# Matthew Foulkes

Faculty of Natural SciencesDepartment of Physics

Professor of Physics

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### Contact

+44 (0)20 7594 7607wmc.foulkes

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### Assistant

Mrs Carolyn Dale +44 (0)20 7594 7579

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### Location

810Blackett LaboratorySouth Kensington Campus

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## Publications

Publication Type
Year
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80 results found

Wells T, Horsfield A, Foulkes WMC, Dudarev Set al., 2019, The microscopic Einstein-de Haas effect, Journal of Chemical Physics, Vol: 150, ISSN: 0021-9606

The Einstein-de Haas (EdH) effect, where the spin angular momentum of electrons is transferred to the mechanical angular momentum of atoms, was established experimentally in 1915. While a semiclassical explanation of the effect exists, modern electronic structure methods have not yet been applied to model the phenomenon. In this paper, we investigate its microscopic origins by means of a noncollinear tight-binding model of an O2 dimer, which includes the effects of spin-orbit coupling, coupling to an external magnetic field, and vector Stoner exchange. By varying an external magnetic field in the presence of spin-orbit coupling, a torque can be generated on the dimer, validating the presence of the EdH effect. The avoided energy level crossings and the rate of change of magnetic field determine the evolution of the spin. We also find that the torque exerted on the nuclei by the electrons in a time-varying B field is not only due to the EdH effect. The other contributions arise from field-induced changes in the electronic orbital angular momentum and from the direct action of the Faraday electric field associated with the time-varying magnetic field.

Journal article

Spencer JS, Blunt NS, Choi S, Etrych J, Filip M-A, Foulkes WMC, Franklin RST, Handley WJ, Malone FD, Neufeld VA, Di Remigio R, Rogers TW, Scott CJC, Shepherd JJ, Vigor WA, Weston J, Xu R, Thom AJWet al., 2019, The HANDE-QMC project: open-source stochastic quantum chemistry from the ground state up, Journal of Chemical Theory and Computation, Vol: 15, Pages: 1728-1742, ISSN: 1549-9618

Building on the success of Quantum Monte Carlo techniques such as diffusion Monte Carlo, alternative stochastic approaches to solve electronic structure problems have emerged over the past decade. The full configuration interaction quantum Monte Carlo (FCIQMC) method allows one to systematically approach the exact solution of such problems, for cases where very high accuracy is desired. The introduction of FCIQMC has subsequently led to the development of coupled cluster Monte Carlo (CCMC) and density matrix quantum Monte Carlo (DMQMC), allowing stochastic sampling of the coupled cluster wave function and the exact thermal density matrix, respectively. In this Article, we describe the HANDE-QMC code, an open-source implementation of FCIQMC, CCMC and DMQMC, including initiator and semistochastic adaptations. We describe our code and demonstrate its use on three example systems; a molecule (nitric oxide), a model solid (the uniform electron gas), and a real solid (diamond). An illustrative tutorial is also included.

Journal article

Coury MEA, Dudarev SL, Foulkes WMC, Horsfield AP, Ma P-W, Spencer JSet al., 2018, Erratum: Hubbard-like Hamiltonians for interacting electrons in s, p, and d orbitals (vol 93, 075101, 2016), Physical Review B, Vol: 98, ISSN: 2469-9950

Journal article

Davies PAG, Foulkes WMC, 2018, A two-phase Hessian approach improves the DFT relaxation of slabs, Journal of Physics: Condensed Matter, Vol: 30, Pages: 315901-315901, ISSN: 0953-8984

A two-phase Hessian approach to DFT slab relaxation of slabs has been implemented and tested. It addresses weaknesses in the modified Broyden and Pfrommer BFGS algorithms specific to relaxing slabs. Complete Hessian and then inverse Hessian matrices with no strain/stress components are first constructed at high force signal-to-noise ratios with no accompanying relaxation. In a second phase the static inverse Hessian is used to relax the slab down to a low force tolerance.

