  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.
