Benchmarking TD-DFT against Vibrationally Resolved Absorption Spectra at Room Temperature: 7‑Aminocoumarins as Test Cases

Time-dependent density functional theory (TD-DFT) is usually benchmarked by evaluating how the vertical excitation energies computed by using different exchange-correlation (XC) functionals compare with the maximum of the absorption spectra. However, the latter does not necessarily coincide with the vertical energies because it is affected by the vibronic band structure that has to be properly taken into account. In this work, we have evaluated the performance of several functionals belonging to different families in reproducing the vibronic structure (band shape) of four 7-aminocoumarin molecules of technological interest, whose spectra have been recorded in methylcyclohexane and acetonitrile solvents. In order to compare the computed vibronic spectra with the experimental ones in the most consistent way, the effect of temperature, often neglected, was also taken into account. We have found that no single functional provides simultaneously accurate band positions and shapes, but the combination of ωB97X vibronic couplings with PBE0 vertical energies can lead to very satisfactory results. In addition to the assessment of XC functionals, several adiabatic and vertical models proposed in the literature to compute vibrationally resolved electronic spectra have been tested and validated with respect to experiments. On these grounds, the adiabatic Hessian model has been used to perform a complete analysis of the ωB97X/PBE0 vibronic transitions contributing to the final band shapes of the investigated aminocoumarin molecules.