How to isolate electrostatic energy components from DFT total energy?

[adelina_carr]

Dear VASP users,

I’m trying to better understand how to extract the electrostatic energy contributions from a DFT total energy calculation using VASP.

As an example, I performed a relaxation of CaHfS₃ (Materials Project ID: mp-1190098) using meta-GGA (R2SCAN). The breakdown of the total free energy is shown in the attached screenshot from the OUTCAR file.

To compute the electrostatic energy, I believe it should consist of the ion-ion, electron-electron, and ion-electron interaction terms. Based on this archived post from 2005, the partitioning appears to be:

Ion-ion interactions:
alpha Z + Ewald energy

Electron-electron interactions:
Hartree energy (possibly divided by 2 to account for double-counting?)

Ion-electron interactions:
This is where I’m unclear. The old forum thread suggests this may be: “embedded in the eigenvalues,” or "the expectation value of the pseudopotential."

However, I’m still not sure how to explicitly extract the ion-electron term, or how to compute it from available OUTCAR data.

Does anyone have insight on how to obtain the ion-electron interaction energy from a standard PAW-based VASP run?

Thanks in advance for your help!

Best,
Adelina

[merzuk.kaltak]

In VASP, extracting the pure ion-electron interaction energy from the OUTCAR is not straightforward, and there isn't a direct way to get this term cleanly separated from the other contributions.
Here's why this is challenging:
The fundamental issue: VASP uses density functional theory where the total energy is calculated through the Kohn-Sham formalism. The energy expression:
TOTEN = EEBANDS - double counting corrections
doesn't cleanly separate into classical electrostatic terms like ion-ion, electron-electron, and ion-electron interactions because:

EEBANDS contains kinetic energy plus all potential energy contributions mixed together
The double counting corrections remove spurious self-interactions but don't correspond to clean physical separations

What you can extract from OUTCAR:

• TOTEN - total energy

• EEBANDS - sum of eigenvalues

• Hartree energy DENC - classical electrostatic energy of electron density

• XC energy XCENC - exchange-correlation energy

• Ewald energy TEWEN - ion-ion electrostatic interaction

• -1/2 Hartree DENC - correction for double counting

Closest approximation:
The ion-electron attraction is buried within the eigenvalue sum (EEBANDS), but you cannot isolate it because the Kohn-Sham eigenvalues inherently mix kinetic and potential contributions in a non-separable way.

A good overview on how the total energy is calculated is also found in PhysRevB.54.11169].