No Arabic abstract
We report all-electron variational and diffusion quantum Monte Carlo (VMC and DMC) calculations for the noble gas atoms He, Ne, Ar, Kr, and Xe. The calculations were performed using Slater-Jastrow wave functions with Hartree-Fock single-particle orbitals. The quality of both the optimized Jastrow factors and the nodal surfaces of the wave functions declines with increasing atomic number Z, but the DMC calculations are tractable and well behaved in all cases. We discuss the scaling of the computational cost of DMC calculations with Z.
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.
We analyze the problem of eliminating finite-size errors from quantum Monte Carlo (QMC) energy data. We demonstrate that both (i) adding a recently proposed [S. Chiesa et al., Phys. Rev. Lett. 97, 076404 (2006)] finite-size correction to the Ewald energy and (ii) using the model periodic Coulomb (MPC) interaction [L. M. Fraser et al., Phys. Rev. B 53, 1814 (1996); P. R. C. Kent et al., Phys. Rev. B 59, 1917 (1999); A. J. Williamson et al., Phys. Rev. B 55, 4851 (1997)] are good solutions to the problem of removing finite-size effects from the interaction energy in cubic systems, provided the exchange-correlation (XC) hole has converged with respect to system size. However, we find that the MPC interaction distorts the XC hole in finite systems, implying that the Ewald interaction should be used to generate the configuration distribution. The finite-size correction of Chiesa et al. is shown to be incomplete in systems of low symmetry. Beyond-leading-order corrections to the kinetic energy are found to be necessary at intermediate and high densities, and we investigate the effect of adding such corrections to QMC data for the homogeneous electron gas. We analyze finite-size errors in two-dimensional systems and show that the leading-order behavior differs from that which has hitherto been supposed. We compare the efficiency of different twist-averaging methods for reducing single-particle finite-size errors and we examine the performance of various finite-size extrapolation formulas. Finally, we investigate the system-size scaling of biases in diffusion QMC.
We have used diffusion Monte Carlo (DMC) simulations to calculate the energy barrier for H$_2$ dissociation on the Mg(0001) surface. The calculations employ pseudopotentials and systematically improvable B-spline basis sets to expand the single particle orbitals used to construct the trial wavefunctions. Extensive tests on system size, time step, and other sources of errors, performed on periodically repeated systems of up to 550 atoms, show that all these errors together can be reduced to $sim 0.03$ eV. The DMC dissociation barrier is calculated to be $1.18 pm 0.03$ eV, and is compared to those obtained with density functional theory using various exchange-correlation functionals, with values ranging between 0.44 and 1.07 eV.
We introduce a simple but efficient method for grand-canonical twist averaging in quantum Monte Carlo calculations. By evaluating the thermodynamic grand potential instead of the ground state total energy, we greatly reduce the sampling errors caused by twist-dependent fluctuations in the particle number. We apply this method to the electron gas and to metallic lithium, aluminum, and solid atomic hydrogen. We show that, even when using a small number of twists, grand-canonical twist averaging of the grand potential produces better estimates of ground state energies than the widely used canonical twist-averaging approach.
We present density-functional theory (DFT) and quantum Monte Carlo (QMC) calculations designed to resolve experimental and theoretical controversies over the optical properties of H-terminated C nanoparticles (diamondoids). The QMC results follow the trends of well-converged plane-wave DFT calculations for the size dependence of the optical gap, but they predict gaps that are 1-2 eV higher. They confirm that quantum confinement effects disappear in diamondoids larger than 1 nm, which have gaps below that of bulk diamond. Our QMC calculations predict a small exciton binding energy and a negative electron affinity (NEA) for diamondoids up to 1 nm, resulting from the delocalized nature of the lowest unoccupied molecular orbital. The NEA suggests a range of possible applications of diamondoids as low-voltage electron emitters.