Understanding a Complex Algorithm: Seeking Insight and Clarity

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SUMMARY

The discussion centers on the construction of an algorithm related to Density Functional Theory (DFT) and its application in calculating electron density. The participants clarify that the density arises from the wave function and the external potential (V-external), emphasizing that the iterative procedure for solving Kohn-Sham equations has been established for decades. The main challenge lies not in the iterative method itself but in reformulating the problem into a generalized eigenvalue problem. The original poster seeks clarity on the relationship between the external potential and electron density within the context of DFT.

PREREQUISITES
  • Understanding of Density Functional Theory (DFT)
  • Familiarity with Kohn-Sham equations
  • Knowledge of eigenvalue problems in quantum mechanics
  • Basic concepts of wave functions and electron density
NEXT STEPS
  • Research the implementation of Kohn-Sham equations in computational software
  • Explore the mathematical formulation of generalized eigenvalue problems
  • Study the relationship between external potentials and electron density in DFT
  • Learn about iterative methods used in solving eigenvalue problems
USEFUL FOR

Researchers, physicists, and computational chemists interested in the theoretical foundations and practical applications of Density Functional Theory and its algorithms.

Karrar
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from my reading to DFT I constructed this algorithm

V ex...>[tex]\rho[/tex] ...[tex]\varphi[/tex]...SCF...new[tex]\varphi[/tex]>>>new[tex]\rho[/tex] ...energy

what your opinion in this algorithm ... is lost to some thing ?

and i need to some one tell me is density come from wave function or from V-external ?
 
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I don't see how that constitutes an algorithm (feel free to prove me wrong by writing an implementation).

Charitably interpreting that as a general statement to the effect of "You can use an SCF-like procedure to calculate the density", then that's true. It's also what everyone's been doing for the last 40 years, solving the Kohn-Sham equations. The difficulty in developing the Roothaan-Hall and Kohn-Sham equations wasn't finding an iterative procedure to solve them. They already knew how to solve eigenvalue problems. The difficulty was reformulating the problem into a generalized eigenvalue problem. You're approaching the problem backwards.
 
I construct this scheme for understanding DFT not for treatment something ... so I have Problem with density equation ... what the equation that include the Vex with electron density ... this my Problem ... thanks alxm for interest
 

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