G=0 term in BSE kernel

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G=0 term in BSE kernel

#1 Post by xiaoming_wang » Wed May 12, 2021 2:17 am


At vanishing momentum, the G=0 term in the electron-hole exchange integral is removed for the BSE calculations as implemented in VASP [PRB 92, 045209 (2015)]. However, this term is important to investigate the longitudinal-transverse splitting. I'm wondering if it is possible to add the G=0 term?

Xiaoming Wang

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Re: G=0 term in BSE kernel

#2 Post by kresse_georg » Mon May 17, 2021 12:26 pm


As alluded to in the quoted paper [PRB 92, 045209 (2015)], the G=0 is
) removed when solving the BSE (see around Equ (52) in the referenced paper). However, when calculating the dielectric function or calculating the binding energies, the G=0 term is added back in exactly [see Equ. (54) and (55)].
) To the best of my knowledge, all BSE codes use this approach. This is discussed in detail in G. Onida, L. Reining, and A. Rubio, Rev. Mod. Phys. 74, 601 (2002). This approach has the advantage to significantly reduce errors related to the TDA as discussed in our paper PRB 92, 045209 (2015).
) Side comment: This affects the RPA or bubble diagrams. Confusingly, literature sometimes refers to these terms as exchange integrals, although they are related to the second derivatives of the Hartree-energy.
) For the second derivatives of the Fock-exchange like interactions (electron-hole ladder diagrams), VASP always accounts for the G=0 term.


Georg Kresse

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