2.0pt solid #800080; background-color: #FFF2FF; color:#000000;} span#colorbox315{background-color:#F2CCF2;} span#colorbox316{background-color:#F2CCF2;} span#colorbox317{background-color:#F2CCF2;} @@ -573,5 +574,9 @@ span#colorbox330{background-color:#F2CCF2;} span#colorbox331{background-color:#F2CCF2;} span#colorbox332{background-color:#F2CCF2;} span#colorbox333{background-color:#F2CCF2;} +span#colorbox334{background-color:#F2CCF2;} +span#colorbox335{background-color:#F2CCF2;} +span#colorbox336{background-color:#F2CCF2;} +span#colorbox337{background-color:#F2CCF2;} /* end css.sty */ diff --git a/gromacs-2024/colvars-refman-gromacs.html b/gromacs-2024/colvars-refman-gromacs.html index 4f0170aca..ab9adf9ad 100644 --- a/gromacs-2024/colvars-refman-gromacs.html +++ b/gromacs-2024/colvars-refman-gromacs.html @@ -12,33 +12,33 @@

-


-

COLLECTIVE VARIABLES MODULE
-

Reference manual for Gromacs
-


Code version: 2023-10-03
-

Updated versions of this manual: [GROMACS] [LAMMPS] [NAMD] [VMD]

-

Colvars logo
Alejandro Bernardin, Haochuan Chen, Jeffrey R. Comer, Giacomo Fiorin, Haohao Fu, Jérôme +


+

COLLECTIVE VARIABLES MODULE
+

Reference manual for GROMACS
+


Code version: 2023-11-28
+

Updated versions of this manual: [GROMACS] [LAMMPS] [NAMD] [Tinker-HP] [VMD]

+

Colvars logo
Alejandro Bernardin, Haochuan Chen, Jeffrey R. Comer, Giacomo Fiorin, Haohao Fu, Jérôme Hénin, Axel Kohlmeyer, Fabrizio Marinelli, Hubert Santuz, Joshua V. Vermaas, Andrew D. White -

(PDF version) +

(PDF version) -

+

-

+

Contents

 1 Overview
 2 Writing a Colvars configuration: a crash course -
 3 Enabling and controlling the Colvars module in Gromacs +
 3 Enabling and controlling the Colvars module in GROMACS
  3.1 Units in the Colvars module -
  3.2 Running Colvars in Gromacs +
  3.2 Running Colvars in GROMACS
  3.3 Configuration syntax used by the Colvars module
  3.4 Global keywords
  3.5 Input state file -
   3.5.1 Contents of the state file. -
   3.5.2 Restarting after a change in Colvars configuration. +
   3.5.1 Restarting in GROMACS. +
   3.5.2 Changing configuration upon restarting.
  3.6 Output files
  3.7 File formats
   3.7.1 Configuration and state files. @@ -164,7 +164,7 @@

Contents

(Go to Contents)

1 Overview

-

+

In molecular dynamics simulations, it is often useful to reduce the large number of degrees of freedom of a physical system into few parameters whose statistical distributions can be analyzed individually, or used to define biasing potentials to alter the dynamics of the system in a controlled manner. These have @@ -212,7 +212,7 @@

1 (Go to Contents)

2 Writing a Colvars configuration: a crash course

-

+

The Colvars configuration is a plain text file or string that defines collective variables, biases, and general parameters of the Colvars module. It is passed to the module using back-end-specific commands documented in section 3. @@ -225,128 +225,143 @@

2 6.5).

-
colvar {
  name dist
  distance {
    group1 { atomNumbersRange 42-55 }
  }
}

harmonic {
  colvars dist
  forceConstant 20.0
  centers 4.0         # initial distance
  targetCenters 15.0  # final distance
  targetNumSteps 500000
}

+

colvar {
  name dist
  distance {
    group1 { atomNumbersRange 42-55 }
    group2 { indexGroup C-alpha_15-30 }
  }
}

harmonic {
  colvars dist
  forceConstant 20.0
  centers 4.0         # initial distance
  targetCenters 15.0  # final distance
  targetNumSteps 500000
}

-

Reading this input in plain English: the variable here named dist consists in a distance +

Reading this input in plain English: the variable here named dist consists in a distance function between the centers of two groups: the ligand (atoms 42 to 55) and the -α-carbon +α-carbon atoms of residues 15 to 30 in the protein . To the “dist" variable, we apply a harmonic potential of force constant -20 kJ/mol/nm2, -initially centered around a value of 4 nm, which will increase to 15 nm over 500,000 simulation +20 kJ/mol/nm2, +initially centered around a value of 4 nm, which will increase to 15 nm over 500,000 simulation steps. -

The atom selection keywords are detailed in section 5. +

The atom selection keywords are detailed in section 5.

-

Example: using multiple variables and multiple biasing/analysis methods together. +

Example: using multiple variables and multiple biasing/analysis methods together. A more complex example configuration is included below, showing how a variable may be constructed by combining multiple existing functions, and how multiple variables or multiple biases may be used concurrently. The colvar indicated below as -“d" +“d" is defined as the difference between two distances (see 4.2): the first distance -(d1) is +(d1) is taken between the center of mass of atoms 1 and 2 and that of atoms 3 to 5, the second -(d2) +(d2) between atom 7 and the center of mass of atoms 8 to 10 (see 5). The difference -d = d1 −d2 is obtained by multiplying -the two by a coefficient C = +1 -or C = −1, respectively (see -4.14). The colvar called “c" +d = d1 −d2 is obtained by multiplying +the two by a coefficient C = +1 +or C = −1, respectively (see +4.14). The colvar called “c" is the coordination number calculated between atoms 1 to 10 and atoms 11 to 20. A harmonic restraint (see 6.5) is -applied to both d and -c: to allow using the -same force constant K, -both d and -c are scaled by their -respective fluctuation widths wd -and wc. The -values of “c" +applied to both d and +c: to allow using the +same force constant K, +both d and +c are scaled by their +respective fluctuation widths wd +and wc. The +values of “c" are also recorded throughout the simulation as a joint 2-dimensional histogram (see 6.10).

-

colvar {
  # difference of two distances
  name d 
  width 0.2 # estimated fluctuation width 
  distance {
    componentCoeff 1.0
    group1 { atomNumbers 1 2 }
    group2 { atomNumbers 3 4 5 }
  }
  distance {
    componentCoeff -1.0
    group1 { atomNumbers 7 }
    group2 { atomNumbers 8 9 10 }
  }
}

colvar {
  name c
  coordNum {
    cutoff 6.0
    group1 { atomNumbersRange 1-10 }
    group2 { atomNumbersRange 11-20 }
    tolerance 1.0e-6
    pairListFrequency 1000
  }
}

harmonic {
  colvars d c
  centers 3.0 4.0
  forceConstant 5.0
}

histogram {
  colvars c
}

+

colvar {
  # difference of two distances
  name d 
  width 0.2 # estimated fluctuation width 
  distance {
    componentCoeff 1.0
    group1 { atomNumbers 1 2 }
    group2 { atomNumbers 3 4 5 }
  }
  distance {
    componentCoeff -1.0
    group1 { atomNumbers 7 }
    group2 { atomNumbers 8 9 10 }
  }
}

colvar {
  name c
  coordNum {
    cutoff 6.0
    group1 { atomNumbersRange 1-10 }
    group2 { atomNumbersRange 11-20 }
    tolerance 1.0e-6
    pairListFrequency 1000
  }
}

harmonic {
  colvars d c
  centers 3.0 4.0
  forceConstant 5.0
}

histogram {
  colvars c
}

-

+

-

+

(Go to Contents)

-

-

3 Enabling and controlling the Colvars module in Gromacs

-

-

Here, we document the syntax of the commands and parameters used to set up and use -the Colvars module in Gromacs [2]. One of these parameters is the configuration file or the +

+

3 Enabling and controlling the Colvars module in GROMACS

+

+

Here, we document the syntax of the commands and parameters used to set up and use the +Colvars module in GROMACS [2]. One of these parameters is the configuration file or the configuration text for the module itself, whose syntax is described in 3.3 and in the following sections.

-

+

(Go to Contents)

-

+

3.1 Units in the Colvars module

-

-

The “internal units" of the Colvars module are the units in which values are expected to be in the -configuration file, and in which collective variable values, energies, etc. are expressed in the output and +

+

The “internal units" of the Colvars module are the units in which values are expressed in the +configuration file, and in which collective variable values, energies, etc. are expressed in the output and colvars trajectory files. Generally the Colvars module uses internally the same units as its back-end MD engine, with the exception of VMD, where different unit sets are supported to allow for easy setup, visualization and analysis of Colvars simulations performed with any simulation engine. -

Note that angles are expressed in degrees, and derived quantities such as force constants -are based on degrees as well. Some colvar components have default values, expressed in -Ångström in this documentation. They are converted to the current length unit as needed. +

Note that angles are expressed in degrees, and derived quantities such as force constants are based +on degrees as well. Some colvar components have default values, expressed in Ångström +(Å) in this documentation. They are converted to the current length unit, if different from Å. Atomic coordinates read from XYZ files (and PDB files where applicable) are expected to be -expressed in Ångström, no matter what unit system is in use by the back-end (Gromacs) or the +expressed in Ångström, no matter what unit system is in use by the back-end (GROMACS) or the Colvars Module. They are converted internally to the current length unit as needed. Note that force constants in harmonic and harmonicWalls biases (6.5) are rescaled according to the width parameter of colvars, so that they are formally in energy units, although if width is given its default value of 1.0, force constants are effectively expressed in kJ/mol/(colvar -unit)2. -

To avoid errors due to reading configuration files written in a different unit system, it can be specified +unit)2. +

To avoid errors due to reading configuration files written in a different unit system, it can be specified within the input:

+
  • Keyword units⟨Unit + system to be used⟩
    Context: global
    Acceptable values: string
    Description: A string defining the units to be used internally by Colvars. In GROMACS the + only supported value is GROMACS native units: gromacs (nm, kJ/mol).
    • -

    +

    (Go to Contents)

    -

    -

    3.2 Running Colvars in Gromacs

    -

    -

    To enable a Colvars-based calculation, just specify one or more Colvars configuration files with the --colvars command-line parameter to gmx mdrun:

    +

    +

    3.2 Running Colvars in GROMACS

    +

    +

    Note: the GROMACS keywords described here are only supported in GROMACS versions 2024 and +later, where Colvars is supported natively. +

    To enable a simulation with Colvars, one or more options should be added to the typical mdp +parameters, for example:

    -

    gmx mdrun -s test.tpr -deffnm md -colvars variables.colvars.dat biases.colvars.dat

    +

    ; MDP file
    ...
    colvars-active = yes
    colvars-configfile = my_config.colvars
    ...
    (other MDP options)

    -

    Note that the standard extension of all files, including configuration files, have to be changed manually to -end with “.dat" to satisfy Gromacs requirements on filenames. -

    Restarting from a previous simulation is done using the -colvars_restart parameter for the Colvars -state file in conjunction with -cpi parameter for the checkpoint file (e.g. “state.cpt"). Altogether, the two -files hold the required information to restart the simulation.

    +

    When the gmx grommp command is called to create a TPR file, the contents of my_config.colvars +and of all files referenced by it are bundled in the TPR file as well. In any run based on the +same TPR file, gmx mdrun will not access any of the original files used to initialize Colvars. +Therefore to modify the Colvars configuration (e.g. adding or removing a bias), a new TPR file +should be built as well. To do this while also continuing a previous simulations, please see +3.5.2. +

    + +

    Then, create the tpr and launch the simulation using a standard gmx mdrun command line:

    -

    gmx mdrun -s test_restart.tpr -deffnm md -cpi state.cpt \
        -colvars config.colvars.dat -colvars_restart md.colvars.state.dat

    +

    gmx grompp -f system.mdp -p system.top -c init.gro -o test.tpr
    gmx mdrun -s test.tpr

    +
    +

    Continuing from a previous simulation is done using the -cpi parameter for the checkpoint +file (e.g. “state.cpt"). This file holds the required information to restart the Colvars-based +simulation.

    +
    +

    gmx convert-tpr -s test.tpr -nsteps $NUMSTEPS -o test_restart.tpr
    gmx mdrun -s test_restart.tpr -cpi state.cpt

    -

    Only checkpoint files generated by a Colvars-enabled Gromacs version are supported. It is also highly -recommended to read checkpoint files that were written by the same major version of Gromacs (as is the -case with unmodified Gromacs). -

    For the output files, the prefix of Colvars output files will use the -defnnm option of mdrun, -or be the same as the Gromacs log file if the option is not set. Otherwise, the prefix will be -output. -

    Note on PBC wrapping in Gromacs. Internally, Gromacs handles only PBC-wrapped atom -coordinates, which may break the calculation of some variables if their atom groups become split across -PBCs. To prevent this, Colvars unwraps coordinates throughout the simulation, by assuming that each -atom group is intact in the initial coordinates, and canceling any later jumps across the periodic box. This -information is propagated across restarts, and communicated between replicas when Gromacs is used -for replica-exchange simulations. Thus, Colvars is compatible with native replica-exchange in -Gromacs. +

    Other output files (not needed for restarting) will be written using as prefix the value of the -e flag of +gmx mdrun (see ??).

    -

    +

    (Go to Contents)

    -

    +

    3.3 Configuration syntax used by the Colvars module

    -

    -

    Configuration for the Colvars module is passed using an external file. Configuration lines follow the +

    +

    Configuration for the Colvars module is passed using an external file. Configuration lines follow the format “keyword value" or “keyword { ... }", where the keyword and its value must be separated by one or more space characters. The following formatting rules apply:

    @@ -381,192 +396,220 @@

    3.3 LC_ALL=C vi.
    -

    +

    (Go to Contents)

    -

    +

    3.4 Global keywords

    -

    -

    The following keywords are available in the global context of the Colvars configuration, i.e. they are +

    +

    The following keywords are available in the global context of the Colvars configuration, i.e. they are not nested inside other keywords:

    -

    +

    (Go to Contents)

    -

    +

    3.5 Input state file

    -

    -

    Several of the sampling methods implemented in Colvars are time- or history-dependent, i.e. they +

    +

    Several of the sampling methods implemented in Colvars are time- or history-dependent, i.e. they work by accumulating data as a simulation progresses, and use these data to determine their biasing forces. If the simulation engine uses a checkpoint or restart file (as GROMACS and LAMMPS do), any -data needed by Colvars are embedded inti that file. Otherwise, a dedicated state file can be loaded into +data needed by Colvars are embedded into that file. Otherwise, a dedicated state file can be loaded into Colvars directly. -

    When a dedicated Colvars state file is used, it may be in either one of two formats:

    +

    When a dedicated Colvars state file is used, it may be in either one of two formats:

    +

    In either format, the state file contains accumulated data as well as the step number at the end of the +run. The step number read from a state file overrides any value that GROMACS provides, and will be +incremented if the simulation proceeds. This means that the step number used internally by Colvars may +not always match the step number reported by GROMACS. +

    -

    +

    (Go to Contents)

    -

    -
    3.5.1 Contents of the state file.
    -

    In either format, the state file contains accumulated data as well as the step number at the end of -the run. The step number read from a state file overrides any value that Gromacs provides, and will be -incremented if the simulation proceeds. This means that the step number used internally by Colvars may -not always match the step number reported by Gromacs. +

    +
    3.5.1 Restarting in GROMACS.
    +

    Beginning with GROMACS 2024, all information necessary to restart Colvars is included in the +checkpoint “.cpt" file. No special provisions are therefore needed compared to a GROMACS simulation +without Colvars enabled. + +
    -

    +

    (Go to Contents)

    -

    -
    3.5.2 Restarting after a change in Colvars configuration.
    -

    It useful in some cases to modify the configuration of variables or biases between consecutive runs: -a typical example would the addition or removal of a restraint in a simulation. By restarting using -text-format Colvars state files, it is possible to read previous data while allowing for changes in -configuration. For each newly defined variable or bias, no information will be read from the state file if this -is unavailable: such new objects will remain uninitialized until the first compute step. Conversely, any -information that the state file has about variables or biases that are no longer defined is silently ignored. -Because these checks are performed based solely on the names of variables and biases, it is -your responsibility to ensure that these names correspond to consistent definitions between +

    +
    3.5.2 Changing configuration upon restarting.
    +

    +

    In some cases, it is useful to modify the configuration of variables or biases between consecutive runs, +for example by adding or removing a restraint. Some special provisions will happen in that case. When a +state file is loaded, no information is available about any newly added variable or bias, which will +thus remain uninitialized until the first compute step. Conversely, any information that the +state file may contain about variables or biases that are no longer defined will be silently +ignored. Please note that these checks are performed based only on the names of variables and +biases: it is your responsibility to ensure that these names have consistent definitions between runs. -

    When restarting using binary state files, configuration changes are not allowed. The easiest solution -would be to produce a text-format state file specifically for that purpose. +

    The flexibility just described carries some limitations: namely, it is only supported when reading +text-format Colvars state files. Instead, restarting from binary files (such as the GROMACS checkpoint +file) after a configuration change will trigger an error. It is also important to remind that when switching to +a different build of GROMACS, the binary format may change slightly, even if the release version is the +same. +

    To work around the potential issues just described, a text-format Colvars state file should be +loaded. Loading such state file requires an exception to the standard behavior in GROMACS +(i.e. loading a checkpoint file): this exception is supported by the following Colvars configuration: +

    + +

    When a Colvars configuration featuring defaultInputStateFile is processed into a TPR file, and a +GROMACS simulation is started from this TPR file but without providing a checkpoint, Colvars will load its +state from the file named by defaultInputStateFile. Later, when that same simulation is continued by +providing a checkpoint file to GROMACS, Colvars will ignore defaultInputStateFile and will read its +data from the checkpoint file. For the sake of clarity, we recommend that as soon as a suitable +GROMACS checkpoint is available, the defaultInputStateFile is removed removed, and a new TPR file +is produced accordingly.

    -

    +

    (Go to Contents)

    -

    +

    3.6 Output files

    -

    -

    If the output prefix output is defined, the following output files are written during a simulation -run: +

    +

    When the output prefix output is defined (in GROMACS, this is automatically set to the value of the +-eflag of mdrun), the following output files are written during a simulation run:

    -

    Other output files may also be written by specific methods, e.g. the ABF or metadynamics methods -(6.2, 6.4). Like the trajectory file, they are needed only for analyzing, not continuing a simulation. All such -files' names also begin with the prefix output. -

    -

    +

    (Go to Contents)

    -

    +

    3.7 File formats

    -

    -

    This section summarizes the file formats of various files that Colvars may be reading or +

    +

    This section summarizes the file formats of various files that Colvars may be reading or writing.

    -

    +

    (Go to Contents)

    -

    +

    3.7.1 Configuration and state files.
    -

    -

    Configuration files are text files that are generally read as input by Gromacs. Starting from version +

    +

    Configuration files are text files that are generally read as input by GROMACS. Starting from version 2017-02-01, changes in newline encodings are handled transparently, i.e. it is possible to typeset a configuration file in Windows (CR-LF newlines) and then use it with Linux or macOS (LF-only newlines). -

    State files, although not written manually, follow otherwise the same text format as configuration -files. +

    Formatted state files, although not written manually, follow otherwise the same text format as +configuration files. Binary state files can only be read by the Colvars code itself.

    -

    +

    (Go to Contents)

    -

    +

    3.7.2 Index (NDX) files
    -

    -

    For atom selections that cannot be specified only by using internal Colvars keywords, external index +

    +

    For atom selections that cannot be specified only by using internal Colvars keywords, external index files may also be used following the NDX format used in GROMACS:

    -
    -

    [ group_1_name ]
      i1  i2  i3  i4  ...
      ...             ...  iN
    [ group_2_name ]
      ...

    +
    +

    [ group_1_name ]
      i1  i2  i3  i4  ...
      ...             ...  iN
    [ group_2_name ]
      ...

    -

    where i1 through iN are 1-based indices. Each group name may not contain spaces or tabs: otherwise, a +

    where i1 through iN are 1-based indices. Each group name may not contain spaces or tabs: otherwise, a parsing error will be raised. -

    Multiple index files may be provided to Colvars, each using the keyword indexFile. Two index files + + +

    Multiple index files may be provided to Colvars, each using the keyword indexFile. Two index files may contain groups with the same names, however these must also represent identical atom selections, i.e. the same sequence of indices including order. -

    Note that although GROMACS reads index files natively, indexFile uses a Colvars internal function. +

    Note that although GROMACS reads index files natively, indexFile uses a Colvars internal function. Thus, index files loaded into GROMACS and Colvars do not need to coincide, but it is recommended that they do for simplicity. -

    Other than with GROMACS, an index group may also be generated from the VMD command-line +

    Other than with GROMACS, an index group may also be generated from the VMD command-line interface, using the helper function write_index_group provided in the colvartools folder:

    -
    -

    source colvartools/write_index_group.tcl
    set sel [atomselect top "resname XXX and not hydrogen"]
    write_index_group indexfile.ndx $sel "Ligand"

    +
    +

    source colvartools/write_index_group.tcl
    set sel [atomselect top "resname XXX and not hydrogen"]
    write_index_group indexfile.ndx $sel "Ligand"

    -

    +

    (Go to Contents)

    -

    +

    3.7.3 XYZ coordinate files
    -

    XYZ coordinate files are text files with the extension “.xyz". They are read by the Colvars module +

    XYZ coordinate files are text files with the extension “.xyz". They are read by the Colvars module using an internal reader, and expect the following format: -

    - - +

    N
    Comment line
    E -1 x1 y1 z1
    E2 x2 y2 z2
    + + - +
    N
    Comment line
    E +1 x1 y1 z1
    E2 x2 y2 z2
    …
    EN xN yN zN
    EN xN yN zN
    -

    where N is the number of atomic -coordinates in the file and Ei is -the chemical element of the i-th -atom. Because Ei +

    where N is the number of atomic +coordinates in the file and Ei is +the chemical element of the i-th +atom. Because Ei is not used in Colvars, any string that does not contain tabs or spaces is acceptable. -

    An XYZ file may contain either one of the following scenarios: +

    Note: all XYZ coordinates are assumed to be expressed in Å units; it is advisable to obtain them from +a PDB file, or using VMD and/or the Colvars Dashboard to avoid inconstencies with GROMACSńm +units. +

    An XYZ file may contain either one of the following scenarios:

    1. The file contains as many coordinates as the atoms that they are being read for: all coordinates will be read from the file following the same order as the atoms appear in the @@ -575,101 +618,105 @@
      3.7.3 The file contains more coordinates than needed, and it is assumed to contain coordinates + + for the entire system: only coordinates that match the numeric indices of the selected atoms are read, in order of increasing number.
    -

    XYZ-file coordinates are read directly by Colvars and stored internally as double-precision floating +

    XYZ-file coordinates are read directly by Colvars and stored internally as double-precision floating point numbers.

    -

    +

    (Go to Contents)

    -

    +

    3.7.4 Grid files: multicolumn text format
    -

    -

    Many simulation methods and analysis tools write files that contain functions of the collective variables +

    +

    Many simulation methods and analysis tools write files that contain functions of the collective variables tabulated on a grid (e.g. potentials of mean force or multidimensional histograms) for the purpose of analyzing results. Such files are produced by ABF (6.2), metadynamics (6.4), multidimensional histograms (6.10), as well as any restraint with optional thermodynamic integration support (6.1). -

    In some cases, these files may also be read as input of a new simulation. Suitable input files for +

    In some cases, these files may also be read as input of a new simulation. Suitable input files for this purpose are typically generated as output files of previous simulations, or directly by the user in the specific case of ensemble-biased metadynamics (6.4.5). This section explains the “multicolumn" format used by these files. For a multidimensional function -f(ξ1, -ξ2, -…) the +f(ξ1, +ξ2, +…) the multicolumn grid format is defined as follows:

    -
    - - - +
    # Ncv
    # min(ξ1) width(ξ1) npoints(ξ1) periodic(ξ1)
    # min(ξ2) width(ξ2) npoints(ξ2) periodic(ξ2)
    # … … … …
    # min(ξNcv) width(ξNcv) npoints(ξNcv) periodic(ξNcv)
    + + + - - + +
    # Ncv
    # min(ξ1) width(ξ1) npoints(ξ1) periodic(ξ1)
    # min(ξ2) width(ξ2) npoints(ξ2) periodic(ξ2)
    # … … … …
    # min(ξNcv) width(ξNcv) npoints(ξNcv) periodic(ξNcv)
    ξ11 ξ21 … ξNcv1 f(ξ11, ξ21, …, ξNcv1)
    ξ11 ξ21 … ξNcv2 f(ξ11, ξ21, …, ξNcv2)
    … … … … …
    ξ11 ξ21 … ξNcv1 f(ξ11, ξ21, …, ξNcv1)
    ξ11 ξ21 … ξNcv2 f(ξ11, ξ21, …, ξNcv2)
    … … … … …
    -

    Lines beginning with the character “#" are the header of the file. -Ncv +

    Lines beginning with the character “#" are the header of the file. +Ncv is the number of collective variables sampled by the grid. For each variable -ξi, -min(ξi) +ξi, +min(ξi) is the lowest value sampled by the grid (i.e. the left-most boundary of the grid along -ξi), -width(ξi) is the width of each -grid step along ξi, -npoints(ξi) is the number -of points and periodic(ξi) +ξi), + + +width(ξi) is the width of each +grid step along ξi, +npoints(ξi) is the number +of points and periodic(ξi) is a flag whose value is 1 or 0 depending on whether the grid is periodic along -ξi. In +ξi. In most situations:

      -
    • min(ξi) - is given by the lowerBoundary keyword of the variable ξi; +
    • min(ξi) + is given by the lowerBoundary keyword of the variable ξi;
      • -
    • width(ξi) +
    • width(ξi) is given by the width keyword;
      • -
    • npoints(ξi) +
    • npoints(ξi) is calculated from the two above numbers and the upperBoundary keyword; - -
      • -
    • periodic(ξi) - is set to 1 if and only if ξi +
    • periodic(ξi) + is set to 1 if and only if ξi is periodic and the grids' boundaries cover its period.
    -

    How the grid's boundaries affect the sequence of points depends on how the contents of the file were +

    How the grid's boundaries affect the sequence of points depends on how the contents of the file were computed. In many cases, such as histograms and PMFs computed by metadynamics (6.4.5), the values -of ξi +of ξi in the first few columns correspond to the midpoints of the corresponding bins, -i.e. ξ11 = min(ξi)+width(ξi)∕2. +i.e. ξ11 = min(ξi)+width(ξi)∕2. However, there is a slightly different format in PMF files computed by ABF (6.2) or other biases that use thermodynamic integration (6.1). In these cases, it is free-energy gradients that are accumulated on an (npoints)-long grid along each variable -ξ: after these +ξ: after these gradients are integrated, the resulting PMF is discretized on a slightly larger grid with (npoints+1) points -along ξ +along ξ (unless the interval is periodic). Therefore, the grid's outer edges extend by -width(ξi)∕2 +width(ξi)∕2 above and below the specified boundaries, so that for instance -min(ξi) in the header appears -to be shifted back by width(ξi)∕2 +min(ξi) in the header appears +to be shifted back by width(ξi)∕2 compared to what would be expected. Please keep this difference in mind when comparing PMFs computed by different methods. -

    After the header, the rest of the file contains values of the tabulated function -f(ξ1, -ξ2, -…ξNcv), one for each line. -The first Ncv columns -contain values of ξ1, -ξ2, -…ξNcv and the last column contains -the value of the function f. +

    After the header, the rest of the file contains values of the tabulated function +f(ξ1, +ξ2, +…ξNcv), one for each line. +The first Ncv columns +contain values of ξ1, +ξ2, + + +…ξNcv and the last column contains +the value of the function f. Points are sorted in ascending order with the fastest-changing values at the right (“C-style" order). Each sweep of the -right-most variable ξNcv +right-most variable ξNcv is terminated by an empty line. For two dimensional grid files, this allows quick visualization by programs such as GNUplot.
    -

    Example 1: multicolumn text file for a one-dimensional histogram with lowerBoundary = 15, +

    Example 1: multicolumn text file for a one-dimensional histogram with lowerBoundary = 15, upperBoundary = 48 and width = 0.1.

    @@ -678,11 +725,9 @@
    3.7.4
    # 1 … …
    47.85 1.65944e-06
    47.95 1.46712e-06
    -

    Example 2: multicolumn text file for a two-dimensional histogram of two dihedral angles (periodic interval -with 6∘ +

    Example 2: multicolumn text file for a two-dimensional histogram of two dihedral angles (periodic interval +with 6∘ bins): - -

    @@ -692,49 +737,49 @@
    3.7.4
    # 2
    # -180.0 6.0 30 1
    # -180.0 6.0 30 1 -171.0 -177.0 2.04702e-05
    … … …
    -

    +

    (Go to Contents)

    -

    +

    3.7.5 Output trajectory files
    -

    -

    The Colvars trajectory file (with a suffix .colvars.traj) is a plain text file (scientific +

    +

    The Colvars trajectory file (with a suffix .colvars.traj) is a plain text file (scientific notation with 14-digit precision) whose columns represent quantities such as colvar values, applied forces, or individual restraints' energies. Under most scenarios, plotting or analyzing this file is straightforward: for example, the following contains a variable -“A" and the energy -of a restraint “rA":

    -
    -

    #       step   A                     E_rA
               0    1.42467449615693e+01  6.30982865292123e+02
             100    1.42282559728026e+01  6.20640585041317e+02
    …

    +“A" and the energy +of a restraint “rA":

    +
    +

    #       step   A                     E_rA
               0    1.42467449615693e+01  6.30982865292123e+02
             100    1.42282559728026e+01  6.20640585041317e+02
    …

    -

    Occasionally, if the Colvars configuration is changed mid-run certain quantities may be +

    Occasionally, if the Colvars configuration is changed mid-run certain quantities may be added or removed, changing the column layout. Labels in comment lines can assist in such cases: for example, consider the trajectory above with the addition of a second variable, -“B", after +“B", after 10,000 steps:

    -
    -

    #       step   A                     E_rA
               0    1.42467449615693e+01  6.30982865292123e+02
             100    1.42282559728026e+01  6.20640585041317e+02
    …
    #       step   A                     B                     E_rA              
           10000    1.38136915830229e+01  9.99574098859265e-01  4.11184644791030e+02
           10100    1.36437184346326e+01  9.99574091957314e-01  3.37726286543895e+02
-

    +
    +

    #       step   A                     E_rA
               0    1.42467449615693e+01  6.30982865292123e+02
             100    1.42282559728026e+01  6.20640585041317e+02
    …
    #       step   A                     B                     E_rA              
           10000    1.38136915830229e+01  9.99574098859265e-01  4.11184644791030e+02
           10100    1.36437184346326e+01  9.99574091957314e-01  3.37726286543895e+02
+

    -

    Analyzing the above file with standard tools is possible, but laborious: a convenience script is provided +

    Analyzing the above file with standard tools is possible, but laborious: a convenience script is provided for this and related purposes. It may be used either as a command-line tool or as a Python module:

    -
    -

    >>> from plot_colvars_traj import Colvars_traj
    >>> traj = Colvars_traj('test.colvars.traj')
    >>> print(traj['A'].steps, traj['A'].values)
    [    0   100  ...  10000 10100] [14.246745 14.228256 ... 13.813692 13.643718]
    >>> print(traj['B'].steps, traj['B'].values)
    [10000 10100] [0.999574  0.9995741]

    +
    +

    >>> from plot_colvars_traj import Colvars_traj
    >>> traj = Colvars_traj('test.colvars.traj')
    >>> print(traj['A'].steps, traj['A'].values)
    [    0   100  ...  10000 10100] [14.246745 14.228256 ... 13.813692 13.643718]
    >>> print(traj['B'].steps, traj['B'].values)
    [10000 10100] [0.999574  0.9995741]

    -

    +

    -

    +

    (Go to Contents)

    -

    +

    4 Defining collective variables

    -

    -

    A collective variable is defined by the keyword colvar followed by its configuration options contained +

    +

    A collective variable is defined by the keyword colvar followed by its configuration options contained within curly braces:

    -
    -

    colvar {
      name xi
       <other options >
      function_name {
         <parameters >
         <atom selection >
      }
    }

    +
    +

    colvar {
      name xi
       <other options >
      function_name {
         <parameters >
         <atom selection >
      }
    }

    -

    There are multiple ways of defining a variable:

    +

    There are multiple ways of defining a variable:

    -

    Choosing a component (function) is the only parameter strictly required to define a collective variable. It is +

    Choosing a component (function) is the only parameter strictly required to define a collective variable. It is also highly recommended to specify a name for the variable:

      -
    •   Keyword name⟨Name - of this colvar⟩
      Context: colvar
      Acceptable values: string
      Default value: “colvar" + numeric id
      Description: The name is an unique case-sensitive string which allows the Colvars module +
    •   Keyword name⟨Name + of this colvar⟩
      Context: colvar
      Acceptable values: string
      Default value: “colvar" + numeric id
      Description: The name is an unique case-sensitive string which allows the Colvars module to identify this colvar unambiguously; it is also used in the trajectory file to label to the columns corresponding to this colvar.
    -

    +

    (Go to Contents)

    -

    +

    4.1 Choosing a function

    -

    -

    In this context, the function that computes a colvar is called a component. A component's choice +

    +

    In this context, the function that computes a colvar is called a component. A component's choice and definition consists of including in the variable's configuration a keyword indicating the type of function (e.g. rmsd), followed by a definition block specifying the atoms involved (see 5) and any additional parameters (cutoffs, “reference" values, …). At least one component must be chosen to define a variable: if none of the keywords listed below is found, an error is raised. -

    The following components implement functions with a scalar value (i.e. a real number): +

    The following components implement functions with a scalar value (i.e. a real number):

    • distance: distance between two groups; @@ -822,7 +867,7 @@

      4.1 inertia: moment of inertia of a group of atoms;

    • inertiaZ: moment of inertia of a group of atoms around a chosen axis;
    -

    Some components do not return scalar, but vector values:

    +

    Some components do not return scalar, but vector values:

    • distanceVec: distance vector between two groups (length: 3); @@ -830,49 +875,49 @@

      4.1 distanceDir: unit vector parallel to distanceVec (length: 3);

      • -
    • cartesian: vector of atomic Cartesian coordinates (length: N +
    • cartesian: vector of atomic Cartesian coordinates (length: N times the number of Cartesian components requested, X, Y or Z);
      • -
    • distancePairs: vector of mutual distances (length: N1 ×N2); +
    • distancePairs: vector of mutual distances (length: N1 ×N2);
    • orientation: best-fit rotation, expressed as a unit quaternion (length: 4).
    -

    The types of components used in a colvar (scalar or not) determine the properties of that colvar, and +

    The types of components used in a colvar (scalar or not) determine the properties of that colvar, and particularly which biasing or analysis methods can be applied. -

    What if “X" is not listed? If a function type is not available on this list, it may be possible to +

    What if “X" is not listed? If a function type is not available on this list, it may be possible to define it as a polynomial superposition of existing ones (see 4.14), a custom function (see 4.15). -

    In the rest of this section, all available component types are listed, along with their physical units and +

    In the rest of this section, all available component types are listed, along with their physical units and their ranges of values, if limited. Such ranges are often used to define automatically default sampling intervals, for example by setting the parameters lowerBoundary and upperBoundary in the parent colvar. -

    For each type of component, the available configurations keywords are listed: when two components +

    For each type of component, the available configurations keywords are listed: when two components share certain keywords, the second component references to the documentation of the first one that uses that keyword. The very few keywords that are available for all types of components are listed in a separate section 4.11.

