W. M. C. Foulkes

Finite-size errors in continuum quantum Monte Carlo calculations

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 R4851 (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. Phys. Rev. Lett. 97 076404 (2006) 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; 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 efficiencies 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.

The treatment of electronic excitations in atomistic models of radiation damage in metals

Atomistic simulations are a primary means of understanding the damage done to metallic materials by high energy particulate radiation. In many situations the electrons in a target material are known to exert a strong influence on the rate and type of damage. The dynamic exchange of energy between electrons and ions can act to damp the ionic motion, to inhibit the production of defects or to quench in damage, depending on the situation. Finding ways to incorporate these electronic effects into atomistic simulations of radiation damage is a topic of current major interest, driven by materials science challenges in diverse areas such as energy production and device manufacture. In this review, we discuss the range of approaches that have been used to tackle these challenges. We compare augmented classical models of various kinds and consider recent work applying semi-classical techniques to allow the explicit incorporation of quantum mechanical electrons within atomistic simulations of radiation damage. We also outline the body of theoretical work on stopping power and electron-phonon coupling used to inform efforts to incorporate electronic effects in atomistic simulations and to evaluate their performance.

The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method

The recently proposed full configuration interaction quantum Monte Carlo method allows access to essentially exact ground-state energies of systems of interacting fermions substantially larger than previously tractable without knowledge of the nodal structure of the ground-state wave function. We investigate the nature of the sign problem in this method and how its severity depends on the system studied. We explain how cancellation of the positive and negative particles sampling the wave function ensures convergence to a stochastic representation of the many-fermion ground state and accounts for the characteristic population dynamics observed in simulations.

How good is damped molecular dynamics as a method to simulate radiation damage in metals

Classical molecular dynamics (MD) is a frequently used technique in the study of radiation damage cascades because it provides information on very small time and length scales inaccessible to experiment. In a radiation damage process, energy transfer from ions to electrons may be important, yet there is continued uncertainty over how to accurately incorporate such effects in MD. We introduce a new technique based on the quantum mechanical Ehrenfest approximation to evaluate different methods of accounting for electronic losses. Our results suggest that a damping force proportional to velocity is sufficient to model energy transfer from ions to electrons in most low energy cascades. We also find, however, that a larger rate of energy transfer is seen when the ionic kinetic energy is confined to a focused sequence of collisions. A viscous damping coefficient dependent on the local atomic environment is shown to be an excellent model for electronic energy losses in low energy cascades in metals.

Finite size errors in quantum many-body simulations of extended systems

Further developments are introduced in the theory of finite-size errors in quantum many-body simulations of extended systems using periodic boundary conditions. We show that our recently introduced model periodic Coulomb interaction @A. J. Williamson et al., Phys. Rev. B 55, R4851 ~1997!# can be applied consistently to all Coulomb interactions in the system. The model periodic Coulomb interaction greatly reduces the finite-size errors in quantum many-body simulations. We illustrate the practical application of our techniques with Hartree-Fock and variational and diffusion quantum Monte Carlo calculations for ground- and excited-state calculations. We demonstrate that the finite-size effects in electron promotion and electron addition/subtraction excitation energy calculations are very similar. @S0163-1829~99!07303-8#

Ab initio calculations of the cohesive energy and the bulk modulus of aluminium

To date there have been few attempts to calculate bulk properties such as the cohesive energy or the bulk modulus of metals using Monte Carlo (MC) methods. We present a variational MC calculation for aluminium and find that methods used to deal with finite-size effects work just as well as for insulators, despite the presence of a Fermi surface. However, the large statistical uncertainties are a problem when evaluating the bulk modulus.

Fate of density functional theory in the study of high-pressure solid hydrogen

This paper investigates some of the successes and failures of density functional theory in the study of high-pressure solid hydrogen at low temperature. We calculate the phase diagram, metallization pressure, phonon spectrum, and proton zero-point energy using three popular exchange-correlation functionals: the local density approximation (LDA), the Perdew-Burke-Ernzerhof (PBE) generalized gradient approximation, and the semilocal Becke-Lee-Yang-Parr (BLYP) functional. We focus on the solid molecular

Electronic damping of atomic dynamics in irradiation damage of metals

P{6}_{3}/m

Quantum Monte Carlo study of high pressure solid molecular hydrogen

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Quantum Monte Carlo Analysis of Exchange and Correlation in the Strongly Inhomogeneous Electron Gas

C2/c