Localized operator partitioning method for electronic excitation energies in the time-dependent density functional formalism

Abstract

We extend the localized operator partitioning method (LOPM) [J. Nagesh, A.F. Izmaylov, and P. Brumer, J. Chem. Phys. 142, 084114 (2015)] to the time-dependent density functional theory (TD-DFT) framework to partition molecular electronic energies of excited states in a rigorous manner. A molecular fragment is defined as a collection of atoms using Stratman-Scuseria-Frisch atomic partitioning. A numerically efficient scheme for evaluating the fragment excitation energy is derived employing a resolution of the identity to preserve standard one-and two-electron integrals in the final expressions. The utility of this partitioning approach is demonstrated by examining several excited states of two bichromophoric compounds: 9−((1−naphthyl)−methyl)−anthracene and 4−((2−naphthyl)−methyl)−benzaldehyde. The LOPM is found to provide nontrivial insights into the nature of electronic energy localization that are not accessible using simple density difference analysis.