Going beyond the vertical approximation with time-dependent density functional theory

Since two decades, time-dependent density functional theory (TD-DFT) has been in the limelight due to its noteworthy efficiency. Indeed, in many cases, TD-DFT provides accurate excited-state properties for a relatively limited computational cost. Recently, there has been a rapidly growing interest in applications of TDDFT (partly) exploring the excited-state potential energy surfaces. In this review, we summarize such TD-DFT investigations going beyond the vertical approximation and devoted to spectroscopic applications, with a focus on both 0-0 energies and vibrationally resolved absorption and emission spectra. We show how these quantities can be computed, considering various models for the latter, and illustrate their advantages compared to vertical estimates in terms of comparisons with experimental data