COSMO-Solvation-Model.md

COSMO Solvation Model

COSMO is the continuum solvation 'COnductor-like Screening MOdel' of A. Klamt and G. Schürmann to describe dielectric screening effects in solvents¹. This model has been enhanced by D.M. York and M. Karplus² to create a smooth potential energy surface. The latter facilitates geometry optimization and dynamics and the implementation has been adapted to take advantage of those ideas.

The NWChem COSMO module implements algorithm for calculation of the energy for the following methods:

1. Restricted Hartree-Fock (RHF),
2. Restricted open-shell Hartree-Fock (ROHF),
3. Restricted Kohn-Sham DFT (DFT),
4. Unrestricted Kohn-Sham DFT (ODFT),

by determining the solvent reaction field self-consistently with the solute charge distribution from the respective methods. Note that COSMO for unrestricted Hartree-Fock (UHF) method can also be performed by invoking the DFT module with appropriate keywords.

Correlation energy of solvent molecules may also be evaluated at

1. MP2,
2. CCSD,
3. CCSD+T(CCSD),
4. CCSD(T),

levels of theory. It is cautioned, however, that these correlated COSMO calculations determine the solvent reaction field using the HF charge distribution of the solute rather than the charge distribution of the correlation theory and are not entirely self consistent in that respect. In other words, these calculations assume that the correlation effect and solvation effect are largely additive, and the combination effect thereof is neglected. COSMO for MCSCF has not been implemented yet.

In the current implementation the code calculates the gas-phase energy of the system followed by the solution-phase energy, and returns the electrostatic contribution to the solvation free energy. At the present gradients are calculated analytically, but frequencies are calculated by finite difference of the gradients.
The non-electrostatic contributions can be calculated by turning on the SMD model. It should be noted that one must in general take into account the standard state correction besides the electrostatic and cavitation/dispersion contribution to the solvation free energy, when a comparison to experimental data is made.

COSMO Input Parameters

Invoking the COSMO solvation model is done by specifying the input COSMO input block with the input options as:

cosmo  
  [off]  
  [dielec  <real dielec default 78.4>]  
  [parameters <filename>]  
  [radius  <real atom1>  
           <real atom2>  
      . . .  
           <real atomN>]  
  [iscren  <integer iscren default 0>]  
  [minbem  <integer minbem default 2>]  
  [ificos  <integer ificos default 0>]  
  [lineq   <integer lineq default 1>]  
  [zeta <real zeta default 0.98>]  
  [gamma_s <real gammas default 1.0>]  
  [sw_tol <real swtol default 1.0e-4>]  
  [do_gasphase  <logical do_gasphase default True>] 
  [do_cosmo_ks]
  [do_cosmo_yk]
  [do_cosmo_smd]
end

followed by the task directive specifying the wavefunction and type of calculation, e.g., task scf energy, task mp2 energy, task dft optimize, etc.

off can be used to turn off COSMO in a compound (multiple task) run. By default, once the COSMO solvation model has been defined it will be used in subsequent calculations. Add the keyword off if COSMO is not needed in subsequent calculations.

dielec is the value of the dielectric constant of the medium, with a default value of 78.4 (the dielectric constant for water).

parameters specifies COSMO radii parameters file that stores custom setting for COSMO parameters. The format for such file consists of the atom or element name followed by the radii. The program will first attempt to match based on atom name and only then the element name. Otherwise radius will be set based on default parameters. The file has to present in one of the three location ( in the order of preference) - directory specified by the environmental variable NWCHEM_COSMO_LIBRARY, permanent directory, and run directory.

radius is an array that specifies the radius of the spheres associated with each atom and that make up the molecule-shaped cavity. These values will override default radii setting including those specified in the COSMO parameter file (if any) Default values are Van der Waals radii. Values are in units of angstroms. The codes uses the following Van der Waals radii by default:

