Publications
99 results found
Sorouri A, Foulkes WMC, Hine NDM, 2006, Accurate and efficient method for the treatment of exchange in a plane-wave basis, JOURNAL OF CHEMICAL PHYSICS, Vol: 124, ISSN: 0021-9606
- Author Web Link
- Open Access Link
- Cite
- Citations: 32
Wood B, Foulkes WMC, Towler MD, et al., 2004, Coulomb finite-size effects in quasi-two-dimensional systems, JOURNAL OF PHYSICS-CONDENSED MATTER, Vol: 16, Pages: 891-902, ISSN: 0953-8984
- Author Web Link
- Open Access Link
- Cite
- Citations: 11
Nekovee M, Foulkes WMC, Needs RJ, 2003, Quantum Monte Carlo investigations of density functional theory of the strongly inhomogeneous electron gas, Physical Review B, Vol: 68, ISSN: 1550-235X
We use a variational quantum Monte Carlo realization of the adiabatic connection technique to calculate the most relevant quantities in Hohenberg-Kohn-Sham density functional theory for several strongly inhomogeneous electron-gas systems. Results for the coupling-constant dependence of the exchange-correlation energy, the pair-correlation function, the exchange-correlation hole, and the exchange and correlation energy densities are presented. Comparisons are made with the interaction strength interpolation (ISI) approximation, the local density approximation (LDA), the gradient expansion approximation (GEA), the generalized gradient approximation (GGA), and the weighted density approximation (WDA). The coupling-constant dependence of the exchange-correlation energy is accurately described by an ISI model that incorporates information on the strong-interaction limit. Unlike either the LDA or GEA, the WDA is successful in describing the nonlocal structure of the exchange-correlation hole. The LDA errors in the exchange-correlation energy density show a remarkable correlation with the Laplacian of the density. The GGA worsens the error in the integrated exchange-correlation energy as the inhomogeneity of the systems increases. This failure is shared by current meta-GGA functionals and is shown to be caused by the inability of these functionals to describe the LDA overestimation (in absolute value) of the exchange energy density around density maxima. It is suggested that this effect could be taken into account by including Laplacian terms in semilocal density functionals.
Nekovee M, WMC F, Needs RJ, 2003, Quantum Monte Carlo studies of density functional theory, MATHEMATICS AND COMPUTERS IN SIMULATION, Vol: 62, Pages: 463-470, ISSN: 0378-4754
We review our variational quantum Monte Carlo (VMC) approach for evaluating the key quantities in the density functional theory of inhomogeneous many-electron systems, and describe the underlying simulation algorithm and its parallel implementation. We discuss the insights gained from our recent application of the method to the study of the density functional theory (DFT) of the strongly inhomogeneous electron gas. (C) 2003 IMACS. Published by Elsevier Science B.V. All rights reserved.
Gaudoin R, WMC F, Rajagopal G, 2002, Ab initio calculations of the cohesive energy and the bulk modulus of aluminium, J PHYS-CONDENS MAT, Vol: 14, Pages: 8787-8793, ISSN: 0953-8984
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.
Gaudoin R, Foulkes WMC, 2002, <i>Ab initio</i> calculations of bulk moduli and comparison with experiment -: art. no. 052104, PHYSICAL REVIEW B, Vol: 66, ISSN: 2469-9950
- Author Web Link
- Open Access Link
- Cite
- Citations: 33
Nekovee M, Foulkes WMC, Needs RJ, 2001, Quantum Monte Carlo analysis of exchange and correlation in the strongly inhomogeneous electron gas, PHYSICAL REVIEW LETTERS, Vol: 87, ISSN: 0031-9007
- Author Web Link
- Open Access Link
- Cite
- Citations: 32
Gaudoin R, Nekovee M, Foulkes WMC, et al., 2001, Inhomogeneous random-phase approximation and many-electron trial wave functions, Phys. Rev. B, Vol: 63, ISSN: 1098-0121
The long-range electronic correlations in a uniform electron gas may be deduced from the random-phase approximation (RPA) of Bohm and Pines [Phys. Rev. 92, 609 (1953)]. Here we generalize the RPA to nonuniform systems and use it to derive many-electron Slater-Jastrow trial wave functions for quantum Monte Carlo simulations. The RPA theory fixes the long-range behavior of the inhomogeneous two-body terms in the Jastrow factor and provides an accurate analytic expression for the one-body terms. It also explains the success of Slater-Jastrow trial functions containing determinants of Hartree-Fock or density-functional orbitals, even though these theories do not include Jastrow factors. After adjusting the RPA Jastrow factor to incorporate the known short-range behavior, we test it using variational Monte Carlo simulations. In the small inhomogeneous electron gas system we consider, the analytic RPA-based Jastrow factor slightly outperforms the standard numerically optimized form. The inhomogeneous RPA theory therefore enables us to reduce or even avoid the costly numerical optimization process.
