Small and large wavelength contributions to the exchange and correlation energy of a nonuniform electron gas

Abstract

For the uniform electron gas, the decomposition of the exchange and correlation energy into its individual wave vectors has proved invaluable for both a deeper understanding of its structure as well as its extensions to the metallic range. Similar efforts made in the nouniform electron gas (and, in particular, surface properties) have also yielded much finer knowledge. However, we show here unequivocally that the particle conservation sum rule does not determine the long-wavelength limit of the structure factor of inhomogeneous many-electron systems in the thermodynamic limit. The short-wavelength region is also examined and shown not to be given rigorously by the local-density approximation.