EXCHANGE AND CORRELATION IN SILICON

A combination of the coupling constant integration technique and the q uantum Monte Carlo method is used to investigate the most relevant qua ntities in Kohn-Sham density-functional theory. Variational quantum Mo nte Carlo is used to construct realistic many-body wave functions for diamond-structure silicon at different values of the Coulomb coupling constant. The exchange-correlation energy density along with the coupl ing constant dependence and the coupling-constant-integrated form of t he pair-correlation function, the exchange-correlation hole, and the e xchange-correlation energy are presented. Comparisons of these functio ns an mode with results obtained from the local-density approximation, the average density approximation, the weighted density approximation , and the generalized gradient approximation. We discuss reasons for t he success of the local-density approximation. The insights provided b y this approach will make it possible to carry out stringent tests of the effectiveness of exchange-correlation functionals and in the long term aid in the search for better functionals. [S0163-1829(98)02115-8] .