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.