WMC F, Mitas L, Needs RJ, et al., 2001, Quantum Monte Carlo simulations of solids, REV MOD PHYS, Vol: 73, Pages: 33-83, ISSN: 0034-6861
This article describes the variational and fixed-node diffusion quantum Monte Carlo methods and how they may be used to calculate the properties of many-electron systems. These stochastic wave-function-based approaches provide a very direct treatment of quantum many-body effects and serve as benchmarks against which other techniques may be compared. They complement the less demanding density-functional approach by providing more accurate results and a deeper understanding of the physics of electronic correlation in real materials. The algorithms are intrinsically parallel, and currently available high-performance computers allow applications to systems containing a thousand or more electrons. With these tools one can study complicated problems such as the properties of surfaces and defects, while including electron correlation effects with high precision. The authors provide a pedagogical overview of the techniques and describe a selection of applications to ground and excited states of solids and clusters.
WMC F, Hood RQ, Needs RJ, 1999, Symmetry constraints and variational principles in diffusion quantum Monte Carlo calculations of excited-state energies, Physical Review B, Vol: 60, ISSN: 1550-235X
Fixed-node diffusion Monte Carlo (DMC) is a stochastic algorithm for finding the lowest energy many-fermion wave function with the same nodal surface as a chosen trial function. It has proved itself among the most accurate methods available for calculating many-electron,ground states, and is one of the few approaches that can be applied to systems large enough to act as realistic models of solids. In attempts to use fixed-node DMC for excited-state calculations, it has often been assumed that the DMC energy must be greater than or equal to the energy of the lowest exact eigenfunction with the same symmetry as the trial function. We show that this assumption is not justified unless the trial function transforms according to a one-dimensional irreducible representation of the symmetry group of the Hamiltonian. If the trial function transforms according to a multidimensional irreducible representation, corresponding to a degenerate energy level, the DMC energy may lie below the energy of the lowest eigenstate of that symmetry. Weaker variational bounds may then be obtained by choosing trial functions transforming according to one-dimensional irreducible representations of subgroups of the full symmetry group. [S0163-1829(99)09331-5].
PRC K, Hood RQ, Williamson AJ, et al., 1999, Finite-size errors in quantum many-body simulations of extended systems, PHYS REV B, Vol: 59, Pages: 1917-1929, ISSN: 0163-1829
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].
Foulkes WMC, Nekovee M, Gaudoin RL, et al., 1999, Quantum Monte Carlo simulations of real solids, High Performance Computing, Editors: Allen, Guest, Simpson, Henty, Nicole, Publisher: Kluwer Academic/Plenum, Pages: 165-174
Nekovee M, Foulkes WMC, Williamson AJ, et al., 1999, A quantum Monte Carlo approach to the adiabatic connection method, Adv. Quantum Chem., Vol: 33, Pages: 189-207
Stedman ML, WMC F, 1998, Talus - A quantum Monte Carlo modelling suite, COMPUT PHYS COMMUN, Vol: 113, Pages: 180-198, ISSN: 0010-4655
We present the Talus Quantum Monte Carlo modelling suite of programs. The suite provides an extensible environment for the study of a diverse range of physical systems with several QMC algorithms. The overriding concern behind the design of the suite has been to enable new algorithms and, in particular, new systems to be studied with minimal implementation and testing overhead. To this end, we have designed the Monte Carlo and measurement functions to be independent of the actual wavefunction. We describe the main algorithms used, discuss the unusual features of the suite's implementation, and provide results for a simple test calculation. (C) 1998 Published by Elsevier Science B.V.
Stedman ML, Foulkes WMC, Nekovee M, 1998, An accelerated Metropolis method, JOURNAL OF CHEMICAL PHYSICS, Vol: 109, Pages: 2630-2634, ISSN: 0021-9606
- Author Web Link
- Open Access Link
- Cite
- Citations: 13
Hood RQ, Chou MY, Williamson AJ, et al., 1997, Quantum Monte Carlo investigation of exchange and correlation in silicon, PHYSICAL REVIEW LETTERS, Vol: 78, Pages: 3350-3353, ISSN: 0031-9007
- Author Web Link
- Open Access Link
- Cite
- Citations: 64
Foulkes WMC, Nekovee M, Hood RQ, et al., 1997, Quantum Monte Carlo studies of exchange and correlation in solids., ABSTRACTS OF PAPERS OF THE AMERICAN CHEMICAL SOCIETY, Vol: 213, Pages: 125-COMP, ISSN: 0065-7727
Williamson AJ, Rajagopal G, Needs RJ, et al., 1997, Elimination of Coulomb finite-size effects in quantum many-body simulations, PHYSICAL REVIEW B, Vol: 55, Pages: R4851-R4854, ISSN: 0163-1829
Kenny SD, Rajagopal G, Needs RJ, et al., 1996, Quantum Monte Carlo calculations of the energy of the relativistic homogeneous electron gas, PHYSICAL REVIEW LETTERS, Vol: 77, Pages: 1099-1102, ISSN: 0031-9007
- Author Web Link
- Open Access Link
- Cite
- Citations: 13
Needs RJ, Rajagopal G, Williamson AJ, et al., 1996, Quantum Monte Carlo studies of electronic systems, Pacific Conference on Condensed Matter Theory - Complex Materials and Strongly Correlated Systems, Publisher: KOREAN PHYSICAL SOC, Pages: S116-S120, ISSN: 0374-4884
Williamson AJ, Kenny SD, Rajagopal G, et al., 1996, Optimized wave functions for quantum Monte Carlo studies of atoms and solids, Physical Review B, Vol: 53, Pages: 9640-9648, ISSN: 1550-235X
Wave functions for the homogeneous electron gas, a germanium pseudosolid, and a germanium pseudoatom are optimized using the method of variance minimization. Forms for the Jastrow factor which are convenient to optimize and may be evaluated rapidly are devised and tested and we stress the advantages of using expressions which are linear in the variable parameters. For each system studied we have performed variational and diffusion quantum Monte Carlo calculations to test the accuracy of the optimized wave functions. The results of our study are very promising for future applications of quantum Monte Carlo methods to real materials.
