About Achieving self-consistency in solving KS equation

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SUMMARY

The discussion focuses on the challenges of achieving self-consistency in solving the Kohn-Sham (KS) equation. It highlights that simply using the output density as the new input can lead to oscillations and slow convergence. Instead, employing intelligent mixing schemes such as conjugate-gradient or Anderson mixing is essential for improving convergence rates. Proper citation practices are also emphasized, requiring detailed references for academic papers.

PREREQUISITES
  • Understanding of Kohn-Sham (KS) equations in density functional theory
  • Familiarity with self-consistent field (SCF) methods
  • Knowledge of numerical methods for iterative solutions
  • Experience with mixing schemes like conjugate-gradient and Anderson mixing
NEXT STEPS
  • Research Kohn-Sham equations and their applications in quantum mechanics
  • Learn about self-consistent field (SCF) methods and their convergence properties
  • Study numerical techniques for improving convergence in iterative algorithms
  • Explore advanced mixing schemes such as Anderson mixing in computational physics
USEFUL FOR

This discussion is beneficial for physicists, computational chemists, and researchers working on density functional theory and numerical methods for solving the Kohn-Sham equation.

pcthu
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Why cannot simply taking the output density as the new input to the next?
I've read the paper by [P.H.Dederichs and R.Zeller],but more physics picture like answer I wonder to know. Thanks all
 
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Usually with self-consistent algorithms like this, the output will have moved in approximately the right direction from the input, but much too far. So if you just take the output as the input for your next iteration, your density will wildly oscillate and never converge. Even if it does converge, it may go extremely slowly, taking thousands of iterations before converging. Implementing some intelligent mixing scheme like conjugate-gradient or Anderson mixing will greatly improve the convergence.

By the way, writing the paper by [author x] is not a proper citation, we need the journal name, volume and page number of the first page (year is good too) to know what paper you are talking about.
 

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