Randolph Q. Hood

Lawrence Livermore National Laboratory, Livermore, CA, United States

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Publications (53)125.74 Total impact

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    Justin B. Haskins, John A. Moriarty, Randolph Q. Hood
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    ABSTRACT: Recent small-cell (< 150-atom) quantum molecular dynamics (QMD) simulations for Ta based on density functional theory (DFT) have predicted a hexagonal omega (hex-omega) phase more stable than the normal bcc phase at high temperature (T) and pressure (P) above 70 GPa [Burakovsky et al., Phys. Rev. Lett. 104, 255702 (2010)]. Here we examine possible high-polymorphism in Ta with complementary DFT-based model generalized pseudopotential theory (MGPT) multi-ion interatomic potentials, which allow accurate treatment of much larger system sizes (up to ~ 80000 atoms). We focus on candidate bcc, A15, fcc, hcp, and hex-omega phases for the high-phase diagram to 420 GPa, studying the mechanical and relative thermodynamic stability of these phases for both small and large computational cells. Our MGPT potentials fully capture the DFT energetics of these phases, while MGPT-MD simulations demonstrate that the higher-energy fcc, hcp and hex-omega structures are only mechanically stabilized at high temperature by large, size-dependent, anharmonic vibrational effects, with the stability of the hex-omega phase also being found to be a sensitive function of its ratio. Both two-phase and Z-method melting techniques have been used in MGPT-MD simulations to determine relative phase stability and its size dependence. In the large-cell limit, the two-phase method yields accurate equilibrium melt curves for all five phases, with bcc producing the highest melt temperatures at all pressures and hence being the most stable phase of those considered. The two-phase bcc melt curve is also in good agreement with dynamic experimental data as well as with the MGPT melt curve calculated from bcc and liquid free energies. In contrast, we find that the Z method produces only an upper bound to the equilibrium melt curve in the large-cell limit. For the bcc and hex-omega structures, however, this is a close upper bound within 5% of the two-phase results, although for the A15, fcc, and hcp structures, the Z-melt curves are 25-35% higher in temperature than the two-phase results. Nonetheless, the Z method has allowed us to study melt size effects in detail. We find these effects to be either small or modest for the cubic bcc, A15, and fcc structures, but to have a large impact on the hexagonal hcp and hex-omega melt curves, which are dramatically pushed above that of bcc for simulation cells less than 150 atoms. The melt size effects are driven by and closely correlated with similar size effects on the mechanical stability and the vibrational anharmonicity. We further show that for the same simulation cell sizes and choice of c/a ratio, the MGPT-MD bcc and hex-omega melt curves are in good agreement with the QMD results, so the QMD prediction is confirmed in the small-cell limit. But in the large-cell limit, the MGPT-MD hex-omega melt curve is always lowered below that of bcc for any choice of c/a, so bcc is the most stable phase. We conclude that for the non-bcc Ta phases studied, one requires simulation cells of at least 250-500 atoms to be free of size effects impacting mechanical and thermodynamic phase stability.
    Physical Review B 12/2012; 86(22):224104. · 3.66 Impact Factor
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    Randolph Q. Hood, P. R. C. Kent, Fernando A. Reboredo
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    ABSTRACT: The many-body diffusion quantum Monte Carlo (DMC) method with twist-averaged boundary conditions is used to calculate the ground-state equation of state and the energetics of point defects in fcc aluminum using supercells up to 1331 atoms. The DMC equilibrium lattice constant differs from experiment by 0.008 A, or 0.2%, while the cohesive energy using DMC with backflow wave functions with improved nodal surfaces differs by 27 meV. DMC-calculated defect formation and migration energies agree with available experimental data, except for the nearest-neighbor divacancy, which is found to be energetically unstable, in agreement with previous density functional theory (DFT) calculations. DMC and DFT calculations of vacancy defects are in reasonably close agreement. Self-interstitial formation energies have larger differences between DMC and DFT, of up to 0.33eV, at the tetrahedral site. We also computed formation energies of helium interstitial defects where energies differed by up to 0.34eV, also at the tetrahedral site. The close agreement with available experiments demonstrates that DMC can be used as a predictive method to obtain benchmark energetics of defects in metals.
    Physical Review B 10/2012; 85(13). · 3.66 Impact Factor