Journal article

Groth S, Dornheim T, Sjostrom T, Malone FD, Foulkes WMC, Bonitz Met al., 2017, Ab initio exchange-correlation free energy of the uniform electron gas at warm dense matter conditions, Physical Review Letters, Vol: 119, ISSN: 0031-9007

In a recent Letter [T.~Dornheim \textit{et al.}, Phys. Rev. Lett.\textbf{117}, 156403 (2016)], we presented the first \textit{ab initio} quantumMonte-Carlo (QMC) results of the warm dense electron gas in the thermodynamiclimit. However, a complete parametrization of the exchange-correlation freeenergy with respect to density, temperature, and spin polarization remained outof reach due to the absence of (i) accurate QMC results below$\theta=k_\text{B}T/E_\text{F}=0.5$ and (ii) of QMC results for spinpolarizations different from the paramagnetic case. Here we overcome bothremaining limitations. By closing the gap to the ground state and by performingextensive QMC simulations for different spin polarizations, we are able toobtain the first complete \textit{ab initio} exchange-correlation free energyfunctional; the accuracy achieved is an unprecedented $\sim 0.3\%$. This alsoallows us to quantify the accuracy and systematic errors of various previousapproximate functionals.

Journal article

Dornheim T, Groth S, Malone FD, Schoof T, Sjostrom T, Foulkes WMC, Bonitz Met al., 2017, Ab initio quantum Monte Carlo simulation of the warm dense electron gas, Physics of Plasmas, Vol: 24, Pages: 056303-1-056303-10, ISSN: 1089-7674

Warm dense matter is one of the most active frontiers in plasma physics due to its relevance for denseastrophysical objects as well as for novel laboratory experiments in which matter is being strongly compressede.g. by high-power lasers. Its description is theoretically very challenging as it contains correlated quantumelectrons at nite temperature|a system that cannot be accurately modeled by standard analytical or groundstate approaches. Recently several breakthroughs have been achieved in the eld of fermionic quantum MonteCarlo simulations. First, it was shown that exact simulations of a nite model system (30 : : : 100 electrons)is possible that avoid any simplifying approximations such as xed nodes [Schoof et al., Phys. Rev. Lett.115, 130402 (2015)]. Second, a novel way to accurately extrapolate these results to the thermodynamic limitwas reported by Dornheim et al. [Phys. Rev. Lett. 117, 156403 (2016)]. As a result, now thermodynamicresults for the warm dense electron gas are available that have an unprecedented accuracy on the order of0:1%. Here we present an overview on these results and discuss limitations and future directions.

Journal article

Azadi S, Drummond ND, Foulkes WMC, 2017, Nature of the metallization transition in solid hydrogen, Physical Review. B, Condensed Matter, Vol: 95, ISSN: 0163-1829

We present an accurate study of the static-nucleus electronic energy band gap of solid molecular hydrogen at high pressure. The excitonic and quasiparticle gaps of the C2/c, Pc, Pbcn, and P63/mstructures at pressures of 250, 300, and 350 GPa are calculated using the fixed-node diffusion quantum Monte Carlo (DMC) method. The difference between the mean-field and many-body band gaps at the same density is found to be almost independent of system size and can therefore be applied as a scissor correction to the mean-field gap of an infinite system to obtain an estimate of the many-body gap in the thermodynamic limit. By comparing our static-nucleus DMC energy gaps with available experimental results, we demonstrate the important role played by nuclear quantum effects in the electronic structure of solid hydrogen.

Journal article

Dornheim T, Groth S, Sjostrom T, Malone FD, Foulkes WMC, Bonitz Met al., 2016, Ab Initio Quantum Monte Carlo Simulation of the Warm Dense Electron Gas in the Thermodynamic Limit, Physical Review Letters, Vol: 117, ISSN: 1079-7114

We perform ab initio quantum Monte Carlo (QMC) simulations of the warm dense uniform electrongas in the thermodynamic limit. By combining QMC data with linear response theory we are able toremove finite-size errors from the potential energy over the entire warm dense regime, overcoming thedeficiencies of the existing finite-size corrections by Brown et al. [PRL 110, 146405 (2013)]. Extensivenew QMC results for up to N = 1000 electrons enable us to compute the potential energy V and theexchange-correlation free energy Fxc of the macroscopic electron gas with an unprecedented accuracyof |∆V |/|V |, |∆Fxc|/|F|xc ∼ 10−3. A comparison of our new data to the recent parametrization ofFxc by Karasiev et al. [PRL 112, 076403 (2014)] reveals significant deviations to the latter.

