Correlation energy of the paramagnetic electron gas at the thermodynamic limit

The variational and diffusion quantum Monte Carlo methods are used to calculate the correlation energy of the paramagnetic three-dimensional homogeneous electron gas at intermediate to high density. Ground-state energies in finite cells are determined using Slater-Jastrow-backflow trial wave functions, and finite-size errors are removed using twist-averaged boundary conditions and extrapolation of the energy per particle to the thermodynamic limit of infinite system size. Our correlation energies in the thermodynamic limit are more accurate than previous results. The present diffusion quantum Monte Carlo energies together with our recently reported [Phys. Rev. B 105, 245135 (2022)] results at low density, are used to parametrize the correlation energy of the electron gas using a functional form that satisfies the exact asymptotic behavior at high density.

Figure 1

Twist-averaged VMC and DMC correlation energies at system size $N=54$ as a function of variance, relative to the correlation energy with a SJ wave function in which the Jastrow factor only contains the isotropic two-body term $U$. Results are shown at density parameters $r_{\mathrm{s}}=0.5$ (left panel) and 20 (right panel).

Figure 2

Correlation energy of the spin-unpolarized 3D HEG as a function of $r_{\mathrm{s}}$. (Left panel) The VMC and DMC correlation energies are fitted to Eq. (7) and are compared with the PZ81 [27] parametrization. (Middle panel) VMC and DMC correlation energies at high density ($r_{\mathrm{s}}=0.5$, 0.75, and 1) are fitted to Gell-Mann and Brueckner's asymptotic formula. The fitting parameters are presented in the main text. (Right panel) Difference between our DMC correlation energy (Present week-DMC) and the PZ81 [27], VWN80 [28], PW92 [29], and DPI [12] DFT functionals.