    -

    +

    (Go to Contents)

    -

    +

    4.2 Distances

    -

    +

    -

    +

    (Go to Contents)

    -

    +

    4.2.1 distance: center-of-mass distance between two groups.
    -

      -

    The distance {...} block defines a distance component between the two atom groups, group1 and +

      +

    The distance {...} block defines a distance component between the two atom groups, group1 and group2. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    •   Keyword group1⟨First - group of atoms⟩
      Context: distance
      Acceptable values: Block group1 {...}
      Description: First group of atoms. +
    •   Keyword group1⟨First + group of atoms⟩
      Context: distance
      Acceptable values: Block group1 {...}
      Description: First group of atoms.
      • -
    •   group2: analogous to group1 +
    •   group2: analogous to group1
      • -
    •   Keyword forceNoPBC⟨Calculate - absolute rather than minimum-image distance?⟩
      Context: distance
      Acceptable values: boolean
      Default value: no
      Description: By default, in calculations with periodic boundary conditions, the distance +
    •   Keyword forceNoPBC⟨Calculate + absolute rather than minimum-image distance?⟩
      Context: distance
      Acceptable values: boolean
      Default value: no
      Description: By default, in calculations with periodic boundary conditions, the distance component returns the distance according to the minimum-image convention. If this parameter is set to yes, PBC will be ignored and the distance between the coordinates as maintained internally will be used. This is only useful in a limited number of special cases, e.g. to describe @@ -880,339 +925,339 @@
      4.2.1   Keyword oneSiteTotalForce⟨Measure - total force on group 1 only?⟩
      Context: angle, dipoleAngle, dihedral
      Acceptable values: boolean
      Default value: no
      Description: If this is set to yes, the total force is measured along a vector field (see +
    •   Keyword oneSiteTotalForce⟨Measure + total force on group 1 only?⟩
      Context: angle, dipoleAngle, dihedral
      Acceptable values: boolean
      Default value: no
      Description: If this is set to yes, the total force is measured along a vector field (see equation (20) in section 6.2) that only involves atoms of group1. This option is only useful for ABF, or custom biases that compute total forces. See section 6.2 for details.
    -

    The value returned is a positive number (in nm), ranging from -0 to the +

    The value returned is a positive number (in nm), ranging from +0 to the largest possible interatomic distance within the chosen boundary conditions (with PBCs, the minimum image convention is used unless the forceNoPBC option is set).

    -

    +

    (Go to Contents)

    -

    +

    4.2.2 distanceZ: projection of a distance vector on an axis.
    -

      -

    The distanceZ {...} block defines a distance projection component, which can be seen as +

      +

    The distanceZ {...} block defines a distance projection component, which can be seen as measuring the distance between two groups projected onto an axis, or the position of a group along such an axis. The axis can be defined using either one reference group and a constant vector, or dynamically based on two reference groups. One of the groups can be set to a dummy atom to allow the use of an absolute Cartesian coordinate. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    •   Keyword main⟨Main - group of atoms⟩
      Context: distanceZ
      Acceptable values: Block main {...}
      Description: Group of atoms whose position r +
    •   Keyword main⟨Main + group of atoms⟩
      Context: distanceZ
      Acceptable values: Block main {...}
      Description: Group of atoms whose position r is measured.
      • -
    •   Keyword ref⟨Reference - group of atoms⟩
      Context: distanceZ
      Acceptable values: Block ref {...}
      Description: Reference group of atoms. The position of its center of mass is noted r1 +
    •   Keyword ref⟨Reference + group of atoms⟩
      Context: distanceZ
      Acceptable values: Block ref {...}
      Description: Reference group of atoms. The position of its center of mass is noted r1 below.
      • -
    •   Keyword ref2⟨Secondary - reference group⟩
      Context: distanceZ
      Acceptable values: Block ref2 {...}
      Default value: none
      Description: Optional group of reference atoms, whose position r2 - can be used to define a dynamic projection axis: e = (∥r2 −r1∥)−1 ×(r2 −r1). - In this case, the origin is rm = 1∕2(r1 +r2), - and the value of the component is e⋅(r−rm). +
    •   Keyword ref2⟨Secondary + reference group⟩
      Context: distanceZ
      Acceptable values: Block ref2 {...}
      Default value: none
      Description: Optional group of reference atoms, whose position r2 + can be used to define a dynamic projection axis: e = (∥r2 −r1∥)−1 ×(r2 −r1). + In this case, the origin is rm = 1∕2(r1 +r2), + and the value of the component is e⋅(r−rm).
      • -
    •   Keyword axis⟨Projection - axis⟩
      Context: distanceZ
      Acceptable values: (x, y, z) triplet
      Default value: (0.0, 0.0, 1.0)
      Description: This vector will be normalized to define a projection axis e - for the distance vector r−r1 - joining the centers of groups ref and main. The value of the component is then e⋅(r−r1). +
    •   Keyword axis⟨Projection + axis⟩
      Context: distanceZ
      Acceptable values: (x, y, z) triplet
      Default value: (0.0, 0.0, 1.0)
      Description: This vector will be normalized to define a projection axis e + for the distance vector r−r1 + joining the centers of groups ref and main. The value of the component is then e⋅(r−r1). The vector should be written as three components separated by commas and enclosed in parentheses.
      • -
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component) +
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component)
      • -
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance +
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance component)
    -

    This component returns a number (in nm) whose range is determined by the chosen boundary conditions. For -instance, if the z +

    This component returns a number (in nm) whose range is determined by the chosen boundary conditions. For +instance, if the z axis is used in a simulation with periodic boundaries, the returned value ranges between -−bz∕2 and -bz∕2, where -bz is the box -length along z +−bz∕2 and +bz∕2, where +bz is the box +length along z (this behavior is disabled if forceNoPBC is set).

    -

    +

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    -

    +

    4.2.3 distanceXY: modulus of the projection of a distance vector on a plane.
    -

      -

    The distanceXY {...} block defines a distance projected on a plane, and accepts the same +

      +

    The distanceXY {...} block defines a distance projected on a plane, and accepts the same keywords as the component distanceZ, i.e. main, ref, either ref2 or axis, and oneSiteTotalForce. It returns the norm of the projection of the distance vector between main and ref onto the plane orthogonal to the axis. The axis is defined using the axis parameter or as the vector joining ref and ref2 (see distanceZ above). -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword main: see definition of main (distanceZ component) +
    • Keyword main: see definition of main (distanceZ component)
      • -
    • Keyword ref: see definition of ref (distanceZ component) +
    • Keyword ref: see definition of ref (distanceZ component)
      • -
    • Keyword ref2: see definition of ref2 (distanceZ component) +
    • Keyword ref2: see definition of ref2 (distanceZ component)
      • -
    • Keyword axis: see definition of axis (distanceZ component) +
    • Keyword axis: see definition of axis (distanceZ component)
      • -
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component) +
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component)
      • -
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance +
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance component)
    -

    +

    (Go to Contents)

    -

    +

    4.2.4 distanceVec: distance vector between two groups.
    -

      -

    The distanceVec {...} block defines a distance vector component, which accepts the same +

      +

    The distanceVec {...} block defines a distance vector component, which accepts the same keywords as the component distance: group1, group2, and forceNoPBC. Its value is the 3-vector joining the centers of mass of group1 and group2. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword group1: see definition of group1 (distance component) +
    • Keyword group1: see definition of group1 (distance component)
      • -
    • group2: analogous to group1 +
    • group2: analogous to group1
      • -
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component) +
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component)
      • -
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance +
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance component)
    -

    +

    (Go to Contents)

    -

    +

    4.2.5 distanceDir: distance unit vector between two groups.
    -

      -

    The distanceDir {...} block defines a distance unit vector component, which accepts the same +

      +

    The distanceDir {...} block defines a distance unit vector component, which accepts the same keywords as the component distance: group1, group2, and forceNoPBC. It returns a 3-dimensional unit -vector d = (dx,dy,dz), -with |d| = 1. -

    List of keywords (see also 4.14 for additional options):

    +vector d = (dx,dy,dz), +with |d| = 1. +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword group1: see definition of group1 (distance component) +
    • Keyword group1: see definition of group1 (distance component)
      • -
    • group2: analogous to group1 +
    • group2: analogous to group1
      • -
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component) +
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component)
      • -
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance +
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance component)
    -

    +

    (Go to Contents)

    -

    +

    4.2.6 distanceInv: mean distance between two groups of atoms.
    -

      -

    The distanceInv {...} block defines a generalized mean distance between +

      +

    The distanceInv {...} block defines a generalized mean distance between two groups of atoms 1 and 2, where each distance is taken to the power -−n:

    +−n:

    - + d1,2[n] = ( 1 N1N2∑i,jdij−n)−1∕n (2)
    -

    where dij is the -distance between atoms i -and j in groups 1 and -2 respectively, and n +

    where dij is the +distance between atoms i +and j in groups 1 and +2 respectively, and n is an even integer. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword group1: see definition of group1 (distance component) +
    • Keyword group1: see definition of group1 (distance component)
      • -
    • group2: analogous to group1 +
    • group2: analogous to group1
      • -
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance +
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance component)
      • -
    • Keyword exponent⟨Exponent - n - in equation 2⟩
      Context: distanceInv
      Acceptable values: positive even integer
      Default value: 6
      Description: Defines the exponent to which the individual distances are elevated before +
    • Keyword exponent⟨Exponent + n + in equation 2⟩
      Context: distanceInv
      Acceptable values: positive even integer
      Default value: 6
      Description: Defines the exponent to which the individual distances are elevated before averaging. The default value of 6 is useful for example to applying restraints based on NOE-measured distances.
    -

    This component returns a number ranging from 0 +

    This component returns a number ranging from 0 to the largest possible distance within the chosen boundary conditions.

    -

    +

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    -

    +

    4.3 Angles

    -

    +

    -

    +

    (Go to Contents)

    -

    +

    4.3.1 angle: angle between three groups.
    -

      -

    The angle {...} block defines an angle, and contains the three blocks group1, group2 +

      +

    The angle {...} block defines an angle, and contains the three blocks group1, group2 and group3, defining the three groups. It returns an angle (in degrees) within the interval -[0 : 180]. -

    List of keywords (see also 4.14 for additional options):

    +[0 : 180]. +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword group1: see definition of group1 (distance component) +
    • Keyword group1: see definition of group1 (distance component)
      • -
    • group2: analogous to group1 +
    • group2: analogous to group1
      • -
    • group3: analogous to group1 +
    • group3: analogous to group1
      • -
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component) +
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component)
      • -
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance +
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance component)
    -

    +

    (Go to Contents)

    -

    +

    4.3.2 dipoleAngle: angle between two groups and dipole of a third group.
    -

      -

    The dipoleAngle {...} block defines an angle, and contains the three blocks group1, group2 and group3, +

      +

    The dipoleAngle {...} block defines an angle, and contains the three blocks group1, group2 and group3, defining the three groups, being group1 the group where dipole is calculated. It returns an angle (in degrees) within -the interval [0 : 180]. -

    List of keywords (see also 4.14 for additional options):

    +the interval [0 : 180]. +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword group1: see definition of group1 (distance component) +
    • Keyword group1: see definition of group1 (distance component)
      • -
    • group2: analogous to group1 +
    • group2: analogous to group1
      • -
    • group3: analogous to group1 +
    • group3: analogous to group1
      • -
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component) +
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component)
      • -
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance +
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance component)
    -

    +

    (Go to Contents)

    -

    +

    4.3.3 dihedral: torsional angle between four groups.
    -

      -

    The dihedral {...} block defines a torsional angle, and contains the blocks group1, group2, +

      +

    The dihedral {...} block defines a torsional angle, and contains the blocks group1, group2, group3 and group4, defining the four groups. It returns an angle (in degrees) within the interval -[−180 : 180]. The +[−180 : 180]. The Colvars module calculates all the distances between two angles taking into account periodicity. For instance, reference values for restraints or range boundaries can be defined by using any real number of choice. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword group1: see definition of group1 (distance component) +
    • Keyword group1: see definition of group1 (distance component)
      • -
    • group2: analogous to group1 +
    • group2: analogous to group1
      • -
    • group3: analogous to group1 +
    • group3: analogous to group1
      • -
    • group4: analogous to group1 +
    • group4: analogous to group1
      • -
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component) +
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component)
      • -
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance +
    • Keyword oneSiteTotalForce: see definition of oneSiteTotalForce (distance component)
    -

    +

    (Go to Contents)

    -

    +

    4.3.4 polarTheta: polar angle in spherical coordinates.
    -

      -

    The polarTheta {...} block defines the polar angle in spherical coordinates, for the center of mass +

      +

    The polarTheta {...} block defines the polar angle in spherical coordinates, for the center of mass of a group of atoms described by the block atoms. It returns an angle (in degrees) within the interval -[0 : 180]. To +[0 : 180]. To obtain spherical coordinates in a frame of reference tied to another group of atoms, use the fittingGroup (5.2) option within the atoms block. An example is provided in file examples/11_polar_angles.in of the Colvars public repository. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    •   Keyword atoms⟨Atom - group⟩
      Context: polarPhi
      Acceptable values: atoms {...} block
      Description: Defines the group of atoms for the COM of which the angle should be calculated. +
    •   Keyword atoms⟨Atom + group⟩
      Context: polarPhi
      Acceptable values: atoms {...} block
      Description: Defines the group of atoms for the COM of which the angle should be calculated.
    -

    +

    (Go to Contents)

    -

    +

    4.3.5 polarPhi: azimuthal angle in spherical coordinates.
    -

      -

    The polarPhi {...} block defines the azimuthal angle in spherical coordinates, for the center of +

      +

    The polarPhi {...} block defines the azimuthal angle in spherical coordinates, for the center of mass of a group of atoms described by the block atoms. It returns an angle (in degrees) within the interval -[−180 : 180]. The +[−180 : 180]. The Colvars module calculates all the distances between two angles taking into account periodicity. For instance, reference values for restraints or range boundaries can be defined by using any real number of choice. To obtain spherical coordinates in a frame of reference tied to another group of atoms, use the fittingGroup (5.2) option within the atoms block. An example is provided in file examples/11_polar_angles.in of the Colvars public repository. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    •   Keyword atoms⟨Atom - group⟩
      Context: polarPhi
      Acceptable values: atoms {...} block
      Description: Defines the group of atoms for the COM of which the angle should be calculated. +
    •   Keyword atoms⟨Atom + group⟩
      Context: polarPhi
      Acceptable values: atoms {...} block
      Description: Defines the group of atoms for the COM of which the angle should be calculated.
    -

    +

    (Go to Contents)

    -

    +

    4.4 Contacts

    -

    +

    -

    +

    (Go to Contents)

    -

    +

    4.4.1 coordNum: coordination number between two groups.
    -

      -

    The coordNum {...} block defines a coordination number (or number of contacts), which calculates the -function (1−(d∕d0)n)∕(1−(d∕d0)m), where -d0 is the “cutoff" -distance, and n -and m are +

      +

    The coordNum {...} block defines a coordination number (or number of contacts), which calculates the +function (1−(d∕d0)n)∕(1−(d∕d0)m), where +d0 is the “cutoff" +distance, and n +and m are exponents that can control its long range behavior and stiffness [3]. This function is summed over all pairs of atoms in group1 and group2:

    - + C(group1,group2) = ∑i∈group1∑j∈group21−(|xi−xj|∕d0)n 1−(|xi−xj|∕d0)m (3)
    -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    •   Keyword group1: see definition of group1 (distance component) +
    •   Keyword group1: see definition of group1 (distance component)
      • -
    •   group2: analogous to group1 +
    •   group2: analogous to group1
      • -
    •   Keyword cutoff⟨“Interaction" - distance (nm)⟩
      Context: coordNum
      Acceptable values: positive decimal
      Default value: 4.0 Å
      Description: This number defines the switching distance to define an interatomic contact: - for d ≪ d0, - the switching function (1−(d∕d0)n)∕(1−(d∕d0)m) - is close to 1, at d = d0 - it has a value of n∕m - (1∕2 - with the default n - and m), - and at d ≫ d0 - it goes to zero approximately like dm−n. - Hence, for a proper behavior, m - must be larger than n. -
      • -
    •   Keyword cutoff3⟨Reference - distance vector (nm)⟩
      Context: coordNum
      Acceptable values: “(x, y, z)" triplet of positive decimals
      Default value: (4.0, 4.0, 4.0) Å
      Description: The three components of this vector define three different cutoffs d0 +
    •   Keyword cutoff⟨“Interaction" + distance (nm)⟩
      Context: coordNum
      Acceptable values: positive decimal
      Default value: 4.0 Å
      Description: This number defines the switching distance to define an interatomic contact: + for d ≪ d0, + the switching function (1−(d∕d0)n)∕(1−(d∕d0)m) + is close to 1, at d = d0 + it has a value of n∕m + (1∕2 + with the default n + and m), + and at d ≫ d0 + it goes to zero approximately like dm−n. + Hence, for a proper behavior, m + must be larger than n. +
      • +
    •   Keyword cutoff3⟨Reference + distance vector (nm)⟩
      Context: coordNum
      Acceptable values: “(x, y, z)" triplet of positive decimals
      Default value: (4.0, 4.0, 4.0) Å
      Description: The three components of this vector define three different cutoffs d0 for each direction. This option is mutually exclusive with cutoff.
      • -
    •   Keyword expNumer⟨Numerator - exponent⟩
      Context: coordNum
      Acceptable values: positive even integer
      Default value: 6
      Description: This number defines the n +
    •   Keyword expNumer⟨Numerator + exponent⟩
      Context: coordNum
      Acceptable values: positive even integer
      Default value: 6
      Description: This number defines the n exponent for the switching function.
      • -
    •   Keyword expDenom⟨Denominator - exponent⟩
      Context: coordNum
      Acceptable values: positive even integer
      Default value: 12
      Description: This number defines the m +
    •   Keyword expDenom⟨Denominator + exponent⟩
      Context: coordNum
      Acceptable values: positive even integer
      Default value: 12
      Description: This number defines the m exponent for the switching function.
      • -
    •   Keyword group2CenterOnly⟨Use +
    •   Keyword group2CenterOnly⟨Use - only group2's center of mass⟩
      Context: coordNum
      Acceptable values: boolean
      Default value: off
      Description: If this option is on, only contacts between each atoms in group1 and the center + only group2's center of mass⟩
      Context: coordNum
      Acceptable values: boolean
      Default value: off
      Description: If this option is on, only contacts between each atoms in group1 and the center of mass of group2 are calculated (by default, the sum extends over all pairs of atoms in group1 and group2). If group2 is a dummyAtom, this option is set to yes by default.
      • -
    •   Keyword tolerance⟨Pairlist - control⟩
      Context: coordNum
      Acceptable values: decimal
      Default value: 0.0
      Description: This controls the pair list feature, dictating the minimum value for each summation +
    •   Keyword tolerance⟨Pairlist + control⟩
      Context: coordNum
      Acceptable values: decimal
      Default value: 0.0
      Description: This controls the pair list feature, dictating the minimum value for each summation element in Eq. 3 such that the pair that contributed the summation element is included in subsequent simulation timesteps until the next pai r list recalculation. For most applications, this value should be small (eg. 0.001) to avoid missing important contributions to the overall @@ -1220,138 +1265,138 @@
      4.4.1 3 is further modified by subtracting the tolerance and then rescaling so that each pair covers the range - [0,1]. + [0,1].
      • -
    •   Keyword pairListFrequency⟨Pairlist - regeneration frequency⟩
      Context: coordNum
      Acceptable values: positive integer
      Default value: 100
      Description: This controls the pairlist feature, dictating how many steps are taken between +
    •   Keyword pairListFrequency⟨Pairlist + regeneration frequency⟩
      Context: coordNum
      Acceptable values: positive integer
      Default value: 100
      Description: This controls the pairlist feature, dictating how many steps are taken between regenerating pair lists if the tolerance is greater than 0.
    -

    This component returns a dimensionless number, which ranges from +

    This component returns a dimensionless number, which ranges from approximately 0 (all interatomic distances are much larger than the cutoff) to -Ngroup1×Ngroup2 (all distances are less -than the cutoff), or Ngroup1 +Ngroup1×Ngroup2 (all distances are less +than the cutoff), or Ngroup1 if group2CenterOnly is used. For performance reasons, at least one of group1 and group2 should be of limited size or group2CenterOnly should be used: the cost of the loop over all pairs grows as -Ngroup1×Ngroup2. Setting -tolerance > 0 +Ngroup1×Ngroup2. Setting +tolerance > 0 ameliorates this to some degree, although every pair is still checked to regenerate the pair list.

    -

    +

    (Go to Contents)

    -

    +

    4.4.2 selfCoordNum: coordination number between atoms within a group.
    -

      -

    The selfCoordNum {...} block defines a coordination number similarly to the component coordNum, +

      +

    The selfCoordNum {...} block defines a coordination number similarly to the component coordNum, but the function is summed over atom pairs within group1:

    - + C(group1) = ∑i∈group1∑j>i 1−(|xi−xj|∕d0)n 1−(|xi−xj|∕d0)m (4)
    -

    The keywords accepted by selfCoordNum are a subset of those accepted by coordNum, namely group1 +

    The keywords accepted by selfCoordNum are a subset of those accepted by coordNum, namely group1 (here defining all of the atoms to be considered), cutoff, expNumer, and expDenom. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword group1: see definition of group1 (coordNum component) +
    • Keyword group1: see definition of group1 (coordNum component)
      • -
    • Keyword cutoff: see definition of cutoff (coordNum component) +
    • Keyword cutoff: see definition of cutoff (coordNum component)
      • -
    • Keyword cutoff3: see definition of cutoff3 (coordNum component) +
    • Keyword cutoff3: see definition of cutoff3 (coordNum component)
      • -
    • Keyword expNumer: see definition of expNumer (coordNum component) +
    • Keyword expNumer: see definition of expNumer (coordNum component)
      • -
    • Keyword expDenom: see definition of expDenom (coordNum component) +
    • Keyword expDenom: see definition of expDenom (coordNum component)
      • -
    • Keyword tolerance: see definition of tolerance (coordNum component) +
    • Keyword tolerance: see definition of tolerance (coordNum component)
      • -
    • Keyword pairListFrequency: see definition of pairListFrequency (coordNum +
    • Keyword pairListFrequency: see definition of pairListFrequency (coordNum component)
    -

    This component returns a dimensionless number, which ranges from +

    This component returns a dimensionless number, which ranges from approximately 0 (all interatomic distances much larger than the cutoff) to -Ngroup1×(Ngroup1−1)∕2 (all distances +Ngroup1×(Ngroup1−1)∕2 (all distances within the cutoff). For performance reasons, group1 should be of limited size, because the cost of the loop over all -pairs grows as Ngroup12. +pairs grows as Ngroup12.

    -

    +

    (Go to Contents)

    -

    +

    4.4.3 hBond: hydrogen bond between two atoms.
    -

      -

    The hBond {...} block defines a hydrogen bond, implemented as a coordination number (eq. 3) +

      +

    The hBond {...} block defines a hydrogen bond, implemented as a coordination number (eq. 3) between the donor and the acceptor atoms. Therefore, it accepts the same options cutoff (with a different default value of 3.3 Å), expNumer (with a default value of 6) and expDenom (with a default value of 8). Unlike coordNum, it requires two atom numbers, acceptor and donor, to be defined. It returns a dimensionless number, with values between 0 (acceptor and donor far outside the cutoff distance) and 1 (acceptor and donor much closer than the cutoff). -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword acceptor⟨Number - of the acceptor atom⟩
      Context: hBond
      Acceptable values: positive integer
      Description: Number that uses the same convention as atomNumbers. +
    • Keyword acceptor⟨Number + of the acceptor atom⟩
      Context: hBond
      Acceptable values: positive integer
      Description: Number that uses the same convention as atomNumbers.
      • -
    • donor: analogous to acceptor +
    • donor: analogous to acceptor
      • -
    • Keyword cutoff: see definition of cutoff (coordNum component)
      Note: default value is 3.3 Å. +
    • Keyword cutoff: see definition of cutoff (coordNum component)
      Note: default value is 3.3 Å.
      • -
    • Keyword expNumer: see definition of expNumer (coordNum component)
      Note: default value is 6. +
    • Keyword expNumer: see definition of expNumer (coordNum component)
      Note: default value is 6.
      • -
    • Keyword expDenom: see definition of expDenom (coordNum component)
      Note: default value is 8.
    +
  • Keyword expDenom: see definition of expDenom (coordNum component)
    Note: default value is 8.
    • -

    +

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    -

    +

    4.5 Collective metrics

    -

    +

    -

    +

    (Go to Contents)

    -

    +

    4.5.1 rmsd: root mean square displacement (RMSD) from reference positions.
    -

      -

    The block rmsd {...} defines the root mean square replacement (RMSD) of a +

      +

    The block rmsd {...} defines the root mean square replacement (RMSD) of a group of atoms with respect to a reference structure. For each set of coordinates -{x1(t),x2(t),… &ApplyFunction;xN(t)}, +{x1(t),x2(t),… &ApplyFunction;xN(t)}, the colvar component rmsd calculates the optimal rotation -U{xi(t)}→{xi(ref)} that best superimposes -the coordinates {xi(t)} onto a set -of reference coordinates {xi(ref)}. +U{xi(t)}→{xi(ref)} that best superimposes +the coordinates {xi(t)} onto a set +of reference coordinates {xi(ref)}. Both the current and the reference coordinates are centered on their centers of geometry, -xcog(t) and -xcog(ref). The +xcog(t) and +xcog(ref). The root mean square displacement is then defined as:

    - + RMSD ( {xi (t)}, {xi(ref)}) = 1 N∑i=1N |U (xi(t)−xcog(t))− (xi(ref) −xcog(ref))|2 (5)
    -

    The optimal rotation U{xi(t)}→{xi(ref)} +

    The optimal rotation U{xi(t)}→{xi(ref)} is calculated within the formalism developed in reference [4], which guarantees a continuous dependence -of U{xi(t)}→{xi(ref)} with -respect to {xi(t)}. -

    List of keywords (see also 4.14 for additional options):

    +of U{xi(t)}→{xi(ref)} with +respect to {xi(t)}. +

    List of keywords (see also 4.14 for additional options):

      -
    •   Keyword atoms⟨Atom - group⟩
      Context: rmsd
      Acceptable values: atoms {...} block
      Description: Defines the group of atoms of which the RMSD should be calculated. Optimal +
    •   Keyword atoms⟨Atom + group⟩
      Context: rmsd
      Acceptable values: atoms {...} block
      Description: Defines the group of atoms of which the RMSD should be calculated. Optimal fit options (such as refPositions and rotateToReference) should typically NOT be set within this block. Exceptions to this rule are the special cases discussed in the Advanced usage paragraph below.
      • -
    •   Keyword refPositions⟨Reference - coordinates⟩
      Context: rmsd
      Acceptable values: space-separated list of (x, y, z) triplets
      Description: This option (mutually exclusive with refPositionsFile) sets the reference +
    •   Keyword refPositions⟨Reference + coordinates⟩
      Context: rmsd
      Acceptable values: space-separated list of (x, y, z) triplets
      Description: This option (mutually exclusive with refPositionsFile) sets the reference coordinates for RMSD calculation, and uses these to compute the roto-translational fit. See the equivalent option refPositions within the atom group definition for details on acceptable formats and other features.
      • -
    •   Keyword refPositionsFile⟨Reference - coordinates file⟩
      Context: rmsd
      Acceptable values: UNIX filename
      Description: This option (mutually exclusive with refPositions) sets the reference coordinates +
    •   Keyword refPositionsFile⟨Reference + coordinates file⟩
      Context: rmsd
      Acceptable values: UNIX filename
      Description: This option (mutually exclusive with refPositions) sets the reference coordinates for RMSD calculation, and uses these to compute the roto-translational fit. See the equivalent option refPositionsFile within the atom group definition for details on acceptable file formats and other features.
      • -
    •   Keyword atomPermutation⟨Alternate - ordering of atoms for RMSD computation⟩
      Context: rmsd
      Acceptable values: List of atom numbers
      Description: If defined, this parameter defines a re-ordering (permutation) of the 1-based +
    •   Keyword atomPermutation⟨Alternate + ordering of atoms for RMSD computation⟩
      Context: rmsd
      Acceptable values: List of atom numbers
      Description: If defined, this parameter defines a re-ordering (permutation) of the 1-based atom numbers that can be used to compute the RMSD, typically due to molecular symmetry. This parameter can be specified multiple times, each one defining a new permutation: the returned RMSD value is the minimum over the set of permutations. For example, if the atoms @@ -1362,14 +1407,14 @@
      4.5.1 fittingGroup, or when fitting is disabled altogether. For details, see reference [5].
    -

    This component returns a positive real number (in nm). +

    This component returns a positive real number (in nm).

    -

    +

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    -

    +

    4.5.2 Advanced usage of the rmsd component.
    -

    In the standard usage as described above, the rmsd component calculates a minimum RMSD, that +

    In the standard usage as described above, the rmsd component calculates a minimum RMSD, that is, current coordinates are optimally fitted onto the same reference coordinates that are used to compute the RMSD value. The fit itself is handled by the atom group object, whose parameters are automatically set by the rmsd component. For very specific applications, however, it may be useful to control @@ -1377,7 +1422,7 @@
    4.5.2 refPositions, etc.) explicitly in the atom group block. This allows for the following non-standard cases: -

    +

    1. applying the optimal translation, but no rotation (rotateToReference off), to bias or restrain the shape and orientation, but not the position of the atom group; @@ -1397,251 +1442,251 @@
      4.5.2 fittingGroup: the RMSD then reflects the deviation from reference coordinates in a separate, moving reference frame (see example in the section on fittingGroup).
    -

    +

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    -

    +

    4.5.3 eigenvector: projection of the atomic coordinates on a vector.
    -

      -

    The block eigenvector {...} defines the projection of the coordinates of a group of +

      +

    The block eigenvector {...} defines the projection of the coordinates of a group of atoms (or more precisely, their deviations from the reference coordinates) onto a vector in -ℝ3n, where -n is the +ℝ3n, where +n is the number of atoms in the group. The computed quantity is the total projection:

    - + p ( {xi (t)}, {xi(ref)}) = ∑ i=1nv i⋅ (U(xi(t)−xcog(t))−(xi(ref) −x cog(ref))), (6)
    -

    where, as in the rmsd component, U -is the optimal rotation matrix, xcog(t) -and xcog(ref) +

    where, as in the rmsd component, U +is the optimal rotation matrix, xcog(t) +and xcog(ref) are the centers of geometry of the current and reference positions respectively, and -vi +vi are the components of the vector for each atom. Example choices for -(vi) are an +(vi) are an eigenvector of the covariance matrix (essential mode), or a normal mode of the system. It is assumed that -∑ &ApplyFunction;ivi = 0: otherwise, the Colvars -module centers the vi +∑ &ApplyFunction;ivi = 0: otherwise, the Colvars +module centers the vi automatically when reading them from the configuration. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component) +
    • Keyword atoms: see definition of atoms (rmsd component)
      • -
    • Keyword refPositions: see definition of refPositions (rmsd component) +
    • Keyword refPositions: see definition of refPositions (rmsd component)
      • -
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component) +
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
      • -
    • Keyword vector⟨Vector - components⟩
      Context: eigenvector
      Acceptable values: space-separated list of (x, y, z) triplets
      Description: This option (mutually exclusive with vectorFile) sets the values of the vector +
    • Keyword vector⟨Vector + components⟩
      Context: eigenvector
      Acceptable values: space-separated list of (x, y, z) triplets
      Description: This option (mutually exclusive with vectorFile) sets the values of the vector components.
      • -
    • Keyword vectorFile⟨file - containing vector components⟩
      Context: eigenvector
      Acceptable values: UNIX filename
      Description: This option (mutually exclusive with vector) sets the name of an XYZ (3.7.3) +
    • Keyword vectorFile⟨file + containing vector components⟩
      Context: eigenvector
      Acceptable values: UNIX filename
      Description: This option (mutually exclusive with vector) sets the name of an XYZ (3.7.3) coordinate file containing the vector components. Note: Reading data from a coordinate file may entail an automatic unit conversion if the length unit currently used by the MD engine is not Å. If this is not the desired behavior, this can be remedied using the normalizeVector option described below.
      • -
    • Keyword normalizeVector⟨Normalize - the vector components when reading them?⟩
      Context: eigenvector
      Acceptable values: boolean
      Default value: off
      Description: If this flag is activated, the norm of the vector |v| = ∑ &ApplyFunction; i |v i |2 - is set equal to 1 by automatically rescaling all the components vi; - alternatively, the value of |v| +
    • Keyword normalizeVector⟨Normalize + the vector components when reading them?⟩
      Context: eigenvector
      Acceptable values: boolean
      Default value: off
      Description: If this flag is activated, the norm of the vector |v| = ∑ &ApplyFunction; i |v i |2 + is set equal to 1 by automatically rescaling all the components vi; + alternatively, the value of |v| is printed.
      • -
    • Keyword differenceVector⟨The - 3n-dimensional - vector is the difference between vector and refPositions⟩
      Context: eigenvector
      Acceptable values: boolean
      Default value: off
      Description: If this option is on, the numbers provided by vector are interpreted as another - set of positions, xi′: - the vector vi - is then defined as vi = (xi′−xi(ref)). - This allows to conveniently define a colvar ξ +
    • Keyword differenceVector⟨The + 3n-dimensional + vector is the difference between vector and refPositions⟩
      Context: eigenvector
      Acceptable values: boolean
      Default value: off
      Description: If this option is on, the numbers provided by vector are interpreted as another + set of positions, xi′: + the vector vi + is then defined as vi = (xi′−xi(ref)). + This allows to conveniently define a colvar ξ as a projection on the linear transformation between two sets of positions, “A" and “B". If this - flag is on, the vector is normalized so that ξ = 0 - when the atoms are at the set of positions “A" and ξ = 1 + flag is on, the vector is normalized so that ξ = 0 + when the atoms are at the set of positions “A" and ξ = 1 at the set of positions “B". Setting normalizeVector on overrides this behavior.
    -

    +

    (Go to Contents)

    -

    +

    4.5.4 gyration: radius of gyration of a group of atoms.
    -

      -

    The block gyration {...} defines the parameters for calculating the radius of gyration of a group of atomic positions -{x1(t),x2(t),… &ApplyFunction;xN(t)} with respect to their -center of geometry, xcog(t): +

      +

    The block gyration {...} defines the parameters for calculating the radius of gyration of a group of atomic positions +{x1(t),x2(t),… &ApplyFunction;xN(t)} with respect to their +center of geometry, xcog(t):

    - + Rgyr = 1 N∑i=1N |xi(t)−xcog(t)|2 (7)
    -

    This component must contain one atoms {...} block to define the atom group, and returns a positive +

    This component must contain one atoms {...} block to define the atom group, and returns a positive number, expressed in nm. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component)
    +
  • Keyword atoms: see definition of atoms (rmsd component)
    • -

    +

    (Go to Contents)

    -

    +

    4.5.5 inertia: total moment of inertia of a group of atoms.
    -

      -

    The block inertia {...} defines the parameters for calculating the total moment of inertia of a group of atomic positions -{x1(t),x2(t),… &ApplyFunction;xN(t)} with respect to their -center of geometry, xcog(t): +

      +

    The block inertia {...} defines the parameters for calculating the total moment of inertia of a group of atomic positions +{x1(t),x2(t),… &ApplyFunction;xN(t)} with respect to their +center of geometry, xcog(t):

    - + I = ∑i=1N |x i(t)−xcog(t)|2 (8)
    -

    Note that all atomic masses are set to 1 for simplicity. This component must contain one +

    Note that all atomic masses are set to 1 for simplicity. This component must contain one atoms {...} block to define the atom group, and returns a positive number, expressed in -nm2. -

    List of keywords (see also 4.14 for additional options):

    +nm2. +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component)
    +
  • Keyword atoms: see definition of atoms (rmsd component)
    • -

    +

    (Go to Contents)

    -

    +

    4.5.6 dipoleMagnitude: dipole magnitude of a group of atoms.
    -

      The dipoleMagnitude {...} block defines the dipole magnitude of a group of atoms (norm of the +

      The dipoleMagnitude {...} block defines the dipole magnitude of a group of atoms (norm of the dipole moment's vector), being atoms the group where dipole magnitude is calculated. It returns the magnitude in -elementary charge e +elementary charge e times nm. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component)
    +
  • Keyword atoms: see definition of atoms (rmsd component)
    • -

    +

    (Go to Contents)

    -

    +

    4.5.7 inertiaZ: total moment of inertia of a group of atoms around a chosen axis.
    -

      -

    The block inertiaZ {...} defines the parameters for calculating the component along the axis -e of the moment of inertia of a group -of atomic positions {x1(t),x2(t),… &ApplyFunction;xN(t)} with respect -to their center of geometry, xcog(t): +

      +

    The block inertiaZ {...} defines the parameters for calculating the component along the axis +e of the moment of inertia of a group +of atomic positions {x1(t),x2(t),… &ApplyFunction;xN(t)} with respect +to their center of geometry, xcog(t):

    - + Ie = ∑i=1N ( (x i(t)−xcog(t))⋅e)2 (9)
    -

    Note that all atomic masses are set to 1 for simplicity. This component must contain one +

    Note that all atomic masses are set to 1 for simplicity. This component must contain one atoms {...} block to define the atom group, and returns a positive number, expressed in -nm2. -

    List of keywords (see also 4.14 for additional options):

    +nm2. +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component) +
    • Keyword atoms: see definition of atoms (rmsd component)
      • -
    • Keyword axis⟨Projection - axis⟩
      Context: inertiaZ
      Acceptable values: (x, y, z) triplet
      Default value: (0.0, 0.0, 1.0)
      Description: The three components of this vector define (when normalized) the projection - axis e. +
    • Keyword axis⟨Projection + axis⟩
      Context: inertiaZ
      Acceptable values: (x, y, z) triplet
      Default value: (0.0, 0.0, 1.0)
      Description: The three components of this vector define (when normalized) the projection + axis e.
    -

    +

    (Go to Contents)

    -

    +

    4.6 Rotations

    -

    -

    The variables discussed in this section quantify the rotations of macromolecules (or other quasi-rigid +

    +

    The variables discussed in this section quantify the rotations of macromolecules (or other quasi-rigid objects) from a given set of reference coordinates to the current coordinates. Such rotations are computed following the same method used for best-fit RMSDs (see rmsd and fittingGroup). The underlying mathematical formalism is described in reference [4], and the implementation in reference [1]. -

    The first of the functions described is the orientation, which describes the full rotation as a unit -quaternion q = (q0,q1,q2,q3), +

    The first of the functions described is the orientation, which describes the full rotation as a unit +quaternion q = (q0,q1,q2,q3), i.e. 4 numbers with one constraint (3 degrees of freedom). The quaternion -q +q is one of only two representations that are both complete and accurate, the other being a -3×3 unit matrix with 3 independent +3×3 unit matrix with 3 independent -parameters. Although q +parameters. Although q is used internally in the Colvars module for features such as the rmsd function and the fittingGroup option, its direct use as a collective variable is more difficult, and mostly limited to fixed or moving restraints. -

    The two functions orientationAngle and orientationProj, with the latter being +

    The two functions orientationAngle and orientationProj, with the latter being the cosine of the former, represent the amplitude of the full rotation described by -q, +q, regardless of the direction of its axis. As one-dimensional scalar variables, both orientationAngle and orientationProj are a much reduced simplification of the full rotation. However, they can be used in a variety of methods including both restraints and PMF computations. -

    A slightly more complete parametrization is achieved by decomposing the full rotation into the two parameters, +

    A slightly more complete parametrization is achieved by decomposing the full rotation into the two parameters, tilt and spinAngle. These quantify the amplitudes of two independent sub-rotations away from a certain axis -e, and around the same -axis e, respectively. -The axis e is chosen +e, and around the same +axis e, respectively. +The axis e is chosen by the user, and is by default the Z axis: under that choice, tilt is equivalent to the sine of the Euler “pitch" angle -𝜃, and spinAngle to the sum -of the other two angles, (ϕ +ψ). +𝜃, and spinAngle to the sum +of the other two angles, (ϕ +ψ). This parameterization is mathematically well defined for almost all full rotations, including small ones when the current coordinates are almost completely aligned with the reference ones. However, a mathematical singularity prevents using the spinAngle function near configurations where the value of tilt tilt is -1 (i.e. a --180∘ rotation around -an axis orthogonal to e). +-180∘ rotation around +an axis orthogonal to e). For these reasons, tilt and spinAngle are useful when the allowed rotations are known to have approximately the same axis, and differ only in the magnitude of the corresponding angle. In this use case, spinAngle measures the angle of the sub-rotation around the chosen axis -e, whereas tilt measures -the dot product between e +e, whereas tilt measures +the dot product between e and the actual axis of the full rotation. -

    Lastly, the traditional Euler angles are also available as the functions eulerPhi, eulerTheta and +

    Lastly, the traditional Euler angles are also available as the functions eulerPhi, eulerTheta and eulerPsi. Altogether, these are sufficient to represent all three degrees of freedom of a full rotation. However, they also suffer from the potential “gimbal lock" problem, which emerges whenever -𝜃 ≃±90∘, which +𝜃 ≃±90∘, which includes also the case where the full rotation is small. Under such conditions, the angles -ϕ and -ψ +ϕ and +ψ are both ill-defined and cannot be used as collective variables. For these reasons, it is highly recommended that Euler angles are used only in simulations where their range of applicability is known ahead of time, and excludes configurations where -𝜃 ≃±90∘ +𝜃 ≃±90∘ altogether.

