Which potential energy should be used in thermodynamic integration

[xiancai]

Dear VASP developers,
I am trying to use the keyword SCALEE to perform thermodynamic integration from the ideal gas reference to the fully interacting system. I understand that I should use the unscaled potential energy to calculate the free energy difference. Following the detailed guidance in your publication titled “Melting Si: Beyond Density Functional Theory” published in Physical Review Letters, I used Fermi-Dirac smearing with SIGMA=kBT to account for the electronic entropy. Therefore, as shown in the following figure, VASP outputs three different potential energies (i.e., free energy TOTEN, energy without entropy, and energy (sigma->0)). I am wondering which one should be used to calculate the free energy difference? Thank you for your time!
Sincerely,
Tian Hua

[fabien_tran1]

Hi,

This is the free energy that has to be used (the value printed next to "free energy TOTEN"). You may have a look at Sec. I of the supplemental material of the PRL that you mentioned.

[xiancai]

Dear Dr. Tran,

Thank you very much for your reply. In the supplemental material of the PRL, the relevant text states, “the electronic entropy is therefore consistently included in the energy in all ab initio calculations (in VASP this means using the reported electronic ‘free energies’).” I personally suggest explicitly mentioning the use of “free energy TOTEN” in the wiki for the SCALEE and VCAIMAGES tags.

Sincerely,
Tian Hua