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It is sometimes observed that when using the BDP thermostat in a sequence of runs, the plot generated by the econste.plt script has discontinuities at the beginning of each run. The reason is the following:

When using no thermostat (NVE simulation) the constant of the motion <econst> is conserved (if the time step is small enough and if the ground state is reached with sufficient accuracy at each MD step. The value of <econst> is <ekin_ion> + <etotal> where <ekin_ion> is the kinetic energy of the nuclei, and <etotal> is the total Kohn-Sham energy.

When using a thermostat, the quantity <ekin_ion>+ <etotal> is not constant since the thermostat modifies the ionic velocities and this changes <ekin_ion>.

In the case of the BDP thermostat, the amount of kinetic energy that is given to (or taken from) the ions can be computed, and in that case the quantity <econst> includes that contribution from the thermostat. This means that in the case of the BDP thermostat, <econst> should be conserved.

This is done by keeping track (i.e. integrating) all the contributions to <ekin_ion> from the thermostat during the run. However, this information is not carried from one run to the next, so at the beginning of each run, it starts from a zero contribution from the thermostat. This causes the discontinuity in the plot of <econst> across multiple runs.

The only information that should be extracted from the econste.plt plot is whether the value of <econst> is reasonably constant during a run. This would indicate that the time step is small enough and the ground state calculations are converged after taking into account the contributions from the thermostat.