CORRELATION-ENERGY FUNCTIONAL AND ITS HIGH-DENSITY LIMIT OBTAINED FROM A COUPLING-CONSTANT PERTURBATION EXPANSION

A perturbation theory is developed for the correlation energy E(c)[n], of a finite-density system, with respect to the coupling constant a which multiplies the electron-electron repulsion operator in H(alpha)=T+alphaV(ee)+SIGMA(i)v(alpha)(r(i)). The external potential v(alpha) is constrained to keep the ground-state density n fixed for all a greater-than-or-equal-to 0. v(alpha) is given completely in terms of functional derivatives at full charge (alpha = 1), from which E(c)[n(lambda)]=e(c,2)[n]+lambda-1e(c,3)[n]+lambda-2e(c,4)[n]+..., where each e(c,j)[n] is expressed in terms of integrals involving Kohn-Sham determinants. Here, n(lambda)(x,y,x)=lambda3n(lambdax,lambday,lambdaz) and lambda=alpha-1. The identification of lim(lambda-->infinity)E(c)[n(lambda)], which is a high-density limit, as the second-order energy e(c,2)[n] allows one to compute bounds upon lim(lambda-->infinity)E(c)[n(lambda)]; the bounds imply that lim(lambda-->infinity)E(c)[n(lambda)]congruent-to E(c)[n] for a large class of small atoms and molecules, and suggest that lim(lambda-->infinity)E(c)[n(lambda)] should be of the same order of magnitude as E(c)[n] infinite insulators and semiconductors. Approximations to E(c)[n] should reflect all this. In contrast, perhaps the well-known overbinding of the local-density approximation (LDA) in molecules and solids is due, in part, to the fact that the LDA correlation energy is too sensitive to a coordinate scaling of n. Indeed, the LDA for E(c)[n(lambda)] diverges when lambda-->infinity because of the presence of the -1n(lambda) term in the Gell-Mann and Brueckner high-density expression for the correlation energy, per particle, of a homogeneous density, which is infinite. In a sense, the derived perturbation expansion transforms the Gell-Mann and Brueckner expression into one that applies specifically to an inhomogeneous density which integrates to a finite number of electrons.