Electron-pair density decomposition for core-valence separable systems

The electron pair density of a core-valence separable system can be decomposed into three parts: core-core, core-valence, and valence-valence. The core-core part has a Hartree-Fock like structure. The core-valence part can be written as Γ(cv) (1,2) = γ(c) (1,1)γ(v) (2,2) - γ(c) (1,2)γ(v) (2,1) + γ(c) (2,2)γ(v) (1,1) - γ(c) (2,1)γ(v) (1,2), where only the 1-matrices from the core and valence orbitals contribute. The valence-valence part is left to be determined from the reduced frozen-core type wave function, which often contains the essential information on the electron correlation and the chemical bond. We demonstrate the analysis to the ground state of negative ion Li(-) and 2(1)Σ(u)(+) excited state of the Li(2) molecule.