  The localized operator partitioning method [Y. Khan and P. Brumer, J. Chem.
Phys. 137, 194112 (2012)] rigorously defines the electronic energy on any
subsystem within a molecule and gives a precise meaning to the subsystem ground
and excited electronic energies, which is crucial for investigating electronic
energy transfer from first principles. However, an efficient implementation of
this approach has been hindered by complicated one- and two-electron integrals
arising in its formulation. Using a resolution of the identity in the
definition of partitioning we reformulate the method in a computationally
efficient manner that involves standard one- and two-electron integrals. We
apply the developed algorithm to the 9-((1-naphthyl)-methyl)-anthracene (A1N)
molecule by partitioning A1N into anthracenyl and CH2-naphthyl groups as
subsystems, and examine their electronic energies and populations for several
excited states using Configuration Interaction Singles method. The implemented
approach shows a wide variety of different behaviors amongst the excited
electronic states.
