Graduate Derivation of Generalized Khon-Sham Scheme

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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.
Mart1234
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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
1700172954424.png


The minimization of this step leads to
1700172984118.png
.
where
1700173019267.png


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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