Quantum Monte Carlo Analysis of Exchange and Correlation in the Strongly Inhomogeneous Electron Gas

We use variational quantum Monte Carlo to calculate the density-functional exchange-correlation hole n_{xc}, the exchange-correlation energy density e_{xc}, and the total exchange-correlation energy E_{xc}, of several electron gas systems in which strong density inhomogeneities are induced by a cosine-wave potential. We compare our results with the local density approximation and the generalized gradient approximation. It is found that the nonlocal contributions to e_{xc} contain an energetically significant component, the magnitude, shape, and sign of which are controlled by the Laplacian of the electron density.