Non-local exchange correlation energy in quasi-two-dimensional electron layers

We introduce a simple, non-local approximation for the exchange-correlation energy of an inhomogeneous electron gas. This approximation is shown to be quantitatively accurate in several important limiting cases. The method is used to calculate the non-local exchange-correlation energy for density distributions representing quasi-two-dimensional electron layers. These energies are compared to the widely used three-dimensional local-density approximation and suggest that the latter approximation may contain errors on the order of 10–30% for layer profiles typical of real systems.