Mean-field theory of an electron solvated in molten salts

A mean-field, microscopic theory of an excess electron solvated in a molten salt is presented. Starting with the grand partition function of the syste m, we reformulate the problem to evaluate a mean field induced by charges a nd calculate self-consistently the electron density distribution. We obtain a Poisson-Boltzmann equation for the mean-field and Schrodinger equation f or the electron wave functions with a potential dependent on the mean field and a local density of melt. We also derive expressions for electron-ion c orrelation functions. We demonstrate that the mean field is weak in molten salts and can be analytically evaluated in the Debye-Huckel limit. Using a simple variational treatment, we calculate energetic and structural propert ies of a solvated electron for a wide range of alkali halide melts. These p roperties are mainly determined by the polaron effect, while the repulsion between the electron and ion cores leads to a remarkable variance of the pr operties. The results obtained are in good agreement with path-integral sim ulations and experimental data on the maximum of the absorption spectrum of an electron solvated in these melts. (C) 2000 American Institute of Physic s. [S0021-9606(00)51107-6].