Comment on “Correlation holes in a spin-polarized dense electron gas”

Rassolov, Pople, and Ratner [Phys. Rev. $\mathrm{B}\hspace{0.5em}59,$ 15 625 (1999)] used first-order perturbation theory to predict the short-range, high-density limit for the Coulomb correlation hole around an electron in a uniform electron gas, and compared their result with the parametrization of Perdew and Wang [Phys. Rev. B 46, 12 947 (1992)] (PW92). We find that their figures do not correctly represent the PW92 expressions, and we present corrected figures. At the highest density ${(r}_s=0.8)$ for which we can make a numerical comparison with the diffusion Monte Carlo method, we show that the PW92 correlation holes are valid. We suggest that the PW92 expressions may also be valid over the range $0.1\lesssim r_s\lesssim 10,$ in which they provide a smooth, controlled interpolation between short- and long-range limits. In particular, the PW92 correlation holes display a remarkable exchangelike scaling relation, and an intuitively appealing noncrossing behavior. The short-range, high-density ${(r}_s\to 0)$ limit suggested by the PW92 correlation hole for the fully spin-polarized case is smaller than the perturbative results of Rassolov, Pople, and Ratner by a factor of about 3, but is consistent with our own study of the approach to this limit within the random-phase approximation. We also suggest an improved spin resolution of the PW92 correlation hole, which for $r_s=0.1\mathrm{}$ agrees with Ueda’s $g^{\uparrow \downarrow }$ [Prog. Theor. Phys. 26, 45 (1961)].