One approach to calculating electronic excited states treats both ground and excited states as single determinants, either by direct optimization or with the aid of constraints. In this work, we extend the theory of occupied-virtual orbitals for chemical valence (OVOCV) to analyze the orbital character of excitations computed in this way. An intermediate frozen state that is polarization-free is introduced to cleanly separate the primary excitation from the accompanying orbital relaxation of spectator orbitals. A variety of chemical examples are reported using the OVOCV excitation analysis on orbital-optimized density functional theory (OO-DFT) calculations, including charge-transfer excitations, core excitations and singly and doubly excited valence states. Orbital relaxation effects are typically collective, and can be as large as 4-5 eV (with roughly 0.1 e- promoted) in charge transfer states, and even larger in core excited states. OVOCV analysis differs from natural transition orbital (NTO) analysis; we show that direct use of NTOs can largely obscure the role of orbital relaxation in favor of the primary excitation.
Shen et al. (Mon,) studied this question.