A Derivation of Generalized Khon-Sham Scheme

Thread starter Mart1234
Start date Nov 16, 2023
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Derivation Physics Quantum mechanics

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The discussion centers on confusion regarding the derivation of the generalized Kohn-Sham equations found on page 14 of a specific paper. The user seeks clarification on the process that leads to the eigenvalue problem associated with the minimization of ground state energy. They request insights or additional resources to better understand this derivation. Participants are encouraged to provide explanations or references that could help clarify the mathematical steps involved. The inquiry highlights the complexities of density functional theory and the need for clear guidance in advanced topics.

Nov 16, 2023

Mart1234

TL;DR: Question dealing with the derivation of the generalized Khon-Sham equations regarding the final eigenvalue.

Hello, I am following the paper: https://www.yumpu.com/en/document/read/42212557/exact-exchange-in-density-functional-calculations and I am confused on page 14 where the generalized Kohn-Sham equations are derived. I follow that the ground state energy is

The minimization of this step leads to

.
where

I'm not sure of the process used to generate this eigenvalue problem. Any insight into how this was done or other resources would be greatly appreciated.

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