Default radii provided by Andreas Klamt (Cosmologic)

vdw radii: 1.17 (± 0.02) * Bondi radius³

optimal vdw radii for H, C, N, O, F, S, Cl, Br, I⁴

for heavy elements: 1.17*1.9

     data (vander(i),i=1,102)  
    1 / 1.300,1.638,1.404,1.053,2.0475,2.00,  
    2   1.830,1.720,1.720,1.8018,1.755,1.638,  
    3   1.404,2.457,2.106,2.160,2.05,2.223,  
    4   2.223,2.223,2.223,2.223,2.223,2.223,  
    5   2.223,2.223,2.223,2.223,2.223,2.223,  
    6   2.223,2.223,2.223,2.223,2.160,2.223,  
    7   2.223,2.223,2.223,2.223,2.223,2.223,  
    8   2.223,2.223,2.223,2.223,2.223,2.223,  
    9   2.223,2.223,2.223,2.223,2.320,2.223,  
    1   2.223,2.223,2.223,2.223,2.223,2.223,  
    2   2.223,2.223,2.223,2.223,2.223,2.223,  
    3   2.223,2.223,2.223,2.223,2.223,2.223,  
    4   2.223,2.223,2.223,2.223,2.223,2.223,  
    5   2.223,2.223,2.223,2.223,2.223,2.223,  
    6   2.223,2.223,2.223,2.223,2.223,2.223,  
    7   2.223,2.223,2.223,2.223,2.223,2.223,  
    7   2.223,2.223,2.223,2.223,2.223,2.223/

For examples see Stefanovich et al.⁵ and Barone et al.⁶

"Rsolv" is no longer used.

iscren is a flag to define the dielectric charge scaling option. iscren 1 implies the original scaling from Klamt and Schürmann, mainly "(ε-1)/(ε+1/2)", where ε is the dielectric constant. iscren 0 implies the modified scaling suggested by Stefanovich and Truong⁷, mainly "(ε-1)/ε". Default is to use the modified scaling. For high dielectric the difference between the scaling is not significant.

The next two parameters define the tesselation of the unit sphere. The approach still follows the original proposal by Klamt and Schürmann to some degree. Basically a tesselation is generated from minbem refining passes starting from either an octahedron or an icosahedron. Each level of refinement partitions the triangles of the current tesselation into four triangles. This procedure is repeated recursively until the desired granularity of the tesselation is reached. The induced point charges from the polarization of the medium are assigned to the centers of the tesselation. The default value is minbem 2. The flag ificos serves to select the original tesselation, ificos 0 for an octahedron (default) and ificos 1 for an icoshedron. Starting from an icosahedron yields a somewhat finer tesselation that converges somewhat faster. Solvation energies are not really sensitive to this choice for sufficiently fine tesselations. The old "maxbem" directive is no longer used.

The lineq parameter serves to select the numerical algorithm to solve the linear equations yielding the effective charges that represent the polarization of the medium. lineq 0 selects a dense matrix linear equation solver (default), lineq 1 selects an iterative method. For large molecules where the number of effective charges is large, the code selects the iterative method.

zeta sets the width of the Gaussian charge distributions that were suggested by York and Karplus to avoid singularities when two surface charges coincide. The default value is zeta 0.98 this value was chosen to ensure that the results of the current implementation are as close as possible to those of the original Klamt and Schürmann based implementation.

gamma_s modifies the width of the smooth switching function that eliminates surface charges when their positions move into the sphere of a neighboring atom. gamma_s 0.0 leads to a heavyside or abrupt switching function, whereas gamma_s 1.0 maximizes the width of the switching function. The default value is gamma_s 1.0.

sw_tol specifies the cutoff of the switching function below which a surface charge at a particular point is eliminated. The values of the switching function lie in the domain from 0 to 1. This value should not be set too small as that leads to instabilities in the linear system solvers. The default value is sw_tol 1.0e-4.

do_gasphase is a flag to control whether the calculation of the solvation energy is preceded by a gas phase calculation. The default is to always perform a gas phase calculation first and then calculate the solvation starting from the converged gas phase electron density. However, in geometry optimizations this approach can double the cost. In such a case setting do_gasphase false suppresses the gas phase calculations and only the solvated system calculations are performed. This option needs to be used with care as in some cases starting the COSMO solvation from an unconverged electron density can generate unphysical charges that lock the calculation into strange electron distributions.

