No abstract

A misprint was found in the last digit of the parameter C 0 of Table II. The correct value is C 0 0:057 238 4. Moreover, to reobtain exactly Fig. 3, one has to use G 0 0:339 97 (not G 0 0:34 as originally printed). The use of the misprinted values of C 0 and G 0 which appear in the original version of Table II does not affect the results for r s & 30; it does, instead, shift the Wigner crystallization to slightly larger r s .Finally, the text following Eq.(3) has two rather obvious misprints: the factors of 2 and 24 instead of 1=2 and 1=24 in the definitions of 1 and 2 . This is completely harmless: all results and equations of the Letter are based on the correct definition, not on the misprinted one.

We propose a simple and accurate model for the electron static structure factors ͑and corresponding paircorrelation functions͒ of the three-dimensional unpolarized homogeneous electron gas. Our spin-resolved paircorrelation function is built up with a combination of analytic constraints and fitting procedures to quantum Monte Carlo data, and, in comparison to previous attempts, ͑i͒ fulfills more known integral and differential properties of the exact pair-correlation function, ͑ii͒ is analytic both in real and in reciprocal space, and ͑iii͒ accurately interpolates the newest, extensive diffusion-Monte Carlo data of Ortiz, Harris, and Ballone ͓Phys. Rev. Lett. 82, 5317 ͑1999͔͒. This can be of interest for the study of electron correlations of real materials and for the construction of new exchange and correlation energy density functionals.

The ground-state energy of the two-dimensional uniform electron gas has been calculated with a fixed-node diffusion Monte Carlo method, including backflow correlations, for a wide range of electron densities as a function of spin polarization. We give a simple analytic representation of the correlation energy which fits our simulation data and includes several known high- and low-density limits. This parametrization provides a reliable local spin density energy functional for two-dimensional systems and an estimate for the spin susceptibility. Within the proposed model for the correlation energy, a weakly first-order polarization transition occurs shortly before Wigner crystallization as the density is lowered.

Based on exact limits and quantum Monte Carlo simulations, we obtain, at any density and spin polarization, an accurate estimate for the energy of a modified homogeneous electron gas where electrons repel each other only with a long-range coulombic tail. This allows us to construct an analytic local-spin-density exchange-correlation functional appropriate to new, multideterminantal versions of the density functional theory, where quantum chemistry and approximate exchange-correlation functionals are combined to optimally describe both long-and short-range electron correlations.