Exchange and correlation in the Si atom: A quantum Monte Carlo study

We have studied the pair-correlation function, the exchange-correlation hole, and the exchange-correlation energy density of the valence electrons in the Si atom using the Coulomb-coupling constant integration technique with the variational quantum Monte Carlo method. These quantities are compared to those derived from various approximate models within the Kohn-Sham density functional theory. We find that the charge density prefactor in the expression for the exchange-correlation hole dominates the errors found in the local spin density approximation (LSDA), that the generalized gradient approximation improves energy calculations by improving the LSDA at long ranges, and that the weighted spin density approximation, which uses the correct charge density prefactor, gives the lowest root mean square error for the exchange-correlation energy density.