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

Abstract

AbstractDamped 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.