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