do_cosmo_ks is a flag to turn on the Klamt-Schürmann model

do_cosmo_yk is a flag to turn on the York-Karplus model (default)

do_cosmo_smd is a flag to turn on the SMD model. More details can be found at the SMD Model documentation page

The following example is for a water molecule in 'water', using the HF/6-31G** level of theory:

start  
 
geometry  
 o                  .0000000000         .0000000000        -.0486020332  
 h                  .7545655371         .0000000000         .5243010666  
 h                 -.7545655371         .0000000000         .5243010666  
end  
basis
 o library 6-31g**  
 h library 6-31g**  
end  
cosmo  
 dielec 78.0  
 radius 1.40  
        1.16  
        1.16  
 lineq  0  
end  
task scf energy

Alternatively, instead of listing COSMO radii parameters in the input, the former can be loaded using an external file through the parameters directive

start  

geometry  
 ow                  .0000000000         .0000000000        -.0486020332  
 hw                  .7545655371         .0000000000         .5243010666  
 h                  -.7545655371         .0000000000         .5243010666  
end  
basis
 * library 6-31g**  
end

cosmo  
 dielec 78.0  
 lineq  0  
 parameters water.par  
end

task scf energy

where the water.par file has the following form:

O 1.40
H 1.16

This will set radii of all oxygen atoms to 1.4 and all hydrogen atoms to 1.16. More fine grained control may be achieved using specific atom names. For example, the following parameter file

O    1.40
H    1.16
HW  1.06

will set a different radii of 1.06 to hydrogen atoms named HW. Note that, as per general rule in NWChem, all names are case insensitive.

and placed in one of the these locations - directory specified by the environmental variable NWCHEM_COSMO_LIBRARY, permanent directory, or run directory.

COSMO Usage Tips

Authors of the paper ⁸ report that
" ... the SMD/COSMO/NWChem calculations we employed finer grids (options minbem=3, maxbem=4, ificos=1) because the default NWChem tessellation parameters (options: minbem=2, maxbem=3, ificos=0) produced very large errors in solvation free energies."
Since the maxbem keyword is no longer in use, this paper's recommended input translate into

cosmo
 minbem 3
 ificos 1
end

References

///Footnotes Go Here///

Solvents List - Solvent keyword

The short name for the solvent from the table can be used with the solvent keyword to define the solvent.
Example with acetonitrile.

