Multiconfigurational Effects on the Density Coherence

This paper is a study of density coherences in multiconfiguration self-consistent field theory and Kohn-Sham (KS) density functional theory. We visualize and compare the nondiagonal elements of the first-order reduced density matrix in the electronic coordinate representation. This is the electronic density coherence, and it also appears in Hartree-Fock (HF) theory in the integrand of the exchange integral. The density coherence is calculated as a function of the internuclear distance for three diatomic molecules (H2, F2, and HF) using both restricted and unrestricted KS and HF theory, as well as the complete active space self-consistent field method. We identify a group of closely associated peaks corresponding to the coherence of electrons on opposite sides of the center of the molecule, and we call this the exchange massif. We find that Slater-determinant methods with a higher percentage of HF exchange tend to underestimate the density coherence at the exchange massif. We explain the trends in terms of a multireference diagnostic and the number of unpaired electrons.