Excess electrons in condensed media: Theory of optical absorption spectrum in molecular solutions

A theoretical formalism is developed for analyzing the spectra of excess electrons in pure molecular solids and liquids. A perturbation decomposition of the Hamiltonian allows the expression for the band shape I (ω) to be written as a sum of a zeroth order part, proportional to dipole transition matrix elements and corresponding Franck–Condon factors, and perturbation terms containing effects of electron hopping and their fluctuations. By using several physically motivated approximations (e.g., the temporally localized nature of electronic transitions which allows a short-time expansion of the time dependence of operators), the expression for I (ω) can be expressed in terms of solvent structure information and the electron–solvent interaction potential. From the general expressions for I (ω) a simplified model was developed in the special case of systems for which bound-to-bound transitions are dominant. This model has been successfully applied to the spectra of excess electrons in ethanol and anthracene glass, thereby providing some optimism for the potential use of the general formalism derived here.