Journal article

Foulkes WMC, 2016, Tight-Binding Models and Coulomb Interactions for s, p, and d Electrons, Quantum Materials: Experiments and Theory, Editors: Pavarini, Koch, van den Brink, Sawatzky, Jülich, Germany, Publisher: Forschungszentrum Jülich GmbH, Pages: 3.1-3.42, ISBN: 978-3-95806-159-0

Book chapter

Malone FD, Blunt NS, Brown EW, Lee DKK, Spencer JS, Foulkes WMC, Shepherd JJet al., 2016, Accurate exchange-correlation energies for the warm dense electron gas, Physical Review Letters, Vol: 117, ISSN: 1079-7114

The density matrix quantum Monte Carlo (DMQMC) method is used to sample exact-on-average N-body density matrices for uniform electron gas systems of up to 10124 matrix elements via a stochastic solution of the Bloch equation. The results of these calculations resolve a current debate over the accuracy of the data used to parametrize finite-temperature density functionals. Exchange-correlation energies calculated using the real-space restricted path-integral formalism and the k-space configuration path-integral formalism disagree by up to ∼10% at certain reduced temperatures T/TF≤0.5 and densities rs≤1. Our calculations confirm the accuracy of the configuration path-integral Monte Carlo results available at high density and bridge the gap to lower densities, providing trustworthy data in the regime typical of planetary interiors and solids subject to laser irradiation. We demonstrate that the DMQMC method can calculate free energies directly and present exact free energies for T/TF≥1 and rs≤2.

Journal article

Horsfield AP, Lim A, Foulkes WMC, Correa AAet al., 2016, Adiabatic perturbation theory of electronic stopping in insulators, Physical Review. B, Condensed Matter, Vol: 93, ISSN: 0163-1829

A model able to explain the complicated structure of electronic stopping at low velocities in insulating materials is presented. It is shown to be in good agreement with results obtained from time-dependent density-functional theory for the stopping of a channeling Si atom in a Si crystal. If we define the repeat frequency f=v/λ, where λ is the periodic repeat length of the crystal along the direction the channeling atom is traveling, and v is the velocity of the channeling atom, we find that electrons experience a perturbing force that varies in time at integer multiples l of f. This enables electronic excitations at low atom velocity, but their contributions diminish rapidly with increasing values of l. The expressions for stopping power are derived using adiabatic perturbation theory for many-electron systems, and they are then specialized to the case of independent electrons. A simple model for the nonadiabatic matrix elements is described, along with the procedure for determining its parameters.

Journal article

Heuer AH, Azar MZ, Guhl H, Foulkes M, Gleeson B, Nakagawa T, Ikuhara Y, Finnis MWet al., 2016, The band structure of polycrystalline Al2O3 and its influence on transport phenomena, Journal of the American Ceramic Society, Vol: 99, Pages: 733-747, ISSN: 1551-2916

Journal article

Coury MEA, Dudarev SL, Foulkes WMC, Horsfield AP, Ma P-W, Spencer JSet al., 2016, Hubbard-like Hamiltonians for interacting electrons in s, p, and d orbitals, Physical Review B, Vol: 93, ISSN: 1550-235X

Hubbard-like Hamiltonians are widely used to describe on-site Coulomb interactions in magnetic and strongly-correlated solids, but there is much confusion in the literature about the form these Hamiltonians should take for shells of p and d orbitals. This paper derives the most general s,p, and d orbital Hubbard-like Hamiltonians consistent with the relevant symmetries, and presents them in ways convenient for practical calculations. We use the full configuration interaction method to study p and d orbital dimers and compare results obtained using the correct Hamiltonian and the collinear and vector Stoner Hamiltonians. The Stoner Hamiltonians can fail to describe properly the nature of the ground state, the time evolution of excited states, and the electronic heat capacity.

