Vertical excitation energies from the adiabatic connection

Vertical single-particle excitations from closed-shell ground states are complicated by the fact that the singlet open-shell states are, even in the first approximation, two-determinantal. Thus two-electron integrals come into play and standard time-independent DFT (density-functional theory) does not apply. In this work, we use the “adiabatic connection” to analyse the role of the two-electron integrals, obtaining a time-independent DFT approach to excitation-energy calculations that is new and simple. A non-empirical modeling of the method works as well as the popular TD-B3LYP time-dependent approach to excited states, and can be made even simpler by introducing one reasonable semi-empirical parameter.