    -

    +

    (Go to Contents)

    -

    +

    4.6.1 orientation: orientation from reference coordinates.
    -

      -

    The block orientation {...} returns the same optimal rotation used in the rmsd component to superimpose the coordinates -{xi(t)} onto a set of reference -coordinates {xi(ref)}. Such component -returns a four dimensional vector q = (q0,q1,q2,q3), -with ∑ &ApplyFunction;iqi2 = 1; this quaternion -expresses the optimal rotation {xi(t)}→{xi(ref)} +

      +

    The block orientation {...} returns the same optimal rotation used in the rmsd component to superimpose the coordinates +{xi(t)} onto a set of reference +coordinates {xi(ref)}. Such component +returns a four dimensional vector q = (q0,q1,q2,q3), +with ∑ &ApplyFunction;iqi2 = 1; this quaternion +expresses the optimal rotation {xi(t)}→{xi(ref)} according to the formalism in reference [4]. The quaternion -(q0,q1,q2,q3) can also be -written as (cos &ApplyFunction; (𝜃∕2),sin &ApplyFunction; (𝜃∕2)u), where -𝜃 is the angle and -u the normalized axis of rotation; -for example, a rotation of 90∘ -around the z axis is +(q0,q1,q2,q3) can also be +written as (cos &ApplyFunction; (𝜃∕2),sin &ApplyFunction; (𝜃∕2)u), where +𝜃 is the angle and +u the normalized axis of rotation; +for example, a rotation of 90∘ +around the z axis is expressed as “(0.707, 0.0, 0.0, 0.707)". The script quaternion2rmatrix.tcl provides Tcl functions for converting -to and from a 4×4 +to and from a 4×4 rotation matrix in a format suitable for usage in VMD. -

    As for the component rmsd, the available options are atoms, refPositionsFile and refPositions. -

    Note: refPositions and refPositionsFile define the set of positions from which the optimal rotation +

    As for the component rmsd, the available options are atoms, refPositionsFile and refPositions. +

    Note: refPositions and refPositionsFile define the set of positions from which the optimal rotation is calculated, but this rotation is not applied to the coordinates of the atoms involved: it is used instead to define the variable itself. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component) +
    • Keyword atoms: see definition of atoms (rmsd component)
      • -
    • Keyword refPositions: see definition of refPositions (rmsd component) +
    • Keyword refPositions: see definition of refPositions (rmsd component)
      • -
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component) +
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
      • -
    • Keyword closestToQuaternion⟨Reference - rotation⟩
      Context: orientation
      Acceptable values: “(q0, q1, q2, q3)" quadruplet
      Default value: (1.0, 0.0, 0.0, 0.0) (“null" rotation)
      Description: Between the two equivalent quaternions (q0,q1,q2,q3) - and (−q0,−q1,−q2,−q3), +
    • Keyword closestToQuaternion⟨Reference + rotation⟩
      Context: orientation
      Acceptable values: “(q0, q1, q2, q3)" quadruplet
      Default value: (1.0, 0.0, 0.0, 0.0) (“null" rotation)
      Description: Between the two equivalent quaternions (q0,q1,q2,q3) + and (−q0,−q1,−q2,−q3), the closer to (1.0, 0.0, 0.0, 0.0) is chosen. This simplifies the visualization of the colvar trajectory when sampled values are a smaller subset of all possible rotations. Note: this only affects the output, never the dynamics.
    -

    Tip: stopping the rotation of a protein. To stop the rotation of an elongated macromolecule in +

    Tip: stopping the rotation of a protein. To stop the rotation of an elongated macromolecule in solution (and use an anisotropic box to save water molecules), it is possible to define a colvar with an @@ -1651,591 +1696,591 @@

    4.6.1 wrapAll otherwise.

    -

    +

    (Go to Contents)

    -

    +

    4.6.2 orientationAngle: angle of rotation from reference coordinates.
    -

      -

    The block orientationAngle {...} accepts the same base options as the component +

      +

    The block orientationAngle {...} accepts the same base options as the component orientation: atoms, refPositions, refPositionsFile. The returned value is the angle of rotation -𝜃 +𝜃 between the current and the reference positions. This angle is expressed in degrees within the range -[0∘:180∘]. -

    List of keywords (see also 4.14 for additional options):

    +[0∘:180∘]. +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component) +
    • Keyword atoms: see definition of atoms (rmsd component)
      • -
    • Keyword refPositions: see definition of refPositions (rmsd component) +
    • Keyword refPositions: see definition of refPositions (rmsd component)
      • -
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component) +
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
    -

    +

    (Go to Contents)

    -

    +

    4.6.3 orientationProj: cosine of the angle of rotation from reference coordinates.
    -

      -

    The block orientationProj {...} accepts the same base options as the component orientation: +

      +

    The block orientationProj {...} accepts the same base options as the component orientation: atoms, refPositions, refPositionsFile. The returned value is the cosine of the angle of rotation -𝜃 +𝜃 between the current and the reference positions. The range of values is [-1:1]. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component) +
    • Keyword atoms: see definition of atoms (rmsd component)
      • -
    • Keyword refPositions: see definition of refPositions (rmsd component) +
    • Keyword refPositions: see definition of refPositions (rmsd component)
      • -
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
    +
  • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
    • -

    +

    (Go to Contents)

    -

    +

    4.6.4 spinAngle: angle of rotation around a given axis.
    -

      -

    The complete rotation described by orientation can optionally be decomposed into two +

      +

    The complete rotation described by orientation can optionally be decomposed into two sub-rotations: one is a “spin" rotation around e, and the other a “tilt" rotation around an axis orthogonal to e. The component spinAngle measures the angle of the “spin" sub-rotation around e. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component) +
    • Keyword atoms: see definition of atoms (rmsd component)
      • -
    • Keyword refPositions: see definition of refPositions (rmsd component) +
    • Keyword refPositions: see definition of refPositions (rmsd component)
      • -
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component) +
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
      • -
    •   Keyword axis⟨Special - rotation axis⟩
      Context: tilt
      Acceptable values: (x, y, z) triplet
      Default value: (0.0, 0.0, 1.0)
      Description: The three components of this vector define (when normalized) the special +
    •   Keyword axis⟨Special + rotation axis⟩
      Context: tilt
      Acceptable values: (x, y, z) triplet
      Default value: (0.0, 0.0, 1.0)
      Description: The three components of this vector define (when normalized) the special rotation axis used to calculate the tilt and spinAngle components.
    -

    The component spinAngle returns an angle (in degrees) within the periodic interval -[−180 : 180]. -

    Note: the value of spinAngle is a continuous function almost everywhere, +

    The component spinAngle returns an angle (in degrees) within the periodic interval +[−180 : 180]. +

    Note: the value of spinAngle is a continuous function almost everywhere, with the exception of configurations with the corresponding “tilt" angle equal to -180∘ (i.e. the tilt -component is equal to −1): +180∘ (i.e. the tilt +component is equal to −1): in those cases, spinAngle is undefined. If such configurations are expected, consider defining a tilt colvar using the same axis e, and restraining it with a lower wall away from -−1. +−1.

    -

    +

    (Go to Contents)

    -

    +

    4.6.5 tilt: cosine of the rotation orthogonal to a given axis.
    -

      -

    The component tilt measures the cosine of the angle of the “tilt" sub-rotation, which +

      +

    The component tilt measures the cosine of the angle of the “tilt" sub-rotation, which combined with the “spin" sub-rotation provides the complete rotation of a group of atoms. The cosine of the tilt angle rather than the tilt angle itself is implemented, because the latter is unevenly distributed even for an isotropic system: consider as an analogy the angle -𝜃 in the +𝜃 in the spherical coordinate system. The component tilt relies on the same options as spinAngle, including the definition of the axis e. The values of tilt are real numbers in the interval -[−1 : 1]: the value -1 represents an orientation fully -parallel to e (tilt angle = 0∘), -and the value −1 +[−1 : 1]: the value +1 represents an orientation fully +parallel to e (tilt angle = 0∘), +and the value −1 represents an anti-parallel orientation. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component) +
    • Keyword atoms: see definition of atoms (rmsd component)
      • -
    • Keyword refPositions: see definition of refPositions (rmsd component) +
    • Keyword refPositions: see definition of refPositions (rmsd component)
      • -
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component) +
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
      • -
    • Keyword axis: see definition of axis (spinAngle component)
    +
  • Keyword axis: see definition of axis (spinAngle component)
    • -

    +

    (Go to Contents)

    -

    +

    4.6.6 eulerPhi: Roll angle from references coordinates.
    -

      -

    Assuming the axes of the original frame are denoted as x, y, z and the axes of the rotated frame as X, +

      +

    Assuming the axes of the original frame are denoted as x, y, z and the axes of the rotated frame as X, Y, Z, the line of nodes, N, can be defined as the intersection of the plane xy and XY. The axis perpendicular to N and z is defined as P. In this case, as illustrated in the figure below, the complete rotation described by orientation can optionally be decomposed into three Euler angles:

      -
    • the “roll" angle ϕ, +
    • the “roll" angle ϕ, i.e. the rotation angle from the x axis to the N axis;
      • -
    • the “pitch" angle 𝜃, +
    • the “pitch" angle 𝜃, i.e. the rotation angle from the P axis to the Z axis, and
      • -
    • the “yaw" angle ψ, +
    • the “yaw" angle ψ, i.e. the rotation angle from the N axis to the X axis.
    -

    -

    PIC

    -

    Although Euler angles are more straightforward to use than quaternions, they are also potentially -subject to the “gimbal lock" problem:
    https://en.wikipedia.org/wiki/Gimbal_lock
    which arises whenever 𝜃 ≃±90∘, +

    +

    PIC

    +

    Although Euler angles are more straightforward to use than quaternions, they are also potentially +subject to the “gimbal lock" problem:
    https://en.wikipedia.org/wiki/Gimbal_lock
    which arises whenever 𝜃 ≃±90∘, including the common case when the simulated coordinates are near the reference coordinates. Therefore, a safe use of Euler angles as collective variables requires the use of restraints to avoid such singularities, such as done in reference [6] and in the protein-ligand binding NAMD tutorial. -

    The eulerPhi component accepts exactly the same options as orientation, and measures the +

    The eulerPhi component accepts exactly the same options as orientation, and measures the rotation angle from the x axis to the N axis. This angle is expressed in degrees within the periodic range -[−180∘ : 180∘]. -

    List of keywords (see also 4.14 for additional options):

    +[−180∘ : 180∘]. +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component) +
    • Keyword atoms: see definition of atoms (rmsd component)
      • -
    • Keyword refPositions: see definition of refPositions (rmsd component) +
    • Keyword refPositions: see definition of refPositions (rmsd component)
      • -
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
    +
  • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
    • -

    +

    (Go to Contents)

    -

    +

    4.6.7 eulerTheta: Pitch angle from references coordinates.
    -

      -

    This component accepts exactly the same options as orientation, and measures the +

      +

    This component accepts exactly the same options as orientation, and measures the rotation angle from the P axis to the Z axis. This angle is expressed in degrees within the range -[−90∘ : 90∘]. -

    Warning: When this angle reaches −90∘ -or 90∘, the +[−90∘ : 90∘]. +

    Warning: When this angle reaches −90∘ +or 90∘, the definition of orientation by euler angles suffers from the gimbal lock issue. You may need to apply a restraint to keep eulerTheta away from the singularities. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component) +
    • Keyword atoms: see definition of atoms (rmsd component)
      • -
    • Keyword refPositions: see definition of refPositions (rmsd component) +
    • Keyword refPositions: see definition of refPositions (rmsd component)
      • -
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
    +
  • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
    • -

    +

    (Go to Contents)

    -

    +

    4.6.8 eulerPsi: Yaw angle from references coordinates.
    -

      -

    This component accepts exactly the same options as orientation, and measures the rotation angle +

      +

    This component accepts exactly the same options as orientation, and measures the rotation angle from the N axis to the X axis. This angle is expressed in degrees within the periodic range -[−180∘ : 180∘]. -

    List of keywords (see also 4.14 for additional options):

    +[−180∘ : 180∘]. +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms: see definition of atoms (rmsd component) +
    • Keyword atoms: see definition of atoms (rmsd component)
      • -
    • Keyword refPositions: see definition of refPositions (rmsd component) +
    • Keyword refPositions: see definition of refPositions (rmsd component)
      • -
    • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
    +
  • Keyword refPositionsFile: see definition of refPositionsFile (rmsd component)
    • -

    +

    (Go to Contents)

    -

    +

    4.7 Raw data: building blocks for custom functions

    -

    +

    -

    +

    (Go to Contents)

    -

    +

    4.7.1 cartesian: vector of atomic Cartesian coordinates.
    -

      -

    The cartesian {...} block defines a component returning a flat vector +

      +

    The cartesian {...} block defines a component returning a flat vector containing the Cartesian coordinates of all participating atoms, in the order -(x1,y1,z1,⋯,xn,yn,zn). -

    List of keywords (see also 4.14 for additional options):

    +(x1,y1,z1,⋯,xn,yn,zn). +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms⟨Group - of atoms⟩
      Context: cartesian
      Acceptable values: Block atoms {...}
      Description: Defines the atoms whose coordinates make up the value of the component. +
    • Keyword atoms⟨Group + of atoms⟩
      Context: cartesian
      Acceptable values: Block atoms {...}
      Description: Defines the atoms whose coordinates make up the value of the component. If rotateToReference, centerToReference, or centerToOrigin are defined, coordinates are evaluated within the moving frame of reference.
    -

    +

    (Go to Contents)

    -

    +

    4.7.2 distancePairs: set of pairwise distances between two groups.
    -

      -

    The distancePairs {...} block defines a -N1 ×N2-dimensional +

      +

    The distancePairs {...} block defines a +N1 ×N2-dimensional variable that includes all mutual distances between the atoms of two groups. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword group1: see definition of group1 (distance component) +
    • Keyword group1: see definition of group1 (distance component)
      • -
    • group2: analogous to group1 +
    • group2: analogous to group1
      • -
    • Keyword forceNoPBC: see definition of forceNoPBC (distance component)
    -

    This component returns a N1 ×N2-dimensional -vector of numbers, each ranging from 0 +

  • Keyword forceNoPBC: see definition of forceNoPBC (distance component)
    • +

    This component returns a N1 ×N2-dimensional +vector of numbers, each ranging from 0 to the largest possible distance within the chosen boundary conditions.

    -

    +

    (Go to Contents)

    -

    +

    4.8 Geometric path collective variables

    -

    -

    The geometric path collective variables define the progress along a path, -s, and the distance -from the path, z. +

    +

    The geometric path collective variables define the progress along a path, +s, and the distance +from the path, z. These CVs are proposed by Leines and Ensing[7] , which differ from that[8] proposed by Branduardi et al., and utilize a set of geometric algorithms. The path is defined as a series of frames in the atomic Cartesian coordinate space or the CV space. -s and -z are +s and +z are computed as

    - + s = m M ± 1 2M ((v 1 ⋅v 3 )2 −|v 3 |2 (|v 1 |2 −|v 2 |2 )−(v1 ⋅v3) |v3|2 −1) (10)
    - + z = (v 1 + 1 2 ((v 1 ⋅v 3 )2 −|v 3 |2 (|v 1 |2 −|v 2 |2 )−(v1 ⋅v3) |v3|2 −1)v4)2 (11)
    -

    where v1 = sm−z +

    where v1 = sm−z is the vector connecting the current position to the closest frame, -v2 = z −sm−1 +v2 = z −sm−1 is the vector connecting the second closest frame to the current position, -v3 = sm+1 −sm +v3 = sm+1 −sm is the vector connecting the closest frame to the third closest frame, and -v4 = sm−sm−1 +v4 = sm−sm−1 is the vector connecting the second closest frame to the closest frame. -m and -M +m and +M are the current index of the closest frame and the total number of frames, respectively. If the current position is on the left of the closest reference frame, the -± in -s turns to +± in +s turns to the positive sign. Otherwise it turns to the negative sign. -

    The equations above assume: (i) the frames are equidistant and (ii) the second and the third closest +

    The equations above assume: (i) the frames are equidistant and (ii) the second and the third closest frames are neighbouring to the closest frame. When these assumptions are not satisfied, this set of path CV should be used carefully.

    -

    +

    (Go to Contents)

    -

    +

    4.8.1 gspath: progress along a path defined in atomic Cartesian coordinate space.
    -

      -

    In the gspath {...} and the gzpath {...} block all vectors, namely -z and -sk +

      +

    In the gspath {...} and the gzpath {...} block all vectors, namely +z and +sk are defined in atomic Cartesian coordinate space. More specifically, -z = [r1,⋯,rn], where -ri is the -i-th atom specified -in the atoms block. sk = [rk,1,⋯,rk,n], -where rk,i means -the i-th atom -of the k-th +z = [r1,⋯,rn], where +ri is the +i-th atom specified +in the atoms block. sk = [rk,1,⋯,rk,n], +where rk,i means +the i-th atom +of the k-th reference frame. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms⟨Group - of atoms⟩
      Context: gspath and gzpath
      Acceptable values: Block atoms {...}
      Description: Defines the atoms whose coordinates make up the value of the component. +
    • Keyword atoms⟨Group + of atoms⟩
      Context: gspath and gzpath
      Acceptable values: Block atoms {...}
      Description: Defines the atoms whose coordinates make up the value of the component.
      • -
    • Keyword refPositionsCol⟨PDB - column containing atom flags⟩
      Context: gspath and gzpath
      Acceptable values: O, B, X, Y, or Z
      Description: If refPositionsFileN is a PDB file that contains all the atoms in the topology, +
    • Keyword refPositionsCol⟨PDB + column containing atom flags⟩
      Context: gspath and gzpath
      Acceptable values: O, B, X, Y, or Z
      Description: If refPositionsFileN is a PDB file that contains all the atoms in the topology, this option may be provided to set which PDB field is used to flag the reference coordinates for atoms.
      • -
    • Keyword refPositionsFileN⟨File - containing the reference positions for fitting⟩
      Context: gspath and gzpath
      Acceptable values: UNIX filename
      Description: The path is defined by multiple refPositionsFiles which are similiar to - refPositionsFile in the rmsd CV. If your path consists of 10 +
    • Keyword refPositionsFileN⟨File + containing the reference positions for fitting⟩
      Context: gspath and gzpath
      Acceptable values: UNIX filename
      Description: The path is defined by multiple refPositionsFiles which are similiar to + refPositionsFile in the rmsd CV. If your path consists of 10 nodes, you can list the coordinate file (in PDB or XYZ format) from refPositionsFile1 to refPositionsFile10.
      • -
    • Keyword useSecondClosestFrame⟨Define - sm−1 - as the second closest frame?⟩
      Context: gspath and gzpath
      Acceptable values: boolean
      Default value: on
      Description: The definition assumes the second closest frame is neighbouring to the +
    • Keyword useSecondClosestFrame⟨Define + sm−1 + as the second closest frame?⟩
      Context: gspath and gzpath
      Acceptable values: boolean
      Default value: on
      Description: The definition assumes the second closest frame is neighbouring to the closest frame. This is not always true especially when the path is crooked. If this option is set - to on (default), sm−1 - is defined as the second closest frame. If this option is set to off, sm−1 + to on (default), sm−1 + is defined as the second closest frame. If this option is set to off, sm−1 is defined as the left or right neighbouring frame of the closest frame.
      • -
    • Keyword useThirdClosestFrame⟨Define - sm+1 - as the third closest frame?⟩
      Context: gspath and gzpath
      Acceptable values: boolean
      Default value: off
      Description: The definition assumes the third closest frame is neighbouring to the closest +
    • Keyword useThirdClosestFrame⟨Define + sm+1 + as the third closest frame?⟩
      Context: gspath and gzpath
      Acceptable values: boolean
      Default value: off
      Description: The definition assumes the third closest frame is neighbouring to the closest frame. This is not always true especially when the path is crooked. If this option is set to on, - sm+1 - is defined as the third closest frame. If this option is set to off (default), sm+1 + sm+1 + is defined as the third closest frame. If this option is set to off (default), sm+1 is defined as the left or right neighbouring frame of the closest frame.
      • -
    • Keyword fittingAtoms⟨The - atoms that are used for alignment⟩
      Context: gspath and gzpath
      Acceptable values: Group of atoms
      Description: Before calculating v1, - v2, - v3 - and v4, +
    • Keyword fittingAtoms⟨The + atoms that are used for alignment⟩
      Context: gspath and gzpath
      Acceptable values: Group of atoms
      Description: Before calculating v1, + v2, + v3 + and v4, the current frame need to be aligned to the corresponding reference frames. This option specifies which atoms are used to do alignment.
    -

    +

    (Go to Contents)

    -

    +

    4.8.2 gzpath: distance from a path defined in atomic Cartesian coordinate space.
    -

      -

    List of keywords (see also 4.14 for additional options):

    +

      +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword useZsquare⟨Compute - z2 - instead of z⟩
      Context: gzpath
      Acceptable values: boolean
      Default value: off
      Description: z +
    • Keyword useZsquare⟨Compute + z2 + instead of z⟩
      Context: gzpath
      Acceptable values: boolean
      Default value: off
      Description: z is not differentiable when it is zero. This implementation workarounds it by setting the derivative - of z - to zero when z = 0. - Another workaround is set this option to on, which computes z2 - instead of z, - and then z2 + of z + to zero when z = 0. + Another workaround is set this option to on, which computes z2 + instead of z, + and then z2 is differentiable when it is zero.
    -

    The usage of gzpath and gspath is illustrated below:

    -
    -

    colvar {
      # Progress along the path
      name gs
      # The path is defined by 5 reference frames (from string-00.pdb to string-04.pdb)
      # Use atomic coordinate from atoms 1, 2 and 3 to compute the path
      gspath {
        atoms {atomnumbers { 1 2 3 }}
        refPositionsFile1 string-00.pdb
        refPositionsFile2 string-01.pdb
        refPositionsFile3 string-02.pdb
        refPositionsFile4 string-03.pdb
        refPositionsFile5 string-04.pdb
      }
    }
    colvar {
      # Distance from the path
      name gz
      # The path is defined by 5 reference frames (from string-00.pdb to string-04.pdb)
      # Use atomic coordinate from atoms 1, 2 and 3 to compute the path
      gzpath {
        atoms {atomnumbers { 1 2 3 }}
        refPositionsFile1 string-00.pdb
        refPositionsFile2 string-01.pdb
        refPositionsFile3 string-02.pdb
        refPositionsFile4 string-03.pdb
        refPositionsFile5 string-04.pdb
      }
    }

    +

    The usage of gzpath and gspath is illustrated below:

    +
    +

    colvar {
      # Progress along the path
      name gs
      # The path is defined by 5 reference frames (from string-00.pdb to string-04.pdb)
      # Use atomic coordinate from atoms 1, 2 and 3 to compute the path
      gspath {
        atoms {atomnumbers { 1 2 3 }}
        refPositionsFile1 string-00.pdb
        refPositionsFile2 string-01.pdb
        refPositionsFile3 string-02.pdb
        refPositionsFile4 string-03.pdb
        refPositionsFile5 string-04.pdb
      }
    }
    colvar {
      # Distance from the path
      name gz
      # The path is defined by 5 reference frames (from string-00.pdb to string-04.pdb)
      # Use atomic coordinate from atoms 1, 2 and 3 to compute the path
      gzpath {
        atoms {atomnumbers { 1 2 3 }}
        refPositionsFile1 string-00.pdb
        refPositionsFile2 string-01.pdb
        refPositionsFile3 string-02.pdb
        refPositionsFile4 string-03.pdb
        refPositionsFile5 string-04.pdb
      }
    }

    -

    +

    (Go to Contents)

    -

    +

    4.8.3 linearCombination: Helper CV to define a linear combination of other CVs
    -

      -

    This is a helper CV which can be defined as a linear combination of other CVs. It maybe useful when +

      +

    This is a helper CV which can be defined as a linear combination of other CVs. It maybe useful when you want to define the gspathCV {...} and the gzpathCV {...} as combinations of other CVs. Total forces (required by ABF) of this CV are not available.

    -

    +

    (Go to Contents)

    -

    +

    4.8.4 customColvar: Helper CV to define a mathematical expression as CV from other CVs
    -

      -

    This is a helper CV which can be defined as a mathematical expression (see 4.15) of other CVs by +

      +

    This is a helper CV which can be defined as a mathematical expression (see 4.15) of other CVs by using customFunction. Currently only the scalar type of customFunction is supported. If customFunction is not provided, this component falls back to linearCombination. It maybe useful when you want to define the gspathCV {...}, the gzpathCV {...} and NeuralNetwork {...} as combinations of other CVs. Total forces (required by ABF) of this CV are not available.

    -

    +

    (Go to Contents)

    -

    +

    4.8.5 gspathCV: progress along a path defined in CV space.
    -

      -

    In the gspathCV {...} and the gzpathCV {...} block all vectors, namely -z and -sk are defined in CV space. -More specifically, z = [ξ1,⋯,ξn], - - -where ξi is -the i-th CV. -sk = [ξk,1,⋯,ξk,n], where -ξk,i means the -i-th CV of -the k-th +

      +

    In the gspathCV {...} and the gzpathCV {...} block all vectors, namely +z and +sk are defined in CV space. +More specifically, z = [ξ1,⋯,ξn], + + +where ξi is +the i-th CV. +sk = [ξk,1,⋯,ξk,n], where +ξk,i means the +i-th CV of +the k-th reference frame. It should be note that these two CVs requires the pathFile option, which specifies a path file. Each line in the path file contains a set of space-seperated CV value of the reference frame. The sequence of reference frames matches the sequence of the lines. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword useSecondClosestFrame⟨Define - sm−1 - as the second closest frame?⟩
      Context: gspathCV and gzpathCV
      Acceptable values: boolean
      Default value: on
      Description: The definition assumes the second closest frame is neighbouring to the +
    • Keyword useSecondClosestFrame⟨Define + sm−1 + as the second closest frame?⟩
      Context: gspathCV and gzpathCV
      Acceptable values: boolean
      Default value: on
      Description: The definition assumes the second closest frame is neighbouring to the closest frame. This is not always true especially when the path is crooked. If this option is set - to on (default), sm−1 - is defined as the second closest frame. If this option is set to off, sm−1 + to on (default), sm−1 + is defined as the second closest frame. If this option is set to off, sm−1 is defined as the left or right neighbouring frame of the closest frame.
      • -
    • Keyword useThirdClosestFrame⟨Define - sm+1 - as the third closest frame?⟩
      Context: gspathCV and gzpathCV
      Acceptable values: boolean
      Default value: off
      Description: The definition assumes the third closest frame is neighbouring to the closest +
    • Keyword useThirdClosestFrame⟨Define + sm+1 + as the third closest frame?⟩
      Context: gspathCV and gzpathCV
      Acceptable values: boolean
      Default value: off
      Description: The definition assumes the third closest frame is neighbouring to the closest frame. This is not always true especially when the path is crooked. If this option is set to on, - sm+1 - is defined as the third closest frame. If this option is set to off (default), sm+1 + sm+1 + is defined as the third closest frame. If this option is set to off (default), sm+1 is defined as the left or right neighbouring frame of the closest frame.
      • -
    • Keyword pathFile⟨The - file name of the path file.⟩
      Context: gspathCV and gzpathCV
      Acceptable values: UNIX filename
      Description: Defines the nodes or images that constitutes the path in CV space. The CVs +
    • Keyword pathFile⟨The + file name of the path file.⟩
      Context: gspathCV and gzpathCV
      Acceptable values: UNIX filename
      Description: Defines the nodes or images that constitutes the path in CV space. The CVs of an image are listed in a line of pathFile using space-seperated format. Lines from top to button in pathFile corresponds images from initial to last.
    -

    +

    (Go to Contents)

    -

    +

    4.8.6 gzpathCV: distance from a path defined in CV space.
    -

      -

    List of keywords (see also 4.14 for additional options):

    +

      +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword useZsquare⟨Compute - z2 - instead of z⟩
      Context: gzpathCV
      Acceptable values: boolean
      Default value: off
      Description: z +
    • Keyword useZsquare⟨Compute + z2 + instead of z⟩
      Context: gzpathCV
      Acceptable values: boolean
      Default value: off
      Description: z is not differentiable when it is zero. This implementation workarounds it by setting the derivative - of z - to zero when z = 0. - Another workaround is set this option to on, which computes z2 - instead of z, - and then z2 + of z + to zero when z = 0. + Another workaround is set this option to on, which computes z2 + instead of z, + and then z2 is differentiable when it is zero.
    -

    The usage of gzpathCV and gspathCV is illustrated below:

    -
    -

    colvar {
      # Progress along the path
      name gs
      # Path defined by the CV space of two dihedral angles
      gspathCV {
        pathFile ./path.txt
        dihedral {
          name 001
          group1 {atomNumbers {5}}
          group2 {atomNumbers {7}}
          group3 {atomNumbers {9}}
          group4 {atomNumbers {15}}
        }
        dihedral {
          name 002
          group1 {atomNumbers {7}}
          group2 {atomNumbers {9}}
          group3 {atomNumbers {15}}
          group4 {atomNumbers {17}}
        }
      }
    }

    colvar {
      # Distance from the path
      name gz
      gzpathCV {
        pathFile ./path.txt
        dihedral {
          name 001
          group1 {atomNumbers {5}}
          group2 {atomNumbers {7}}
          group3 {atomNumbers {9}}
          group4 {atomNumbers {15}}
        }
        dihedral {
          name 002
          group1 {atomNumbers {7}}
          group2 {atomNumbers {9}}
          group3 {atomNumbers {15}}
          group4 {atomNumbers {17}}
        }
      }
    }

    +

    The usage of gzpathCV and gspathCV is illustrated below:

    +
    +

    colvar {
      # Progress along the path
      name gs
      # Path defined by the CV space of two dihedral angles
      gspathCV {
        pathFile ./path.txt
        dihedral {
          name 001
          group1 {atomNumbers {5}}
          group2 {atomNumbers {7}}
          group3 {atomNumbers {9}}
          group4 {atomNumbers {15}}
        }
        dihedral {
          name 002
          group1 {atomNumbers {7}}
          group2 {atomNumbers {9}}
          group3 {atomNumbers {15}}
          group4 {atomNumbers {17}}
        }
      }
    }

    colvar {
      # Distance from the path
      name gz
      gzpathCV {
        pathFile ./path.txt
        dihedral {
          name 001
          group1 {atomNumbers {5}}
          group2 {atomNumbers {7}}
          group3 {atomNumbers {9}}
          group4 {atomNumbers {15}}
        }
        dihedral {
          name 002
          group1 {atomNumbers {7}}
          group2 {atomNumbers {9}}
          group3 {atomNumbers {15}}
          group4 {atomNumbers {17}}
        }
      }
    }

    -

    +

    (Go to Contents)

    -

    +

    4.9 Arithmetic path collective variables

    -

    -

    The arithmetic path collective variable in CV space uses a similar formula as the one proposed by Branduardi[8] et al., -except that it computes s -and z in +

    +

    The arithmetic path collective variable in CV space uses a similar formula as the one proposed by Branduardi[8] et al., +except that it computes s +and z in CV space instead of RMSDs in Cartesian space. Moreover, this implementation allows different coefficients for each CV components as described in [9]. Assuming a path is composed of -N reference frames and -defined in an M-dimensional CV -space, then the equations of s -and z of +N reference frames and +defined in an M-dimensional CV +space, then the equations of s +and z of the path are

    - + s = 1 N −1 ∑i=0N−1iexp &ApplyFunction; (−λ∑j=1Mcj2 (xj−xi,j)2) ∑i=0N−1exp &ApplyFunction; (−λ∑j=1Mcj2 (xj−xi,j)2) (12)
    - + z = −1 λln &ApplyFunction; (∑i=0N−1exp &ApplyFunction; (−λ∑ j=1Mc j2 (x j−xi,j)2)) (13)
    -

    where cj is the -coefficient(weight) of the j-th -CV, xi,j is the value -of j-th CV of -i-th reference frame -and xj is the value of -j-th CV of current frame. -λ is a parameter to -smooth the variation of s -and z. It should be -noted that the index i -ranges from 0 to -N −1, and the definition -of s is normalized -by 1∕(N −1). Consequently, -the scope of s -is [0 : 1]. +

    where cj is the +coefficient(weight) of the j-th +CV, xi,j is the value +of j-th CV of +i-th reference frame +and xj is the value of +j-th CV of current frame. +λ is a parameter to +smooth the variation of s +and z. It should be +noted that the index i +ranges from 0 to +N −1, and the definition +of s is normalized +by 1∕(N −1). Consequently, +the scope of s +is [0 : 1].

