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

The pair-correlation function, exchange-correlation hole, and exchange-correlation energy density for an atomic system were computed using the variational Monte Carlo (VMC) methodology. From the VMC wave functions, it was explained how the spin components of the pair-correlation function are calculated and how they may be combined to produce the exchange-correlation hole and the exchange-correlation energy density. The results were compared to those from the local spin density approximation (LSDA) and other approximation methods within density functional theory (DFT).