Fraser LM, Foulkes WMC, Rajagopal G, et al., 1996, Finite-size effects and Coulomb interactions in quantum Monte Carlo calculations for homogeneous systems with periodic boundary conditions, PHYSICAL REVIEW B, Vol: 53, Pages: 1814-1832, ISSN: 2469-9950
- Author Web Link
- Open Access Link
- Cite
- Citations: 188
RAJAGOPAL G, NEEDS RJ, JAMES A, et al., 1995, VARIATIONAL AND DIFFUSION QUANTUM MONTE-CARLO CALCULATIONS AT NONZERO WAVE VECTORS - THEORY AND APPLICATION TO DIAMOND-STRUCTURE GERMANIUM, PHYSICAL REVIEW B, Vol: 51, Pages: 10591-10600, ISSN: 0163-1829
- Author Web Link
- Open Access Link
- Cite
- Citations: 76
Rajagopal G, Needs RJ, Kenny S, et al., 1994, Quantum Monte Carlo calculations for solids using special k points methods., Phys Rev Lett, Vol: 73, Pages: 1959-1962
ANNETT JF, MATTHEW W, FOULKES C, et al., 1994, A recursive solution of Heisenberg's equation and its interpretation, J PHYS-CONDENS MAT, Vol: 6, Pages: 6455-6475, ISSN: 0953-8984
We present the generalization of the recursion method of Haydock and co-workers to systems of many interacting particles. This new method has close similarities to the memory function or Mori formalism, but with some important differences. Heisenberg's equation for the time evolution of a microscopic operator is recursively transformed into a tridiagonal matrix equation. This equation resolves the operator into components corresponding to transitions of different energies. The projected spectrum of transitions has a continued fraction expansion given by the elements of the tridiagonal matrix, We show that for an appropriate choice of inner product this density of transitions obeys a generalization of the black body theorem of electromagnetism, in that it is exponentially insensitive to distant parts of the system. This implies that the projected density of transitions is computationally stable and can be calculated even in macroscopic many-body systems. We argue that the physical content of the density of transitions is determined by the nature of its singular points, such as discrete transitions, continuous spectrum, band edges and van Hove singularities.
Foulkes WMC, 1993, Accuracy of the chemical-pseudopotential method for tetrahedral semiconductors., Phys Rev B, Vol: 48, Pages: 14216-14225, ISSN: 0163-1829
FOULKES WMC, 1993, FEYNMAN-KAC PATH-INTEGRAL CALCULATION OF THE GROUND-STATE ENERGIES OF ATOMS - COMMENT, PHYSICAL REVIEW LETTERS, Vol: 71, Pages: 2158-2158, ISSN: 0031-9007
- Author Web Link
- Cite
- Citations: 6
Foulkes WMC, Edwards DM, 1993, Perfect localized basis functions for solids: chemical pseudopotentials and the Kronig-Penney model, J. Phys. Condensed Matter, Vol: 5, Pages: 7987-8004
CAMPBELL IG, FREEMONT PS, FOULKES W, et al., 1992, AN OVARIAN TUMOR-MARKER WITH HOMOLOGY TO VACCINIA VIRUS CONTAINS AN IGV-LIKE REGION AND MULTIPLE TRANSMEMBRANE DOMAINS, CANCER RESEARCH, Vol: 52, Pages: 5416-5420, ISSN: 0008-5472
- Author Web Link
- Cite
- Citations: 123
Hybertsen MS, Stechel EB, Foulkes WM, et al., 1992, Model for low-energy electronic states probed by x-ray absorption in high-Tc cuprates., Phys Rev B, Vol: 45, Pages: 10032-10050, ISSN: 0163-1829
This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.