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

We use the variational quantum Monte Carlo method to calculate the density-functional exchange-correlation hole nxc , the exchange-correlation energy density exc , and the total exchange-correlation energy Exc of several strongly inhomogeneous electron gas systems. We compare our results with the local density approximation and the generalized gradient approximation. It is found that the nonlocal contributions to exc contain an energetically significant component, the magnitude, shape, and sign of which are controlled by the Laplacian of the electron density