Benchmark Quantum Monte Carlo calculations of the ground-state kinetic, interaction, and total energy of the three-dimensional electron gas

We report variational and diffusion Quantum Monte Carlo ground-state energies of the three-dimensional electron gas using a model periodic Coulomb interaction and backflow corrections for N=54, 102, 178, and 226 electrons. We remove finite-size effects by extrapolation and we find lower energies than previously reported. Using the Hellman-Feynman operator sampling method introduced in Phys. Rev. Lett. 99, 126406 (2007), we compute accurately, within the fixed-node pproximation, the separate kinetic and interaction contributions to the total ground-state energy. The difference between the interaction energies obtained from the original Slater-determinant nodes and the backflow-displaced nodes is found to be considerably larger than the difference between the corresponding kinetic energies.