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I want to discuss the stability of two polymorphs (such as rutile and anatase TiO2) under high pressure by plotting the difference in free energy between them as a function of pressure.

I found that one typical way to do this is to calculate the energy at different volumes and fit it using an equation of state (such as Birch-Murnaghan). On the other hand, there is an option in the VASP INCAR file called "PSTRESS", which allows setting the external pressure and obtaining the energy under that pressure.

My question is: what is the difference between the energy obtained by the EoS method and the PSTRESS option? Which method is more accurate for discussing phase stability under high pressure?

I would say both approaches should yield the same result.
In one case, you control the volume and obtain a pressure and the energy, in the other case you control the pressure and obtain the volume and energy.
Since the stress tensor is computed in the same way, I would expect you to get the exact same results.
Did you encounter a significant difference from using one method instead of the other?

Thank you very much for your response.

I tried PRTRESS one, but haven't tried E-V plot yet.
I will try both and compare them