I've calculated the bulk modulus by following the procedure described in Furukawa et al. First-Principles Prediction of Densities of Amorphous Materials: The Case of Amorphous Silicon. J. Phys. Soc. Japan 2018. That is a multitude of relaxations are performed for each fixed volume (hence density) and the average energy at each is fitted to the Murnaghan EOS to determined the bulk modulus. Amorphous systems are generated by random placement of 140 atoms in a cubic cell followed by melting and quenching using a ReaxFF potential under constant cell volume and shape. These structures are then relaxed in VASP under the following settings.
ISIF=4
EDIFFG=-1e-3
PREC=HIGH
ENCUT=550 eV (>1.3 the ENMAX)
This is performed for 20 simulations of each volume. However, the minimum in the energy vs volume relation and does not coincide with the 0 pressure in the pressure vs volume plot. I am curious if this might be attributable to a collective shift from the Pulay stress despite the higher than recommended energy cutoff. If so, should I perform a simulation with an even higher cutoff to benchmark the Pulay stress for corrections?
Discrepancy between Minimum Energy and 0 Pressure of Amorphous Simulations
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ccrook
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marie-therese.huebsch
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Re: Discrepancy between Minimum Energy and 0 Pressure of Amorphous Simulations
Dear ccrook,
Very interesting work!
The source of the discrepancy could be Pulay stress. You can try to devise a convergence test without repeating the entire calculation to clarify this. The energy at each volume should not change when increasing the energy cutoff.
Another source could be that 20 simulations might not suffice to enter the realm of statistics. Maybe you can find an error estimate and/or increase statistics.
Additionally, EDIFFG is a negative number, which invokes a convergence criterion of the ionic relaxation on the force and not on the energy. As you then analyze the energy vs. volume plot, it is prudent to check if your calculations are also converged with respect to energy.
These are just some ideas where you could start investigating. Maybe other users have more suggestions.
All the best,
Marie-Therese
Very interesting work!
The source of the discrepancy could be Pulay stress. You can try to devise a convergence test without repeating the entire calculation to clarify this. The energy at each volume should not change when increasing the energy cutoff.
Another source could be that 20 simulations might not suffice to enter the realm of statistics. Maybe you can find an error estimate and/or increase statistics.
Additionally, EDIFFG is a negative number, which invokes a convergence criterion of the ionic relaxation on the force and not on the energy. As you then analyze the energy vs. volume plot, it is prudent to check if your calculations are also converged with respect to energy.
These are just some ideas where you could start investigating. Maybe other users have more suggestions.
All the best,
Marie-Therese