Knowledge Bank

A theoretical formalism for the optical Spectroscopy of charged and neutral species in mixed solvents is developed and generalized to treat the case of charge-transfer spectra. The Hamiltonian of the solvent molecules and the single excess electron is decomposed in such a way that the equilibrium average of the electron-solvent interaction is included in the zero-the order part, while fluctuations away from this average are treated as a perturbation. With several approximations based on solvent structure and the relevant time scale of the experiment, the intensity spectrum $I(\omega )$ is written as the sum of 0-th, 1st, and 2nd order contributions. The 0-th order contribution involves, in the charge-transfer case, a direct dipole transition from the donor to the acceptor; whereas the 1st and 2nd order expressions involve dipole transitions modified by the effects of intermolecular electron ``hopping” and its fluctuations, respectively. Using the so-called hopping (or resonance) and fluctuation integrals as adjustable parameters, the theory is used to reproduce the experimentally observed electronic absorption spectrum of the well-known benzene-iodine charge-transfer complex.