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

TL;DR

This paper extends a localized operator partitioning method to time-dependent density functional theory, enabling rigorous analysis of excited state energies in molecular fragments, providing new insights into electronic energy localization.

Contribution

The paper introduces a novel extension of the LOPM to TD-DFT, allowing for rigorous partitioning of excited state energies in molecules.

Findings

Provides a numerically efficient scheme for energy partitioning.

Demonstrates the method on bichromophoric compounds.

Reveals insights into electronic energy localization.

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.