Journal article

Lim A, Foulkes WM, Horsfield AP, Mason DR, Schleife A, Draeger EW, Correa AAet al., 2016, Electron elevator: excitations across the band gap via a dynamical gap state, Physical Review Letters, Vol: 116, ISSN: 1079-7114

We use time-dependent density functional theory to study self-irradiated Si. We calculate the electronic stopping power of Si in Si by evaluating the energy transferred to the electrons per unit path length by an ion of kinetic energy from 1 eV to 100 keV moving through the host. Electronic stopping is found to be significant below the threshold velocity normally identified with transitions across the band gap. A structured crossover at low velocity exists in place of a hard threshold. An analysis of the time dependence of the transition rates using coupled linear rate equations enables one of the excitation mechanisms to be clearly identified: a defect state induced in the gap by the moving ion acts like an elevator and carries electrons across the band gap.

Journal article

Spencer JS, Blunt NS, Vigor WA, Malone FD, Foulkes WMC, Shepherd JJ, Thom AJWet al., 2015, Open-source development experiences in scientific software: the HANDE quantum Monte Carlo project, Journal of Open Research Software, Vol: 3, ISSN: 2049-9647

The HANDE quantum Monte Carlo project offers accessible stochastic algorithmsfor general use for scientists in the field of quantum chemistry. HANDE is anambitious and general high-performance code developed by ageographically-dispersed team with a variety of backgrounds in computationalscience. In the course of preparing a public, open-source release, we havetaken this opportunity to step back and look at what we have done and what wehope to do in the future. We pay particular attention to development processes,the approach taken to train students joining the project, and how a flathierarchical structure aids communication

Journal article

Edmunds DM, Tangney P, Vvedensky DD, Foulkes WMCet al., 2015, Free-energy coarse-grained potential for C₆₀, Journal of Chemical Physics, Vol: 143, Pages: 164509-164509, ISSN: 1089-7690

We propose a new deformable free energy method for generating a free-energy coarse-graining potentialfor C₆₀. Potentials generated from this approach exhibit a strong temperature dependence and produceexcellent agreement with benchmark fully atomistic molecular dynamics simulations. Parametersets for analytical fits to this potential are provided at four different temperatures.

Journal article

Guhl H, Lee H-S, Tangney P, Foulkes WMC, Heuer AH, Nakagawa T, Ikuhara Y, Finnis MWet al., 2015, Structural and Electronic Properties of Sigma7 Grain Boundaries in alpha-Al2O3, Acta Materialia, Vol: 99, Pages: 16-28, ISSN: 1873-2453

Applying simulated annealing with a classical potential followed by screening of low-energy structures with density functional theory, we examined the atomic and electronic structures of the View the MathML source and View the MathML source symmetric tilt grain boundaries in α-Al2O3. The lowest energy View the MathML source boundary exhibits a pronounced pattern of alternating columns of exclusively four- or fivefold coordinated Al atoms, with a grain boundary energy of 1.84 Jm−2. For the View the MathML source boundary, numerous structures were found with energy just below 2.11 Jm−2. Furthermore, by analysing the full set of candidate structures generated by simulated annealing for the two grain boundaries, we find that the number of fivefold coordinated Al atoms tends to increase with grain boundary energy, which we can also correlate with the behaviour of the electronic density of states. On the other hand, we find no systematic trend with energy that might be expected for other quantities, notably the excess volume of the interface. We compare simulated high-resolution transmission electron microscope (HRTEM) images of the lowest energy calculated structures with experimental images. The disparate structural and electronic features of these two boundaries suggest reasons for their very different oxygen diffusion coefficients that have been observed experimentally.

