Extended solids are frequently simulated as finite systems with periodic boundary conditions, which due to the long-range nature of the Coulomb interaction may lead to slowly decaying finite- size errors. In the case of Quantum-Monte-Carlo simulation
s, which are based on real space, both real-space and momentum-space solutions to this problem exist. Here, we describe a hybrid method which using real-space data models the spherically averaged structure factor in momentum space. We show that (i) by integration our hybrid method exactly maps onto the real-space model periodic Coulomb-interaction (MPC) method and (ii) therefore our method combines the best of both worlds (real-space and momentum-space). One can use known momentum-resolved behavior to improve convergence where MPC fails (e.g., at surface-like systems). In contrast to pure momentum-space methods, our method only deals with a simple single-valued function and, hence, better lends itself to interpolation with exact small-momentum data as no directional information is needed. By virtue of integration, the resulting finite-size corrections can be written as an addition to MPC.
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 effec
ts 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.
In a recent Letter we introduced Hellmann-Feynman operator sampling in diffusion Monte Carlo calculations. Here we derive, by evaluating the second derivative of the total energy, an efficient method for the calculation of the static density-response
function of a many-electron system. Our analysis of the effect of the nodes suggests that correlation is described correctly and we find that the effect of the nodes can be dealt with.
Diffusion Monte Carlo (DMC) calculations typically yield highly accurate results in solid-state and quantum-chemical calculations. However, operators that do not commute with the Hamiltonian are at best sampled correctly up to second order in the err
or of the underlying trial wavefunction, once simple corrections have been applied. This error is of the same order as that for the energy in variational calculations. Operators that suffer from these problems include potential energies and the density. This paper presents a new method, based on the Hellman-Feynman theorem, for the correct DMC sampling of all operators diagonal in real space. Our method is easy to implement in any standard DMC code.
