Stochastic theory of inhomogeneous spectroscopic line shapes reinvestigated

The inhomogeneous distribution of an ensemble of absorption or fluorescence lines in a disordered matrix can be described by a stochastic theory whose fundamental ideas have been known for many decades. Due to its very general principles, it can be applied to inhomogeneous effects of many different types, including inhomogeneous broadening in optical spectra and spectral diffusion in magnetic resonance and line-narrowed optical experiments. In the case of absorption and luminescence bands, it is often convenient to perform the so-called Gaussian approximation, which is valid in the limit that the density of the matrix molecules is high compared to the reciprocal volume of the cavity containing the absorbing or fluorescing center; this leads to the analytical result that the line shapes of the optical bands are Gaussian. Numerical calculations beyond the Gaussian approximation help to clarify its physical meaning and to interpret inhomogeneous bandwidths from a statistical point of view. Three types of intermolecular potentials are examined, namely, dipole–dipole, van der Waals, and a modified Lennard-Jones-type interaction.