Journal article

Malone FDARA, 2015, Interaction picture density matrix quantum Monte Carlo, Journal of Chemical Physics, Vol: 143, ISSN: 1089-7690

The recently developed density matrix quantum Monte Carlo (DMQMC) algorithm stochastically samplesthe N-body thermal density matrix and hence provides access to exact properties of many-particle quantumsystems at arbitrary temperatures. We demonstrate that moving to the interaction picture provides substan-tial benefits when applying DMQMC to interacting fermions. In this first study, we focus on a system ofmuch recent interest: the uniform electron gas in the warm dense regime. The basis set incompleteness errorat finite temperature is investigated and extrapolated via a simple Monte Carlo sampling procedure. Finally,we provide benchmark calculations for a four-electron system, comparing our results to previous work wherepossible.

Journal article

Azadi S, Foulkes WMC, 2015, Systematic study of finite-size effects in quantum Monte Carlo calculations of real metallic systems, Journal of Chemical Physics, Vol: 143, ISSN: 1089-7690

We present a systematic and comprehensive study of finite-size effects in diffusion quantum Monte Carlo calculations of metals. Several previously introduced schemes for correcting finite-size errors are compared for accuracy and efficiency, and practical improvements are introduced. In particular, we test a simple but efficient method of finite-size correction based on an accurate combination of twist averaging and density functional theory. Our diffusion quantum Monte Carlo results for lithium and aluminum, as examples of metallic systems, demonstrate excellent agreement between all of the approaches considered.

Journal article

Drummond ND, Needs RJ, Sorouri A, Foulkes WMCet al., 2014, Erratum: Finite-size errors in continuum quantum Monte Carlo calculations (Physical Review B - Condensed Matter and Materials Physics (2008) 78 (125106)), Physical Review B - Condensed Matter and Materials Physics, Vol: 90, ISSN: 1098-0121

Journal article

Blunt NS, Rogers TW, Spencer JS, Foulkes WMCet al., 2014, Density-matrix quantum Monte Carlo method, PHYSICAL REVIEW B, Vol: 89, ISSN: 1098-0121

Journal article

Azadi S, Foulkes WMC, Kuehne TD, 2013, Quantum Monte Carlo study of high pressure solid molecular hydrogen, NEW JOURNAL OF PHYSICS, Vol: 15, ISSN: 1367-2630

Journal article

Azadi S, Foulkes WMC, 2013, Fate of density functional theory in the study of high-pressure solid hydrogen (vol 88, 014115, 2013), PHYSICAL REVIEW B, Vol: 88, ISSN: 1098-0121

Journal article

Heuer AH, Nakagawa T, Azar MZ, Hovis DB, Smialek JL, Gleeson B, Hine NDM, Guhl H, Lee H-S, Tangney P, Foulkes WMC, Finnis MWet al., 2013, On the Growth of Al_2 O_3 Scales, Acta Materialia, Vol: 61, Pages: 6670-6683

Journal article

Race CP, Mason DR, Foo MHF, Foulkes WMC, Horsfield AP, Sutton APet al., 2013, Quantum-classical simulations of the electronic stopping force and charge on slow heavy channelling ions in metals, JOURNAL OF PHYSICS-CONDENSED MATTER, Vol: 25, ISSN: 0953-8984

Journal article

Kolodrubetz MH, Spencer JS, Clark BK, Foulkes WMCet al., 2013, The effect of quantization on the full configuration interaction quantum Monte Carlo sign problem, JOURNAL OF CHEMICAL PHYSICS, Vol: 138, ISSN: 0021-9606

Journal article

Mason DR, Race CP, Foo MHF, Horsfield AP, Foulkes WMC, Sutton APet al., 2012, Resonant charging and stopping power of slow channelling atoms in a crystalline metal, NEW JOURNAL OF PHYSICS, Vol: 14, ISSN: 1367-2630

Journal article

Spencer JS, Blunt NS, Foulkes WMC, 2012, The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method, JOURNAL OF CHEMICAL PHYSICS, Vol: 136, ISSN: 0021-9606

Journal article

Mason DR, Race CP, Foulkes WMC, Finnis MW, Horsfield AP, Sutton APet al., 2011, Quantum mechanical simulations of electronic stopping in metals, Nucl. Instrum. Meth. Phys. Res. B, Vol: 269, Pages: 1640-1645, ISSN: 0168-583X

Journal article

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