How to calculate for single-particle Kohn-Sham energies/core energies for bulk VBM alignment?

[reynaldo.putra]

Hello,

IP-image.png

I have a question on the alignment of the ionization potential (IP) of bulks after calculating the vacuum level of a slab model. In the case where the surface effects are important, we can immediately use the IP of the surface slab if we are interested in e.g., band bending and dangling bond effects (the blue IP in the image).

In the case where it is not, I found here that we can find the IP of the bulk (the green IP in the image) to align the references by following this equation:

IP-bulk.png

I have a question about the single-particle Kohn-Sham energies/core energies mentioned here because I am frankly quite unsure about the terminology used here. What is the single-particle Kohn-Sham energies/core energies? Are they related to the ICORELEVEL tag?

Thank you for your attention.

[jonathan_lahnsteiner2]

Dear Reynaldo Putra,

Single-particle Kohn-Sham energies refer to the eigenvalues ε_i obtained by solving the Kohn-Sham equations:

H_KS ψi(r) = εi ψ_i(r)   (i = 1,...,N)

where H_KS is the Kohn-Sham Hamiltonian, ψi(r) are the Kohn-Sham orbitals, and εi are the single-particle energies.

Core energies typically refer to eigenvalues corresponding to orbitals that are tightly bound and lie energetically well below the Fermi level. In a pseudopotential or PAW method (as in VASP), core states are not treated explicitly, but their energies may be referenced as part of atomic data (e.g., for calculating total energies or reference chemical potentials).

All the best Jonathan