Multiscale Modeling of Electronic Spectra Including Nuclear Quantum Effects

Theoretical prediction of electronic absorption spectra without input from experiment is no easy feat as it requires addressing all the factors that affect line shapes. In practice, however, the methodologies are limited to treat these ingredients only to a certain extent. Here we present a multiscale protocol that addresses the temperature, solvent and nuclear quantum effects, anharmonicity and reconstruction of the final spectra from the individual transitions. First, QM/MM molecular dynamics is conducted to obtain trajectories of solute-solvent configurations, from which the corresponding quantum corrected ensembles are generated through the Generalized Smoothed Trajectory Analysis (GSTA). The optical spectra of the ensembles are then produced by calculating vertical transitions using TDDFT with implicit solvation. To obtain the final spectral shapes, the stick spectra from TDDFT are convoluted with Gaussian kernels where the half-widths are determined by a statistically motivated strategy. We have tested our method by calculating the UV-vis spectra of a recently discovered acridine photocatalyst in two redox states. Vibronic progressions and broadenings due to the finite lifetime of the excited states are not included into the methodology yet. Nuclear quantization affects the relative peak intensities and widths, which is necessary to reproduce the experimental spectrum. We have also found that using only the optimized geometry of each molecule works surprisingly well if a proper empirical broadening factor is applied. This is explained by the rigidity of the conjugated chromophore moieties of the selected molecules which are mainly responsible for the excitations in the spectra. In contrast, we have also shown that other parts of the molecules are flexible enough to feature anharmonicities that impair the use of other techniques such as Wigner sampling.