Quasi-local-density Approximation for a Van Der Waals Energy Functional

We discuss a possible form for a theory akin to local density functional theory, but able to produce van der Waals energies in a natural fashion. The usual Local Density Approximation (LDA) for the exchange and correlation energy Exc of an inhomogeneous electronic system can be derived by making a quasilocal approximation for the interacting density-density response function χ(~r, ~r , ω), then using the fluctuation-dissipation theorem and a Feynman coupling-constant integration to generate Exc. The first new idea proposed here is to use the same approach except that one makes a quasilocal approximation for the bare response χ, rather than for χ. The interacting response is then obtained by solving a nonlocal screening integral equation in real space. If the nonlocal screening is done at the time-dependent Hartree level, then the resulting energy is an approximation to the full inhomogeneous RPA energy: we show here that the inhomogeneous RPA correlation energy contains a van der Waals term for the case of widely-separated neutral subsystems. The second new idea is to use a particularly simple way of introducing LDA-like local field corrrections into the screening equations, giving a theory which should remain reasonable for all separations of a pair of subsystems, encompassing both the van der Waals limit much as in RPA and the bonding limit much as in LDA theory. The resulting functional is an explicit recipe which takes a trial electron density distribution n(r) as its input and yields Exc as its output. The reason that it includes the van der Waals energy is that, like the RPA formalism but unlike LDA, it involves spatially nonlocal screening for inhomogeneous systems. It differs from earlier theories which effectively use hydrodnamics to generate χ, in that rapid spatial variations in electron density, such as those at subsystem boundaries, can be handled more effectively; LDA-like local correlations are also included. Thus the theory has credibility even at small separations outside