    -

    +

    (Go to Contents)

    -

    +

    4.9.1 aspathCV: progress along a path defined in CV space.
    -

    -

    This colvar component computes the s +

    +

    This colvar component computes the s variable. -

      -

    List of keywords (see also 4.14 for additional options):

    +

      +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword weights⟨Coefficients - of the collective variables⟩
      Context: aspathCV and azpathCV
      Acceptable values: space-separated numbers in a {...} block
      Default value: {1.0 ...}
      Description: Define the coefficients. The j-th - value in the {...} block corresponds the cj +
    • Keyword weights⟨Coefficients + of the collective variables⟩
      Context: aspathCV and azpathCV
      Acceptable values: space-separated numbers in a {...} block
      Default value: {1.0 ...}
      Description: Define the coefficients. The j-th + value in the {...} block corresponds the cj in the equations.
      • -
    • Keyword lambda⟨Smoothness - of the variation of s - and z⟩
      Context: aspathCV and azpathCV
      Acceptable values: decimal
      Default value: inverse of the mean square displacements of successive reference frames
      Description: The value of λ +
    • Keyword lambda⟨Smoothness + of the variation of s + and z⟩
      Context: aspathCV and azpathCV
      Acceptable values: decimal
      Default value: inverse of the mean square displacements of successive reference frames
      Description: The value of λ in the equations.
      • -
    • Keyword pathFile⟨The - file name of the path file.⟩
      Context: aspathCV and azpathCV
      Acceptable values: UNIX filename
      Description: Defines the nodes or images that constitutes the path in CV space. The CVs +
    • Keyword pathFile⟨The + file name of the path file.⟩
      Context: aspathCV and azpathCV
      Acceptable values: UNIX filename
      Description: Defines the nodes or images that constitutes the path in CV space. The CVs of an image are listed in a line of pathFile using space-separated format. Lines from top to button in pathFile corresponds images from initial to last.
    -

    +

    (Go to Contents)

    -

    +

    4.9.2 azpathCV: distance from a path defined in CV space.
    -

    -

    This colvar component computes the z +

    +

    This colvar component computes the z variable. Options are the same as in 4.9.1. -

    The usage of azpathCV and aspathCV is illustrated below:

    -
    -

    colvar {
      # Progress along the path
      name as
      # Path defined by the CV space of two dihedral angles
      aspathCV {
        pathFile ./path.txt
        weights {1.0 1.0}
        lambda 0.005
        dihedral {
          name 001
          group1 {atomNumbers {5}}
          group2 {atomNumbers {7}}
          group3 {atomNumbers {9}}
          group4 {atomNumbers {15}}
        }
        dihedral {
          name 002
          group1 {atomNumbers {7}}
          group2 {atomNumbers {9}}
          group3 {atomNumbers {15}}
          group4 {atomNumbers {17}}
        }
      }
    }

    colvar {
      # Distance from the path
      name az
      azpathCV {
        pathFile ./path.txt
        weights {1.0 1.0}
        lambda 0.005
        dihedral {
          name 001
          group1 {atomNumbers {5}}
          group2 {atomNumbers {7}}
          group3 {atomNumbers {9}}
          group4 {atomNumbers {15}}
        }
        dihedral {
          name 002
          group1 {atomNumbers {7}}
          group2 {atomNumbers {9}}
          group3 {atomNumbers {15}}
          group4 {atomNumbers {17}}
        }
      }
    }

    +

    The usage of azpathCV and aspathCV is illustrated below:

    +
    +

    colvar {
      # Progress along the path
      name as
      # Path defined by the CV space of two dihedral angles
      aspathCV {
        pathFile ./path.txt
        weights {1.0 1.0}
        lambda 0.005
        dihedral {
          name 001
          group1 {atomNumbers {5}}
          group2 {atomNumbers {7}}
          group3 {atomNumbers {9}}
          group4 {atomNumbers {15}}
        }
        dihedral {
          name 002
          group1 {atomNumbers {7}}
          group2 {atomNumbers {9}}
          group3 {atomNumbers {15}}
          group4 {atomNumbers {17}}
        }
      }
    }

    colvar {
      # Distance from the path
      name az
      azpathCV {
        pathFile ./path.txt
        weights {1.0 1.0}
        lambda 0.005
        dihedral {
          name 001
          group1 {atomNumbers {5}}
          group2 {atomNumbers {7}}
          group3 {atomNumbers {9}}
          group4 {atomNumbers {15}}
        }
        dihedral {
          name 002
          group1 {atomNumbers {7}}
          group2 {atomNumbers {9}}
          group3 {atomNumbers {15}}
          group4 {atomNumbers {17}}
        }
      }
    }

    -

    +

    (Go to Contents)

    -

    +

    4.9.3 aspath: progress along a path defined in atomic Cartesian coordinate space.
    -

      -

    This CV computes a special case of Eq. 12, where -xj is the -j-th atomic -position, xi,j is the -j-th atomic position of -the i-th reference frame. -The subtraction xj−xi,j is -actually calculated as xj−Rixi,j, -where Ri is a +

      +

    This CV computes a special case of Eq. 12, where +xj is the +j-th atomic +position, xi,j is the +j-th atomic position of +the i-th reference frame. +The subtraction xj−xi,j is +actually calculated as xj−Rixi,j, +where Ri is a 3x3 rotation matrix that minimizes the RMSD between the current atomic positions of simulation and the -i-th reference -frame. Bold xj +i-th reference +frame. Bold xj is used since an atomic position is a vector. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    • Keyword atoms⟨Group - of atoms⟩
      Context: aspath and azpath
      Acceptable values: Block atoms {...}
      Description: Defines the atoms whose coordinates make up the value of the component. +
    • Keyword atoms⟨Group + of atoms⟩
      Context: aspath and azpath
      Acceptable values: Block atoms {...}
      Description: Defines the atoms whose coordinates make up the value of the component.
      • -
    • Keyword refPositionsCol⟨PDB - column containing atom flags⟩
      Context: aspath and azpath
      Acceptable values: O, B, X, Y, or Z
      Description: If refPositionsFileN is a PDB file that contains all the atoms in the topology, +
    • Keyword refPositionsCol⟨PDB + column containing atom flags⟩
      Context: aspath and azpath
      Acceptable values: O, B, X, Y, or Z
      Description: If refPositionsFileN is a PDB file that contains all the atoms in the topology, this option may be provided to set which PDB field is used to flag the reference coordinates for atoms.
      • -
    • Keyword refPositionsFileN⟨File - containing the reference positions for fitting⟩
      Context: aspath and azpath
      Acceptable values: UNIX filename
      Description: The path is defined by multiple refPositionsFiles which are similiar to - refPositionsFile in the rmsd CV. If your path consists of 10 +
    • Keyword refPositionsFileN⟨File + containing the reference positions for fitting⟩
      Context: aspath and azpath
      Acceptable values: UNIX filename
      Description: The path is defined by multiple refPositionsFiles which are similiar to + refPositionsFile in the rmsd CV. If your path consists of 10 nodes, you can list the coordinate file (in PDB or XYZ format) from refPositionsFile1 to refPositionsFile10.
      • -
    • Keyword fittingAtoms⟨The - atoms that are used for alignment⟩
      Context: aspath and azpath
      Acceptable values: Group of atoms
      Description: Before calculating v1, - v2, - v3 - and v4, +
    • Keyword fittingAtoms⟨The + atoms that are used for alignment⟩
      Context: aspath and azpath
      Acceptable values: Group of atoms
      Description: Before calculating v1, + v2, + v3 + and v4, the current frame need to be aligned to the corresponding reference frames. This option specifies which atoms are used to do alignment.
    -

    +

    (Go to Contents)

    -

    +

    4.9.4 azpath: distance from a path defined in atomic Cartesian coordinate space.
    -

      -

    Similar to aspath, this CV computes a special case of Eq. 13, and shares the same options as +

      +

    Similar to aspath, this CV computes a special case of Eq. 13, and shares the same options as aspath. -

    The usage of azpath and aspath is illustrated below:

    -
    -

    colvar {
      # Progress along the path
      name as
      # The path is defined by 5 reference frames (from string-00.pdb to string-04.pdb)
      # Use atomic coordinate from atoms 1, 2 and 3 to compute the path
      aspath {
        atoms {atomnumbers { 1 2 3 }}
        refPositionsFile1 string-00.pdb
        refPositionsFile2 string-01.pdb
        refPositionsFile3 string-02.pdb
        refPositionsFile4 string-03.pdb
        refPositionsFile5 string-04.pdb
      }
    }
    colvar {
      # Distance from the path
      name az
      # The path is defined by 5 reference frames (from string-00.pdb to string-04.pdb)
      # Use atomic coordinate from atoms 1, 2 and 3 to compute the path
      azpath {
        atoms {atomnumbers { 1 2 3 }}
        refPositionsFile1 string-00.pdb
        refPositionsFile2 string-01.pdb
        refPositionsFile3 string-02.pdb
        refPositionsFile4 string-03.pdb
        refPositionsFile5 string-04.pdb
      }
    }

    +

    The usage of azpath and aspath is illustrated below:

    +
    +

    colvar {
      # Progress along the path
      name as
      # The path is defined by 5 reference frames (from string-00.pdb to string-04.pdb)
      # Use atomic coordinate from atoms 1, 2 and 3 to compute the path
      aspath {
        atoms {atomnumbers { 1 2 3 }}
        refPositionsFile1 string-00.pdb
        refPositionsFile2 string-01.pdb
        refPositionsFile3 string-02.pdb
        refPositionsFile4 string-03.pdb
        refPositionsFile5 string-04.pdb
      }
    }
    colvar {
      # Distance from the path
      name az
      # The path is defined by 5 reference frames (from string-00.pdb to string-04.pdb)
      # Use atomic coordinate from atoms 1, 2 and 3 to compute the path
      azpath {
        atoms {atomnumbers { 1 2 3 }}
        refPositionsFile1 string-00.pdb
        refPositionsFile2 string-01.pdb
        refPositionsFile3 string-02.pdb
        refPositionsFile4 string-03.pdb
        refPositionsFile5 string-04.pdb
      }
    }

    -

    +

    (Go to Contents)

    -

    +

    4.10 Dense neural network in CV space (MLCV)

    -

      -

    This colvar component computes a non-linear combination of other scalar colvar components, where +

      +

    This colvar component computes a non-linear combination of other scalar colvar components, where the transformation is defined by a dense neural network.[10] The network can be optimized using any framework, and its parameters are provided to Colvars in plain text files, as detailed below. An example Python script to export the parameters of a TensorFlow model is provided in @@ -2243,162 +2288,162 @@

    4.10
    -

    Dense neural network +

    Dense neural network

    Figure 1: Graphical representation of an example dense neural network with two hidden layers -y1 -and y2. -Both the input layer x -and the output layer z +y1 +and y2. +Both the input layer x +and the output layer z have two nodes. The input nodes can be any existing scalar CVs.
    -

    The output of the j-th -node of a k-th -layer that has Nk +

    The output of the j-th +node of a k-th +layer that has Nk nodes is computed by

    - + yk,j = fk (∑i=1Nk−1w (k,j),(k−1,i)yk−1,i+bk,j), (14)
    -

    where fk is the activation -function of the k-th -layer, w(k,j),(k−1,i) is the weight of -j-th node with respect -to the i-th output of -previous layer, and bk,j -is the bias of j-th -node of k-th +

    where fk is the activation +function of the k-th +layer, w(k,j),(k−1,i) is the weight of +j-th node with respect +to the i-th output of +previous layer, and bk,j +is the bias of j-th +node of k-th layer. -

    List of keywords (see also 4.14 for additional options):

    +

    List of keywords (see also 4.14 for additional options):

      -
    •   Keyword output_component⟨The - j-th - node of the output or the last layer⟩
      Context: NeuralNetwork
      Acceptable values: integer starting from 0
      Description: The value of this option specifies the output node to be used as the value of +
    •   Keyword output_component⟨The + j-th + node of the output or the last layer⟩
      Context: NeuralNetwork
      Acceptable values: integer starting from 0
      Description: The value of this option specifies the output node to be used as the value of this CV.
      • -
    •   Keyword layeri_WeightsFile -⟨The - weights from layer i−1 - to layer i⟩
      Context: NeuralNetwork
      Acceptable values: UNIX filename
      Description: The letter i +
    •   Keyword layeri_WeightsFile +⟨The + weights from layer i−1 + to layer i⟩
      Context: NeuralNetwork
      Acceptable values: UNIX filename
      Description: The letter i in this option needs to be replaced with the indexing number starting from 1, for example, layer1_WeightsFile and layer2_WeightsFile. The value of this option specifies a plain text - file containing the weights from layer i−1 + file containing the weights from layer i−1 - to layer i. - In the file, the number at k-th - column and l-th - row represents the weight from node k - at layer i−1 - to node l - at layer i. -
      • -
    •   Keyword layeri_BiasesFile -⟨The - biases from layer i−1 - to layer i⟩
      Context: NeuralNetwork
      Acceptable values: UNIX filename
      Description: The letter i + to layer i. + In the file, the number at k-th + column and l-th + row represents the weight from node k + at layer i−1 + to node l + at layer i. +
      • +
    •   Keyword layeri_BiasesFile +⟨The + biases from layer i−1 + to layer i⟩
      Context: NeuralNetwork
      Acceptable values: UNIX filename
      Description: The letter i in this option needs to be replaced with the indexing number starting from 1, for example, layer1_BiasesFile and layer2_BiasesFile. The value of this option specifies a plain text - file containing the weights of layer i. - The file should have only one column, where the number at l-th - row represents the bias of node l - from layer i−1 - to layer i. -
      • -
    •   Keyword layeri_activation -⟨The - activation function from layer i−1 - to layer i⟩
      Context: NeuralNetwork
      Acceptable values: tanh, sigmoid, linear, relu, lrelu100, elu
      Description: The letter i + file containing the weights of layer i. + The file should have only one column, where the number at l-th + row represents the bias of node l + from layer i−1 + to layer i. +
      • +
    •   Keyword layeri_activation +⟨The + activation function from layer i−1 + to layer i⟩
      Context: NeuralNetwork
      Acceptable values: tanh, sigmoid, linear, relu, lrelu100, elu
      Description: The letter i in this option needs to be replaced with the indexing number starting from 1, for example, - layer1_activation and layer2_activation. The activation function from layer i−1 - to layer i. + layer1_activation and layer2_activation. The activation function from layer i−1 + to layer i. Available choices are tanh, sigmoid, linear (identity), relu, lrelu100 (a leaky rely with - coefficients 10−2 + coefficients 10−2 and 1), and elu (with coefficient 1).
      • -
    •   Keyword layeri_custom_activation -⟨An - alternative custom expression as the activation function from layer i−1 - to layer i⟩
      Context: NeuralNetwork
      Acceptable values: string
      Description: Mathematical expression to define the activation function from layer i−1 - to layer i. +
    •   Keyword layeri_custom_activation +⟨An + alternative custom expression as the activation function from layer i−1 + to layer i⟩
      Context: NeuralNetwork
      Acceptable values: string
      Description: Mathematical expression to define the activation function from layer i−1 + to layer i. The input value must be written as x. For example, the ELU activation function can be expressed as select(step(x), alpha*(exp(x)-1), x). For details of the expression syntax, see customFunction. This option is mutually exclusive with colvar|NeuralNetwork|layeri_activation
    -

    An example of configuration using NeuralNetwork is shown below: -

    colvar {
      # Define a neural network with 2 layers
      # The inputs are two torsion angles
      # and the first node at the output layer is used as the final CV
      name nn_output_1
      NeuralNetwork {
        output_component 0
        layer1_WeightsFile dense_1_weights.txt
        layer1_BiasesFile dense_1_biases.txt
        layer1_activation tanh
        layer2_WeightsFile dense_2_weights.txt
        layer2_BiasesFile dense_2_biases.txt
        layer2_activation tanh
        # The component coefficient is used for normalization
        componentCoeff 180.0
        dihedral {
          name 001
          # normalization factor 1.0/180.0
          componentCoeff 0.00555555555555555556
          group1 {atomNumbers {5}}
          group2 {atomNumbers {7}}
          group3 {atomNumbers {9}}
          group4 {atomNumbers {15}}
        }
        dihedral {
          name 002
          # normalization factor 1.0/180.0
          componentCoeff 0.00555555555555555556
          group1 {atomNumbers {7}}
          group2 {atomNumbers {9}}
          group3 {atomNumbers {15}}
          group4 {atomNumbers {17}}
        }
      }
    } +

    An example of configuration using NeuralNetwork is shown below: +

    colvar {
      # Define a neural network with 2 layers
      # The inputs are two torsion angles
      # and the first node at the output layer is used as the final CV
      name nn_output_1
      NeuralNetwork {
        output_component 0
        layer1_WeightsFile dense_1_weights.txt
        layer1_BiasesFile dense_1_biases.txt
        layer1_activation tanh
        layer2_WeightsFile dense_2_weights.txt
        layer2_BiasesFile dense_2_biases.txt
        layer2_activation tanh
        # The component coefficient is used for normalization
        componentCoeff 180.0
        dihedral {
          name 001
          # normalization factor 1.0/180.0
          componentCoeff 0.00555555555555555556
          group1 {atomNumbers {5}}
          group2 {atomNumbers {7}}
          group3 {atomNumbers {9}}
          group4 {atomNumbers {15}}
        }
        dihedral {
          name 002
          # normalization factor 1.0/180.0
          componentCoeff 0.00555555555555555556
          group1 {atomNumbers {7}}
          group2 {atomNumbers {9}}
          group3 {atomNumbers {15}}
          group4 {atomNumbers {17}}
        }
      }
    }

    -

    +

    (Go to Contents)

    -

    +

    4.11 Shared keywords for all components

    -

    -

    The following options can be used for any of the above colvar components in order to obtain a +

    +

    The following options can be used for any of the above colvar components in order to obtain a polynomial combination.

      -
    • Keyword name⟨Name - of this component⟩
      Context: any component
      Acceptable values: string
      Default value: type of component + numeric id
      Description: The name is an unique case-sensitive string which allows the Colvars module +
    • Keyword name⟨Name + of this component⟩
      Context: any component
      Acceptable values: string
      Default value: type of component + numeric id
      Description: The name is an unique case-sensitive string which allows the Colvars module to identify this component. It also defines the variable name representing the component's value in a customFunction expression.
      • -
    • Keyword scalable⟨Attempt - to calculate this component in parallel?⟩
      Context: any component
      Acceptable values: boolean
      Default value: on, if available
      Description: If set to on (default), the Colvars module will attempt to calculate this component +
    • Keyword scalable⟨Attempt + to calculate this component in parallel?⟩
      Context: any component
      Acceptable values: boolean
      Default value: on, if available
      Description: If set to on (default), the Colvars module will attempt to calculate this component in parallel to reduce overhead. Whether this option is available depends on the type of component: currently supported are distance, distanceZ, distanceXY, distanceVec, distanceDir, angle and dihedral. This flag influences computational cost, but does not affect numerical results: therefore, it should only be turned off for debugging or testing purposes.
    -

    +

    (Go to Contents)

    -

    +

    4.12 Periodic components

    -

    The following components returns real numbers that lie in a periodic interval: +

    The following components returns real numbers that lie in a periodic interval:
    • dihedral: torsional angle between four groups;
    • spinAngle: angle of rotation around a predefined axis in the best-fit from a set of reference coordinates.
    -

    In certain conditions, distanceZ can also be periodic, namely when periodic boundary conditions (PBCs) are +

    In certain conditions, distanceZ can also be periodic, namely when periodic boundary conditions (PBCs) are defined in the simulation and distanceZ's axis is parallel to a unit cell vector. -

    In addition, a custom scalar colvar may be periodic depending on its user-defined expression. It will +

    In addition, a custom scalar colvar may be periodic depending on its user-defined expression. It will only be treated as such by the Colvars module if the period is specified using the period keyword, while wrapAround is optional. -

    The following keywords can be used within periodic components, or within custom variables +

    The following keywords can be used within periodic components, or within custom variables (4.15)).

      -
    • Keyword period⟨Period - of the component⟩
      Context: distanceZ, custom colvars
      Acceptable values: positive decimal
      Default value: 0.0
      Description: Setting this number enables the treatment of distanceZ as a periodic component: +
    • Keyword period⟨Period + of the component⟩
      Context: distanceZ, custom colvars
      Acceptable values: positive decimal
      Default value: 0.0
      Description: Setting this number enables the treatment of distanceZ as a periodic component: by default, distanceZ is not considered periodic. The keyword is supported, but irrelevant within dihedral or spinAngle, because their period is always 360 degrees.
      • -
    • Keyword wrapAround⟨Center - of the wrapping interval for periodic variables⟩
      Context: distanceZ, dihedral, spinAngle, custom colvars
      Acceptable values: decimal
      Default value: 0.0
      Description: By default, values of the periodic components are centered around zero, - ranging from −P∕2 - to P∕2, - where P +
    • Keyword wrapAround⟨Center + of the wrapping interval for periodic variables⟩
      Context: distanceZ, dihedral, spinAngle, custom colvars
      Acceptable values: decimal
      Default value: 0.0
      Description: By default, values of the periodic components are centered around zero, + ranging from −P∕2 + to P∕2, + where P is the period. Setting this number centers the interval around this value. This can be useful for convenience of output, or to set the walls for a harmonicWalls in an order that would not otherwise be allowed.
    -

    Internally, all differences between two values of a periodic colvar follow the minimum image +

    Internally, all differences between two values of a periodic colvar follow the minimum image convention: they are calculated based on the two periodic images that are closest to each other. -

    Note: linear or polynomial combinations of periodic components (see 4.14) may become meaningless +

    Note: linear or polynomial combinations of periodic components (see 4.14) may become meaningless when components cross the periodic boundary. Use such combinations carefully: estimate the range of possible values of each component in a given simulation, and make use of wrapAround to limit this problem whenever possible.

    -

    +

    (Go to Contents)

    -

    +

    4.13 Non-scalar components

    -

    -

    When one of the following components are used, the defined colvar returns a value that is not a scalar +

    +

    When one of the following components are used, the defined colvar returns a value that is not a scalar number:

    -

    The distance between two 3-dimensional unit vectors is computed as the angle +

    The distance between two 3-dimensional unit vectors is computed as the angle between them. The distance between two quaternions is computed as the angle between the two 4-dimensional unit vectors: because the orientation represented by -q is the same as the -one represented by −q, +q is the same as the +one represented by −q, distances between two quaternions are computed considering the closest of the two symmetric images. -

    Non-scalar components carry the following restrictions:

    +

    Non-scalar components carry the following restrictions:

    -

    Note: while these restrictions apply to individual colvars based on non-scalar components, no limit is +

    Note: while these restrictions apply to individual colvars based on non-scalar components, no limit is set to the number of scalar colvars. To compute multi-dimensional histograms and PMFs, use sets of scalar colvars of arbitrary size.

    -

    +

    (Go to Contents)

    -

    +

    4.13.1 Calculating total forces
    -

    In addition to the restrictions due to the type of value computed (scalar or non-scalar), a final +

    In addition to the restrictions due to the type of value computed (scalar or non-scalar), a final restriction can arise when calculating total force (outputTotalForce option or application of a abf bias). total forces are available currently only for the following components: distance, distanceZ, distanceXY, angle, dihedral, rmsd, eigenvector and gyration.
    -

    +

    (Go to Contents)

    -

    +

    4.14 Linear and polynomial combinations of components

    -

    -

    To extend the set of possible definitions of colvars -ξ(r), multiple -components qi(r) +

    +

    To extend the set of possible definitions of colvars +ξ(r), multiple +components qi(r) can be summed with the formula:

    - + ξ (r) = ∑ici[qi(r)]ni (15)
    -

    where each component appears with a unique coefficient -ci (1.0 by default) the -positive integer exponent ni +

    where each component appears with a unique coefficient +ci (1.0 by default) the +positive integer exponent ni (1 by default). -

    Any set of components can be combined within a colvar, provided that they return the same type of +

    Any set of components can be combined within a colvar, provided that they return the same type of values (scalar, unit vector, vector, or quaternion). By default, the colvar is the sum of its components. Linear or polynomial combinations (following equation (15)) can be obtained by setting the following parameters, which are common to all components:

      -
    • Keyword componentCoeff⟨Coefficient - of this component in the colvar⟩
      Context: any component
      Acceptable values: decimal
      Default value: 1.0
      Description: Defines the coefficient by which this component is multiplied (after being raised +
    • Keyword componentCoeff⟨Coefficient + of this component in the colvar⟩
      Context: any component
      Acceptable values: decimal
      Default value: 1.0
      Description: Defines the coefficient by which this component is multiplied (after being raised to componentExp) before being added to the sum.
      • -
    • Keyword componentExp⟨Exponent - of this component in the colvar⟩
      Context: any component
      Acceptable values: integer
      Default value: 1
      Description: Defines the power at which the value of this component is raised before being +
    • Keyword componentExp⟨Exponent + of this component in the colvar⟩
      Context: any component
      Acceptable values: integer
      Default value: 1
      Description: Defines the power at which the value of this component is raised before being added to the sum. When this exponent is different than 1 (non-linear sum), total forces and the Jacobian force are not available, making the colvar unsuitable for ABF calculations (eABF remains possible).
    -

    Example: To define the average of a colvar across different parts of the system, +

    Example: To define the average of a colvar across different parts of the system, simply define within the same colvar block a series of components of the same type (applied to different atom groups), and assign to each component a componentCoeff of -1∕N. +1∕N.

    -

    +

    (Go to Contents)

    -

    +

    4.15 Custom functions

    -

    -

    Collective variables may be defined by specifying a custom function of multiple components, i.e. an +

    +

    Collective variables may be defined by specifying a custom function of multiple components, i.e. an analytical expression that is more general than the linear combinations described in 4.14. Such expression is parsed and calculated by Lepton, the lightweight expression parser written by Peter Eastman (https://simtk.org/projects/lepton) that produces efficient evaluation @@ -2488,19 +2533,19 @@

    4.15 -
  •   Keyword customFunction⟨Compute - colvar as a custom function of its components⟩
    Context: colvar
    Acceptable values: string
    Description: Mathematical expression to define the colvar as a closed-form function of +
  •   Keyword customFunction⟨Compute + colvar as a custom function of its components⟩
    Context: colvar
    Acceptable values: string
    Description: Mathematical expression to define the colvar as a closed-form function of its colvar components. See below for the detailed syntax of Lepton expressions. Multiple mentions of this keyword can be used to define a vector variable (as in the example below).
    • -
  • Keyword customFunctionType⟨Type - of value returned by the custom function⟩
    Context: colvar
    Acceptable values: string
    Default value: scalar
    Description: With this flag, the user may specify whether the colvar is a scalar or one of +
  • Keyword customFunctionType⟨Type + of value returned by the custom function⟩
    Context: colvar
    Acceptable values: string
    Default value: scalar
    Description: With this flag, the user may specify whether the colvar is a scalar or one of the following vector types: vector3 (a 3D vector), unit_vector3 (a normalized 3D vector), or unit_quaternion (a normalized quaternion), or vector. Note that the scalar and vector cases are not necessary, as they are detected automatically.
    • -

    The expression may use the collective variable components as variables, referred to by their +

    The expression may use the collective variable components as variables, referred to by their user-defined name. Scalar elements of vector components may be accessed by appending a 1-based index to their name, as in the example below. When implementing generic functions of Cartesian coordinates rather than functions of existing components, the cartesian component may be particularly @@ -2509,20 +2554,20 @@

    4.15 4.12 for details). A vector variable may be defined by specifying the customFunction parameter several times: each expression defines one scalar element of the vector colvar, as in this example:

    -
    -

    colvar {
      name custom

      # A 2-dimensional vector function of a scalar x and a 3-vector r
      customFunction cos(x) * (r1 + r2 + r3)
      customFunction sqrt(r1 * r2)

      distance {
        name x
        group1 { atomNumbers 1 }
        group2 { atomNumbers 50 }
      }
      distanceVec {
        name r
        group1 { atomNumbers 10 11 12 }
        group2 { atomNumbers 20 21 22 }
      }
    }

    +
    +

    colvar {
      name custom

      # A 2-dimensional vector function of a scalar x and a 3-vector r
      customFunction cos(x) * (r1 + r2 + r3)
      customFunction sqrt(r1 * r2)

      distance {
        name x
        group1 { atomNumbers 1 }
        group2 { atomNumbers 50 }
      }
      distanceVec {
        name r
        group1 { atomNumbers 10 11 12 }
        group2 { atomNumbers 20 21 22 }
      }
    }

    -

    Numeric constants may be given in either decimal or exponential form (e.g. 3.12e-2). An expression +

    Numeric constants may be given in either decimal or exponential form (e.g. 3.12e-2). An expression may be followed by definitions for intermediate values that appear in the expression, separated by semicolons. For example, the expression:
    a^2 + a*b + b^2; a = a1 + a2; b = b1 + b2
    is exactly equivalent to:
    (a1 + a2)^2 + (a1 + a2) * (b1 + b2) + (b1 + b2)^2.
    The definition of an intermediate value may itself involve other intermediate values. All uses of a value must appear before that value's definition. -

    Lepton supports the usual arithmetic operators +, -, *, /, and ^ (power), as well as the following +

    Lepton supports the usual arithmetic operators +, -, *, /, and ^ (power), as well as the following functions:

    -

    +

    @@ -2546,27 +2591,27 @@

    4.15

    - - - + + +
    sqrt Square root
    exp Exponential ceil Ceiling
    min Minimum of two values
    max Maximum of two values
    delta delta(x) = 1 if x = 0, 0 otherwise
    step step(x) = 0 if x < 0, 1 if x >= 0
    select select(x,y,z) = z if x = 0, y otherwise
    delta delta(x) = 1 if x = 0, 0 otherwise
    step step(x) = 0 if x < 0, 1 if x >= 0
    select select(x,y,z) = z if x = 0, y otherwise
    -

    +

    (Go to Contents)

    -

    +

    4.16 Defining grid parameters for a colvar

    -

    -

    Many algorithms require the definition of two boundaries and a bin width for each colvar, which are +

    +

    Many algorithms require the definition of two boundaries and a bin width for each colvar, which are necessary to compute discrete “states" for a collective variable's otherwise continuous values. The following keywords define these parameters for a specific variable, and will be used by all bias that refer to that variable unless otherwise specified.

      -
    •   Keyword lowerBoundary⟨Lower +
    •   Keyword lowerBoundary⟨Lower - boundary of the colvar⟩
      Context: colvar
      Acceptable values: decimal
      Default value: natural boundary of the function
      Description: Defines the lowest end of the interval of “relevant" values for the variable. This + boundary of the colvar⟩
      Context: colvar
      Acceptable values: decimal
      Default value: natural boundary of the function
      Description: Defines the lowest end of the interval of “relevant" values for the variable. This number can be, for example, a true physical boundary imposed by the choice of function (e.g. the distance function is always larger than zero): if this is the case, and only one function is used to define the variable, the default value of this number is set to the lowest @@ -2577,75 +2622,75 @@

      4.16 harmonicWalls restraint, 6.7), or (b) instruct the code that this is a true physical boundary by setting hardLowerBoundary.

      • -
    •   Keyword upperBoundary⟨Upper - boundary of the colvar⟩
      Context: colvar
      Acceptable values: decimal
      Default value: natural boundary of the function
      Description: Similarly to lowerBoundary, defines the highest of the “relevant" values of the +
    •   Keyword upperBoundary⟨Upper + boundary of the colvar⟩
      Context: colvar
      Acceptable values: decimal
      Default value: natural boundary of the function
      Description: Similarly to lowerBoundary, defines the highest of the “relevant" values of the variable.
      • -
    •   Keyword width⟨grid - spacing, or unit of the variable⟩
      Context: colvar
      Acceptable values: positive decimal
      Default value: 1.0
      Description: This number defines the width of a discrete “state" for a collective variable, +
    •   Keyword width⟨grid + spacing, or unit of the variable⟩
      Context: colvar
      Acceptable values: positive decimal
      Default value: 1.0
      Description: This number defines the width of a discrete “state" for a collective variable, and is used by the many biasing methods to achieve different purposes. Histograms (6.10), ABF (6.2) and metadynamics (6.4) all use this number as the initial choice for the grid spacing along this variable. As a typical rule of thumb, width should be no larger than the standard deviation of the colvar in an unbiased simulation (to characterize a local free-energy minimum with at least two points). -

      Further, many restraints such as harmonic potentials (6.5), harmonic walls (6.7) and linear +

      Further, many restraints such as harmonic potentials (6.5), harmonic walls (6.7) and linear restraints (6.8) also use this parameter to define the expected fluctuations of the colvar, allowing to express the force constant in terms of this unit. This is most useful with multi-dimensional restraints acting on variables that have very different units (for examples, working with nm - and degrees ∘ + and degrees ∘ simultaneously): a single force constant can be used for all, which is converted to the respective unit of each variable when forces are applied (the are printed at initialization time.

      • -
    •   Keyword hardLowerBoundary⟨Whether - the lower boundary is the physical lower limit⟩
      Context: colvar
      Acceptable values: boolean
      Default value: provided by the component
      Description: When the colvar has a “natural" boundary (for example, a distance colvar +
    •   Keyword hardLowerBoundary⟨Whether + the lower boundary is the physical lower limit⟩
      Context: colvar
      Acceptable values: boolean
      Default value: provided by the component
      Description: When the colvar has a “natural" boundary (for example, a distance colvar cannot go below 0) this flag is automatically enabled. For more complex variable definitions, or when lowerBoundary is provided directly by the user, it may be useful to set this flag explicitly. This option does not affect simulation results, but enables some internal optimizations by letting the code know that the variable is unable to cross the lower boundary, regardless of whether restraints are applied to it.
      • -
    •   Keyword hardUpperBoundary⟨Whether - the upper boundary is the physical upper limit of the colvar's values⟩
      Context: colvar
      Acceptable values: boolean
      Default value: provided by the component
      Description: Analogous to hardLowerBoundary. +
    •   Keyword hardUpperBoundary⟨Whether + the upper boundary is the physical upper limit of the colvar's values⟩
      Context: colvar
      Acceptable values: boolean
      Default value: provided by the component
      Description: Analogous to hardLowerBoundary.
      • -
    •   Keyword expandBoundaries⟨Allow - to expand the two boundaries if needed⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: If defined, lowerBoundary and upperBoundary may be automatically expanded +
    •   Keyword expandBoundaries⟨Allow + to expand the two boundaries if needed⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: If defined, lowerBoundary and upperBoundary may be automatically expanded to accommodate colvar values that do not fit in the initial range. Currently, this option is used by the metadynamics bias (6.4) to keep all of its hills fully within the grid. Enabling this option does not affect any boundaries that are defined as “hard" (see above), or any boundaries that span the full period of a periodic colvar.
    -

    +

    (Go to Contents)

    -

    +

    4.17 Trajectory output

    -

    +

      -
    • Keyword outputValue⟨Output - a trajectory for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: on
      Description: If colvarsTrajFrequency is non-zero, the value of this colvar is written to the - trajectory file every colvarsTrajFrequency steps in the column labeled “ <name >". +
    • Keyword outputValue⟨Output + a trajectory for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: on
      Description: If colvarsTrajFrequency is non-zero, the value of this colvar is written to the + trajectory file every colvarsTrajFrequency steps in the column labeled “ <name >".
      • -
    • Keyword outputVelocity⟨Output - a velocity trajectory for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: If colvarsTrajFrequency is defined, the finite-difference calculated velocity of - this colvar are written to the trajectory file under the label “v_ <name >". +
    • Keyword outputVelocity⟨Output + a velocity trajectory for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: If colvarsTrajFrequency is defined, the finite-difference calculated velocity of + this colvar are written to the trajectory file under the label “v_ <name >".
      • -
    • Keyword outputEnergy⟨Output - an energy trajectory for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: This option applies only to extended Lagrangian colvars. If colvarsTrajFrequency +
    • Keyword outputEnergy⟨Output + an energy trajectory for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: This option applies only to extended Lagrangian colvars. If colvarsTrajFrequency is defined, the kinetic energy of the extended degree and freedom and the potential energy of - the restraining spring are are written to the trajectory file under the labels “Ek_ <name >" - and “Ep_ <name >". + the restraining spring are are written to the trajectory file under the labels “Ek_ <name >" + and “Ep_ <name >".
      • -
    •   Keyword outputTotalForce⟨Output - a total force trajectory for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: If colvarsTrajFrequency is defined, the total force on this colvar (i.e. the +
    •   Keyword outputTotalForce⟨Output + a total force trajectory for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: If colvarsTrajFrequency is defined, the total force on this colvar (i.e. the projection of all atomic total forces onto this colvar — see equation (20) in section 6.2) are - written to the trajectory file under the label “fs_ <name >". + written to the trajectory file under the label “fs_ <name >". For extended Lagrangian colvars, the “total force" felt by the extended degree of freedom is simply the force from the harmonic spring. Note: not all components support this option. The physical unit for this force is kJ/mol/(colvar unit).
      • -
    •   Keyword outputAppliedForce⟨Output - an applied force trajectory for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: If colvarsTrajFrequency is defined, the total force applied on this colvar by - Colvars biases are written to the trajectory under the label “fa_ <name >". +
    •   Keyword outputAppliedForce⟨Output + an applied force trajectory for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: If colvarsTrajFrequency is defined, the total force applied on this colvar by + Colvars biases are written to the trajectory under the label “fa_ <name >". For extended Lagrangian colvars, this force is actually applied to the extended degree of @@ -2653,93 +2698,93 @@

      4.17 unit).

