Graduate 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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SUMMARY

The discussion centers on the derivation of the generalized Kohn-Sham equations as presented in the paper "Exact Exchange in Density Functional Calculations." The user expresses confusion regarding the minimization process that leads to the eigenvalue problem associated with the ground state energy. Key elements include the mathematical formulation of the Kohn-Sham equations and the specific steps involved in deriving the eigenvalue problem. Clarification on these processes is sought, indicating a need for deeper understanding of the theoretical framework.

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Understanding of Density Functional Theory (DFT)
Familiarity with Kohn-Sham equations
Basic knowledge of eigenvalue problems in quantum mechanics
Proficiency in mathematical minimization techniques

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Researchers in theoretical chemistry, physicists specializing in quantum mechanics, and students studying Density Functional Theory will benefit from this discussion.

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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