cosmo
  solvent acetntrl
end

Long name	short name	dielec
acetic acid	acetacid	6.2528
acetone	acetone	20.493
acetonitrile	acetntrl	35.688
acetophenone	acetphen	17.440
aniline	aniline	6.8882
anisole	anisole	4.2247
benzaldehyde	benzaldh	18.220
benzene	benzene	2.2706
benzonitrile	benzntrl	25.592
benzyl chloride	benzylcl	6.7175
1-bromo-2-methylpropane	brisobut	7.7792
bromobenzene	brbenzen	5.3954
bromoethane	brethane	9.01
bromoform	bromform	4.2488
1-bromooctane	broctane	5.0244
1-bromopentane	brpentan	6.269
2-bromopropane	brpropa2	9.3610
1-bromopropane	brpropan	8.0496
butanal	butanal	13.450
butanoic acid	butacid	2.9931
1-butanol	butanol	17.332
2-butanol	butanol2	15.944
butanone	butanone	18.246
butanonitrile	butantrl	24.291
butyl acetate	butile	4.9941
butylamine	nba	4.6178
n-butylbenzene	nbutbenz	2.360
sec-butylbenzene	sbutbenz	2.3446
tert-butylbenzene	tbutbenz	2.3447
carbon disulfide	cs2	2.6105
carbon tetrachloride	carbntet	2.2280
chlorobenzene	clbenzen	5.6968
sec-butyl chloride	secbutcl	8.3930
chloroform	chcl3	4.7113
1-chlorohexane	clhexane	5.9491
1-chloropentane	clpentan	6.5022
1-chloropropane	clpropan	8.3548
o-chlorotoluene	ocltolue	4.6331
m-cresol	m-cresol	12.440
o-cresol	o-cresol	6.760
cyclohexane	cychexan	2.0165
cyclohexanone	cychexon	15.619
cyclopentane	cycpentn	1.9608
cyclopentanol	cycpntol	16.989
cyclopentanone	cycpnton	13.58
cis-decalin	declncis	2.2139
trans-decalin	declntra	2.1781
decalin (cis/trans mixture)	declnmix	2.196
n-decane	decane	1.9846
1-decanol	decanol	7.5305
1,2-dibromoethane	edb12	4.9313
dibromomethane	dibrmetn	7.2273
dibutyl ether	butyleth	3.0473
o-dichlorobenzene	odiclbnz	9.9949
1,2-dichloroethane	edc12	10.125
cis-dichloroethylene	c12dce	9.200
trans-dichloroethylene	t12dce	2.140
dichloromethane	dcm	8.930
diethyl ether	ether	4.2400
diethyl sulfide	et2s	5.723
diethylamine	dietamin	3.5766
diiodomethane	mi	5.320
diisopropyl ether	dipe	3.380
dimethyl disulfide	dmds	9.600
dimethylsulfoxide	dmso	46.826
N,N-dimethylacetamide	dma	37.781
cis-1,2-dimethylcyclohexane	cisdmchx	2.060
N,N-dimethylformamide	dmf	37.219
2,4-dimethylpentane	dmepen24	1.8939
2,4-dimethylpyridine	dmepyr24	9.4176
2,6-dimethylpyridine	dmepyr26	7.1735
1,4-dioxane	dioxane	2.2099
diphenyl ether	phoph	3.730
dipropylamine	dproamin	2.9112
n-dodecane	dodecan	2.0060
1,2-ethanediol	meg	40.245
ethanethiol	etsh	6.667
ethanol	ethanol	24.852
ethyl acetate	etoac	5.9867
ethyl formate	etome	8.3310
ethylbenzene	eb	2.4339
ethylphenyl ether	phenetol	4.1797
fluorobenzene	c6h5f	5.420
1-fluorooctane	foctane	3.890
formamide	formamid	108.94
formic acid	formacid	51.100
n-heptane	heptane	1.9113
1-heptanol	heptanol	11.321
2-heptanone	heptnon2	11.658
4-heptanone	heptnon4	12.257
n-hexadecane	hexadecn	2.0402
n-hexane	hexane	1.8819
hexanoic acid	hexnacid	2.600
1-hexanol	hexanol	12.51
2-hexanone	hexanon2	14.136
1-hexene	hexene	2.0717
1-hexyne	hexyne	2.615
iodobenzene	c6h5i	4.5470
1-iodobutane	iobutane	6.173
iodoethane	c2h5i	7.6177
1-iodohexadecane	iohexdec	3.5338
iodomethane	ch3i	6.8650
1-iodopentane	iopentan	5.6973
1-iodopropane	iopropan	6.9626
isopropylbenzene	cumene	2.3712
p-isopropyltoluene	p-cymene	2.2322
mesitylene	mesityln	2.2650
methanol	methanol	32.613
2-methoxyethanol	egme	17.200
methyl acetate	meacetat	6.8615
methyl benzoate	mebnzate	6.7367
methyl butanoate	mebutate	5.5607
methyl formate	meformat	8.8377
4-methyl-2-pentanone	mibk	12.887
methyl propanoate	mepropyl	6.0777
2-methyl-1-propanol	isobutol	16.777
2-methyl-2-propanol	terbutol	12.470
N-methylaniline	nmeaniln	5.9600
methylcyclohexane	mecychex	2.024
N-methylformamide (E/Z mixture)	nmfmixtr	181.56
2-methylpentane	isohexan	1.890
2-methylpyridine	mepyrid2	9.9533
3-methylpyridine	mepyrid3	11.645
4-methylpyridine	mepyrid4	11.957
nitrobenzene	c6h5no2	34.809
nitroethane	c2h5no2	28.290
nitromethane	ch3no2	36.562
1-nitropropane	ntrprop1	23.730
2-nitropropane	ntrprop2	25.654
o-nitrotoluene	ontrtolu	25.669
n-nonane	nonane	1.9605
1-nonanol	nonanol	8.5991
5-nonanone	nonanone	10.600
n-octane	octane	1.9406
1-octanol	octanol	9.8629
2-octanone	octanon2	9.4678
n-pentadecane	pentdecn	2.0333
pentanal	pentanal	10.000
n-pentane	npentane	1.8371
pentanoic acid	pentacid	2.6924
1-pentanol	pentanol	15.130
2-pentanone	pentnon2	15.200
3-pentanone	pentnon3	16.780
1-pentene	pentene	1.9905
E-2-pentene	e2penten	2.051
pentyl acetate	pentacet	4.7297
pentylamine	pentamin	4.2010
perfluorobenzene	pfb	2.029
phenylmethanol	benzalcl	12.457
propanal	propanal	18.500
propanoic acid	propacid	3.440
1-propanol	propanol	20.524
2-propanol	propnol2	19.264
propanonitrile	propntrl	29.324
2-propen-1-ol	propenol	19.011
propyl acetate	propacet	5.5205
propylamine	propamin	4.9912
pyridine	pyridine	12.978
tetrachloroethene	c2cl4	2.268
tetrahydrofuran	thf	7.4257
tetrahydrothiophene-S,S-dioxide	sulfolan	43.962
tetralin	tetralin	2.771
thiophene	thiophen	2.7270
thiophenol	phsh	4.2728
toluene	toluene	2.3741
tributyl phosphate	tbp	8.1781
1,1,1-trichloroethane	tca111	7.0826
1,1,2-trichloroethane	tca112	7.1937
trichloroethene	tce	3.422
triethylamine	et3n	2.3832
2,2,2-trifluoroethanol	tfe222	26.726
1,2,4-trimethylbenzene	tmben124	2.3653
2,2,4-trimethylpentane	isoctane	1.9358
n-undecane	undecane	1.9910
m-xylene	m-xylene	2.3478
o-xylene	o-xylene	2.5454
p-xylene	p-xylene	2.2705
xylene (mixture)	xylenemx	2.3879
water	h2o	78.400

