👌 PwBaseWorkChain: Improve handling of SCF convergence issues

The current error handler for the `PwBaseWorkChain` that deals with SCF convergence
issues only tries to reduce the `mixing-beta` by 20% each time the calculation fails,
and doesn't consider the rate of convergence.

Here we improve the error handling for this case by calculating the slope on the
logarithm of the "scf accuracy". Based on some statistics presented in

#961

We noted two points:

1. Most of the calculations that converge do so within 50 SCF steps.
2. For those that don't, there is a very low chance of convergence in case the scf
   accuracy slope is higher than -0.1.

Hence, we:

* Limit the default number of maximum steps (`electron_maxstep`) to 50.
* In case of SCF convergence failure, check the scf accuracy slope. If < -0.1, do a
  full restart.
* Else, check the `mixing_beta`. If above 0.1, half it and restart the calculation.

src/aiida_quantumespresso/workflows/protocols/pw/base.yaml

@@ -25,7 +25,7 @@ default_inputs:
                 smearing: cold
                 degauss: 0.01
             ELECTRONS:
-                electron_maxstep: 80
+                electron_maxstep: 50
                 mixing_beta: 0.4
 default_protocol: moderate
 protocols:

src/aiida_quantumespresso/workflows/pw/base.py

@@ -29,10 +29,11 @@ class PwBaseWorkChain(ProtocolMixin, BaseRestartWorkChain):
         'qe': qe_defaults,
         'delta_threshold_degauss': 30,
         'delta_factor_degauss': 0.1,
-        'delta_factor_mixing_beta': 0.8,
+        'delta_factor_mixing_beta': 0.5,
         'delta_factor_max_seconds': 0.95,
         'delta_factor_nbnd': 0.05,
         'delta_minimum_nbnd': 4,
+        'conv_slope_threshold': -0.1,
     })
 
     @classmethod
@@ -563,16 +564,36 @@ def handle_electronic_convergence_not_reached(self, calculation):
 
         Decrease the mixing beta and fully restart from the previous calculation.
         """
-        factor = self.defaults.delta_factor_mixing_beta
+        import numpy
+
+        scf_accuracy = calculation.tools.get_scf_accuracy(0)
+        scf_accuracy_slope = numpy.polyfit(numpy.arange(0, len(scf_accuracy)), numpy.log(scf_accuracy), 1)[0]
+
+        if scf_accuracy_slope < self.defaults.conv_slope_threshold:
+
+            action = (
+                'electronic convergence not reached but the scf accuracy is decreasing: restart from the last '
+                'calculation.'
+            )
+            self.set_restart_type(RestartType.FULL, calculation.outputs.remote_folder)
+            self.report_error_handled(calculation, action)
+            return ProcessHandlerReport(True)
+
         mixing_beta = self.ctx.inputs.parameters.get('ELECTRONS', {}).get('mixing_beta', self.defaults.qe.mixing_beta)
-        mixing_beta_new = mixing_beta * factor
 
-        self.ctx.inputs.parameters['ELECTRONS']['mixing_beta'] = mixing_beta_new
-        action = f'reduced beta mixing from {mixing_beta} to {mixing_beta_new} and restarting from the last calculation'
+        if mixing_beta > 0.1:
 
-        self.set_restart_type(RestartType.FULL, calculation.outputs.remote_folder)
-        self.report_error_handled(calculation, action)
-        return ProcessHandlerReport(True)
+            mixing_beta_new = mixing_beta * self.defaults.delta_factor_mixing_beta
+
+            self.ctx.inputs.parameters['ELECTRONS']['mixing_beta'] = mixing_beta_new
+            action = (
+                f'reduced beta mixing from {mixing_beta} to {mixing_beta_new} and restarting from the last '
+                'calculation'
+            )
+
+            self.set_restart_type(RestartType.FULL, calculation.outputs.remote_folder)
+            self.report_error_handled(calculation, action)
+            return ProcessHandlerReport(True)
 
     @process_handler(priority=420, exit_codes=[
         PwCalculation.exit_codes.WARNING_ELECTRONIC_CONVERGENCE_NOT_REACHED,

tests/workflows/protocols/pw/test_bands/test_default.yml

@@ -20,7 +20,7 @@ bands:
         conv_thr: 4.0e-10
         diago_full_acc: true
         diagonalization: paro
-        electron_maxstep: 80
+        electron_maxstep: 50
         mixing_beta: 0.4
         startingpot: file
       SYSTEM:
@@ -60,7 +60,7 @@ relax:
           tstress: true
         ELECTRONS:
           conv_thr: 4.0e-10
-          electron_maxstep: 80
+          electron_maxstep: 50
           mixing_beta: 0.4
         SYSTEM:
           degauss: 0.01
@@ -95,7 +95,7 @@ scf:
         tstress: true
       ELECTRONS:
         conv_thr: 4.0e-10
-        electron_maxstep: 80
+        electron_maxstep: 50
         mixing_beta: 0.4
       SYSTEM:
         degauss: 0.01

tests/workflows/protocols/pw/test_base/test_default.yml

@@ -18,7 +18,7 @@ pw:
       tstress: true
     ELECTRONS:
       conv_thr: 4.0e-10
-      electron_maxstep: 80
+      electron_maxstep: 50
       mixing_beta: 0.4
     SYSTEM:
       degauss: 0.01

tests/workflows/protocols/pw/test_relax/test_default.yml

@@ -22,7 +22,7 @@ base:
         tstress: true
       ELECTRONS:
         conv_thr: 4.0e-10
-        electron_maxstep: 80
+        electron_maxstep: 50
         mixing_beta: 0.4
       SYSTEM:
         degauss: 0.01
@@ -54,7 +54,7 @@ base_final_scf:
         tstress: true
       ELECTRONS:
         conv_thr: 4.0e-10
-        electron_maxstep: 80
+        electron_maxstep: 50
         mixing_beta: 0.4
       SYSTEM:
         degauss: 0.01

tests/workflows/protocols/test_pdos/test_default.yml

@@ -32,7 +32,7 @@ nscf:
         tstress: true
       ELECTRONS:
         conv_thr: 4.0e-10
-        electron_maxstep: 80
+        electron_maxstep: 50
         mixing_beta: 0.4
       SYSTEM:
         ecutrho: 240.0
@@ -74,7 +74,7 @@ scf:
         tstress: true
       ELECTRONS:
         conv_thr: 4.0e-10
-        electron_maxstep: 80
+        electron_maxstep: 50
         mixing_beta: 0.4
       SYSTEM:
         degauss: 0.01

tests/workflows/protocols/xspectra/test_core/test_default.yml

@@ -37,7 +37,7 @@ scf:
         tstress: true
       ELECTRONS:
         conv_thr: 4.0e-10
-        electron_maxstep: 80
+        electron_maxstep: 50
         mixing_beta: 0.4
       SYSTEM:
         degauss: 0.01

tests/workflows/protocols/xspectra/test_crystal/test_default.yml

@@ -25,7 +25,7 @@ core:
           tstress: true
         ELECTRONS:
           conv_thr: 4.0e-10
-          electron_maxstep: 80
+          electron_maxstep: 50
           mixing_beta: 0.4
         SYSTEM:
           degauss: 0.01
@@ -100,7 +100,7 @@ relax:
           tstress: true
         ELECTRONS:
           conv_thr: 4.0e-10
-          electron_maxstep: 80
+          electron_maxstep: 50
           mixing_beta: 0.4
         SYSTEM:
           degauss: 0.01