    -

    +

    (Go to Contents)

    -

    +

    4.18 Extended Lagrangian

    -

    -

    The following options enable extended-system dynamics, where a colvar is coupled to an +

    +

    The following options enable extended-system dynamics, where a colvar is coupled to an additional degree of freedom (fictitious particle) by a harmonic spring. This extended coordinate masks the colvar and replaces it transparently from the perspective of biasing and analysis methods. Biasing forces are then applied to the extended degree of freedom, and the actual geometric colvar (function of Cartesian coordinates) only feels the force from the harmonic spring. This is particularly useful when combined with an abf bias to perform eABF simulations (6.3). -

    Note that for some biases (harmonicWalls, histogram), this masking behavior is controlled by the +

    Note that for some biases (harmonicWalls, histogram), this masking behavior is controlled by the keyword bypassExtendedLagrangian. Specifically for harmonicWalls, the default behavior is to bypass extended Lagrangian coordinates and act directly on the actual colvars.

      -
    • Keyword extendedLagrangian⟨Add - extended degree of freedom⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: Adds a fictitious particle to be coupled to the colvar by a harmonic spring. +
    • Keyword extendedLagrangian⟨Add + extended degree of freedom⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: Adds a fictitious particle to be coupled to the colvar by a harmonic spring. The fictitious mass and the force constant of the coupling potential are derived from the parameters extendedTimeConstant and extendedFluctuation, described below. Biasing forces on the colvar are applied to this fictitious particle, rather than to the atoms directly. This implements the extended Lagrangian formalism used in some metadynamics simulations [3]. .
      • -
    • Keyword extendedFluctuation⟨Standard - deviation between the colvar and the fictitious particle (colvar unit)⟩
      Context: colvar
      Acceptable values: positive decimal
      Description: Defines the spring stiffness for the extendedLagrangian mode, by setting the +
    • Keyword extendedFluctuation⟨Standard + deviation between the colvar and the fictitious particle (colvar unit)⟩
      Context: colvar
      Acceptable values: positive decimal
      Description: Defines the spring stiffness for the extendedLagrangian mode, by setting the typical deviation between the colvar and the extended degree of freedom due to thermal - fluctuation. The spring force constant is calculated internally as kBT ∕σ2, - where σ + fluctuation. The spring force constant is calculated internally as kBT ∕σ2, + where σ is the value of extendedFluctuation.
      • -
    • Keyword extendedTimeConstant⟨Oscillation - period of the fictitious particle (fs)⟩
      Context: colvar
      Acceptable values: positive decimal
      Default value: 200
      Description: Defines the inertial mass of the fictitious particle, by setting the oscillation +
    • Keyword extendedTimeConstant⟨Oscillation + period of the fictitious particle (fs)⟩
      Context: colvar
      Acceptable values: positive decimal
      Default value: 200
      Description: Defines the inertial mass of the fictitious particle, by setting the oscillation period of the harmonic oscillator formed by the fictitious particle and the spring. The period should be much larger than the MD time step to ensure accurate integration of the extended - particle's equation of motion. The fictitious mass is calculated internally as kBT (τ∕2πσ)2, - where τ - is the period and σ + particle's equation of motion. The fictitious mass is calculated internally as kBT (τ∕2πσ)2, + where τ + is the period and σ is the typical fluctuation (see above).
      • -
    • Keyword extendedTemp⟨Temperature - for the extended degree of freedom (K)⟩
      Context: colvar
      Acceptable values: positive decimal
      Default value: thermostat temperature
      Description: Temperature used for calculating the coupling force constant of the extended +
    • Keyword extendedTemp⟨Temperature + for the extended degree of freedom (K)⟩
      Context: colvar
      Acceptable values: positive decimal
      Default value: thermostat temperature
      Description: Temperature used for calculating the coupling force constant of the extended variable (see extendedFluctuation) and, if needed, as a target temperature for extended Langevin dynamics (see extendedLangevinDamping). This should normally be left at its default value.
      • -
    • Keyword extendedLangevinDamping⟨Damping - factor for extended Langevin dynamics (ps−1)⟩
      Context: colvar
      Acceptable values: positive decimal
      Default value: 1.0
      Description: If this is non-zero, the extended degree of freedom undergoes Langevin +
    • Keyword extendedLangevinDamping⟨Damping + factor for extended Langevin dynamics (ps−1)⟩
      Context: colvar
      Acceptable values: positive decimal
      Default value: 1.0
      Description: If this is non-zero, the extended degree of freedom undergoes Langevin dynamics at temperature extendedTemp. The friction force is minus extendedLangevinDamping times the velocity. This is useful because the extended dynamics coordinate may heat up in the transient non-equilibrium regime of ABF. Use moderate damping values, to limit viscous friction (potentially slowing down diffusive sampling) and stochastic noise (increasing the variance of statistical measurements). In doubt, use the default value.
      • -
    •   Keyword reflectingLowerBoundary⟨Whether - the lower boundary reflects the extended Lagrangian particle⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: This turns the specified lowerBoundary into a reflecting wall for the extended +
    •   Keyword reflectingLowerBoundary⟨Whether + the lower boundary reflects the extended Lagrangian particle⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: This turns the specified lowerBoundary into a reflecting wall for the extended particle: upon collision, the particle is reflected with opposite momentum.
      • -
    •   Keyword reflectingUpperBoundary⟨Whether - the upper boundary reflects the extended Lagrangian particle⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: This turns the specified upperBoundary into a reflecting wall for the extended +
    •   Keyword reflectingUpperBoundary⟨Whether + the upper boundary reflects the extended Lagrangian particle⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: This turns the specified upperBoundary into a reflecting wall for the extended particle: upon collision, the particle is reflected with opposite momentum.
    -

    +

    (Go to Contents)

    -

    +

    4.19 Multiple time-step variables

    -

    +

      -
    • Keyword timeStepFactor⟨Compute - this colvar once in a certain number of timesteps⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 1
      Description: Instructs this colvar to activate at a time interval equal to the base (MD) +
    • Keyword timeStepFactor⟨Compute + this colvar once in a certain number of timesteps⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 1
      Description: Instructs this colvar to activate at a time interval equal to the base (MD) timestep times timeStepFactor.[11] At other time steps, the value of the variable is not updated, and no biasing forces are applied. Any forces exerted by biases are accumulated over the given time interval, then applied as an impulse at the next update.
    -

    +

    (Go to Contents)

    -

    +

    4.20 Backward-compatibility

    -

    +

      -
    • Keyword subtractAppliedForce⟨Do - not include biasing forces in the total force for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: If the colvar supports total force calculation (see 4.13.1), all forces applied to +
    • Keyword subtractAppliedForce⟨Do + not include biasing forces in the total force for this colvar⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: If the colvar supports total force calculation (see 4.13.1), all forces applied to this colvar by biases will be removed from the total force. This keyword allows to recover some of the “system force" calculation available in the Colvars module before version 2016-08-10. Please note that removal of all other external forces (including biasing forces applied to a @@ -2749,99 +2794,99 @@

      4.20 option is not recommended.

    -

    +

    (Go to Contents)

    -

    +

    4.21 Statistical analysis

    -

    -

    Run-time calculations of statistical properties that depend explicitly on time can be performed for +

    +

    Run-time calculations of statistical properties that depend explicitly on time can be performed for individual collective variables. Currently, several types of time correlation functions, running averages and running standard deviations are implemented. For run-time computation of histograms, please see the histogram bias (6.10).

      -
    •   Keyword corrFunc⟨Calculate - a time correlation function?⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: Whether or not a time correlaction function should be calculated for this colvar. +
    •   Keyword corrFunc⟨Calculate + a time correlation function?⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: Whether or not a time correlaction function should be calculated for this colvar.
      • -
    • Keyword corrFuncWithColvar⟨Colvar - name for the correlation function⟩
      Context: colvar
      Acceptable values: string
      Description: By default, the auto-correlation function (ACF) of this colvar, ξi, +
    • Keyword corrFuncWithColvar⟨Colvar + name for the correlation function⟩
      Context: colvar
      Acceptable values: string
      Description: By default, the auto-correlation function (ACF) of this colvar, ξi, is calculated. When this option is specified, the correlation function is calculated instead with - another colvar, ξj, - which must be of the same type (scalar, vector, or quaternion) as ξi. -
      • -
    • Keyword corrFuncType⟨Type - of the correlation function⟩
      Context: colvar
      Acceptable values: velocity, coordinate or coordinate_p2
      Default value: velocity
      Description: With coordinate or velocity, the correlation function Ci,j(t) = - ⟨Π (ξi(t0),ξj(t0 +t))⟩ - is calculated between the variables ξi - and ξj, - or their velocities. Π(ξi,ξj) + another colvar, ξj, + which must be of the same type (scalar, vector, or quaternion) as ξi. +
      • +
    • Keyword corrFuncType⟨Type + of the correlation function⟩
      Context: colvar
      Acceptable values: velocity, coordinate or coordinate_p2
      Default value: velocity
      Description: With coordinate or velocity, the correlation function Ci,j(t) = + ⟨Π (ξi(t0),ξj(t0 +t))⟩ + is calculated between the variables ξi + and ξj, + or their velocities. Π(ξi,ξj) is the scalar product when calculated between scalar or vector values, whereas for quaternions it is the cosine between the two corresponding rotation axes. With coordinate_p2, the - second order Legendre polynomial, (3cos &ApplyFunction; (𝜃)2 −1)∕2, + second order Legendre polynomial, (3cos &ApplyFunction; (𝜃)2 −1)∕2, is used instead of the cosine.
      • -
    • Keyword corrFuncNormalize⟨Normalize - the time correlation function?⟩
      Context: colvar
      Acceptable values: boolean
      Default value: on
      Description: If enabled, the value of the correlation function at t = - 0 is normalized to 1; otherwise, it equals to ⟨O (ξi,ξj)⟩. +
    • Keyword corrFuncNormalize⟨Normalize + the time correlation function?⟩
      Context: colvar
      Acceptable values: boolean
      Default value: on
      Description: If enabled, the value of the correlation function at t = + 0 is normalized to 1; otherwise, it equals to ⟨O (ξi,ξj)⟩.
      • -
    • Keyword corrFuncLength⟨Length - of the time correlation function⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 1000
      Description: Length (in number of points) of the time correlation function. +
    • Keyword corrFuncLength⟨Length + of the time correlation function⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 1000
      Description: Length (in number of points) of the time correlation function.
      • -
    • Keyword corrFuncStride⟨Stride - of the time correlation function⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 1
      Description: Number of steps between two values of the time correlation function. +
    • Keyword corrFuncStride⟨Stride + of the time correlation function⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 1
      Description: Number of steps between two values of the time correlation function.
      • -
    • Keyword corrFuncOffset⟨Offset - of the time correlation function⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 0
      Description: The starting time (in number of steps) of the time correlation function (default: - t = - 0). Note: the value at t = +
    • Keyword corrFuncOffset⟨Offset + of the time correlation function⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 0
      Description: The starting time (in number of steps) of the time correlation function (default: + t = + 0). Note: the value at t = 0 is always used for the normalization.
      • -
    • Keyword corrFuncOutputFile⟨Output - file for the time correlation function⟩
      Context: colvar
      Acceptable values: UNIX filename
      Default value: output. <name >.corrfunc.dat +
    • Keyword corrFuncOutputFile⟨Output + file for the time correlation function⟩
      Context: colvar
      Acceptable values: UNIX filename
      Default value: output. <name >.corrfunc.dat
      Description: The time correlation function is saved in this file.
      • -
    •   Keyword runAve⟨Calculate - the running average and standard deviation⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: Whether or not the running average and standard deviation should be calculated +
    •   Keyword runAve⟨Calculate + the running average and standard deviation⟩
      Context: colvar
      Acceptable values: boolean
      Default value: off
      Description: Whether or not the running average and standard deviation should be calculated for this colvar.
      • -
    • Keyword runAveLength⟨Length - of the running average window⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 1000
      Description: Length (in number of points) of the running average window. +
    • Keyword runAveLength⟨Length + of the running average window⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 1000
      Description: Length (in number of points) of the running average window.
      • -
    • Keyword runAveStride⟨Stride - of the running average window values⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 1
      Description: Number of steps between two values within the running average window. +
    • Keyword runAveStride⟨Stride + of the running average window values⟩
      Context: colvar
      Acceptable values: positive integer
      Default value: 1
      Description: Number of steps between two values within the running average window.
      • -
    • Keyword runAveOutputFile⟨Output - file for the running average and standard deviation⟩
      Context: colvar
      Acceptable values: UNIX filename
      Default value: output. <name >.runave.traj +
    • Keyword runAveOutputFile⟨Output + file for the running average and standard deviation⟩
      Context: colvar
      Acceptable values: UNIX filename
      Default value: output. <name >.runave.traj
      Description: The running average and standard deviation are saved in this file.
    -

    +

    -

    +

    (Go to Contents)

    -

    +

    5 Selecting atoms

    -

    -

    To define collective variables, atoms are usually selected as groups. Each group is defined +

    +

    To define collective variables, atoms are usually selected as groups. Each group is defined using an identifier that is unique in the context of the specific colvar component (e.g. for a distance component, the two groups are group1 and group2). The identifier is followed by a brace-delimited block containing selection keywords and other parameters, including an optional name:

      -
    • Keyword name⟨Unique - name for the atom group⟩
      Context: atom group
      Acceptable values: string
      Description: This parameter defines a unique name for this atom group, which can be +
    • Keyword name⟨Unique + name for the atom group⟩
      Context: atom group
      Acceptable values: string
      Description: This parameter defines a unique name for this atom group, which can be referred to in the definition of other atom groups (including in other colvars) by invoking atomsOfGroup as a selection keyword.
    -

    +

    (Go to Contents)

    -

    +

    5.1 Atom selection keywords

    -

    -

    Selection keywords may be used individually or in combination with each other, and each can be +

    +

    Selection keywords may be used individually or in combination with each other, and each can be repeated any number of times. Selection is incremental: each keyword adds the corresponding atoms to the selection, so that different sets of atoms can be combined. However, atoms included by multiple keywords are only counted once. Below is an example configuration @@ -2849,63 +2894,63 @@

    5.1 keywords, demonstrating how they can be combined together: most simulations only use one of them.

    -
    -

    atoms {

      # add atoms 1 and 3 to this group (note: first atom in the system is 1)
      atomNumbers { 
        1 3
      }

      # add atoms starting from 20 up to and including 50
      atomNumbersRange 20-50
      # add index group (requires a .ndx file to be provided globally)
      indexGroup Water
    }

    +
    +

    atoms {

      # add atoms 1 and 3 to this group (note: first atom in the system is 1)
      atomNumbers { 
        1 3
      }

      # add atoms starting from 20 up to and including 50
      atomNumbersRange 20-50
      # add index group (requires a .ndx file to be provided globally)
      indexGroup Water
    }

    -

    The resulting selection includes atoms 1 and 3, those between 20 and 50, and those in the index +

    The resulting selection includes atoms 1 and 3, those between 20 and 50, and those in the index group called “Water". The indices of this group are read from the file provided by the global keyword indexFile. -

    The complete list of selection keywords available in Gromacs is: +

    The complete list of selection keywords available in GROMACS is:

      -
    • Keyword atomNumbers⟨List - of atom numbers⟩
      Context: atom group
      Acceptable values: space-separated list of positive integers
      Description: This option adds to the group all the atoms whose numbers are in the list. The +
    • Keyword atomNumbers⟨List + of atom numbers⟩
      Context: atom group
      Acceptable values: space-separated list of positive integers
      Description: This option adds to the group all the atoms whose numbers are in the list. The number of the first atom in the system is 1: to convert from a VMD selection, use “atomselect get serial".
      • -
    • Keyword indexGroup⟨Name - of index group to be used (GROMACS format)⟩
      Context: atom group
      Acceptable values: string
      Description: If the name of an index file has been provided by indexFile, this option allows +
    • Keyword indexGroup⟨Name + of index group to be used (GROMACS format)⟩
      Context: atom group
      Acceptable values: string
      Description: If the name of an index file has been provided by indexFile, this option allows to select one index group from that file: the atoms from that index group will be used to define the current group.
      • -
    • Keyword atomsOfGroup⟨Name - of group defined previously⟩
      Context: atom group
      Acceptable values: string
      Description: Refers to a group defined previously using its user-defined name. This adds all +
    • Keyword atomsOfGroup⟨Name + of group defined previously⟩
      Context: atom group
      Acceptable values: string
      Description: Refers to a group defined previously using its user-defined name. This adds all atoms of that named group to the current group.
      • -
    • Keyword atomNumbersRange⟨Atoms +
    • Keyword atomNumbersRange⟨Atoms - within a number range⟩
      Context: atom group
      Acceptable values: <Starting - number >- <Ending - number > + within a number range⟩
      Context: atom group
      Acceptable values: <Starting + number >- <Ending + number >
      Description: This option includes in the group all atoms whose numbers are within the range specified. The number of the first atom in the system is 1.
      • -
    • Keyword dummyAtom⟨Dummy - atom position (nm)⟩
      Context: atom group
      Acceptable values: (x, y, z) triplet
      Description: Instead of selecting any atom, this option makes the group a virtual particle at +
    • Keyword dummyAtom⟨Dummy + atom position (nm)⟩
      Context: atom group
      Acceptable values: (x, y, z) triplet
      Description: Instead of selecting any atom, this option makes the group a virtual particle at a fixed position in space. This is useful e.g. to replace a group's center of geometry with a user-defined position.
    -

    +

    (Go to Contents)

    -

    +

    5.2 Moving frame of reference.

    -

    -

    The following options define an automatic calculation of an optimal translation (centerToReference) or +

    +

    The following options define an automatic calculation of an optimal translation (centerToReference) or optimal rotation (rotateToReference), that superimposes the positions of this group to a provided set of reference coordinates. Alternately, centerToOrigin applies a translation to place the geometric center of the group at (0, 0, 0). This can allow, for example, to effectively remove from certain colvars the effects of molecular tumbling and of diffusion. Given the set of atomic positions -xi, the colvar -ξ can be defined on a set of -roto-translated positions xi′ = R(xi−xC)+xref. -xC is the geometric -center of the xi, -R is the optimal rotation matrix -to the reference positions and xref +xi, the colvar +ξ can be defined on a set of +roto-translated positions xi′ = R(xi−xC)+xref. +xC is the geometric +center of the xi, +R is the optimal rotation matrix +to the reference positions and xref is the geometric center of the reference positions. -

    Components that are defined based on pairwise distances are naturally invariant under global +

    Components that are defined based on pairwise distances are naturally invariant under global roto-translations. Other components are instead affected by global rotations or translations: however, they can be made invariant if they are expressed in the frame of reference of a chosen group of atoms, using the centerToReference and rotateToReference options. Finally, a few components are defined by @@ -2915,7 +2960,7 @@

    5.2 Warning on rotating frames of reference and periodic boundary conditions. +

    Warning on rotating frames of reference and periodic boundary conditions. rotateToReference affects coordinates that depend on minimum-image distances in periodic boundary conditions (PBC). After rotation of the coordinates, the periodic cell vectors become irrelevant: the rotated system is effectively non-periodic. A safe way to handle this is to ensure that the relevant @@ -2924,26 +2969,26 @@

    5.2 Warning on rotating frames of reference and ABF. +

    Warning on rotating frames of reference and ABF. Note that centerToReference and rotateToReference may affect the Jacobian derivative of colvar components in a way that is not taken into account by default. Be careful when using these options in ABF simulations or when using total force values.

      -
    • Keyword centerToReference⟨Implicitly - remove translations for this group⟩
      Context: atom group
      Acceptable values: boolean
      Default value: off
      Description: If this option is on, the center of geometry of the group will be aligned with +
    • Keyword centerToReference⟨Implicitly + remove translations for this group⟩
      Context: atom group
      Acceptable values: boolean
      Default value: off
      Description: If this option is on, the center of geometry of the group will be aligned with that of the reference positions provided by refPositions or refPositionsFile. Colvar components will only have access to the aligned positions. Note: unless otherwise specified, rmsd and eigenvector set this option to on by default.
      • -
    • Keyword centerToOrigin⟨Implicitly - remove translations for this group by keeping its center at the origin⟩
      Context: atom group
      Acceptable values: boolean
      Default value: off
      Description: This option implies centerToReference. If this option is on, coordinates from +
    • Keyword centerToOrigin⟨Implicitly + remove translations for this group by keeping its center at the origin⟩
      Context: atom group
      Acceptable values: boolean
      Default value: off
      Description: This option implies centerToReference. If this option is on, coordinates from the group will be translated so that the center of geometry of the group remains at (0, 0, 0), except if fittingGroup is enabled. In that case, the translation applied is the translation that brings the center of geometry of the fitting group to (0, 0, 0).
      • -
    • Keyword rotateToReference⟨Implicitly - remove rotations for this group⟩
      Context: atom group
      Acceptable values: boolean
      Default value: off
      Description: If this option is on, the coordinates of this group will be optimally superimposed +
    • Keyword rotateToReference⟨Implicitly + remove rotations for this group⟩
      Context: atom group
      Acceptable values: boolean
      Default value: off
      Description: If this option is on, the coordinates of this group will be optimally superimposed to the reference positions provided by refPositions or refPositionsFile. The rotation will be performed around the center of geometry if centerToReference is on, or around the origin otherwise. The algorithm used is the same employed by the orientation colvar @@ -2951,20 +2996,20 @@

      5.2 Note: unless otherwise specified, rmsd and eigenvector set this option to on by default.

      • -
    •   Keyword refPositions⟨Reference - positions for fitting (nm)⟩
      Context: atom group
      Acceptable values: space-separated list of (x, y, z) triplets
      Description: This option provides a list of reference coordinates for centerToReference +
    •   Keyword refPositions⟨Reference + positions for fitting (nm)⟩
      Context: atom group
      Acceptable values: space-separated list of (x, y, z) triplets
      Description: This option provides a list of reference coordinates for centerToReference and/or rotateToReference, and is mutually exclusive with refPositionsFile. If only centerToReference is on, the list may contain a single (x, y, z) triplet; if also rotateToReference is on, the list should be as long as the atom group, and its order must match the order in which atoms were defined.
      • -
    •   Keyword refPositionsFile⟨File - containing the reference positions for fitting⟩
      Context: atom group
      Acceptable values: UNIX filename
      Description: This option provides a list of reference coordinates for centerToReference +
    •   Keyword refPositionsFile⟨File + containing the reference positions for fitting⟩
      Context: atom group
      Acceptable values: UNIX filename
      Description: This option provides a list of reference coordinates for centerToReference and/or rotateToReference, and is mutually exclusive with refPositions. The acceptable file format is XYZ (3.7.3), which is read in double precision. .
      • -
    •   Keyword fittingGroup⟨Use - an alternate set of atoms to define the roto-translation⟩
      Context: atom group
      Acceptable values: Block fittingGroup { ... }
      Default value: This atom group itself
      Description: If either centerToReference or rotateToReference is defined, this keyword +
    •   Keyword fittingGroup⟨Use + an alternate set of atoms to define the roto-translation⟩
      Context: atom group
      Acceptable values: Block fittingGroup { ... }
      Default value: This atom group itself
      Description: If either centerToReference or rotateToReference is defined, this keyword defines an alternate atom group to calculate the optimal roto-translation. Use this option to define a continuous rotation if the structure of the group involved changes significantly (a typical symptom would be the message “Warning: discontinuous rotation!"). Performance @@ -2973,52 +3018,72 @@

      5.2 enableFitGradients for details.

    -

    The following two options have default values appropriate for the vast majority of applications, and are -only provided to support rare, special cases.

    +

    The following options have default values appropriate for the vast majority of applications, and are only +provided to support rare, special cases.

      -
    •   Keyword enableFitGradients⟨Include - the roto-translational contribution to colvar gradients⟩
      Context: atom group
      Acceptable values: boolean
      Default value: on
      Description: When either centerToReference or rotateToReference is on, the gradients of - some colvars include terms proportional to ∂R∕∂xi - (rotational gradients) and ∂xC∕∂xi +
    •   Keyword enableFitGradients⟨Include + the roto-translational contribution to colvar gradients⟩
      Context: atom group
      Acceptable values: boolean
      Default value: on
      Description: When either centerToReference or rotateToReference is on, the gradients of + some colvars include terms proportional to ∂R∕∂xi + (rotational gradients) and ∂xC∕∂xi (translational gradients). By default, these terms are calculated and included in the total gradients; if this option is set to off, they are neglected. In the case of a minimum RMSD component, this flag is automatically disabled because the contributions of those derivatives to the gradients cancel out; other types of variable will require projecting each of the gradients - of the variable onto each of the gradients of the roto-translation (i.e. a O(N2) - loop). When fittingGroup is enabled, the computation is a O(N ×M) + of the variable onto each of the gradients of the roto-translation (i.e. a O(N2) + loop). When fittingGroup is enabled, the computation is a O(N ×M) loop for all variables, including RMSDs.
    -

    +

    (Go to Contents)

    -

    +

    5.3 Treatment of periodic boundary conditions.

    -

    -

    -

      +

    +

    In simulations with periodic boundary conditions (PBCs), Colvars computes all distances between two +points following the nearest-image convention, using PBC parameters provided by GROMACS. However, +many common variables rely on a consistent definition of the center of mass or geometry of a group of +atoms. This requires the use of unwrapped coordinates, which are not subject to “jumps" when they +diffuse across periodic boundaries. +

    Internally, GROMACS wraps individual atom coordinates into a single periodic cell, which +may break the calculation of some variables if their atom groups become split across PBCs. +To prevent this, Colvars unwraps coordinates throughout the simulation, by assuming that +each atom group is intact in the initial coordinates, and canceling any later jumps across +the periodic box. This information is propagated across restarts using a checkpoint (cpt) +file. +

    Whenever preparing a new simulation input with gmx grompp, users should provide input coordinates +such that the atoms involved in collective variables will not be artificially moved across the boundary +conditions, but occupy their relevant positions relative to each other -- usually the nearest ones. +Unwrapped coordinates are communicated between replicas when GROMACS is used for +replica-exchange simulations. Thus, Colvars is compatible with native replica-exchange in +GROMACS. +

    In general, internal coordinate wrapping by GROMACS does not affect the calculation of colvars if +each atom group satisfies one or more of the following: + + +

    1. it is composed by only one atom;
    2. it is used by a colvar component which does not make use of its center of geometry, but only of pairwise distances (distanceInv, coordNum, hBond, alpha, dihedralPC);
    3. it is used by a colvar component that ignores the ill-defined Cartesian components of its - center of mass (such as the x - and y + center of mass (such as the x + and y components of a membrane's center of mass modeled with distanceZ).
    -

    +

    (Go to Contents)

    -

    +

    5.4 Performance of a Colvars calculation based on group size.

    -

    -

    In simulations performed with message-passing programs (such as NAMD or LAMMPS), the -calculation of energy and forces is distributed (i.e., parallelized) across multiple nodes, as well as over the -processor cores of each node. When Colvars is enabled, certain atomic coordinates are collected on a -single node, where the calculation of collective variables and of their biases is executed. This means that -for simulations over large numbers of nodes, a Colvars calculation may produce a significant +

    +

    In simulations performed with message-passing programs (such as NAMD, LAMMPS or GROMACS), +the calculation of energy and forces is distributed (i.e., parallelized) across multiple nodes, as well as over +the processor cores of each node. When Colvars is enabled, certain atomic coordinates are collected on +a single node, where the calculation of collective variables and of their biases is executed. This means +that for simulations over large numbers of nodes, a Colvars calculation may produce a significant overhead, coming from the costs of transmitting atomic coordinates to one node and of processing them. -

    Performance can be improved in multiple ways:

    +

    Performance can be improved in multiple ways:

    -

    +

    -

    +

    (Go to Contents)

    -

    +

    6 Biasing and analysis methods

    -

    -

    A biasing or analysis method can be applied to existing collective variables by using the following +

    +

    A biasing or analysis method can be applied to existing collective variables by using the following configuration:

    -
    -

    -
     <biastype > {
      name  <name >
-
      colvars  <xi1 >  <xi2 > ...
       <parameters >
    }

    +
    +

    +
     <biastype > {
      name  <name >
+
      colvars  <xi1 >  <xi2 > ...
       <parameters >
    }

    -

    The keyword <biastype > +

    The keyword <biastype > indicates the method of choice. There can be multiple instances of the same method, e.g. using multiple harmonic blocks allows defining multiple restraints. -

    All biasing and analysis methods implemented recognize the following options:

    +

    All biasing and analysis methods implemented recognize the following options:

      -
    •   Keyword name⟨Identifier - for the bias⟩
      Context: colvar bias
      Acceptable values: string
      Default value: <type -of bias ><bias -index > +
    •   Keyword name⟨Identifier + for the bias⟩
      Context: colvar bias
      Acceptable values: string
      Default value: <type +of bias ><bias +index >
      Description: This string is used to identify the bias or analysis method in the output, and to name some output files. Tip: although a unique name is assigned automatically, you are strongly encouraged to give a name to a bias that you may want to analyze later. For @@ -3067,23 +3134,23 @@

      6 smd" for a moving harmonic restraint or “us" for a static one.

      • -
    •   Keyword colvars⟨Collective - variables involved⟩
      Context: colvar bias
      Acceptable values: space-separated list of colvar names
      Description: This option selects by name all the variables to which this bias or analysis will +
    •   Keyword colvars⟨Collective + variables involved⟩
      Context: colvar bias
      Acceptable values: space-separated list of colvar names
      Description: This option selects by name all the variables to which this bias or analysis will be applied.
      • -
    •   Keyword outputEnergy⟨Write - the current bias energy to the trajectory file⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: If this option is chosen and colvarsTrajFrequency is not zero, the current +
    •   Keyword outputEnergy⟨Write + the current bias energy to the trajectory file⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: If this option is chosen and colvarsTrajFrequency is not zero, the current value of the biasing energy will be written to the trajectory file during the simulation.
      • -
    •   Keyword outputFreq⟨Frequency - (number of steps) at which output files are written⟩
      Context: colvar bias
      Acceptable values: positive integer
      Default value: colvarsRestartFrequency
      Description: If this bias produces aggregated data that needs to be written to disk (for +
    •   Keyword outputFreq⟨Frequency + (number of steps) at which output files are written⟩
      Context: colvar bias
      Acceptable values: positive integer
      Default value: colvarsRestartFrequency
      Description: If this bias produces aggregated data that needs to be written to disk (for example, a PMF), this number specifies the number of steps after which these data are written to files. A value of zero disables writing files for this bias during the simulation (except for outputEnergy, which is controlled by colvarsTrajFrequency). All output files are also written at the end of a simulation run, regardless of the value of this number.
      • -
    •   Keyword bypassExtendedLagrangian⟨Apply - bias to actual colvars, bypassing extended coordinates⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: This option is implemented by the harmonicWalls and histogram biases. It +
    •   Keyword bypassExtendedLagrangian⟨Apply + bias to actual colvars, bypassing extended coordinates⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: This option is implemented by the harmonicWalls and histogram biases. It is only relevant if the bias is applied to one or several extended-Lagrangian colvars (4.18), for example within an eABF (6.3) simulation. Usually, biases use the value of the extended coordinate as a proxy for the actual colvar, and their biasing forces are applied to the @@ -3091,8 +3158,8 @@

      6   Keyword stepZeroData⟨Accumulate - data starting at step 0 of a simulation run⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: This option is meaningful for biases that record and accumulate data during +
    •   Keyword stepZeroData⟨Accumulate + data starting at step 0 of a simulation run⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: This option is meaningful for biases that record and accumulate data during a simulation, such as ABF (6.2), metadynamics (6.4), histograms (6.10) and in general any bias that accumulates free-energy samples with thermodynamic integration, or TI (6.1). When this option is disabled (default), data will only be recorded into the bias after the first @@ -3101,178 +3168,178 @@

      6   Keyword scaledBiasingForce⟨Scale - biasing force by a factor in an external histogram⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: If this option is set to on, the biasing force at each step will be scaled by +
    •   Keyword scaledBiasingForce⟨Scale + biasing force by a factor in an external histogram⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: If this option is set to on, the biasing force at each step will be scaled by a factor provided in the grid of an external histogram. The histogram file is provided by scaledBiasingForceFactorsGrid. It ought to be noted that if the variables are not in any grids of the histogram, the scaling factor is 1.0.
      • -
    •   Keyword scaledBiasingForceFactorsGrid⟨A - histogram file with the scaling factor of biasing force in each bin⟩
      Context: colvar bias
      Acceptable values: string
      Description: If scaledBiasingForce is set to on, this option accepts the filename of the +
    •   Keyword scaledBiasingForceFactorsGrid⟨A + histogram file with the scaling factor of biasing force in each bin⟩
      Context: colvar bias
      Acceptable values: string
      Description: If scaledBiasingForce is set to on, this option accepts the filename of the histogram file that contains the scaling factors. The histogram file is expected to be in “multicolumn" format (3.7.4), similar to the low-dimensional the PMF files written by metadynamics and ABF.

    -

    +

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    -

    +

    6.1 Thermodynamic integration

    -

    -

    The methods implemented here provide a variety of estimators of conformational free-energies. These +

    +

    The methods implemented here provide a variety of estimators of conformational free-energies. These are carried out at run-time, or with the use of post-processing tools over the generated output files. The specifics of each estimator are discussed in the documentation of each biasing or analysis method. -

    A special case is the traditional thermodynamic integration (TI) method, used for example to compute +

    A special case is the traditional thermodynamic integration (TI) method, used for example to compute potentials of mean force (PMFs). Most types of restraints (6.5, 6.7, 6.8, ...) as well as metadynamics (6.4) can optionally use TI alongside their own estimator, based on the keywords documented below.

      -
    •   Keyword writeTIPMF⟨Write - the PMF computed by thermodynamic integration⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: If the bias is applied to a variable that supports the calculation of total forces +
    •   Keyword writeTIPMF⟨Write + the PMF computed by thermodynamic integration⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: If the bias is applied to a variable that supports the calculation of total forces (see outputTotalForce and 4.13.1), this option allows calculating the corresponding PMF by - thermodynamic integration, and writing it to the file output. <name >.ti.pmf, - where <name > + thermodynamic integration, and writing it to the file output. <name >.ti.pmf, + where <name > is the name of the bias and the contents of the file are in multicolumn text format (3.7.4). The total force includes the forces applied to the variable by all bias, except those from this bias itself. If any bias applies time-dependent forces besides the one using this option, an error is raised.
      • -
    •   Keyword writeTISamples⟨Write - the free-energy gradient samples⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: This option allows to compute total forces for use with thermodynamic integration +
    •   Keyword writeTISamples⟨Write + the free-energy gradient samples⟩
      Context: colvar bias
      Acceptable values: boolean
      Default value: off
      Description: This option allows to compute total forces for use with thermodynamic integration as done by the keyword writeTIPMF. The names of the files containing the variables' histogram - and mean thermodynamic forces are output. <name >.ti.count - and output. <name >.ti.force, + and mean thermodynamic forces are output. <name >.ti.count + and output. <name >.ti.force, respectively: these can be used by abf_integrate (see 6.2.4) or similar utility. Note that because the .force file contains mean forces instead of free-energy gradients, abf_integrate - <filename > + <filename > -s -1.0 should be used. This option is on by default when writeTIPMF is on, but can be enabled separately if the bias is applied to more than one variable, making not possible the direct integration of the PMF at runtime. If any bias applies time-dependent forces besides the one using this option, an error is raised.
    -

    In adaptive biasing force (ABF) (6.2) the above keywords are not recognized, because their +

    In adaptive biasing force (ABF) (6.2) the above keywords are not recognized, because their functionality is either included already (conventional ABF) or not available (extended-system ABF).

