An Introduction to Electronic Structure Calculation

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An Introduction to Electronic Structure
Calculation

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??????Schrodinger ??

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• Hartree approximation (1928)
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Hartree-Fock ??
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Hohenberg-Kohn??

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  electronic density (within a trivial
  constant)! ???????????,?????????????????
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Kohn-Sham ??

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K-S?????

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• ??????local??,KS ??? Hartree?????????,??KS????????
  ???,??????non-local??HF??????
• ??Hartree?Hartree-Fock ?Kohn-Sham?????????????????
  ??,?????????,????????????,?Kohn-Sham????????

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• Hohenberg?Kohn?Sham?60?????????????????
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Kohn-Sham?????

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????????????(?)??,?Hamitonian???? ?n?????????,????
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• ??i??Kohn-Sham??,
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• ??????cij,??Hamitonia H, ??S ???,????????,?????c
  ij?????????????cij?????,????????,???????cij??????
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Iterative Method

• CAR-Parrinello ??
• Which give

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Integration of equations of motion Verlet ??

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• FFT
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• In the standard CP it is still basis
  dependent!

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• Steepest decent
• Conjugate gradient

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Kohn-Sham ???FD??Kohn-Sham???FD?????????

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FD??????

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• ???FFT
• Sparse, structured Hamitonia Matrices
• ???basis???
• Grid ??
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FE??
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Application to H2
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FE??

• Basis
• Sparse ans structured matrices, less sparse than
  FD and less structured than FD
• No FFT
• Adaptive grid
• Generalized eigen value problem, harder to
  implement than FD or PW.