Nonlocal density-functional description of exchange and correlation in silicon

We investigate a range of pair-correlation functions in the nonlocal weighted density approximation (WDA) by calculating the lattice constant, bulk modulus, and band structure of Si. Exchange-correlation holes are also determined at specific points in the [110] plane of Si and a comparison is made with data from variational Monte Carlo simulations. We show that the WDA is particularly sensitive to the pair-correlation function used and that the accuracy of the lattice constant and bulk modulus is directly related to the quality of the exchange-correlation hole in high density regions. The form of the pair-correlation function also has a significant effect on the electronic band gap.