    -

    +

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    -

    +

    6.2 Adaptive Biasing Force

    -

    -

    For a full description of the Adaptive Biasing Force method, see reference [12]. For details about this +

    +

    For a full description of the Adaptive Biasing Force method, see reference [12]. For details about this implementation, see references [13] and [14]. When publishing research that makes use of this functionality, please cite references [12] and [14]. -

    An alternate usage of this feature is the application of custom tabulated biasing potentials to one or +

    An alternate usage of this feature is the application of custom tabulated biasing potentials to one or more colvars. See inputPrefix and updateBias below. -

    Combining ABF with the extended Lagrangian feature (4.18) of the variables produces the +

    Combining ABF with the extended Lagrangian feature (4.18) of the variables produces the extended-system ABF variant of the method (6.3). -

    ABF is based on the thermodynamic integration (TI) scheme for computing +

    ABF is based on the thermodynamic integration (TI) scheme for computing free energy profiles. The free energy as a function of a set of collective variables -ξ = (ξi)i∈[1,n] is defined from the -canonical distribution of ξ, -𝒫(ξ): +ξ = (ξi)i∈[1,n] is defined from the +canonical distribution of ξ, +𝒫(ξ):

    - + A (ξ) = −1 βln &ApplyFunction; 𝒫(ξ)+A0 (16)
    -

    In the TI formalism, the free energy is obtained from its gradient, which is generally calculated in the form of the -average of a force Fξ -exerted on ξ, taken -over an iso-ξ +

    In the TI formalism, the free energy is obtained from its gradient, which is generally calculated in the form of the +average of a force Fξ +exerted on ξ, taken +over an iso-ξ surface:

    - + ∇ &ApplyFunction;ξA (ξ) = ⟨−Fξ⟩ξ (17)
    -

    Several formulae that take the form of (17) have been proposed. This implementation +

    Several formulae that take the form of (17) have been proposed. This implementation relies partly on the classic formulation [15], and partly on a more versatile scheme originating in a work by Ruiz-Montero et al. [16], generalized by den Otter [17] and extended to multiple variables by Ciccotti et al. [18]. Consider a system subject to constraints of the form -σk(x) = 0. Let +σk(x) = 0. Let -(vi)i∈[1,n] be arbitrarily chosen -vector fields (ℝ3N → ℝ3N) -verifying, for all i, -j, and -k: +(vi)i∈[1,n] be arbitrarily chosen +vector fields (ℝ3N → ℝ3N) +verifying, for all i, +j, and +k:

    - + vi⋅∇ &ApplyFunction;xξj = δij (18) vi⋅∇ &ApplyFunction;xσk = 0 (19) -

    +

    -

    then the following holds [18]: +

    then the following holds [18]:

    - + ∂A ∂ξi = ⟨vi⋅∇ &ApplyFunction;xV −kBT ∇ &ApplyFunction;x⋅vi⟩ξ (20)
    -

    where V is the potential -energy function. vi +

    where V is the potential +energy function. vi can be interpreted as the direction along which the force acting on variable -ξi is measured, +ξi is measured, whereas the second term in the average corresponds to the geometric entropy contribution that appears as a Jacobian correction in the classic formalism [15]. Condition (18) states that the direction along which the total force on -ξi is measured is orthogonal to +ξi is measured is orthogonal to -the gradient of ξj, which means -that the force measured on ξi -does not act on ξj. -

    Equation (19) implies that constraint forces are orthogonal to the directions along which the free +the gradient of ξj, which means +that the force measured on ξi +does not act on ξj. +

    Equation (19) implies that constraint forces are orthogonal to the directions along which the free energy gradient is measured, so that the measurement is effectively performed on unconstrained degrees of freedom. -

    In the framework of ABF, Fξ is -accumulated in bins of finite size δξ, +

    In the framework of ABF, Fξ is +accumulated in bins of finite size δξ, thereby providing an estimate of the free energy gradient according to equation (17). The biasing force applied along the collective variables to overcome free energy barriers is calculated as:

    - + FABF = α(N ξ)×∇ &ApplyFunction;xA~(ξ) (21)
    -

    where ∇ &ApplyFunction;xA~ +

    where ∇ &ApplyFunction;xA~ denotes the current estimate of the free energy gradient at the current point -ξ in the collective -variable subspace, and α(Nξ) +ξ in the collective +variable subspace, and α(Nξ) is a scaling factor that is ramped from 0 to 1 as the local number of samples -Nξ +Nξ increases to prevent non-equilibrium effects in the early phase of the simulation, when the gradient estimate has a large variance. See the fullSamples parameter below for details. -

    As sampling of the phase space proceeds, the estimate -∇ &ApplyFunction;xA~ is +

    As sampling of the phase space proceeds, the estimate +∇ &ApplyFunction;xA~ is progressively refined. The biasing force introduced in the equations of motion guarantees that in the bin centered -around ξ, +around ξ, the forces acting along the selected collective variables average to zero over time. Eventually, as the underlying free energy surface is canceled by the adaptive bias, evolution of the system along -ξ is +ξ is governed mainly by diffusion. Although this implementation of ABF can in principle be used in arbitrary dimension, a higher-dimension collective variable space is likely to be difficult to sample and visualize. Most commonly, the number of variables is one or two, sometimes three.

    -

    +

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    -

    +

    6.2.1 ABF requirements on collective variables
    -

    -

    The following conditions must be met for an ABF simulation to be possible and to produce an accurate +

    +

    The following conditions must be met for an ABF simulation to be possible and to produce an accurate estimate of the free energy profile. Note that these requirements do not apply when using the extended-system ABF method (6.3). -

    +

    1. Only linear combinations of colvar components can be used in ABF calculations.
      2. @@ -3282,27 +3349,27 @@
      6.2.1 oneSiteTotalForce, if available.
    2. Mutual orthogonality of colvars. In a multidimensional ABF calculation, equation (18) must be satisfied for any - two colvars ξi - and ξj. + two colvars ξi + and ξj. Various cases fulfill this orthogonality condition:
        -
      • ξi - and ξj +
      • ξi + and ξj are based on non-overlapping sets of atoms.
        • -
      • atoms involved in the force measurement on ξi - do not participate in the definition of ξj. +
      • atoms involved in the force measurement on ξi + do not participate in the definition of ξj. This can be obtained using the option oneSiteTotalForce of the distance, angle, and - dihedral components (example: Ramachandran angles ϕ, - ψ). + dihedral components (example: Ramachandran angles ϕ, + ψ).
        • -
      • ξi - and ξj +
      • ξi + and ξj are orthogonal by construction. Useful cases are the sum and difference of two components, or distance_z and distance_xy using the same axis.
    3. Mutual orthogonality of components: when several components are combined into a colvar, it is assumed that - their vectors vi + their vectors vi (equation (20)) are mutually orthogonal. The cases described for colvars in the previous paragraph apply. @@ -3316,53 +3383,53 @@
      6.2.1 distance component.
    -

    +

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    -

    +

    6.2.2 Parameters for ABF
    -

    -

    ABF depends on parameters from each collective variable to define the grid on which free energy +

    +

    ABF depends on parameters from each collective variable to define the grid on which free energy gradients are computed: see 4.16 for detauls. Other parameters to control the ABF runtime can be set in the ABF configuration block:

      -
    • Keyword name: see definition of name (biasing and analysis methods) +
    • Keyword name: see definition of name (biasing and analysis methods)
      • -
    • Keyword colvars: see definition of colvars (biasing and analysis methods) +
    • Keyword colvars: see definition of colvars (biasing and analysis methods)
      • -
    • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods) +
    • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods)
      • -
    • Keyword outputFreq: see definition of outputFreq (biasing and analysis methods) +
    • Keyword outputFreq: see definition of outputFreq (biasing and analysis methods)
      • -
    • Keyword stepZeroData: see definition of stepZeroData (biasing and analysis methods) +
    • Keyword stepZeroData: see definition of stepZeroData (biasing and analysis methods)
      • -
    • Keyword fullSamples⟨Number - of samples in a bin prior to application of the ABF⟩
      Context: abf
      Acceptable values: positive integer
      Default value: 200
      Description: To avoid non-equilibrium effects due to large fluctuations of the force exerted +
    • Keyword fullSamples⟨Number + of samples in a bin prior to application of the ABF⟩
      Context: abf
      Acceptable values: positive integer
      Default value: 200
      Description: To avoid non-equilibrium effects due to large fluctuations of the force exerted along the colvars, it is recommended to apply a biasing force only after a the estimate has started converging. If fullSamples is non-zero, the applied biasing force is scaled by a factor - α(Nξ) - between 0 and 1. If the number of samples Nξ + α(Nξ) + between 0 and 1. If the number of samples Nξ in the current bin is higher than fullSamples, the factor is one. If it is less than half of fullSamples, the factor is zero and no bias is applied. Between those two thresholds, the - factor follows a linear ramp from 0 to 1: α(Nξ) = (2Nξ∕fullSamples)−1 + factor follows a linear ramp from 0 to 1: α(Nξ) = (2Nξ∕fullSamples)−1 .
      • -
    • Keyword maxForce⟨Maximum - magnitude of the ABF force⟩
      Context: abf
      Acceptable values: positive decimals (one per colvar)
      Default value: disabled
      Description: This option enforces a cap on the magnitude of the biasing force effectively +
    • Keyword maxForce⟨Maximum + magnitude of the ABF force⟩
      Context: abf
      Acceptable values: positive decimals (one per colvar)
      Default value: disabled
      Description: This option enforces a cap on the magnitude of the biasing force effectively applied by this ABF bias on each colvar. This can be useful in the presence of singularities in the PMF such as hard walls, where the discretization of the average force becomes very inaccurate, causing the colvar's diffusion to get “stuck" at the singularity. To enable this cap, provide one non-negative value for each colvar. The unit of force is kJ/mol/(colvar unit).
      • -
    • Keyword hideJacobian⟨Remove - geometric entropy term from calculated free energy gradient?⟩
      Context: abf
      Acceptable values: boolean
      Default value: no
      Description: In a few special cases, most notably distance-based variables, an alternate +
    • Keyword hideJacobian⟨Remove + geometric entropy term from calculated free energy gradient?⟩
      Context: abf
      Acceptable values: boolean
      Default value: no
      Description: In a few special cases, most notably distance-based variables, an alternate definition of the potential of mean force is traditionally used, which excludes the Jacobian term describing the effect of geometric entropy on the distribution of the variable. This results, for example, in particle-particle potentials of mean force being flat at large separations. The Jacobian term is exactly represented in equation (20) by the second term of the average, - −kBT ∇ &ApplyFunction;x⋅vi. + −kBT ∇ &ApplyFunction;x⋅vi. Enabling the hideJacobian option causes the output data to follow the traditional potential of mean force convention, by omitting this contribution from the measured free energy gradients. To ensure uniform sampling despite the incomplete description of the free energy, an additional @@ -3373,18 +3440,18 @@
      6.2.2 Keyword historyFreq⟨Frequency - (in timesteps) at which ABF history files are accumulated⟩
      Context: abf
      Acceptable values: positive integer
      Default value: 0
      Description: If this number is non-zero, the free energy gradient estimate and sampling +
    • Keyword historyFreq⟨Frequency + (in timesteps) at which ABF history files are accumulated⟩
      Context: abf
      Acceptable values: positive integer
      Default value: 0
      Description: If this number is non-zero, the free energy gradient estimate and sampling histogram (and the PMF in one-dimensional calculations) are written to files on disk at the given time interval. History file names use the same prefix as output files, with “.hist" appended (output.hist.pmf). historyFreq must be a multiple of outputFreq.
      • -
    •   Keyword inputPrefix⟨Filename - prefix for reading ABF data⟩
      Context: abf
      Acceptable values: list of strings
      Description: If this parameter is set, for each item in the list, ABF tries to read a gradient and - a sampling files named <inputPrefix >.grad - and <inputPrefix >.count. +
    •   Keyword inputPrefix⟨Filename + prefix for reading ABF data⟩
      Context: abf
      Acceptable values: list of strings
      Description: If this parameter is set, for each item in the list, ABF tries to read a gradient and + a sampling files named <inputPrefix >.grad + and <inputPrefix >.count. This is done at startup and sets the initial state of the ABF algorithm. The data from all provided files is combined appropriately. Also, the grid definition (min and max values, width) need not be the same that for the current run. This command is useful to piece together @@ -3393,66 +3460,66 @@
      6.2.2 Keyword applyBias⟨Apply - the ABF bias?⟩
      Context: abf
      Acceptable values: boolean
      Default value: yes
      Description: If this is set to no, the calculation proceeds normally but the adaptive biasing +
    • Keyword applyBias⟨Apply + the ABF bias?⟩
      Context: abf
      Acceptable values: boolean
      Default value: yes
      Description: If this is set to no, the calculation proceeds normally but the adaptive biasing force is not applied. Data is still collected to compute the free energy gradient. This is mostly intended for testing purposes, and should not be used in routine simulations.
      • -
    • Keyword updateBias⟨Update - the ABF bias?⟩
      Context: abf
      Acceptable values: boolean
      Default value: yes
      Description: If this is set to no, the initial biasing force (e.g. read from a restart file or +
    • Keyword updateBias⟨Update + the ABF bias?⟩
      Context: abf
      Acceptable values: boolean
      Default value: yes
      Description: If this is set to no, the initial biasing force (e.g. read from a restart file or through inputPrefix) is not updated during the simulation. As a result, a constant bias is applied. This can be used to apply a custom, tabulated biasing potential to any combination of colvars. To that effect, one should prepare a gradient file containing the gradient of the potential to be applied (negative of the bias force), and a count file containing only values greater than fullSamples. These files must match the grid parameters of the colvars.
    -

    +

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    -

    +

    6.2.3 Output files
    -

    -

    The ABF bias produces the following files, all in multicolumn text format (3.7.4):

    +

    +

    The ABF bias produces the following files, all in multicolumn text format (3.7.4):

    • output.grad: current estimate of the free energy gradient (grid), in multicolumn;
    • output.count: histogram of samples collected, on the same grid;
    • output.pmf: integrated free energy profile or PMF (for dimension 1, and dimension 2 or 3).
    -

    Also in the case of one-dimensional calculations, the ABF bias can report its current energy via +

    Also in the case of one-dimensional calculations, the ABF bias can report its current energy via outputEnergy; in higher dimensions, such computation is not implemented and the energy reported is zero. -

    If several ABF biases are defined concurrently, their name is inserted to produce unique filenames for +

    If several ABF biases are defined concurrently, their name is inserted to produce unique filenames for output, as in output.abf1.grad. This should not be done routinely and could lead to meaningless results: only do it if you know what you are doing! -

    If the colvar space has been partitioned into sections (windows) in which independent ABF +

    If the colvar space has been partitioned into sections (windows) in which independent ABF simulations have been run, the resulting data can be merged using the inputPrefix option described above (a run of 0 steps is enough).

    -

    +

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    -

    +

    6.2.4 Multidimensional free energy surfaces
    -

    -

    The ABF method only produces an estimate of the free energy gradient. The free energy surface itself +

    +

    The ABF method only produces an estimate of the free energy gradient. The free energy surface itself can be computed depending on the value of integrate and related options.

      -
    • Keyword integrate⟨Integrate +
    • Keyword integrate⟨Integrate free energy surface from ABF gradients (dim < - 3)⟩
      Context: abf
      Acceptable values: boolean
      Default value: yes
      Description: This option, active by default when the dimension of the colvar space is 3 or less, + 3)⟩
      Context: abf
      Acceptable values: boolean
      Default value: yes
      Description: This option, active by default when the dimension of the colvar space is 3 or less, enables the calculation of an integrated free energy surface every time ABF output files are written. In dimension 2 or 3, integration is performed by solving a Poisson equation: [19]
      - + ∇ &ApplyFunction;2A t = ∇ &ApplyFunction;⋅Gt (22)
      -

      wehere Gt is the estimated - gradient at time t, - and At +

      wehere Gt is the estimated + gradient at time t, + and At is corresponding free energy surface. The free energy surface is written under the file name <outputName>.pmf, in a plain text format (see 3.7.4) that can be read by most data plotting and analysis programs (e.g. Gnuplot). Periodic boundary conditions are applied to periodic coordinates, @@ -3461,30 +3528,30 @@

      6.2.4 [19] for details.

      • -
    • Keyword integrateTol⟨Tolerance - for free energy integration⟩
      Context: abf
      Acceptable values: positive decimal
      Default value: 1e-6
      Description: The conjugate gradients algorithm used to integrate the free energy surface is +
    • Keyword integrateTol⟨Tolerance + for free energy integration⟩
      Context: abf
      Acceptable values: positive decimal
      Default value: 1e-6
      Description: The conjugate gradients algorithm used to integrate the free energy surface is stopped when the RMS error reaches integrateTol.
      • -
    • Keyword integrateMaxIterations -⟨Maximum iterations for - free energy integration⟩
      Context: abf
      Acceptable values: integer
      Default value: 10000
      Description: The conjugate gradients algorithm used to integrate the free energy surface is +
    • Keyword integrateMaxIterations +⟨Maximum iterations for + free energy integration⟩
      Context: abf
      Acceptable values: integer
      Default value: 10000
      Description: The conjugate gradients algorithm used to integrate the free energy surface is stopped when the number of iterations reaches integrateMaxIterations, unless the RMS error has reached integrateTol before.
    -

    In dimension 4 or greater, integrating the discretized gradient becomes non-trivial. The +

    In dimension 4 or greater, integrating the discretized gradient becomes non-trivial. The standalone utility abf_integrate is provided to perform that task. Because 4D ABF calculations are uncommon, this tool is practically deprecated by the Poisson integration described above. -

    abf_integrate reads the gradient data and uses it to perform a Monte-Carlo (M-C) simulation in +

    abf_integrate reads the gradient data and uses it to perform a Monte-Carlo (M-C) simulation in discretized collective variable space (specifically, on the same grid used by ABF to discretize the free energy gradient). By default, a history-dependent bias (similar in spirit to metadynamics) is used: at each M-C step, the bias at the current position is incremented by a preset amount (the hill height). Upon convergence, this bias counteracts optimally the underlying gradient; it is negated to obtain the estimate of the free energy surface. -

    abf_integrate is invoked using the command-line:
    abf_integrate <gradient_file> [-n <nsteps>] [-t <temp>] [-m (0|1)] [-h <hill_height>] [-f +

    abf_integrate is invoked using the command-line:
    abf_integrate <gradient_file> [-n <nsteps>] [-t <temp>] [-m (0|1)] [-h <hill_height>] [-f <factor>] -

    The gradient file name is provided first, followed by other parameters in any order. They are described +

    The gradient file name is provided first, followed by other parameters in any order. They are described below, with their default value in square brackets:

    -

    Using the default values of all parameters should give reasonable results in most cases. -

    abf_integrate produces the following output files:

    +

    Using the default values of all parameters should give reasonable results in most cases. +

    abf_integrate produces the following output files:

    -

    Note: Typically, the “deviation" vector field does not vanish as the integration converges. This happens +

    Note: Typically, the “deviation" vector field does not vanish as the integration converges. This happens because the numerical estimate of the gradient does not exactly derive from a potential, due to numerical approximations used to obtain it (finite sampling and discretization on a grid). See Ref.[19] for details.

    -

    +

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    -

    +

    6.3 Extended-system Adaptive Biasing Force (eABF)

    -

    -

    Extended-system ABF (eABF) is a variant of ABF (6.2) where the bias is not applied +

    +

    Extended-system ABF (eABF) is a variant of ABF (6.2) where the bias is not applied directly to the collective variable, but to an extended coordinate (“fictitious variable") -λ that +λ that evolves dynamically according to Newtonian or Langevin dynamics. Such an extended coordinate is enabled for a given colvar using the extendedLagrangian and associated keywords (4.18). The theory of eABF and the present implementation are documented in detail in reference [20]. -

    Defining an ABF bias on a colvar wherein the extendedLagrangian option is active will perform eABF +

    Defining an ABF bias on a colvar wherein the extendedLagrangian option is active will perform eABF automatically; there is no dedicated option. -

    The extended variable λ is -coupled to the colvar z = ξ(q) by the -harmonic potential (k∕2)(z−λ)2. Under eABF -dynamics, the adaptive bias on λ +

    The extended variable λ is +coupled to the colvar z = ξ(q) by the +harmonic potential (k∕2)(z−λ)2. Under eABF +dynamics, the adaptive bias on λ is the running estimate of the average spring force:

    - + Fbias(λ∗) = ⟨k(λ −z)⟩ λ∗ (23)
    -

    where the angle brackets indicate a canonical average conditioned by -λ = λ∗. +

    where the angle brackets indicate a canonical average conditioned by +λ = λ∗. At long simulation times, eABF produces a flat histogram of the extended variable -λ, and a flattened -histogram of ξ, +λ, and a flattened +histogram of ξ, whose exact shape depends on the strength of the coupling as defined by extendedFluctuation in the colvar. Coupling should be somewhat loose for faster exploration and convergence, but strong enough that the bias does help overcome barriers along the colvar -ξ.[20] +ξ.[20] Distribution of the colvar may be assessed by plotting its histogram, which is written to the output.zcount file in every eABF simulation. Note that a histogram bias (6.10) applied to an extended-Lagrangian colvar will access the extended degree of freedom -λ, not the original -colvar ξ; +λ, not the original +colvar ξ; however, the joint histogram may be explicitly requested by listing the name of the colvar twice in a row within the colvars parameter of the histogram block. -

    The eABF PMF is that of the coordinate λ, -it is not exactly the free energy profile of ξ. +

    The eABF PMF is that of the coordinate λ, +it is not exactly the free energy profile of ξ. That quantity can be calculated based on the CZAR estimator.

    -

    +

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    -

    +

    6.3.1 CZAR estimator of the free energy
    -

    -

    The corrected z-averaged restraint (CZAR) estimator is described in detail in reference [20]. It is +

    +

    The corrected z-averaged restraint (CZAR) estimator is described in detail in reference [20]. It is computed automatically in eABF simulations, regardless of the number of colvars involved. Note that ABF may also be applied on a combination of extended and non-extended colvars; in that case, CZAR still provides an unbiased estimate of the free energy gradient. -

    CZAR estimates the free energy gradient as:

    - +

    CZAR estimates the free energy gradient as:

    + A′(z) = −1 β dln &ApplyFunction; ρ~(z) dz +k(⟨λ⟩z−z). (24)
    -

    where z = ξ(q) is the colvar, -λ is the extended variable -harmonically coupled to z -with a force constant k, -and ρ~(z) is the observed -distribution (histogram) of z, +

    where z = ξ(q) is the colvar, +λ is the extended variable +harmonically coupled to z +with a force constant k, +and ρ~(z) is the observed +distribution (histogram) of z, affected by the eABF bias. -

    Parameters for the CZAR estimator are:

    +

    Parameters for the CZAR estimator are:

      -
    • Keyword CZARestimator⟨Calculate - CZAR estimator of the free energy?⟩
      Context: abf
      Acceptable values: boolean
      Default value: yes
      Description: This option is only available when ABF is performed on extended-Lagrangian +
    • Keyword CZARestimator⟨Calculate + CZAR estimator of the free energy?⟩
      Context: abf
      Acceptable values: boolean
      Default value: yes
      Description: This option is only available when ABF is performed on extended-Lagrangian colvars. When enabled, it triggers calculation of the free energy following the CZAR estimator.
      • -
    • Keyword writeCZARwindowFile⟨Write - internal data from CZAR to a separate file?⟩
      Context: abf
      Acceptable values: boolean
      Default value: no
      Description: When this option is enabled, eABF simulations will write a file containing the - z-averaged +
    • Keyword writeCZARwindowFile⟨Write + internal data from CZAR to a separate file?⟩
      Context: abf
      Acceptable values: boolean
      Default value: no
      Description: When this option is enabled, eABF simulations will write a file containing the + z-averaged restraint force under the name output.zgrad. The same information is always included in the colvars state file, which is sufficient for restarting an eABF simulation. These separate file is only useful when joining adjacent windows from a stratified eABF simulation, either to @@ -3612,91 +3679,91 @@
      6.3.1 Similar to ABF, the CZAR estimator produces two output files in multicolumn text format (3.7.4): +

      Similar to ABF, the CZAR estimator produces two output files in multicolumn text format (3.7.4):

      • output.czar.grad: current estimate of the free energy gradient (grid), in multicolumn;
      • output.czar.pmf: only for one-dimensional calculations, integrated free energy profile or PMF.
      -

      The sampling histogram associated with the CZAR estimator is the -z-histogram, +

      The sampling histogram associated with the CZAR estimator is the +z-histogram, which is written in the file output.zcount.

      -

      +

      (Go to Contents)

      -

      +

      6.4 Metadynamics

      -

      -

      The metadynamics method uses a history-dependent potential [21] that generalizes to +

      +

      The metadynamics method uses a history-dependent potential [21] that generalizes to any type of colvars the conformational flooding [22] and local elevation [23] methods, originally formulated to use as colvars the principal components of a covariance matrix or a set of dihedral angles, respectively. The metadynamics potential on the colvars -ξ = (ξ1,ξ2,… &ApplyFunction;,ξNcv) is +ξ = (ξ1,ξ2,… &ApplyFunction;,ξNcv) is defined as:

      - + Vmeta (ξ (t)) = ∑t′=δt,2δt,…t′<tW∏ i=1Ncv exp &ApplyFunction; (−(ξi(t)−ξi(t′))2 2σξi2 ), (25)
      -

      where Vmeta +

      where Vmeta is the history-dependent potential acting on the current values of the colvars -ξ, +ξ, and depends only parametrically on the previous values of the colvars. -Vmeta is constructed as a -sum of Ncv-dimensional +Vmeta is constructed as a +sum of Ncv-dimensional repulsive Gaussian “hills", whose height is a chosen energy constant -W, +W, and whose centers are the previously explored configurations - (ξ(δt),ξ(2δt),… &ApplyFunction;). -

      During the simulation, the system evolves towards the nearest minimum of the “effective" potential of mean -force Ã(ξ), + (ξ(δt),ξ(2δt),… &ApplyFunction;). +

      During the simulation, the system evolves towards the nearest minimum of the “effective" potential of mean +force Ã(ξ), which is the sum of the “real" underlying potential of mean force -A(ξ) and the the -metadynamics potential, Vmeta(ξ). +A(ξ) and the the +metadynamics potential, Vmeta(ξ). Therefore, at any given time the probability of observing the configuration -ξ∗ is proportional -to exp &ApplyFunction; (−Ã(ξ∗)∕κBT ): +ξ∗ is proportional +to exp &ApplyFunction; (−Ã(ξ∗)∕κBT ): this is also the probability that a new Gaussian “hill" is added at that configuration. If the simulation is run for a sufficiently long time, each local minimum is canceled out by the sum of the Gaussian “hills". At that stage the “effective" potential of mean force -Ã(ξ) is constant, and -−Vmeta(ξ) is an estimator of the “real" -potential of mean force A(ξ), +Ã(ξ) is constant, and +−Vmeta(ξ) is an estimator of the “real" +potential of mean force A(ξ), save for an additive constant:

      - + A(ξ) ≃−Vmeta(ξ)+K (26)
      -

      Such estimate of the free energy can be provided by enabling writeFreeEnergyFile. +

      Such estimate of the free energy can be provided by enabling writeFreeEnergyFile. Assuming that the set of collective variables includes all relevant degrees of freedom, the predicted error of the estimate is a simple function of the correlation times of the colvars -τξi, and of the user-defined -parameters W, -σξi and -δt +τξi, and of the user-defined +parameters W, +σξi and +δt [24]. In typical applications, a good rule of thumb can be to choose the ratio -W∕δt much smaller -than κBT ∕τξ, where -τξ is the longest -among ξ's -correlation times: σξi +W∕δt much smaller +than κBT ∕τξ, where +τξ is the longest +among ξ's +correlation times: σξi then dictates the resolution of the calculated PMF. -

      If the metadynamics parameters are chosen correctly, after an equilibration time, -te, +

      If the metadynamics parameters are chosen correctly, after an equilibration time, +te, the estimator provided by eq. 26 oscillates on time around the “real" free energy, thereby a better estimate of the latter can be obtained as the time average of the bias potential after -te +te [25, 26]:

      - + A (ξ) = − 1 ttot−te∫ tettot Vmeta(ξ,t)dt (27)
      -

      where te +

      where te is the time after which the bias potential grows (approximately) evenly during the simulation and -ttot is the +ttot is the total simulation time. The free energy calculated according to eq. 27 can thus be obtained averaging on time multiple time-dependent free energy estimates, that can be printed out through the keyword keepFreeEnergyFiles. An alternative is to obtain the free energy profiles by summing the hills @@ -3706,289 +3773,289 @@

      6.4 -

      +

      (Go to Contents)

      -

      +

      6.4.1 Treatment of the PMF boundaries
      -

      -

      In typical scenarios the Gaussian hills of a metadynamics potential are interpolated and summed +

      +

      In typical scenarios the Gaussian hills of a metadynamics potential are interpolated and summed together onto a grid, which is much more efficient than computing each hill independently at every step (the keyword useGrids is on by default). This numerical approximation typically yields negligible errors in the resulting PMF [1]. However, due to the finite thickness of the Gaussian function, the metadynamics potential would suddenly vanish each time a variable exceeds its grid boundaries. -

      To avoid such discontinuity the Colvars metadynamics code will keep an explicit copy +

      To avoid such discontinuity the Colvars metadynamics code will keep an explicit copy of each hill that straddles a grid's boundary, and will use it to compute metadynamics forces outside the grid. This measure is taken to protect the accuracy and stability of a metadynamics simulation, except in cases of “natural" boundaries (for example, the -[0 : 180] interval +[0 : 180] interval of an angle colvar) or when the flags hardLowerBoundary and hardUpperBoundary are explicitly set by the user. Unfortunately, processing explicit hills alongside the potential and force grids could easily become inefficient, slowing down the simulation and increasing the state file's size. -

      In general, it is a good idea to define a repulsive potential to avoid hills from coming too close to the +

      In general, it is a good idea to define a repulsive potential to avoid hills from coming too close to the grid's boundaries, for example as a harmonicWalls restraint (see 6.7).
      -

      Example: Using harmonic walls to protect the grid's boundaries.

      -
      -

      colvar {
        name r
        distance { ... }
        upperBoundary 15.0
        width 0.2
      }

      metadynamics {
        name meta_r
        colvars r
        hillWeight 0.001
        hillWidth 2.0
      }

      harmonicWalls {
        name wall_r
        colvars r
        upperWalls 13.0
        upperWallConstant 2.0
      }

      +

      Example: Using harmonic walls to protect the grid's boundaries.

      +
      +

      colvar {
        name r
        distance { ... }
        upperBoundary 15.0
        width 0.2
      }

      metadynamics {
        name meta_r
        colvars r
        hillWeight 0.001
        hillWidth 2.0
      }

      harmonicWalls {
        name wall_r
        colvars r
        upperWalls 13.0
        upperWallConstant 2.0
      }

      -

      In the colvar r, the distance function used has a lowerBoundary automatically set to 0 by +

      In the colvar r, the distance function used has a lowerBoundary automatically set to 0 by default, thus the keyword lowerBoundary itself is not mandatory and hardLowerBoundary is set to yes internally. However, upperBoundary does not have such a “natural" choice of value. The metadynamics potential meta_r will individually process any hill whose center is too close to the upperBoundary, more precisely within fewer grid points than 6 times the Gaussian -σ +σ parameter plus one. It goes without saying that if the colvar r represents a distance between two freely-moving molecules, it will cross this “threshold" rather frequently. -

      In this example, where the value of hillWidth -(2σ) amounts +

      In this example, where the value of hillWidth +(2σ) amounts to 2 grid points, the threshold is 6+1 = 7 grid points away from upperBoundary. In explicit units, the width -of r is -wr = 0.2 Å, and the -threshold is 15.0 - 7×0.2 +of r is +wr = 0.2 Å, and the +threshold is 15.0 - 7×0.2 = 13.6 Å. -

      The wall_r restraint included in the example prevents this: the position of its upperWall is 13 Å, i.e. 3 grid +

      The wall_r restraint included in the example prevents this: the position of its upperWall is 13 Å, i.e. 3 grid points below the buffer's threshold (13.6 Å). For the chosen value of upperWallConstant, the energy of the wall_r -bias at r = rupper +bias at r = rupper = 13.6 Å is:

      - + E∗ = 1 2k (r−rupper wr )2 = 1 22.0 (−3)2 = 9kcal∕mol
      -

      which results in a relative probability exp &ApplyFunction; (−E∗∕κBT ) ≃ -3×10−7 that r +

      which results in a relative probability exp &ApplyFunction; (−E∗∕κBT ) ≃ +3×10−7 that r crosses the threshold. The probability that r exceeds upperBoundary, which is further away, has also become vanishingly small. At that point, you may want to set hardUpperBoundary to yes for r, and let meta_r know that no special treatment near the grid's boundaries will be needed. -

      What is the impact of the wall restraint onto the PMF? Not a very complicated one: the PMF reconstructed +

      What is the impact of the wall restraint onto the PMF? Not a very complicated one: the PMF reconstructed by metadynamics will simply show a sharp increase in free-energy where the wall potential kicks in -(r  > +(r  > 13 Å). You may then choose between using the PMF only up until that point and discard the rest, or subtracting the energy of the harmonicWalls restraint from the PMF itself. Keep in mind, however, that the statistical convergence of metadynamics may be less accurate where the wall potential is strong. -

      In summary, although it would be simpler to set the wall's position upperWall and the grid's boundary +

      In summary, although it would be simpler to set the wall's position upperWall and the grid's boundary upperBoundary to the same number, the finite width of the Gaussian hills calls for setting the former strictly within the latter.

      -

      +

      (Go to Contents)

      -

      +

      6.4.2 Required metadynamics keywords
      -

      -

      To enable a metadynamics-based calculation, a metadynamics {...} block must be included in the +

      +

      To enable a metadynamics-based calculation, a metadynamics {...} block must be included in the Colvars configuration file. -

      By default, metadynamics bias energy and forces will be recorded onto a grid, the parameters of +

      By default, metadynamics bias energy and forces will be recorded onto a grid, the parameters of which can be defined within the definition of each colvar, as described in 4.16. -

      Other required keywords will be specified within the metadynamics block: these +

      Other required keywords will be specified within the metadynamics block: these are colvars (the names of the variables involved), hillWeight (the weight parameter -W), and the -widths 2σ +W), and the +widths 2σ of the Gaussian hills in each dimension that can be given either as the single dimensionless parameter hillWidth, or explicitly for each colvar with gaussianSigmas.

