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Pair density in frozen core + valence electron system Jian Wang Huzhou Univ.

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Presentation on theme: "Pair density in frozen core + valence electron system Jian Wang Huzhou Univ."— Presentation transcript:

1 Pair density in frozen core + valence electron system Jian Wang Huzhou Univ. jwang572@hotmail.com

2 CI wave function

3 Why do we make core + valence separation? At the moment, we are here

4 Wave function in core + valence separation corevalence Core orbitals: doubly occupied appear in each

5 Electronic energy of a many-electron system

6 Energy expressed in reduced density matrices Pair density density 1-matrix

7 Hartree-Fock Approximation: Dirac, Proc. Cambridge Phil. Soc. 27, 240(1931)

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11 Hartree-Fock Approximation: Proof:

12 Hartree-Fock Approximation: Proof:

13 General CI wave function:

14 reduction of 1-matrix for a core + valence wave function

15 Natural orbitals In natural orbitals

16 reduction of pair density for core + valence wave function

17 reduction of pair density for core + valence interaction

18 Valence electron pair density N n v

19 Two valence-electron system For two-electron system, Löwdin and Shull, PR101, 1730(1956): Löwdin and Shulls natural orbitals functional is thus extended to N-electron, two- valence-electron system,

20 Summary

21 Li 2 pair density analysis with core-core core-valence valence-valence

22 Benzene, HOMO valence electron pair density

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24 Acknowledgements Thanks for your attention! Prof. Evert Jan Baerends, Prof. Kwang S. Kim


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