Variational Monte Carlo study of the partially polarized electron gas

The variational Monte Carlo (VMC) method, using Jastrow-Slater (JS) wave functions, is used to study the partially polarized interacting electron gas for densities spanning the range encountered in bulk metals. We concentrate on a spin polarization {ζ}=0.42 which allows direct comparison of polarized and unpolarized states for a fixed total number of electrons in the simulation supercell. The radial distribution functions g₊₊(r), g_--(r), and g_+-(r) are given particular attention and compared with a model developed by Perdew and Wang (PW) that satisfies known constraints. At high density the agreement with the PW model is good. At the lower densities (electron-gas parameter rₛ=4--8) there are differences that can be roughly characterized as the PW model giving a somewhat more extended exchange-correlation hole than the VMC calculations. These discrepancies could be due to limitations either of the PW model or of the JS wave functions used here. Both the VMC and PW results are contrasted with the Hartree-Fock result for parallel spins.