We introduce a density-functional approach to calculate electron transfer (ET) between atoms during a process of reaction or collision. Charge transfer of this kind is due entirely to differences of chemical potentials that are quantities relevant in the density-functional formalism, statistical mechanics, and thermodynamics. ET here is independent of electromagnetic interactions if we disregard their influences on the chemical potential. This subject still under intensive investigation in physics is attributed to the transition state described in the Franck-Condon principle. After introducing the main theory, we calculate frontier functions for hydrogen-like and helium-like atoms. Results of single-atom systems confirm concepts of the density of states or accumulations of electrons in semiconductor physics, many-body theories etc., but they imply more physics, particularly in statistical mechanics, about such accumulation from results of two-atom cases.
