Disentangling vibronic and solvent broadening effects in the absorption spectra of coumarin derivatives for dye sensitized solar cells

We simulate from first-principles the absorption spectra of five structure-related coumarin derivatives utilized in dye sensitized solar cells (DSSCs), investigating the vibronic and solvent contributions to the position and width of the spectra in ethanol. Ground and excited state potential energy surfaces (PESs) are modeled by Density Functional Theory (DFT) and its time-dependent (TD) expression for the excited state (TD-DFT). The solute vibronic structure associated with the spectrum is calculated by a TD formalism, accounting for both Duschinsky and temperature effects, while solvent inhomogeneous broadening is evaluated according to Marcus' theory, computing the solvent reorganization energy by the state-specific implementation of the polarizable continuum model (PCM) within TD-DFT. We adopted both the standard hybrid PBE0 and the range separated CAM-B3LYP functionals showing that the latter performs better both concerning the vibronic and solvent-induced contributions to the absorption lineshape. The different predictions of the two functionals are then rationalized in terms of the charge transfer (CT) character of the transitions showing that, in this class of compounds, it is strongly dependent on the nuclear structure. Such a dependence introduces a bias in the PBE0 PES that has a drastic impact on the vibronic spectra. We show that both the intrinsic vibronic structure and the solvent broadening play a relevant role in differentiating the absorption width of the five dyes. In this sense, our results provide a guide to understand the sources of spectral broadening of this family of dyes, a valuable help for a rational design of new molecules to improve DSSC devices.