Energy component analysis for electronically excited states of molecules: why the lowest excited state is not always the HOMO/LUMO transition

The ability to tune excited-state energies is crucial to many areas of molecular design. In many cases, this is done based on the energies of the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). However, this viewpoint is incomplete neglecting the many-body nature of the underlying excited-state wave functions. Within this work, we highlight the importance of two crucial terms, other than orbital energies, that contribute to the excitation energies and show how to quantify them from quantum chemistry computations: a Coulomb attraction and a repulsive exchange interaction. Using this framework, we explain under which circumstances the lowest excited state of a molecule, of either singlet or triplet multiplicity, is not accessed via the HOMO/LUMO transition and show two paradigmatic examples. In the case of the push-pull molecule ACRFLCN, we highlight how the lowest triplet excited state is a locally excited state lying below the HOMO/LUMO charge transfer state due to enhanced Coulomb binding. In the case of the naphthalene molecule, we highlight how the HOMO/LUMO transition (the ¹L_a state) becomes the second excited singlet state due to its enhanced exchange repulsion term. More generally, we explain why excitation energies do not always behave like orbital energy gaps, providing insight into photophysical processes as well as methodogical challenges in describing them.