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

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CI wave function

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

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

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Electronic energy of a many-electron system

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

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

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Hartree-Fock Approximation: Proof:

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Hartree-Fock Approximation: Proof:

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General CI wave function:

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

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Natural orbitals In natural orbitals

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reduction of pair density for core + valence wave function

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reduction of pair density for core + valence interaction

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Valence electron pair density N n v

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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,

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Summary

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

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Benzene, HOMO valence electron pair density

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

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