We present a framework for long-range density-functional theory which is valid for interactions between isolated fragments of matter at large separation. The van der Waals coefficients for interactions between a large number of pairs of atoms are calculated and compared to available first-principles calculations. The success in this test case shows a way of extending density-functional theory calculations with local or semilocal approximations to include van der Waals forces.

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A progress report is given of an extension of the density functional formalism to include long-range interactions such as van der Waals or dispersion forces. This is done by proving a general expression for the so-called exchange-correlation energy to contain and to describe such interactions just as well as any other treatment. The proper long-range forms of the interactions are derived explicitly in the cases of two neutral atoms, an atom outside a metal surface, and two parallel metal surfaces. The long-standing problem of treating the attractive and repulsive forces on the same footing in this way gets a solution. For practical calculations, an approximate form, based on an analysis in the weakly inhomogeneous limit and on a limiting form of the three-point function given by Rapcewicz and Ashcroft, is proposed and applied to some prototype cases. 0 1995 John Wiley & Sons, Inc.well-known R -6 form of London [4]. The asymptotic z p 3 form of the interaction potential between a neutral atom and a surface was first identified by , with subsequent refined treatments of the atom and surface polarizabilities [6,7]. For the interaction between solid bodies, general formulas have been derived [S], which for flat sur-

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