Derivation of the dispersion energy as an explicit density- and exchange-hole functional

Through some simple derivations, it is shown that the nonexpanded dispersion interaction energy between two molecules can entirely be written in terms of the densities and the exchange-holes of the monomers. Thus the suspicion of Becke and Johnson [J. Chem. Phys. 122, 154104 (2005)] that the dispersion energy might be related to fluctuating dipoles produced by the electrons and their accompanying exchange-holes is confirmed. However, it will be shown that the current asymptotic result for the dispersion energy is different from the Becke–Johnson model. Some preliminary results for the polarizabilities and dispersion coefficients of a few atoms and small molecules demonstrate that the approach described in this work might be useful to estimate response properties and long-range correlation energies of molecular systems in general.