        -
      • Keyword name: see definition of name (biasing and analysis methods) +
      • Keyword name: see definition of name (biasing and analysis methods)
        • -
      • Keyword colvars: see definition of colvars (biasing and analysis methods) +
      • Keyword colvars: see definition of colvars (biasing and analysis methods)
        • -
      • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods) +
      • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods)
        • -
      • Keyword outputFreq: see definition of outputFreq (biasing and analysis methods) +
      • Keyword outputFreq: see definition of outputFreq (biasing and analysis methods)
        • -
      • Keyword writeTIPMF: see definition of writeTIPMF (biasing and analysis methods) +
      • Keyword writeTIPMF: see definition of writeTIPMF (biasing and analysis methods)
        • -
      • Keyword writeTISamples: see definition of writeTISamples (biasing and analysis +
      • Keyword writeTISamples: see definition of writeTISamples (biasing and analysis methods)
        • -
      • Keyword stepZeroData: see definition of stepZeroData (biasing and analysis methods) +
      • Keyword stepZeroData: see definition of stepZeroData (biasing and analysis methods)
        • -
      •   Keyword hillWeight⟨Height - of each hill (kJ/mol)⟩
        Context: metadynamics
        Acceptable values: positive decimal
        Description: This option sets the height W +
      •   Keyword hillWeight⟨Height + of each hill (kJ/mol)⟩
        Context: metadynamics
        Acceptable values: positive decimal
        Description: This option sets the height W of the Gaussian hills that are added during this run. Lower values provide more accurate sampling of the system's degrees of freedom at the price of longer simulation times to complete a PMF calculation based on metadynamics.
        • -
      •   Keyword hillWidth⟨Width - 2σ - of a Gaussian hill, measured in number of grid points⟩
        Context: metadynamics
        Acceptable values: positive decimal
        Description: This keyword sets the Gaussian width 2σξi +
      •   Keyword hillWidth⟨Width + 2σ + of a Gaussian hill, measured in number of grid points⟩
        Context: metadynamics
        Acceptable values: positive decimal
        Description: This keyword sets the Gaussian width 2σξi for all colvars, expressed in number of grid points, with the grid spacing along each colvar - ξ + ξ determined by the respective value of width. Values between 1 and 3 are recommended for this option: smaller numbers will fail to adequately interpolate each Gaussian function [1], while larger values may be unable to account for steep free-energy gradients. The values of - each half-width σξi - in the physical units of ξi - are also printed by Gromacs at initialization time; alternatively, they may be set explicitly via - gaussianSigmas. -
        • -
      •   Keyword gaussianSigmas⟨Half-widths - σ - of the Gaussian hill (one for each colvar)⟩
        Context: metadynamics
        Acceptable values: space-separated list of decimals
        Description: This option sets the parameters σξi - of the Gaussian hills along each colvar ξi, - expressed in the same unit of ξi. + each half-width σξi + in the physical units of ξi + are also printed by GROMACS at initialization time; alternatively, they may be set explicitly + via gaussianSigmas. +
        • +
      •   Keyword gaussianSigmas⟨Half-widths + σ + of the Gaussian hill (one for each colvar)⟩
        Context: metadynamics
        Acceptable values: space-separated list of decimals
        Description: This option sets the parameters σξi + of the Gaussian hills along each colvar ξi, + expressed in the same unit of ξi. No restrictions are placed on each value, but a warning will be printed if useGrids is on and - the Gaussian width 2σξi - is smaller than the corresponding grid spacing, width(ξi). + the Gaussian width 2σξi + is smaller than the corresponding grid spacing, width(ξi). If not given, default values will be computed from the dimensionless number hillWidth.
        • -
      •   Keyword newHillFrequency⟨Frequency - of hill creation⟩
        Context: metadynamics
        Acceptable values: positive integer
        Default value: 1000
        Description: This option sets the number of steps after which a new Gaussian hill is added +
      •   Keyword newHillFrequency⟨Frequency + of hill creation⟩
        Context: metadynamics
        Acceptable values: positive integer
        Default value: 1000
        Description: This option sets the number of steps after which a new Gaussian hill is added to the metadynamics potential. The product of this number and the integration time-step - defines the parameter δt + defines the parameter δt in eq. 25. Higher values provide more accurate statistical sampling, at the price of longer simulation times to complete a PMF calculation.
      -

      +

      (Go to Contents)

      -

      +

      6.4.3 Output files
      -

      -

      When interpolating grids are enabled (default behavior), the PMF is written by default every +

      +

      When interpolating grids are enabled (default behavior), the PMF is written by default every colvarsRestartFrequency steps to the file output.pmf in multicolumn text format (3.7.4). The following two options allow to disable or control this behavior and to track statistical convergence:

        -
      • Keyword writeFreeEnergyFile⟨Periodically - write the PMF for visualization⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: on
        Description: When useGrids and this option are on, the PMF is written every outputFreq +
      • Keyword writeFreeEnergyFile⟨Periodically + write the PMF for visualization⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: on
        Description: When useGrids and this option are on, the PMF is written every outputFreq steps.
        • -
      • Keyword keepFreeEnergyFiles⟨Keep - all the PMF files⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: When writeFreeEnergyFile and this option are on, the step number is included +
      • Keyword keepFreeEnergyFiles⟨Keep + all the PMF files⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: When writeFreeEnergyFile and this option are on, the step number is included in the file name, thus generating a series of PMF files. Activating this option can be useful to follow more closely the convergence of the simulation, by comparing PMFs separated by short times.
        • -
      •   Keyword writeHillsTrajectory⟨Write - a log of new hills⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: If this option is on, a file containing the Gaussian hills written by the metadynamics - bias, with the name:
        “output.colvars. <name >.hills.traj",
        which can be useful to post-process the time series of the Gassian hills. Each line is written +
      •   Keyword writeHillsTrajectory⟨Write + a log of new hills⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: If this option is on, a file containing the Gaussian hills written by the metadynamics + bias, with the name:
        “output.colvars. <name >.hills.traj",
        which can be useful to post-process the time series of the Gassian hills. Each line is written every newHillFrequency, regardless of the value of outputFreq. When multipleReplicas - is on, its name is changed to:
        “output.colvars. <name >. <replicaID >.hills.traj".
        The columns of this file are the centers of the hills, ξi(t′), - followed by the half-widths, σξi, - and the weight, W. - Note: prior to version 2020-02-24, the full-width 2σ - of the Gaussian was reported in lieu of σ. + is on, its name is changed to:
        “output.colvars. <name >. <replicaID >.hills.traj".
        The columns of this file are the centers of the hills, ξi(t′), + followed by the half-widths, σξi, + and the weight, W. + Note: prior to version 2020-02-24, the full-width 2σ + of the Gaussian was reported in lieu of σ.
      -

      +

      (Go to Contents)

      -

      +

      6.4.4 Performance optimization
      -

      The following options control the computational cost of metadynamics calculations, +

      The following options control the computational cost of metadynamics calculations, but do not affect results. Default values are chosen to minimize such cost with no loss of accuracy.
        -
      •   Keyword useGrids⟨Interpolate - the hills with grids⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: on
        Description: This option discretizes all hills for improved performance, accumulating their +
      •   Keyword useGrids⟨Interpolate + the hills with grids⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: on
        Description: This option discretizes all hills for improved performance, accumulating their energy and their gradients on two separate grids of equal spacing. Grids are defined by the values of lowerBoundary, upperBoundary and width for each colvar. Currently, this option is implemented for all types of variables except the non-scalar types (distanceDir or orientation). If expandBoundaries is defined in one of the colvars, grids are automatically expanded along the direction of that colvar.
        • -
      • Keyword rebinGrids⟨Recompute - the grids when reading a state file⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: When restarting from a state file, the grid's parameters (boundaries and +
      • Keyword rebinGrids⟨Recompute + the grids when reading a state file⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: When restarting from a state file, the grid's parameters (boundaries and widths) saved in the state file override those in the configuration file. Enabling this option forces the grids to match those in the current configuration file.
        • -
      • Keyword keepHills⟨Write - each individual hill to the state file⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: When useGrids and this option are on, all hills are saved to the state file in +
      • Keyword keepHills⟨Write + each individual hill to the state file⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: When useGrids and this option are on, all hills are saved to the state file in their analytic form, alongside their grids. This makes it possible to later use exact analytic Gaussians for rebinGrids. To only keep track of the history of the added hills, writeHillsTrajectory is preferable.
      -

      +

      (Go to Contents)

      -

      +

      6.4.5 Ensemble-Biased Metadynamics
      -

      -

      The ensemble-biased metadynamics (EBMetaD) approach [27] is designed to reproduce a target +

      +

      The ensemble-biased metadynamics (EBMetaD) approach [27] is designed to reproduce a target probability distribution along selected collective variables. Standard metadynamics can be seen as a special case of EBMetaD with a flat distribution as target. This is achieved by weighing the Gaussian functions used in the metadynamics approach by the inverse of the target probability distribution:

      - + VEBmetaD (ξ (t)) = ∑t′=δt,2δt,…t′<t W exp &ApplyFunction; (Sρ)ρexp(ξ(t′))∏i=1Ncv exp &ApplyFunction; (−(ξi(t)−ξi(t′))2 2σξi2 ), (28)
      -

      where ρexp(ξ) is the target -probability distribution and Sρ = −∫ +

      where ρexp(ξ) is the target +probability distribution and Sρ = −∫ &ApplyFunction;ρexp(ξ)log &ApplyFunction; ρexp(ξ)dξ its corresponding differential entropy. The method is designed so that during the simulation the resulting distribution of -the collective variable ξ -converges to ρexp(ξ). +the collective variable ξ +converges to ρexp(ξ). A practical application of EBMetaD is to reproduce an “experimental" probability distribution, for example the distance distribution between spectroscopic labels inferred from Förster resonance energy transfer (FRET) or double electron-electron resonance (DEER) experiments [27]. -

      The PMF along ξ +

      The PMF along ξ can be estimated from the bias potential and the target ditribution [27]:

      - + A(ξ) ≃−VEBmetaD(ξ)−κBT log &ApplyFunction; ρexp(ξ) (29)
      -

      and obtained by enabling writeFreeEnergyFile. Similarly to eq. 27, a more accurate estimate of the +

      and obtained by enabling writeFreeEnergyFile. Similarly to eq. 27, a more accurate estimate of the free energy can be obtained by averaging (after an equilibration time) multiple time-dependent free energy estimates (see keepFreeEnergyFiles). -

      The following additional options define the configuration for the ensemble-biased metadynamics +

      The following additional options define the configuration for the ensemble-biased metadynamics approach:

        -
      •   Keyword ebMeta⟨Perform - ensemble-biased metadynamics⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: If enabled, this flag activates the ensemble-biased metadynamics as described +
      •   Keyword ebMeta⟨Perform + ensemble-biased metadynamics⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: If enabled, this flag activates the ensemble-biased metadynamics as described by Marinelli et al.[27]. The target distribution file, targetdistfile, is then required. The keywords lowerBoundary, upperBoundary and width for the respective variables are also needed to set the binning (grid) of the target distribution file.
        • -
      •   Keyword targetDistFile⟨Target - probability distribution file for ensemble-biased metadynamics⟩
        Context: metadynamics
        Acceptable values: multicolumn text file
        Description: This file provides the target probability distribution, ρexp(ξ), +
      •   Keyword targetDistFile⟨Target + probability distribution file for ensemble-biased metadynamics⟩
        Context: metadynamics
        Acceptable values: multicolumn text file
        Description: This file provides the target probability distribution, ρexp(ξ), reported in eq. 28. The latter distribution must be a tabulated function provided in a multicolumn text format (see 3.7.4). The provided distribution is then normalized.
        • -
      • Keyword ebMetaEquilSteps⟨Number - of equilibration steps for ensemble-biased metadynamics⟩
        Context: metadynamics
        Acceptable values: positive integer
        Description: The EBMetaD approach may introduce large hills in regions with small values +
      • Keyword ebMetaEquilSteps⟨Number + of equilibration steps for ensemble-biased metadynamics⟩
        Context: metadynamics
        Acceptable values: positive integer
        Description: The EBMetaD approach may introduce large hills in regions with small values of the target probability distribution (eq. 28). This happens, for example, if the probability distribution sampled by a conventional molecular dynamics simulation is significantly different from the target distribution. This may lead to instabilities at the beginning of the simulation related to large biasing forces. In this case, it is useful to introduce an equilibration stage in which the bias potential gradually switches from standard metadynamics (eq. 25) to EBmetaD - (eq. 28) as λVmeta(ξ)+(1−λ)VEBmetaD(ξ), - where λ = (ebMetaEquilSteps−step)∕ebMetaEquilSteps + (eq. 28) as λVmeta(ξ)+(1−λ)VEBmetaD(ξ), + where λ = (ebMetaEquilSteps−step)∕ebMetaEquilSteps and step is the current simulation step number.
        • -
      • Keyword targetDistMinVal⟨Minimum - value of the target distribution in reference to its maximum value⟩
        Context: metadynamics
        Acceptable values: positive decimal
        Description: It is useful to set a minimum value of the target probability distribution to +
      • Keyword targetDistMinVal⟨Minimum + value of the target distribution in reference to its maximum value⟩
        Context: metadynamics
        Acceptable values: positive decimal
        Description: It is useful to set a minimum value of the target probability distribution to avoid values of the latter that are nearly zero, leading to very large hills. This parameter sets the minimum value of the target probability distribution that is expressed as a fraction of its maximum value: minimum value = maximum value X targetDistMinVal. This implies that 0 <targetDistMinVal< 1 and its default value is set to 1/1000000. To avoid divisions by zero - (see eq. 28), if targetDistMinVal is set as zero, values of ρexp + (see eq. 28), if targetDistMinVal is set as zero, values of ρexp equal to zero are replaced by the smallest positive value read in the same file.
      -

      As with standard metadynamics, multidimensional probability distributions can be targeted using a +

      As with standard metadynamics, multidimensional probability distributions can be targeted using a single metadynamics block using multiple colvars and a multidimensional target distribution file (see 3.7.4). Instead, multiple probability distributions on different variables can be targeted separately in the same simulation by introducing multiple metadynamics blocks with the ebMeta option.
      -

      Example: EBmetaD configuration for a single variable.

      -
      -

      colvar {
        name r 
        distance {
          group1 { atomNumbers 991 992 }
          group2 { atomNumbers 1762 1763 }
        }
        upperBoundary 100.0 
        width 0.1 
      }

      metadynamics {
        name ebmeta
        colvars r
        hillWeight 0.01
        hillWidth 3.0
        ebMeta on
        targetDistFile targetdist1.dat
        ebMetaEquilSteps 500000
      }

      +

      Example: EBmetaD configuration for a single variable.

      +
      +

      colvar {
        name r 
        distance {
          group1 { atomNumbers 991 992 }
          group2 { atomNumbers 1762 1763 }
        }
        upperBoundary 100.0 
        width 0.1 
      }

      metadynamics {
        name ebmeta
        colvars r
        hillWeight 0.01
        hillWidth 3.0
        ebMeta on
        targetDistFile targetdist1.dat
        ebMetaEquilSteps 500000
      }

      -

      where targetdist1.dat is a text file in “multicolumn" format (3.7.4) with the same width as the variable r +

      where targetdist1.dat is a text file in “multicolumn" format (3.7.4) with the same width as the variable r (0.1 in this case):

      @@ -3997,48 +4064,48 @@
      6.4.5
      # 1
      # 0.0 0.1 1000 0
      0.05 0.0012 99.95 0.0010
      -

      Tip: Besides setting a meaningful value for targetDistMinVal, the exploration of unphysically low +

      Tip: Besides setting a meaningful value for targetDistMinVal, the exploration of unphysically low values of the target distribution (which would lead to very large hills and possibly numerical instabilities) can be also prevented by restricting sampling to a given interval, using e.g. harmonicWalls restraint (6.7).

      -

      +

      (Go to Contents)

      -

      +

      6.4.6 Well-tempered metadynamics
      -

      The following options define the configuration for the “well-tempered" metadynamics approach +

      The following options define the configuration for the “well-tempered" metadynamics approach [28]:
        -
      • Keyword wellTempered⟨Perform - well-tempered metadynamics⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: If enabled, this flag causes well-tempered metadynamics as described by +
      • Keyword wellTempered⟨Perform + well-tempered metadynamics⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: If enabled, this flag causes well-tempered metadynamics as described by Barducci et al.[28] to be performed, rather than standard metadynamics. The parameter biasTemperature is then required. This feature was contributed by Li Li (Luthey-Schulten group, Department of Chemistry, UIUC).
        • -
      • Keyword biasTemperature⟨Temperature +
      • Keyword biasTemperature⟨Temperature - bias for well-tempered metadynamics⟩
        Context: metadynamics
        Acceptable values: positive decimal
        Description: When running metadynamics in the long time limit, collective variable space is - sampled to a modified temperature T +ΔT . - In conventional metadynamics, the temperature “boost" ΔT - would constantly increases with time. Instead, in well-tempered metadynamics ΔT + bias for well-tempered metadynamics⟩
        Context: metadynamics
        Acceptable values: positive decimal
        Description: When running metadynamics in the long time limit, collective variable space is + sampled to a modified temperature T +ΔT . + In conventional metadynamics, the temperature “boost" ΔT + would constantly increases with time. Instead, in well-tempered metadynamics ΔT must be defined by the user via biasTemperature. The written PMF includes the scaling - factor (T +ΔT )∕ΔT -[28]. A careful choice of ΔT + factor (T +ΔT )∕ΔT +[28]. A careful choice of ΔT determines the sampling and convergence rate, and is hence crucial to the success of a well-tempered metadynamics simulation.
      -

      +

      (Go to Contents)

      -

      +

      6.4.7 Multiple-walker metadynamics
      -

      Metadynamics calculations can be performed concurrently by multiple replicas that share a +

      Metadynamics calculations can be performed concurrently by multiple replicas that share a common history. This variant of the method is called multiple-walker metadynamics [29]: the Gaussian hills of all replicas are periodically combined into a single biasing potential, intended to converge to a single PMF. -

      In the implementation here described [1], replicas communicate through files. This arrangement +

      In the implementation here described [1], replicas communicate through files. This arrangement allows launching the replicas either (1) as a bundle (i.e. a single job in a cluster's queueing system) or (2) as fully independent runs (i.e. as separate jobs for the queueing system). One advantage of the use case (1) is that an identical Colvars configuration can be used for all replicas (otherwise, replicaID needs to @@ -4047,7 +4114,7 @@

      6.4.7 Whichever way the replicas are started (coupled or not), a shared filesystem is needed so that each +

      Whichever way the replicas are started (coupled or not), a shared filesystem is needed so that each replica can read the files created by the others: paths to these files are stored in the shared file replicasRegistry. This file, and those listed in it, are read every replicaUpdateFrequency steps. Each time the Colvars state file is written (for example, colvarsRestartFrequency steps), the file @@ -4055,132 +4122,132 @@

      6.4.7 output.colvars.name.replicaID.hills
      Both files are only used for communication, and may be deleted after the replica begins writing files with a new output.
      -

      Example: Multiple-walker metadynamics with file-based communication.

      -
      -

      metadynamics {
        name mymtd
        colvars x
        hillWeight 0.001
        newHillFrequency 1000
        hillWidth 3.0
        
        multipleReplicas on
        replicasRegistry /shared-folder/mymtd-replicas.txt
        replicaUpdateFrequency 50000 # Best if larger than newHillFrequency
      }

      +

      Example: Multiple-walker metadynamics with file-based communication.

      +
      +

      metadynamics {
        name mymtd
        colvars x
        hillWeight 0.001
        newHillFrequency 1000
        hillWidth 3.0
        
        multipleReplicas on
        replicasRegistry /shared-folder/mymtd-replicas.txt
        replicaUpdateFrequency 50000 # Best if larger than newHillFrequency
      }

      -

      The following are the multiple-walkers related options: +

      The following are the multiple-walkers related options:

        -
      • Keyword multipleReplicas⟨Enable - multiple-walker metadynamics⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: This option turns on multiple-walker communication between replicas. +
      • Keyword multipleReplicas⟨Enable + multiple-walker metadynamics⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: This option turns on multiple-walker communication between replicas.
        • -
      • Keyword replicasRegistry⟨Multiple - replicas database file⟩
        Context: metadynamics
        Acceptable values: UNIX filename
        Description: If multipleReplicas is on, this option sets the path to the replicas' shared +
      • Keyword replicasRegistry⟨Multiple + replicas database file⟩
        Context: metadynamics
        Acceptable values: UNIX filename
        Description: If multipleReplicas is on, this option sets the path to the replicas' shared database file. It is best to use an absolute path (especially when running individual replicas in separate folders).
        • -
      • Keyword replicaUpdateFrequency⟨How - often hills are shared between replicas⟩
        Context: metadynamics
        Acceptable values: positive integer
        Description: If multipleReplicas is on, this option sets the number of steps after which +
      • Keyword replicaUpdateFrequency⟨How + often hills are shared between replicas⟩
        Context: metadynamics
        Acceptable values: positive integer
        Description: If multipleReplicas is on, this option sets the number of steps after which each replica tries to read the other replicas' files. On a networked file system, it is best to use a number of steps that corresponds to at least a minute of wall time.
        • -
      • Keyword replicaID⟨Set - the identifier for this replica (required only for independent jobs)⟩
        Context: metadynamics
        Acceptable values: string
        Default value: replica index (only if MPI is used)
        Description: If multipleReplicas is on, this option sets a unique identifier for this replicas. +
      • Keyword replicaID⟨Set + the identifier for this replica (required only for independent jobs)⟩
        Context: metadynamics
        Acceptable values: string
        Default value: replica index (only if MPI is used)
        Description: If multipleReplicas is on, this option sets a unique identifier for this replicas. Specifying this option is thus only required when the replicas are launched as independent computations: when the replicas share a common parallel communication framework (i.e. they are all launched together as a single message-passing computation via MPI) the default value of this keyword is the replica's numeric index (zero-based).
        • -
      • Keyword writePartialFreeEnergyFile⟨Periodically - write the contribution to the PMF from this replica⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: If multipleReplicas is on, enabling this option produces an additional file +
      • Keyword writePartialFreeEnergyFile⟨Periodically + write the contribution to the PMF from this replica⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: If multipleReplicas is on, enabling this option produces an additional file output.partial.pmf, which can be useful to monitor the contribution of each replica to the total PMF (which is written to the file output.pmf). Note: the name of this file is chosen for consistency and convenience, but its content is not a PMF and it is not expected to converge, even if the total PMF does.
      -

      +

      (Go to Contents)

      -

      +

      6.5 Harmonic restraints

      -

      -

      The harmonic biasing method may be used to enforce fixed or moving restraints, including variants of +

      +

      The harmonic biasing method may be used to enforce fixed or moving restraints, including variants of Steered and Targeted MD. Within energy minimization runs, it allows for restrained minimization, e.g. to calculate relaxed potential energy surfaces. In the context of the Colvars module, harmonic potentials are meant according to their textbook definition:

      - + V (ξ ) = 1 2k (ξ −ξ0 wξ )2 (30)
      -

      There are two noteworthy aspects of this expression: +

      There are two noteworthy aspects of this expression:

        -
      1. Because the standard coefficient of 1∕2 +
      2. Because the standard coefficient of 1∕2 of the harmonic potential is included, this expression differs from harmonic bond and angle potentials historically used in common force fields, where the factor was typically omitted resulting in a non-standard definition of the force constant.
        3. -
      3. The variable ξ - is not only centered at ξ0, - but is also scaled by its characteristic length scale wξ - (keyword width). The resulting dimensionless variable z = (ξ −ξ0)∕wξ +
      4. The variable ξ + is not only centered at ξ0, + but is also scaled by its characteristic length scale wξ + (keyword width). The resulting dimensionless variable z = (ξ −ξ0)∕wξ is typically easier to treat numerically: for example, when the forces typically experienced by - ξ - are much smaller than k∕wξ - and k - is chosen equal to κBT - (thermal energy), the resulting probability distribution of z + ξ + are much smaller than k∕wξ + and k + is chosen equal to κBT + (thermal energy), the resulting probability distribution of z is approximately a Gaussian with mean equal to 0 and standard deviation equal to 1. -

        This property can be used for setting the force constant in umbrella-sampling ensemble runs: - if the restraint centers are chosen in increments of wξ, - the resulting distributions of ξ +

        This property can be used for setting the force constant in umbrella-sampling ensemble runs: + if the restraint centers are chosen in increments of wξ, + the resulting distributions of ξ are most often optimally overlapped. In regions where the underlying free-energy landscape - induces highly skewed distributions of ξ, - additional windows may be added as needed, with spacings finer than wξ.

      -

      Beyond one dimension, the use of a scaled harmonic potential also allows a standard definition of a + induces highly skewed distributions of ξ, + additional windows may be added as needed, with spacings finer than wξ.

      +

      Beyond one dimension, the use of a scaled harmonic potential also allows a standard definition of a multi-dimensional restraint with a unified force constant:

      - + V (ξ1,… &ApplyFunction;,ξM) = 1 2k∑i=1M (ξi−ξ0 wξ )2 (31)
      -

      If one-dimensional or homogeneous multi-dimensional restraints are defined, and there are no other uses for the -parameter wξ, width can be -left at its default value of 1. -

      A harmonic restraint is defined by a harmonic {...} block, which may contain the following keywords: +

      If one-dimensional or homogeneous multi-dimensional restraints are defined, and there are no other uses for the +parameter wξ, width can be +left at its default value of 1. +

      A harmonic restraint is defined by a harmonic {...} block, which may contain the following keywords:

        -
      • Keyword name: see definition of name (biasing and analysis methods) +
      • Keyword name: see definition of name (biasing and analysis methods)
        • -
      • Keyword colvars: see definition of colvars (biasing and analysis methods) +
      • Keyword colvars: see definition of colvars (biasing and analysis methods)
        • -
      • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods) +
      • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods)
        • -
      • Keyword writeTIPMF: see definition of writeTIPMF (biasing and analysis methods) +
      • Keyword writeTIPMF: see definition of writeTIPMF (biasing and analysis methods)
        • -
      • Keyword writeTISamples: see definition of writeTISamples (biasing and analysis +
      • Keyword writeTISamples: see definition of writeTISamples (biasing and analysis methods)
        • -
      • Keyword stepZeroData: see definition of stepZeroData (biasing and analysis methods) +
      • Keyword stepZeroData: see definition of stepZeroData (biasing and analysis methods)
        • -
      •   Keyword forceConstant⟨Scaled - force constant (kJ/mol)⟩
        Context: harmonic
        Acceptable values: positive decimal
        Default value: 1.0
        Description: This option defines a scaled force constant k +
      •   Keyword forceConstant⟨Scaled + force constant (kJ/mol)⟩
        Context: harmonic
        Acceptable values: positive decimal
        Default value: 1.0
        Description: This option defines a scaled force constant k for the harmonic potential (eq. 31). To ensure consistency for multidimensional restraints, it is divided internally by the square of the specific width of each variable (which is 1 by default). This makes all values effectively dimensionless and of commensurate size. For - instance, if this force constant is set to the thermal energy κBT - (equal to RT + instance, if this force constant is set to the thermal energy κBT + (equal to RT if molar units are used), then the amplitude of the thermal fluctuations of each variable - ξ - will be on the order of its width, wξ. + ξ + will be on the order of its width, wξ. This can be used to estimate the optimal spacing of umbrella-sampling windows (under the assumption that the force constant is larger than the curvature of the underlying free energy). - The values of the actual force constants k∕wξ2 + The values of the actual force constants k∕wξ2 are always printed when the restraint is defined.
        • -
      •   Keyword centers⟨Initial - harmonic restraint centers⟩
        Context: harmonic
        Acceptable values: space-separated list of colvar values
        Description: The centers (equilibrium values) of the restraint, ξ0, +
      •   Keyword centers⟨Initial + harmonic restraint centers⟩
        Context: harmonic
        Acceptable values: space-separated list of colvar values
        Description: The centers (equilibrium values) of the restraint, ξ0, are entered here. The number of values must be the number of requested colvars. Each value is a decimal number if the corresponding colvar returns a scalar, a “(x, y, z)" triplet if it returns a unit vector or a vector, and a “(q0, q1, q2, q3)" quadruplet if it returns a rotational quaternion. If a colvar has periodicities or symmetries, its closest image to the restraint center is considered when calculating the harmonic potential.
      -

      Tip: A complex set of restraints can be applied to a system, by defining several colvars, and applying +

      Tip: A complex set of restraints can be applied to a system, by defining several colvars, and applying one or more harmonic restraints to different groups of colvars. In some cases, dozens of colvars can be defined, but their value may not be relevant: to limit the size of the colvars trajectory file, it may be wise to disable outputValue for such “ancillary" variables, and leave it enabled only for “relevant" @@ -4189,83 +4256,83 @@

      6.5 -

      +

      (Go to Contents)

      -

      +

      6.5.1 Moving restraints: steered molecular dynamics
      -

      -

      The following options allow to change gradually the centers of the harmonic restraints during a +

      +

      The following options allow to change gradually the centers of the harmonic restraints during a simulations. When the centers are changed continuously, a steered MD in a collective variable space is carried out.

        -
      • Keyword targetCenters⟨Steer - the restraint centers towards these targets⟩
        Context: harmonic
        Acceptable values: space-separated list of colvar values
        Description: When defined, the current centers will be moved towards these values during +
      • Keyword targetCenters⟨Steer + the restraint centers towards these targets⟩
        Context: harmonic
        Acceptable values: space-separated list of colvar values
        Description: When defined, the current centers will be moved towards these values during the simulation. By default, the centers are moved over a total of targetNumSteps steps by a linear interpolation, in the spirit of Steered MD. If targetNumStages is set to a nonzero value, the change is performed in discrete stages, lasting targetNumSteps steps each. This second mode may be used to sample successive windows in the context of an Umbrella Sampling simulation. When continuing a simulation run, the centers specified in the configuration file - <colvarsConfig > - are overridden by those saved in the restart file <colvarsInput >. + <colvarsConfig > + are overridden by those saved in the restart file <colvarsInput >. To perform Steered MD in an arbitrary space of colvars, it is sufficient to use this option and enable outputAccumulatedWork and/or outputAppliedForce within each of the colvars involved.
        • -
      • Keyword targetNumSteps⟨Number - of steps for steering⟩
        Context: harmonic
        Acceptable values: positive integer
        Description: In single-stage (continuous) transformations, defines the number of MD steps +
      • Keyword targetNumSteps⟨Number + of steps for steering⟩
        Context: harmonic
        Acceptable values: positive integer
        Description: In single-stage (continuous) transformations, defines the number of MD steps required to move the restraint centers (or force constant) towards the values specified with targetCenters or targetForceConstant. After the target values have been reached, the centers (resp. force constant) are kept fixed. In multi-stage transformations, this sets the number of MD steps per stage.
        • -
      • Keyword outputCenters⟨Write +
      • Keyword outputCenters⟨Write - the current centers to the trajectory file⟩
        Context: harmonic
        Acceptable values: boolean
        Default value: off
        Description: If this option is chosen and colvarsTrajFrequency is not zero, the positions + the current centers to the trajectory file⟩
        Context: harmonic
        Acceptable values: boolean
        Default value: off
        Description: If this option is chosen and colvarsTrajFrequency is not zero, the positions of the restraint centers will be written to the trajectory file during the simulation. This option allows to conveniently extract the PMF from the Colvars trajectory files in a steered MD calculation.
      -

      Note on restarting moving restraint simulations: Information about the current step and stage of a +

      Note on restarting moving restraint simulations: Information about the current step and stage of a simulation with moving restraints is stored in the restart file (state file). Thus, such simulations can be run in several chunks, and restarted directly using the same colvars configuration file. In case of a restart, the values of parameters such as targetCenters, targetNumSteps, etc. should not be changed manually.

      -

      +

      (Go to Contents)

      -

      +

      6.5.2 Moving restraints: umbrella sampling
      -

      -

      The centers of the harmonic restraints can also be changed in discrete stages: in this cases a +

      +

      The centers of the harmonic restraints can also be changed in discrete stages: in this cases a one-dimensional umbrella sampling simulation is performed. The sampling windows in simulation are calculated in sequence. The colvars trajectory file may then be used both to evaluate the correlation times between consecutive windows, and to calculate the frequency distribution of the colvar of interest in each window. Furthermore, frequency distributions on a predefined grid can be automatically obtained by using the histogram bias (see 6.10). -

      To activate an umbrella sampling simulation, the same keywords as in the previous section can be +

      To activate an umbrella sampling simulation, the same keywords as in the previous section can be used, with the addition of the following:

        -
      • Keyword targetNumStages⟨Number - of stages for steering⟩
        Context: harmonic
        Acceptable values: non-negative integer
        Default value: 0
        Description: If non-zero, sets the number of stages in which the restraint centers or force +
      • Keyword targetNumStages⟨Number + of stages for steering⟩
        Context: harmonic
        Acceptable values: non-negative integer
        Default value: 0
        Description: If non-zero, sets the number of stages in which the restraint centers or force constant are changed to their target values. If zero, the change is continuous. Each stage lasts targetNumSteps MD steps. To sample both ends of the transformation, the simulation - should be run for targetNumSteps× + should be run for targetNumSteps× (targetNumStages + 1).
      -

      +

      (Go to Contents)

      -

      +

      6.5.3 Changing force constant
      -

      -

      The force constant of the harmonic restraint may also be changed to equilibrate [30]. +

      +

      The force constant of the harmonic restraint may also be changed to equilibrate [30].

