Efficient evaluation of electron correlation along the bond-dissociation coordinate in the ground and excited ionic states with dynamic correlation suppression and enhancement functions of the on-top pair density

Abstract

Calculation of the electron correlation energy ${E}_{c}$ of ground and excited states through the partitioning and evaluation of the dynamic ${E}_{c}^{d}$ and nondynamic ${E}_{c}^{nd}$ components requires one to account for the interplay of these correlation modes as well as for the excitation effect. In this paper it is demonstrated that both local suppression of dynamic correlation (SDC) by nondynamic correlation and enhancement of dynamic correlation (EDC) due to excitation to a state of the ionic nature can be quantified with the ratio $x(\mathbit{r})$ between the correlated and uncorrelated on-top pair densities $\mathrm{\ensuremath{\Pi}}(\mathbit{r})$. A $\mathrm{CAS}\mathrm{\ensuremath{\Pi}}\mathrm{DFT}$ scheme is proposed, in which ${E}_{c}^{nd}$ is calculated with the complete active space approach in a small basis, while ${E}_{c}^{d}$ is calculated in the same basis with a functional of density functional theory corrected for SDC and EDC with an original correction function of $x(\mathbit{r})$. Correlation energies calculated with $\mathrm{CAS}\mathrm{\ensuremath{\Pi}}\mathrm{DFT}$ along the bond-dissociation coordinate for the paradigmatic ${\mathrm{H}}_{2}$ and ${\mathrm{N}}_{2}$ molecules as well as for the ${\mathrm{C}}_{2}$ molecule with strong nondynamic correlation at the equilibrium agree well with the reference data, thus providing a proof of concept for $\mathrm{CAS}\mathrm{\ensuremath{\Pi}}\mathrm{DFT}$.