Quantum Monte Carlo investigation of exchange and correlation in silicon

Abstract

Abstract QMC calculations can be used to calculate wavefunctions, electron densities, and a wide variety of functions and integrals, all of which may in turn be useful in improving other types of electronic structure calculations. In this variational QMC study of diamond-structure silicon, the quantities of central importance in Kohn-Sham density functional theory were calculated and compared to those from local-density and average-density approximations. In this case, the quantities were the coupling-constantintegrated pair correlation function, the exchange-correlation hole, and the exchange-correlation energy density. All are related to the total exchange-correlation energy. The calculations were carried out for 3 x 3 x 3 fee unit cells containing 54 nuclei with pseudopotentials and 216 valence electrons. The VQMC wave functions were optimized Slater-Jastrow functions giving 85% of the fixed-node correlation energy. Several different techniques were used in sampling to accumulate the diamond quantities, which were illustrated in full-color contour plots showing variations with position in the lattice. Differences between VQMC and local density approximation (LDA) results were similarly illustrated, and the largest errors in the LDA exchangecorrelation energy densities were found in the bonding regions and around the pseudoatoms. As pointed out by the authors, such calculations should aid in developing better functionals by providing much more data than the total energy and the bulk moduli previously available for comparison.