Pair density in frozen core + valence electron system Jian Wang Huzhou Univ. [email protected].

Pair density in “frozen core + valence electron” system

Jian WangHuzhou Univ.

[email protected]

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

Pair density

density

1-matrix

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, PR101, 1730(1956):

Löwdin and Shull’s natural orbitals functional is thus extended to N-electron, two- valence-electron system,

Summary

Li2 pair density analysis with

core-core

core-valence valence-valence

Benzene, HOMO valence electron pair density

Benzene, HOMO valence electron pair density

Acknowledgements

Thanks for your attention!

Prof. Evert Jan Baerends,Prof. Kwang S. Kim