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van der Waals interactions in density-functional theory.

The history of van der Waals or dispersion forces dates a long way back [1, 2]. The recent book Van der Waals and Molecular Sciences [1] gives a detailed account of van der Waals’s own contributions and life-long interest in the field. It is interesting to note that this truly quantum-mechanical problem [3, 4, 5] has been addressed by theorists long before the birth of quantum mechanics. The force between atoms, molecules, clusters, complexes, surfaces, and other fragments of matter is dominated by the weak but long-ranged van der Waals interactions at large separations. This is the region that has been primarily addressed. Calculations of the interaction potential between neutral species were first done for molecules [6, 7], leading to the well known asymptotic R −6 form of London [5]. The asymptotic z −3 form of the interaction potential between a neutral atom and a surface was first identified by Lennard-Jones [8], with subsequent refined treatments of the atom and surface polarizabilities [9, 10]. For the interaction between solid bodies, general formulas have been derived [11], which for flat surfaces a long distance d apart give an interaction energy that varies as d −2 [12]. For very large distances, where the limited magnitude of the velocity of light matters, retardation effects are important [13]. Such relativistic effects are physically interesting but beyond the scope of the present work.