Kubo's Line Shape Function for a Linear-Quadratic Chromophore-Solvent Coupling

An exact, closed-form solution is obtained for the line shape function of an optical transition with the transition frequency depending linearly plus quadratically on a Gaussian coordinate of the thermal bath. The dynamical modulation of the line shape involves two parameters corresponding to the linear and quadratic components of the transition frequency. The increase of the second component results in a non-Gaussian line shape that splits into two Lorenzian lines in the limit of fast modulation. (Figure Presented).