Franck-Condon factors within damped displacement harmonic oscillators: Solvent-enhanced absorption and fluorescence spectra

Damped harmonic oscillators that take into account local-mode nuclear vibrations interacting with solvent molecules are developed into Franck-Condon factors within displaced harmonic oscillator approximation. This is practically done by scaling an unperturbed Hessian matrix that represents local modes of force constants for molecules in a gaseous phase, and then by diagonalizing the perturbed Hessian matrix it results in direct modification of Huang-Rhys factors which represent normal modes of solute molecule perturbed by solvent environment. For highly symmetric polycyclic aromatic hydrocarbon molecules in which hydrogen atom vibrations in a solution can be scaled equally, one-set scaling parameters constructed into damped Franck-Condon factors can reproduce solvent-enhanced absorption and fluorescence spectra in solution. However, for low symmetry molecules with atoms other than hydrogen and carbon atoms, multi-set scaling parameters constructed into damped Franck-Condon factors can also reproduce solvent-enhanced absorption and fluorescence spectra in solution. Examples for high symmetry perylene in benzene solution with one-set scaling parameters and for low symmetry carbazole in n-hexane solution with multi-set scaling parameters are given, in both cases, the present damped Franck-Condon simulation can reproduce solvent-enhanced absorption and fluorescence spectra in solution.