An Efficient PCM Scheme for ESA Oscillator Strengths within the Unrelaxed TD-DFT Approximation

We propose a TD-DFT protocol for computing unrelaxed excited-state absorption (ESA) oscillator strengths in solution. Our model is formulated within the popular PCM framework and includes both linear-response and state-specific solvent effects through the cLR² scheme. This protocol can be applied in two regimes: fast and slow. The former corresponds to situations where the time scale of the entire photophysical process is too short to allow relaxation of the nuclear degrees of freedom of the solvent, whereas the latter allows such relaxation. For selected illustrative examples of S₁-S_n ESA transitions in organic dyes, we compare solvated and gas phase transition energies, oscillator strengths, and transition dipole moments. This analysis reveals that solvent-induced shifts in oscillator strengths are predominantly driven by the variations of the transition dipole moment. The magnitude of the solvent effect is strongly system- and state-dependent. For transitions for which S₀-geometry states could be unambiguously assigned to their S₁-geometry counterparts, we found that the two solvation regimes can lead to significantly different effects on the ESA transition properties. This observation is further confirmed by comparing the two solvation regimes, as well as gas phase results, with experimental ESA spectra extracted from transient spectroscopy measurements. Our scheme exhibits clear improvement over the in vacuo outcomes and correctly reproduces the main regions with intense ESA, although an unambiguous choice between the two regimes remains challenging.