The Exchange-correlation Hole of the Si Atom, A Quantum Monte Carlo   Study
  We have studied the exchange-correlation hole and pair correlation function in the valence shell of the ground-state of the Si atom, using accurate Slater-Jastrow wavefunctions 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 3p orbital onto the axis perpendicular to the occupied 3p 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. 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. 
Antonio C. Cancio, C. Y. Fong and J. S. Nelson