        -
      •   Keyword targetForceConstant⟨Change - the force constant towards this value⟩
        Context: harmonic
        Acceptable values: positive decimal
        Description: When defined, the current forceConstant will be moved towards this value +
      •   Keyword targetForceConstant⟨Change + the force constant towards this value⟩
        Context: harmonic
        Acceptable values: positive decimal
        Description: When defined, the current forceConstant will be moved towards this value during the simulation. Time evolution of the force constant is dictated by the lambdaExponent parameter (see below). By default, the force constant is changed smoothly over a total of targetNumSteps steps. This is useful to introduce or remove restraints in a progressive @@ -4279,18 +4346,18 @@
        6.5.3 [30]
        • -
      • Keyword lambdaExponent⟨Exponent - in the time-dependence of the force constant⟩
        Context: harmonic
        Acceptable values: decimal equal to or greater than 1.0
        Default value: 1.0
        Description: Sets the exponent, α, +
      • Keyword lambdaExponent⟨Exponent + in the time-dependence of the force constant⟩
        Context: harmonic
        Acceptable values: decimal equal to or greater than 1.0
        Default value: 1.0
        Description: Sets the exponent, α, in the function used to vary the force constant as a function of time. The force is varied - according to a coupling parameter λ, - raised to the power α: - kλ = k0 +λα(k1 −k0), - where k0, + according to a coupling parameter λ, + raised to the power α: + kλ = k0 +λα(k1 −k0), + where k0, - kλ, - and k1 - are the initial, current, and final values of the force constant. The parameter λ + kλ, + and k1 + are the initial, current, and final values of the force constant. The parameter λ evolves linearly from 0 to 1, either smoothly, or in targetNumStages equally spaced discrete stages, or according to an arbitrary schedule set with lambdaSchedule. When the initial value of the force constant is zero, an exponent greater than 1.0 distributes the effects of @@ -4299,52 +4366,52 @@
        6.5.3 decoupling option.
        • -
      • Keyword decoupling⟨Perform - a restraint decoupling transformation⟩
        Context: harmonic
        Acceptable values: boolean
        Default value: off
        Description: When this option is enabled, the restraint is decoupled by changing the +
      • Keyword decoupling⟨Perform + a restraint decoupling transformation⟩
        Context: harmonic
        Acceptable values: boolean
        Default value: off
        Description: When this option is enabled, the restraint is decoupled by changing the force constant from forceConstant to 0.0 over the course of the simulation, as specified by targetNumSteps and, optionally, targetNumStages. The force constant is then varied as: - kλ = (1−λ)αk, - where α + kλ = (1−λ)αk, + where α is the value of lambdaExponent. Setting lambdaExponent to a value greater than 1 (e.g. 4) - ensures a smoother dependence of the energy on λ - around kλ = 0. + ensures a smoother dependence of the energy on λ + around kλ = 0.
        • -
      • Keyword targetEquilSteps⟨Number - of steps discarded from TI estimate⟩
        Context: harmonic
        Acceptable values: positive integer
        Description: Defines the number of steps within each stage that are considered equilibration +
      • Keyword targetEquilSteps⟨Number + of steps discarded from TI estimate⟩
        Context: harmonic
        Acceptable values: positive integer
        Description: Defines the number of steps within each stage that are considered equilibration and discarded from the restraint free energy derivative estimate reported reported in the output.
        • -
      • Keyword lambdaSchedule⟨Schedule - of lambda-points for changing force constant⟩
        Context: harmonic
        Acceptable values: list of real numbers between 0 and 1
        Description: If specified together with targetForceConstant, sets the sequence of discrete - λ +
      • Keyword lambdaSchedule⟨Schedule + of lambda-points for changing force constant⟩
        Context: harmonic
        Acceptable values: list of real numbers between 0 and 1
        Description: If specified together with targetForceConstant, sets the sequence of discrete + λ values that will be used for different stages.
      -

      +

      (Go to Contents)

      -

      +

      6.6 Computing the work of a changing restraint

      -

      -

      If the restraint centers or force constant are changed continuosly (targetNumStages undefined) it is +

      +

      If the restraint centers or force constant are changed continuosly (targetNumStages undefined) it is possible to record the net work performed by the changing restraint:

        -
      • Keyword outputAccumulatedWork⟨Write - the accumulated work of the changing restraint to the Colvars trajectory file⟩
        Context: harmonic
        Acceptable values: boolean
        Default value: off
        Description: If targetCenters or targetForceConstant are defined and this option is +
      • Keyword outputAccumulatedWork⟨Write + the accumulated work of the changing restraint to the Colvars trajectory file⟩
        Context: harmonic
        Acceptable values: boolean
        Default value: off
        Description: If targetCenters or targetForceConstant are defined and this option is enabled, the accumulated work from the beginning of the simulation will be written to the trajectory file (colvarsTrajFrequency must be non-zero). When the simulation is continued from a state file, the previously accumulated work is included in the integral. This option allows to conveniently extract the estimated PMF of a steered MD calculation (when targetCenters is used), or of other simulation protocols.
      -

      +

      (Go to Contents)

      -

      +

      6.7 Harmonic wall restraints

      -

      -

      The harmonicWalls {...} bias is closely related to the harmonic bias (see 6.5), with the following two +

      +

      The harmonicWalls {...} bias is closely related to the harmonic bias (see 6.5), with the following two differences: (i) instead of a center a lower wall and/or an upper wall are defined, outside of which the bias implements a half-harmonic potential;

      - + V (ξ ) = { 1 2k (ξ−ξupper wξ ) 2 ifξ > ξupper 0 ifξlower ≤ ξ ≤ ξupper @@ -4352,56 +4419,56 @@

      6.7 ) 2 ifξ < ξlower

      		(32)
      -

      where ξlower -and ξupper are +

      where ξlower +and ξupper are the lower and upper wall thresholds, respectively; (ii) because an interval between two walls is defined, only scalar variables can be used (but any number of variables can be defined, and the wall bias is intrinsically multi-dimensional).
      -

      Note: this bias replaces the keywords lowerWall, lowerWallConstant, upperWall and +

      Note: this bias replaces the keywords lowerWall, lowerWallConstant, upperWall and upperWallConstant defined in the colvar context. Those keywords are deprecated. -

      The harmonicWalls bias implements the following options:

      +

      The harmonicWalls bias implements the following options:

        -
      • Keyword name: see definition of name (biasing and analysis methods) +
      • Keyword name: see definition of name (biasing and analysis methods)
        • -
      • Keyword colvars: see definition of colvars (biasing and analysis methods) +
      • Keyword colvars: see definition of colvars (biasing and analysis methods)
        • -
      • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods) +
      • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods)
        • -
      • Keyword writeTIPMF: see definition of writeTIPMF (biasing and analysis methods) +
      • Keyword writeTIPMF: see definition of writeTIPMF (biasing and analysis methods)
        • -
      • Keyword writeTISamples: see definition of writeTISamples (biasing and analysis +
      • Keyword writeTISamples: see definition of writeTISamples (biasing and analysis methods)
        • -
      • Keyword stepZeroData: see definition of stepZeroData (biasing and analysis methods) +
      • Keyword stepZeroData: see definition of stepZeroData (biasing and analysis methods)
        • -
      • Keyword lowerWalls⟨Position - of the lower wall(s)⟩
        Context: colvar
        Acceptable values: Space-separated list of decimals
        Description: Defines the values ξlower - below which a confining restraint on the colvar is applied to each colvar ξ. +
      • Keyword lowerWalls⟨Position + of the lower wall(s)⟩
        Context: colvar
        Acceptable values: Space-separated list of decimals
        Description: Defines the values ξlower + below which a confining restraint on the colvar is applied to each colvar ξ.
        • -
      • Keyword upperWalls⟨Position - of the upper wall(s)⟩
        Context: colvar
        Acceptable values: Space-separated list of decimals
        Description: Defines the values ξupper - above which a confining restraint on the colvar is applied to each colvar ξ. +
      • Keyword upperWalls⟨Position + of the upper wall(s)⟩
        Context: colvar
        Acceptable values: Space-separated list of decimals
        Description: Defines the values ξupper + above which a confining restraint on the colvar is applied to each colvar ξ.
        • -
      • Keyword forceConstant: see definition of forceConstant (Harmonic restraints) +
      • Keyword forceConstant: see definition of forceConstant (Harmonic restraints)
        • -
      • Keyword lowerWallConstant⟨Force - constant for the lower wall⟩
        Context: harmonicWalls
        Acceptable values: positive decimal
        Default value: forceConstant
        Description: When both sets of walls are defined (lower and upper), this keyword allows +
      • Keyword lowerWallConstant⟨Force + constant for the lower wall⟩
        Context: harmonicWalls
        Acceptable values: positive decimal
        Default value: forceConstant
        Description: When both sets of walls are defined (lower and upper), this keyword allows setting different force constants for them. As with forceConstant, the specified constant is divided internally by the square of the specific width of each variable (see also the equivalent keyword for the harmonic restraint, forceConstant). The force constant reported in the - output as “k", + output as “k", and used in the change of force constant scheme, is the geometric mean of upperWallConstant and upperWallConstant.
        • -
      • upperWallConstant: analogous to lowerWallConstant +
      • upperWallConstant: analogous to lowerWallConstant
        • -
      • Keyword targetForceConstant: see definition of targetForceConstant (harmonic +
      • Keyword targetForceConstant: see definition of targetForceConstant (harmonic restraints)
        • -
      • Keyword targetForceConstant⟨Change - the force constant(s) towards this value⟩
        Context: harmonicWalls
        Acceptable values: positive decimal
        Description: This keyword allows changing either one or both of the wall force constants +
      • Keyword targetForceConstant⟨Change + the force constant(s) towards this value⟩
        Context: harmonicWalls
        Acceptable values: positive decimal
        Description: This keyword allows changing either one or both of the wall force constants over time. In the case that lowerWallConstant and upperWallConstant have the same value, the behavior of this keyword is identical to the corresponding keyword in the harmonic restraint; otherwise, the change schedule is applied to the geometric mean of the two constant. @@ -4410,23 +4477,23 @@

        6.7 harmonicWalls, and apply the changing schedule only to one of them.

        • -
      • Keyword targetNumSteps: see definition of targetNumSteps (harmonic restraints) +
      • Keyword targetNumSteps: see definition of targetNumSteps (harmonic restraints)
        • -
      • Keyword lambdaExponent: see definition of lambdaExponent (harmonic restraints) +
      • Keyword lambdaExponent: see definition of lambdaExponent (harmonic restraints)
        • -
      • Keyword targetEquilSteps: see definition of targetEquilSteps (harmonic restraints) +
      • Keyword targetEquilSteps: see definition of targetEquilSteps (harmonic restraints)
        • -
      • Keyword targetNumStages: see definition of targetNumStages (harmonic restraints) +
      • Keyword targetNumStages: see definition of targetNumStages (harmonic restraints)
        • -
      • Keyword lambdaSchedule: see definition of lambdaSchedule (harmonic restraints) +
      • Keyword lambdaSchedule: see definition of lambdaSchedule (harmonic restraints)
        • -
      • Keyword outputAccumulatedWork: see definition of outputAccumulatedWork (harmonic +
      • Keyword outputAccumulatedWork: see definition of outputAccumulatedWork (harmonic restraints)
        • -
      •   Keyword bypassExtendedLagrangian⟨Apply - bias to actual colvars, bypassing extended coordinates⟩
        Context: harmonicWalls
        Acceptable values: boolean
        Default value: on
        Description: This option behaves as bypassExtendedLagrangian for other biases, but it +
      •   Keyword bypassExtendedLagrangian⟨Apply + bias to actual colvars, bypassing extended coordinates⟩
        Context: harmonicWalls
        Acceptable values: boolean
        Default value: on
        Description: This option behaves as bypassExtendedLagrangian for other biases, but it defaults to on, unlike in the general case. Thus, by default, the harmonicWalls bias applies to the actual colvars, so that the distribution of the colvar between the walls is unaffected by the bias, which then applies a flat-bottom potential as a function of the colvar value. This bias @@ -4435,96 +4502,96 @@

        6.7 coordinate. Conversely, this bias will then modify the distribution of the actual colvar value near the walls.

      -

      Example 1: harmonic walls for one variable with two different force constants.

      -
      -

      harmonicWalls {
        name mywalls
        colvars dist
        lowerWalls 22.0 
        upperWalls 38.0 
        lowerWallConstant 2.0 
        upperWallConstant 10.0 
      }

      -
      -

      Example 2: harmonic walls for two variables with a single force constant.

      +

      Example 1: harmonic walls for one variable with two different force constants.

      -

      harmonicWalls {
        name mywalls
        colvars phi psi
        lowerWalls -180.0 0.0
        upperWalls 0.0 180.0
        forceConstant 5.0 
      }

      +

      harmonicWalls {
        name mywalls
        colvars dist
        lowerWalls 22.0 
        upperWalls 38.0 
        lowerWallConstant 2.0 
        upperWallConstant 10.0 
      }

      +
      +

      Example 2: harmonic walls for two variables with a single force constant.

      +
      +

      harmonicWalls {
        name mywalls
        colvars phi psi
        lowerWalls -180.0 0.0
        upperWalls 0.0 180.0
        forceConstant 5.0 
      }

      -

      +

      (Go to Contents)

      -

      +

      6.8 Linear restraints

      -

      -

      The linear keyword defines a linear potential:

      - +

      +

      The linear keyword defines a linear potential:

      + V (ξ ) = k (ξ −ξ0 wξ ) (33)
      -

      whose force is simply given by the constant k∕wξ +

      whose force is simply given by the constant k∕wξ itself:

      - + f(ξ) = k∕wξ (34)
      -

      This type of bias is therefore most useful in situations where a constant force is desired. As all other +

      This type of bias is therefore most useful in situations where a constant force is desired. As all other restraints, it can be defined on one or more CVs, with each contribution added to the total potential and the -parameters wξ +parameters wξ determining the relative magnitude for each. -

      Example: A possible use case of the linear bias is mimicking a constant electric field acting on a +

      Example: A possible use case of the linear bias is mimicking a constant electric field acting on a specific particle, or the center of mass of many particles. In the following example, a linear restraint is applied on a distanceZ variable (4.2.2), generating a constant force parallel to the Z axis of magnitude 5 kJ/mol/nm:

      -
      -

      colvar {
        name z
        distanceZ {
          ...
        }
      }

      linear {
        colvars z
        forceConstant 5.0
        centers 0.0
      }

      +
      +

      colvar {
        name z
        distanceZ {
          ...
        }
      }

      linear {
        colvars z
        forceConstant 5.0
        centers 0.0
      }

      -

      Another useful application of a linear restraint is to enforce experimental constraints in a simulation, +

      Another useful application of a linear restraint is to enforce experimental constraints in a simulation, with a lower non-equilibrium work than e.g. harmonic restraints [31]. There is generally a unique strength of bias for each CV center, which means you must know the bias force constant specifically for the center of the CV. This force constant may be found by using experiment directed simulation described in section 6.9.

        -
      • Keyword name: see definition of name (biasing and analysis methods) +
      • Keyword name: see definition of name (biasing and analysis methods)
        • -
      • Keyword colvars: see definition of colvars (biasing and analysis methods) +
      • Keyword colvars: see definition of colvars (biasing and analysis methods)
        • -
      • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods) +
      • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods)
        • -
      • Keyword forceConstant⟨Scaled - force constant (kJ/mol)⟩
        Context: linear
        Acceptable values: Decimal
        Default value: 1.0
        Description: This option defines a scaled force constant k +
      • Keyword forceConstant⟨Scaled + force constant (kJ/mol)⟩
        Context: linear
        Acceptable values: Decimal
        Default value: 1.0
        Description: This option defines a scaled force constant k for the linear bias. To ensure consistency for multidimensional restraints, it is divided internally by the specific width of each variable (which is 1 by default), so that all variables are - effectively dimensionless and of commensurate size. The values of k∕wξ + effectively dimensionless and of commensurate size. The values of k∕wξ are always printed when the restraint is defined.
        • -
      • Keyword centers⟨Initial - linear restraint centers⟩
        Context: linear
        Acceptable values: space-separated list of colvar values
        Description: These are analogous to the centers keyword of the harmonic restraint. Although +
      • Keyword centers⟨Initial + linear restraint centers⟩
        Context: linear
        Acceptable values: space-separated list of colvar values
        Description: These are analogous to the centers keyword of the harmonic restraint. Although they do not affect dynamics, they are here necessary to ensure a well-defined energy for the linear bias.
        • -
      • Keyword writeTIPMF: see definition of writeTIPMF (biasing and analysis methods) +
      • Keyword writeTIPMF: see definition of writeTIPMF (biasing and analysis methods)
        • -
      • Keyword writeTISamples: see definition of writeTISamples (biasing and analysis +
      • Keyword writeTISamples: see definition of writeTISamples (biasing and analysis methods)
        • -
      • Keyword targetForceConstant: see definition of targetForceConstant (Harmonic +
      • Keyword targetForceConstant: see definition of targetForceConstant (Harmonic restraints)
        • -
      • Keyword targetNumSteps: see definition of targetNumSteps (Harmonic restraints) +
      • Keyword targetNumSteps: see definition of targetNumSteps (Harmonic restraints)
        • -
      • Keyword lambdaExponent: see definition of lambdaExponent (Harmonic restraints) +
      • Keyword lambdaExponent: see definition of lambdaExponent (Harmonic restraints)
        • -
      • Keyword targetEquilSteps: see definition of targetEquilSteps (Harmonic restraints) +
      • Keyword targetEquilSteps: see definition of targetEquilSteps (Harmonic restraints)
        • -
      • Keyword targetNumStages: see definition of targetNumStages (Harmonic restraints) +
      • Keyword targetNumStages: see definition of targetNumStages (Harmonic restraints)
        • -
      • Keyword lambdaSchedule: see definition of lambdaSchedule (Harmonic restraints) +
      • Keyword lambdaSchedule: see definition of lambdaSchedule (Harmonic restraints)
        • -
      • Keyword outputAccumulatedWork: see definition of outputAccumulatedWork (Harmonic +
      • Keyword outputAccumulatedWork: see definition of outputAccumulatedWork (Harmonic restraints)
      -

      +

      (Go to Contents)

      -

      +

      6.9 Adaptive Linear Bias/Experiment Directed Simulation

      -

      -

      Experiment directed simulation applies a linear bias with a changing force constant. Please cite White +

      +

      Experiment directed simulation applies a linear bias with a changing force constant. Please cite White and Voth [32] when using this feature. As opposed to that reference, the force constant here is scaled by the width corresponding to the biased colvar. In White and Voth, each force constant is scaled by the colvars set center. The bias converges to a linear bias, after which it will be the minimal possible bias. You @@ -4535,172 +4602,172 @@

      6.9 converged.

        -
      • Keyword name: see definition of name (biasing and analysis methods) +
      • Keyword name: see definition of name (biasing and analysis methods)
        • -
      • Keyword colvars: see definition of colvars (biasing and analysis methods) +
      • Keyword colvars: see definition of colvars (biasing and analysis methods)
        • -
      • Keyword centers⟨Collective - variable centers⟩
        Context: alb
        Acceptable values: space-separated list of colvar values
        Description: The desired center (equilibrium values) which will be sought during the adaptive +
      • Keyword centers⟨Collective + variable centers⟩
        Context: alb
        Acceptable values: space-separated list of colvar values
        Description: The desired center (equilibrium values) which will be sought during the adaptive linear biasing. The number of values must be the number of requested colvars. Each value is a decimal number if the corresponding colvar returns a scalar, a “(x, y, z)" triplet if it returns a unit vector or a vector, and a “q0, q1, q2, q3)" quadruplet if it returns a rotational quaternion. If a colvar has periodicities or symmetries, its closest image to the restraint center is considered when calculating the linear potential.
        • -
      • Keyword updateFrequency⟨The - duration of updates⟩
        Context: alb
        Acceptable values: An integer
        Description: This is, N, +
      • Keyword updateFrequency⟨The + duration of updates⟩
        Context: alb
        Acceptable values: An integer
        Description: This is, N, the number of simulation steps to use for each update to the bias. This determines how long - the system requires to equilibrate after a change in force constant (N∕2), - how long statistics are collected for an iteration (N∕2), - and how quickly energy is added to the system (at most, A∕2N, - where A + the system requires to equilibrate after a change in force constant (N∕2), + how long statistics are collected for an iteration (N∕2), + and how quickly energy is added to the system (at most, A∕2N, + where A is the forceRange). Until the force constant has converged, the method as described is an optimization procedure and not an integration of a particular statistical ensemble. It is important that each step should be uncorrelated from the last so that iterations are independent. - Therefore, N + Therefore, N should be at least twice the autocorrelation time of the collective variable. The system should - also be able to dissipate energy as fast as N∕2, - which can be done by adjusting thermostat parameters. Practically, N + also be able to dissipate energy as fast as N∕2, + which can be done by adjusting thermostat parameters. Practically, N has been tested successfully at significantly shorter than the autocorrelation time of the collective variables being biased and still converge correctly.
        • -
      • Keyword forceRange⟨The - expected range of the force constant in units of energy⟩
        Context: alb
        Acceptable values: A space-separated list of decimal numbers
        Default value: 3 kbT +
      • Keyword forceRange⟨The + expected range of the force constant in units of energy⟩
        Context: alb
        Acceptable values: A space-separated list of decimal numbers
        Default value: 3 kbT
        Description: This is largest magnitude of the force constant which one expects. If this parameter is too low, the simulation will not converge. If it is too high the simulation will waste - time exploring values that are too large. A value of 3 kbT + time exploring values that are too large. A value of 3 kbT has worked well in the systems presented as a first choice. This parameter is dynamically adjusted over the course of a simulation. The benefit is that a bad guess for the forceRange can be corrected. However, this can lead to large amounts of energy being added over time to the system. To prevent this dynamic update, add hardForceRange yes as a parameter
        • -
      • Keyword rateMax⟨The - maximum rate of change of force constant⟩
        Context: alb
        Acceptable values: A list of space-separated real numbers
        Description: This optional parameter controls how much energy is added to the system +
      • Keyword rateMax⟨The + maximum rate of change of force constant⟩
        Context: alb
        Acceptable values: A list of space-separated real numbers
        Description: This optional parameter controls how much energy is added to the system from this bias. Tuning this separately from the updateFrequency and forceRange can allow for large bias changes but with a low rateMax prevents large energy changes that can lead to instability in the simulation.
      -

      +

      (Go to Contents)

      -

      +

      6.10 Multidimensional histograms

      -

      -

      The histogram feature is used to record the distribution of a set of collective variables in the form of a +

      +

      The histogram feature is used to record the distribution of a set of collective variables in the form of a N-dimensional histogram. Defining such a histogram is generally useful for analysis purposes, but it has no effect on the simulation. -

      Example 1: the two-dimensional histogram of a distance and an angle can be generated +

      Example 1: the two-dimensional histogram of a distance and an angle can be generated using the configuration below. The histogram code requires that each variable is a scalar number that is confined within a pre-defined interval. The interval's boundaries may be specified by hand (e.g. through lowerBoundary and upperBoundary in the variable definition), or auto-detected based on the type of function. In this example, the lower boundary for the distance variable “r" is automatically set to zero, and interval for the three-body angle “theta" is -0∘ and -180∘: however, that +0∘ and +180∘: however, that an upper boundary for the distance “r" still needs to be specified manually. The grid spacings for the two variables -are 0.2 nmand -3.0∘, +are 0.2 nmand +3.0∘, respectively.

      -
      -

      colvar {
        name r
        width 0.2
        upperBoundary 20.0
        distance { ... }
      }

      colvar {
        name theta
        width 3.0
        dihedral { ... }
      }

      histogram {
        name hist2d
        colvars r theta
      }

      +
      +

      colvar {
        name r
        width 0.2
        upperBoundary 20.0
        distance { ... }
      }

      colvar {
        name theta
        width 3.0
        dihedral { ... }
      }

      histogram {
        name hist2d
        colvars r theta
      }

      -

      Example 2: This example is similar to the previous one, but with the important difference +

      Example 2: This example is similar to the previous one, but with the important difference that the parameters for the histogram's grid are defined explicitly for this histogram instance. Therefore, this histogram's grid may differ from the one defined from parameters embedded in the colvar { ... } block (for example, narrower intervals and finer grid spacings may be selected).

      -
      -

      colvar {
        name r
        upperBoundary 20.0
        distance { ... }
      }

      colvar {
        name theta
        dihedral { ... }
      }

      histogram {
        name hist2d
        colvars r theta
        histogramGrid {
          widths  0.1 1.0
          lowerBoundaries   2.0 30.0
          upperBoundaries  10.0 90.0
        }
      }

      +
      +

      colvar {
        name r
        upperBoundary 20.0
        distance { ... }
      }

      colvar {
        name theta
        dihedral { ... }
      }

      histogram {
        name hist2d
        colvars r theta
        histogramGrid {
          widths  0.1 1.0
          lowerBoundaries   2.0 30.0
          upperBoundaries  10.0 90.0
        }
      }

      -

      The standard keywords below are used to control the histogram's computation and to select the +

      The standard keywords below are used to control the histogram's computation and to select the variables that are sampled. See also 6.10.1 for keywords used to define the grid, 6.10.2 for output parameters and 6.10.3 for more advanced keywords.

        -
      • Keyword name: see definition of name (biasing and analysis methods) +
      • Keyword name: see definition of name (biasing and analysis methods)
        • -
      • Keyword colvars: see definition of colvars (biasing and analysis methods) +
      • Keyword colvars: see definition of colvars (biasing and analysis methods)
        • -
      • Keyword stepZeroData: see definition of stepZeroData (biasing and analysis methods) +
      • Keyword stepZeroData: see definition of stepZeroData (biasing and analysis methods)
      -

      +

      (Go to Contents)

      -

      +

      6.10.1 Defining grids for multidimensional histograms
      -

      -

      Grid parameters for the histogram may be provided at the level of the individual variables, or via a +

      +

      Grid parameters for the histogram may be provided at the level of the individual variables, or via a dedicated configuration block histogramGrid { …} inside the configuration of this histogram. The options supported inside this block are:

        -
      • Keyword lowerBoundaries⟨Lower - boundaries of the grid⟩
        Context: histogramGrid
        Acceptable values: list of space-separated decimals
        Description: This option defines the lower boundaries of the grid, overriding any values +
      • Keyword lowerBoundaries⟨Lower + boundaries of the grid⟩
        Context: histogramGrid
        Acceptable values: list of space-separated decimals
        Description: This option defines the lower boundaries of the grid, overriding any values defined by the lowerBoundary keyword of each colvar. Note that when gatherVectorColvars is on, each vector variable is automatically treated as a scalar, and a single value should be provided for it.
        • -
      • upperBoundaries: analogous to lowerBoundaries +
      • upperBoundaries: analogous to lowerBoundaries
        • -
      • widths: analogous to lowerBoundaries
      +
    • widths: analogous to lowerBoundaries
      • -

      +

      (Go to Contents)

      -

      +

      6.10.2 Output options for multi-dimensional histograms
      -

      -

      The accumulated histogram is written in the Colvars state file, allowing for its accumulation +

      +

      The accumulated histogram is written in the Colvars state file, allowing for its accumulation across continued runs. Additionally, the following files are written depending on the histogram's dimensionality:

        -
      • Keyword outputFreq: see definition of outputFreq (biasing and analysis methods) +
      • Keyword outputFreq: see definition of outputFreq (biasing and analysis methods)
        • -
      • Keyword outputFile⟨Write - the histogram to a file⟩
        Context: histogram
        Acceptable values: UNIX filename
        Default value: output. <name >.dat +
      • Keyword outputFile⟨Write + the histogram to a file⟩
        Context: histogram
        Acceptable values: UNIX filename
        Default value: output. <name >.dat
        Description: Name of the file containing histogram data (multicolumn format, see 3.7.4), which is written every outputFreq steps. If outputFile is set to none, the file is not written.
        • -
      • Keyword outputFileDX⟨Write - the histogram to a file⟩
        Context: histogram
        Acceptable values: UNIX filename
        Default value: output. <name >.dx +
      • Keyword outputFileDX⟨Write + the histogram to a file⟩
        Context: histogram
        Acceptable values: UNIX filename
        Default value: output. <name >.dx
        Description: Name of the file containing histogram data (OpenDX format), which is written every outputFreq steps. For the special case of 3 variables, VMD may be used to visualize this file. This file is written by default if the dimension is 3 or more (you cannot visualize it easily for dimensions 4 and above, but the DX format is still more compact than the multicolumn format). If outputFileDX is set to none, the file is not written.
        -

        +

        (Go to Contents)

        -

        +

        6.10.3 Histogramming vector variables
        -

        +

        • -
      • Keyword gatherVectorColvars⟨Treat +
      • Keyword gatherVectorColvars⟨Treat vector variables as multiple observations of a scalar - variable?⟩
        Context: histogram
        Acceptable values: UNIX filename
        Default value: off
        Description: When this is set to on, the components of a multi-dimensional colvar + variable?⟩
        Context: histogram
        Acceptable values: UNIX filename
        Default value: off
        Description: When this is set to on, the components of a multi-dimensional colvar (e.g. one based on cartesian, distancePairs) are treated as multiple observations of a scalar variable. This results in the histogram being accumulated multiple times for each simulation step). When multiple vector variables are included in histogram, these must have the same length because their components are accumulated together. For example, if - ξ, - λ and - τ + ξ, + λ and + τ are three variables of dimensions 5, 5 and 1, respectively, for each iteration 5 triplets - (ξi,λi,τ) - (i = 1,… &ApplyFunction;5) + (ξi,λi,τ) + (i = 1,… &ApplyFunction;5) are accumulated into a 3-dimensional histogram.
        • -
      • Keyword weights⟨Relative +
      • Keyword weights⟨Relative contributions of each vector component to the - histogram⟩
        Context: histogram
        Acceptable values: list of space-separated decimals
        Default value: all weights equal to 1
        Description: When gatherVectorColvars is on, the components of each + histogram⟩
        Context: histogram
        Acceptable values: list of space-separated decimals
        Default value: all weights equal to 1
        Description: When gatherVectorColvars is on, the components of each multi-dimensional colvar are accumulated with a different weight. For example, if - x and - y + x and + y are two distinct cartesian variables defined on the same group of atoms, the corresponding 2D histogram can be weighted on a per-atom basis in the definition of histogram.
      -

      As with any other biasing and analysis method, when a histogram is applied to an extended-system +

      As with any other biasing and analysis method, when a histogram is applied to an extended-system colvar (4.18), it accesses the value of the extended coordinate rather than that of the actual colvar. This can be overridden by enabling the bypassExtendedLagrangian option. A joint histogram of the actual colvar and the extended coordinate may be collected by specifying the @@ -4709,109 +4776,109 @@

      6.10.3 -
    • Keyword bypassExtendedLagrangian: see definition of bypassExtendedLagrangian +
    • Keyword bypassExtendedLagrangian: see definition of bypassExtendedLagrangian (biasing and analysis methods)
      • -

      +

      (Go to Contents)

      -

      +

      6.11 Probability distribution-restraints

      -

      -

      The histogramRestraint bias implements a continuous potential of many variables (or of a single +

      +

      The histogramRestraint bias implements a continuous potential of many variables (or of a single high-dimensional variable) aimed at reproducing a one-dimensional statistical distribution that is provided by the -user. The M -variables (ξ1,… &ApplyFunction;,ξM) +user. The M +variables (ξ1,… &ApplyFunction;,ξM) are interpreted as multiple observations of a random variable -ξ +ξ with unknown probability distribution. The potential is minimized when the histogram -h(ξ), estimated as a sum of Gaussian -functions centered at (ξ1,… &ApplyFunction;,ξM), is equal -to the reference histogram h0(ξ): +h(ξ), estimated as a sum of Gaussian +functions centered at (ξ1,… &ApplyFunction;,ξM), is equal +to the reference histogram h0(ξ):

      - + V (ξ1,… &ApplyFunction;,ξM) = 1 2k∫ (h(ξ)−h0(ξ))2dξ (35)
      - + h (ξ ) = 1 M2πσ2∑i=1Mexp &ApplyFunction; (−(ξ −ξi)2 2σ2 ) (36)
      -

      When used in combination with a distancePairs multi-dimensional variable, this bias +

      When used in combination with a distancePairs multi-dimensional variable, this bias implements the refinement algorithm against ESR/DEER experiments published by Shen et al [33]. -

      This bias behaves similarly to the histogram bias with the gatherVectorColvars option, with the +

      This bias behaves similarly to the histogram bias with the gatherVectorColvars option, with the important difference that all variables are gathered, resulting in a one-dimensional histogram. Future versions will include support for multi-dimensional histograms. -

      The list of options is as follows:

      +

      The list of options is as follows:

        -
      • Keyword name: see definition of name (biasing and analysis methods) +
      • Keyword name: see definition of name (biasing and analysis methods)
        • -
      • Keyword colvars: see definition of colvars (biasing and analysis methods) +
      • Keyword colvars: see definition of colvars (biasing and analysis methods)
        • -
      • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods) +
      • Keyword outputEnergy: see definition of outputEnergy (biasing and analysis methods)
        • -
      • Keyword lowerBoundary⟨Lower - boundary of the colvar grid⟩
        Context: histogramRestraint
        Acceptable values: decimal
        Description: Defines the lowest end of the interval where the reference distribution h0(ξ) +
      • Keyword lowerBoundary⟨Lower + boundary of the colvar grid⟩
        Context: histogramRestraint
        Acceptable values: decimal
        Description: Defines the lowest end of the interval where the reference distribution h0(ξ) is defined. Exactly one value must be provided, because only one-dimensional histograms are supported by the current version.
        • -
      • upperBoundary: analogous to lowerBoundary +
      • upperBoundary: analogous to lowerBoundary
        • -
      • Keyword width⟨Width - of the colvar grid⟩
        Context: histogramRestraint
        Acceptable values: positive decimal
        Description: Defines the spacing of the grid where the reference distribution h0(ξ) +
      • Keyword width⟨Width + of the colvar grid⟩
        Context: histogramRestraint
        Acceptable values: positive decimal
        Description: Defines the spacing of the grid where the reference distribution h0(ξ) is defined.
        • -
      • Keyword gaussianSigma⟨Standard - deviation of the approximating Gaussian⟩
        Context: histogramRestraint
        Acceptable values: positive decimal
        Default value: 2 × -width
        Description: Defines the parameter σ +
      • Keyword gaussianSigma⟨Standard + deviation of the approximating Gaussian⟩
        Context: histogramRestraint
        Acceptable values: positive decimal
        Default value: 2 × +width
        Description: Defines the parameter σ in eq. 36.
        • -
      • Keyword forceConstant⟨Force - constant (kJ/mol)⟩
        Context: histogramRestraint
        Acceptable values: positive decimal
        Default value: 1.0
        Description: Defines the parameter k +
      • Keyword forceConstant⟨Force + constant (kJ/mol)⟩
        Context: histogramRestraint
        Acceptable values: positive decimal
        Default value: 1.0
        Description: Defines the parameter k in eq. 35.
        • -
      • Keyword refHistogram⟨Reference - histogram h0(ξ)⟩
        Context: histogramRestraint
        Acceptable values: space-separated list of M - positive decimals
        Description: Provides the values of h0(ξ) +
      • Keyword refHistogram⟨Reference + histogram h0(ξ)⟩
        Context: histogramRestraint
        Acceptable values: space-separated list of M + positive decimals
        Description: Provides the values of h0(ξ) consecutively. The mid-point convention is used, i.e. the first point that should be included is - for ξ - = lowerBoundary+width/2. If the integral of h0(ξ) - is not normalized to 1, h0(ξ) + for ξ + = lowerBoundary+width/2. If the integral of h0(ξ) + is not normalized to 1, h0(ξ) is rescaled automatically before use.
        • -
      • Keyword refHistogramFile⟨Reference - histogram h0(ξ)⟩
        Context: histogramRestraint
        Acceptable values: UNIX file name
        Description: Provides the values of h0(ξ) +
      • Keyword refHistogramFile⟨Reference + histogram h0(ξ)⟩
        Context: histogramRestraint
        Acceptable values: UNIX file name
        Description: Provides the values of h0(ξ) as contents of the corresponding file (mutually exclusive with refHistogram). The format is - that of a text file, with each line containing the space-separated values of ξ - and h0(ξ). + that of a text file, with each line containing the space-separated values of ξ + and h0(ξ). The same numerical conventions as refHistogram are used.
        • -
      • Keyword writeHistogram⟨Periodically - write the instantaneous histogram h(ξ)⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: If on, the histogram h(ξ) - is written every colvarsRestartFrequency steps to a file with the name output. <name >.hist.dat - This is useful to diagnose the convergence of h(ξ) - against h0(ξ). +
      • Keyword writeHistogram⟨Periodically + write the instantaneous histogram h(ξ)⟩
        Context: metadynamics
        Acceptable values: boolean
        Default value: off
        Description: If on, the histogram h(ξ) + is written every colvarsRestartFrequency steps to a file with the name output. <name >.hist.dat + This is useful to diagnose the convergence of h(ξ) + against h0(ξ).
      -

      +

      -

      +

      (Go to Contents)

      -

      +

      7 Syntax changes from older versions

      -

      -

      The following is a list of syntax changes in Colvars since its first release. Many of the older keywords +

      +

      The following is a list of syntax changes in Colvars since its first release. Many of the older keywords are still recognized by the current code, thanks to specific compatibility code. This is not a list of new features: its primary purpose is to make you aware of those improvements that affect the use of old configuration files with new versions of the code. -

      Note: if you are using any of the NAMD and VMD tutorials:
      https://www.ks.uiuc.edu/Training/Tutorials/
      please be aware that several of these tutorials are not actively maintained: for those cases, this list will +

      Note: if you are using any of the NAMD and VMD tutorials:
      https://www.ks.uiuc.edu/Training/Tutorials/
      please be aware that several of these tutorials are not actively maintained: for those cases, this list will help you reconcile any inconsistencies.

        @@ -4827,13 +4894,13 @@

        7 Colvars version 2018-11-15 or later .
        The global analysis keyword has been discontinued: specific analysis tasks are controlled directly by the keywords         corrFunc and runAve, which continue to remain off by default. -
      • Colvars version 2020-02-25 or later.
        The parameter hillWidth, expressing the Gaussian width 2σ +
      • Colvars version 2020-02-25 or later.
        The parameter hillWidth, expressing the Gaussian width 2σ in relative units (number of grid points), does not have a default value any more. A new - alternative parameter gaussianSigmas allows setting the σ + alternative parameter gaussianSigmas allows setting the σ - parameters explicitly for each variable if needed.
        Furthermore, to facilitate the use of other analysis tools such as for example sum_hills:
        https://www.plumed.org/doc-v2.6/user-doc/html/sum_hills.html
        the format of the file written by writeHillsTrajectory has also been changed to use σ - instead of 2σ. + parameters explicitly for each variable if needed.
        Furthermore, to facilitate the use of other analysis tools such as for example sum_hills:
        https://www.plumed.org/doc-v2.6/user-doc/html/sum_hills.html
        the format of the file written by writeHillsTrajectory has also been changed to use σ + instead of 2σ. This change does not affect how the biasing potential is written in the state file, or the simulated trajectory.
        • @@ -4849,19 +4916,19 @@

        7 Up-to-date documentation can always be accessed at:
        https://colvars.github.io/\cvreleaselabel/colvars-refman-gromacs.html -

        +

        An up-to-date version of this manual for the latest version of Colvars may be accessed here. +

        -

        +

        (Go to Contents)

        -

        +

        8 Compilation notes

        -

        -

        The Colvars module is typically built using the recipes of each supported software package: for this +

        +

        The Colvars module is typically built using the recipes of each supported software package: for this reason, no installation instructions are needed, and the vast majority of the features described in this manual are supported in the most common builds of each package. -

        This section lists the few cases where the choice of compilation settings affects the availability +

        This section lists the few cases where the choice of compilation settings affects the availability features in the Colvars module.

          @@ -4872,13 +4939,14 @@

          8 The Lepton library (https://simtk.org/projects/lepton) used to implement the customFunction feature is currently included only in NAMD (always on), in LAMMPS (on by - default) and in the Colvars-patched GROMACS releases. For VMD, a patch that allows to - link Lepton is available. - -
        • Colvars requires the C++11 language standard, which is either supported (VMD) or required - (GROMACS, LAMMPS, NAMD) by all the engines. However, many of the VMD official builds - are produced on very old architectures. For details please see:
          https://colvars.github.io/README-c++11.html

        -

        + default) and in the Colvars-patched GROMACS releases (but currently, not in the standard + releases). For VMD, a patch that allows to link Lepton is available. + +

      • Colvars requires the C++11 language standard or higher, which is either supported (VMD) + or required (GROMACS, LAMMPS, NAMD) by all the engines. However, many of the VMD + official builds are produced on very old architectures, where C++11 features are disabled at + build time, thus limiting functionality. For details please see:
        https://colvars.github.io/README-c++11.html

      +

      References

      @@ -5036,6 +5104,6 @@

      References

      non-interacting molecular fragments. PLoS Comput. Biol., 11(10):e1004368, 2015.

      -

      +

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