Abstract
A new, fundamental linear relationship between the mean energy of a solvated electron and the mean energy of a representative solvent molecule of the system is derived for solvated-electron optical absorption bands which exhibit spectral shape stability. In simplified form, [ωav(T)+ 4Neff(T)Esolv(T)] is independent of temperature T, where (in atomic units)ωav(T) is the mean absorption frequency of the band, Esolv(T) is the equilibrium-averaged molecular energy of the solvent and Neff(T) is an effective number of solvent molecules about which localization of a solvated electron presumably occurs. Temperature-independent, possibly solvent-dependent values of Neff ranging from 0.4 to 1.0 are obtained from available data for a number of solvents. When spectral shape stability obtains it further follows that the energy of the solvent must decrease in the threshold absorption process occurring at the zero of absolute temperature.