We have studied the exchange-correlation hole $n_{\mathrm{xc}}$ and pair-correlation function in the valence shell of the Si atom in its ${}^{3}P$ ground state, using highly accurate Slater-Jastrow wave functions and the variational Monte Carlo method. The exchange-correlation hole shows a number of interesting features caused by the open shell structure of Si, including a marked transition from efficient to poor screening behavior as a test majority-spin electron is moved from the center of a valence p orbital onto the axis perpendicular to the occupied p orbitals. This behavior results from the dramatic difference in the exchange hole in the two cases, which is partially compensated by a corresponding anisotropy in the correlation hole. In addition we observe an anisotropic change in the spin density induced by Coulomb correlation, reducing the spatial overlap between the different spin components of the density and contributing to the anisotropy of the correlation hole. The exclusion effect correlation, in which a ${3s}^2\to {3p}^2$ substitution excitation is allowed along the unoccupied axis and prohibited along the other axes, was found to have a noticeable effect on the correlation hole and is partially accountable for its anisotropy; however, it is inconsistent with the observed changes in spin density. In contrast to the longer-range features, we find that the “on-top” correlation hole is well described by linear density-functional theory for a large range of local density and magnetization.

• Received 20 March 2000

DOI:https://doi.org/10.1103/PhysRevA.62.062507