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We extend the localized operator partitioning method (LOPM) [J. Nagesh, A.F.Izmaylov, and P. Brumer, J. Chem. Phys. 142, 084114 (2015)] to thetime-dependent density functional theory (TD-DFT) framework to partitionmolecular electronic energies of excited states in a rigorous manner. Amolecular fragment is defined as a collection of atoms usingStratman-Scuseria-Frisch atomic partitioning. A numerically efficient schemefor evaluating the fragment excitation energy is derived employing a resolutionof the identity to preserve standard one- and two-electron integrals in thefinal expressions. The utility of this partitioning approach is demonstrated byexamining 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 electronicenergy localization that are not accessible using simple density differenceanalysis.

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