Footnotes

1. Klamt, A; Schürmann, G (1993). "COSMO: A new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient". Journal of the Chemical Society, Perkin Transactions 2: 799-805. DOI:10.1039/P29930000799 ↩

2. York, D.M.; Karplus, M. (1999). "A smooth solvation potential based on the conductor-like screening model". Journal of physical chemistry A 103: 11060-11079. DOI:10.1021/jp992097l ↩

3. A. Bondi (1964). "van der Waals volums and radii". Journal of Physical Chemistry 68: 441-451. DOI:10.1021/j100785a001 ↩

4. A. Klamt, V. Jonas (1998). "Refinement and parametrization of COSMO-RS". Journal of physical chemistry A 102: 5074-5085. DOI:10.1021/jp980017s ↩

5. E. V. Stefanovich, T. N. Truong (1995). "Optimized atomic radii for quantum dielectric continuum solvation models". Chemical Physics Letters 244: 65-74. DOI:10.1016/0009-2614(95)00898-E ↩

6. V. Barone, M. Cossi (1997). "A new definition of cavities for the computation of solvation free energies by the polarizable continuum model". Journal of Chemical Physics 107: 3210-3221. DOI:10.1063/1.474671 ↩

7. E. V. Stefanovich, T. N. Truong (1995). "Optimized atomic radii for quantum dielectric continuum solvation models". Chemical Physics Letters 244: 65-74. DOI:10.1016/0009-2614(95)00898-E ↩

8. A. V. Marenich, C. J. Cramer, D. G. Truhlar (2009). "Universal Solvation Model Based on Solute Electron Density and on a Continuum Model of the Solvent Defined by the Bulk Dielectric Constant and Atomic Surface Tensions". The Journal of Physical Chemistry B 113: 6378-6396. DOI:10.1021/jp810292n. ↩