Bader, Atoms in Molecules: A Quantum Theory ( University of Oxford Press, Oxford, 1990). Pullman ( Wiley Interscience, New York, 1978), Vol. Claverie, in Intermolecular Interactions: From Diatomics to Biopolymers, edited by B. Thus a connection could be established between the conventional fluctuating charge density model of London dispersion forces and the notion of the “exchange-hole dipole moment” shedding some light on the true nature of the approximations implicit in the Becke-Johnson model. In order to get a formula analogous to that of Becke and Johnson, which involves the exchange-hole only, further assumptions are needed, related to the difficulties of obtaining the expectation value of a two-electron operator from a single determinant. Alternatively, by expanding the Coulomb interaction around the center of charge (centroid) of the exchange-correlation hole associated with each point in the molecular volume, a multicenter expansion is obtained around the centroids of electron localization domains, always in terms of the exchange-correlation hole. In the framework of a dipolar approximation of the Coulomb interaction around the molecular origin, one obtains the so-called Salem-Tang-Karplus approximation to the C 6 dispersion coefficient. A one-term approximation is used for the dynamic charge density response function, and it is shown that a central nonempirical ingredient of the approximate nonexpanded dispersion energy is the charge density autocorrelation function, a two-particle property, related to the exchange-correlation hole. First-principles derivation is given for the heuristic exchange-hole model of London dispersion forces by Becke and Johnson.
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