Pair density in frozen core valence electron system

Pair density in “frozen core + valence electron” system Jian Wang Huzhou Univ. jwang 572@hotmail. com

CI wave function

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

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

Electronic energy of a many-electron system

Energy expressed in reduced density matrices 1 -matrix Pair density

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

Hartree-Fock Approximation: Proof:

Hartree-Fock Approximation: Proof:

General CI wave function:

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

Natural orbitals In natural orbitals

reduction of pair density for core + valence wave function

reduction of pair density for core + valence interaction

Valence electron pair density N nv

Two valence-electron system For two-electron system, Löwdin and Shull, PR 101, 1730(1956): Löwdin and Shull’s natural orbitals functional is thus extended to N-electron, twovalence-electron system,

Summary

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

Benzene, HOMO valence electron pair density

Benzene, HOMO valence electron pair density

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