Localized Molecular Orbitals for Single Excitation Theories

Excited states of systems composed of linked fragments or stacked molecules are important for understanding their optoelectronic properties. These states, when projected to individual fragments, are either local (LEs) or charge transfer excitons (CTEs). However, the canonical molecular orbitals (CMOs) obtained from a typical calculation tend to delocalize, which makes the subsequent analysis of excited states cumbersome. In this work, we report a simple approach to address this problem by employing localized molecular orbitals (LMOs) as linear combinations of the CMOs in the occupied and virtual subspaces separately after a self-consistent field calculation. This separated linear combination ensures that configuration interaction singles (CIS), random phase approximation (RPA), and their corresponding density functional theory (DFT) counterparts [Tamm-Dancoff approximation time-dependent DFT (TDA-TDDFT) and TDDFT] calculations with LMOs are mathematically equivalent to those performed with CMOs. We performed tests on simple symmetric and asymmetric dimer systems and found that the excited states are numerically identical in excitation energies and transition moments for both LMOs and CMOs, except for very few states that are only found in either LMO or CMO (in symmetric cases). The LMO basis makes both qualitative and quantitative analyses of the excited states much more accessible, as the extent of LE and CTE contributions can be easily defined. Consequently, this simple yet robust approach can be useful for characterizing excitons in multichromophoric systems and in condensed phases, which is useful when studying problems pertaining to electron/excitation energy transfer processes.