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

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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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Valence Electrons. Electrons Electrons are found in orbitals within energy levels The regions in an atom where electrons are found are called orbitals.

Valence Electrons. Electrons Electrons are found in orbitals within energy levels The regions in an atom where electrons are found are called orbitals.

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