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    ABSTRACT: Since Dmitri Mendeleev developed a table in 1869 to illustrate recurring ("periodic") trends of the elements, it has been understood that most chemical and physical properties can be described by taking into account the outer most electrons of the atoms. These valence electrons are mainly responsible for the chemical bond. In many ab-initio approaches only valence electrons are taken into account and a pseudopotential is used to mimic the response of the core electrons. Typically an all-electron calculation is used to generate a pseudopotential that is used either within density functional theory or quantum chemistry approaches. In this talk we explain and demonstrate a new method to generate pseudopotentials directly from all-electron many-body diffusion Monte Carlo (DMC) calculations and discuss the results of of the transferability of these pseudopotentials. The advantages of incorporating the exchange and correlation directly from DMC into the pseudopotential are also discussed.
    02/2012;
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    ABSTRACT: Difficulties can arise in simulating various Hamiltonian operators efficiently in diffusion Monte Carlo (DMC) such as those associated with non-local pseudopotentials which require the introduction of an approximate form. The locality approximation and T-moves are two widely used techniques in fixed-node diffusion Monte Carlo (FN-DMC) that provide a tractable approach for treating non-local pseudopotentials, however their use introduces an uncontrolled approximation. Exact treatment of the non-local pseudopotentials in FN-DMC introduces a sign problem with the associated Green's function matrix elements which take on both positive and negative values. Here we present an analysis of the nature of the sign problem that non-local operators introduce into the Green's function. We then consider the feasibility of running DMC simulations in which the non-local pseudopotentials are treated exactly and demonstrate the algorithm on a few molecular systems.
    02/2012;
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    John A Moriarty, Randolph Q Hood, Lin H Yang
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    ABSTRACT: In narrow d-band transition metals, electron temperature T(el) can impact the underlying electronic structure for temperatures near and above melt, strongly coupling the ion- and electron-thermal degrees of freedom and producing T(el)-dependent interatomic forces. Starting from the Mermin formulation of density functional theory, we have extended first-principles generalized pseudopotential theory to finite electron temperature and then developed efficient T(el)-dependent model generalized pseudopotential theory interatomic potentials for a Mo prototype. Unlike potentials based on the T(el)=0 electronic structure, the T(el)-dependent model generalized pseudopotential theory potentials yield a high-pressure Mo melt curve consistent with density functional theory quantum simulations, as well as with dynamic experiments, and also support a rich polymorphism in the high-(T,P) phase diagram.
    Physical Review Letters 01/2012; 108(3):036401. · 7.73 Impact Factor
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    ABSTRACT: We perform release-node quantum Monte Carlo simulations on the first row diatomic molecules in order to assess how accurately their ground-state energies can be obtained. An analysis of the fermion-boson energy difference is shown to be strongly dependent on the nuclear charge, Z, which in turn determines the growth of variance of the release-node energy. It is possible to use maximum entropy analysis to extrapolate to ground-state energies only for the low Z elements. For the higher Z dimers beyond boron, the error growth is too large to allow accurate data for long enough imaginary times. Within the limit of our statistics we were able to estimate, in atomic units, the ground-state energy of Li(2) (-14.9947(1)), Be(2) (-29.3367(7)), and B(2)(-49.410(2)).
    The Journal of Chemical Physics 11/2011; 135(18):184109. · 3.12 Impact Factor
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    ABSTRACT: We use first-principles fixed-node diffusion quantum Monte Carlo to calculate the energetics of point defects in bulk FCC aluminum demonstrating a very high accuracy when compared to experiment. Aluminum has been well studied experimentally as a "simple" metal prototype for investigating the effects of radiation damage such as void formation and helium embrittlement. Often accuracies at the level of milli-electronvolts are required, which is not achieved even for the simple case of pairs of vacancies in aluminum, using common density functionals. Perhaps surprisingly, even single vacancy energies are not reliable in many simple structural materials. Also presented are results for the bulk properties of aluminum - the equilibrium lattice constant, the cohesive energy, and the bulk modulus. These calculations bring a new level of rigor to the study of defects in metals.
    03/2011;
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    ABSTRACT: Release-Node quantum Monte Carlo (RN-QMC) is a method that calculates unbiased ground-state energies of fermionic systems. However, while RN-QMC has been successfully applied to the homogeneous electron gas with more than one hundred electrons, obtaining converged results for molecular systems has proven to be problematic for all but the smallest systems. A promising route to extending the method's success to a wider class of physically interesting Hamiltonians lies in the application of projection techniques such as Maximum Entropy (MaxEnt) which, in principle, allows for extrapolation to the converged ground-state energy. Direct application of MaxEnt to higher Z elements is, however, not entirely straightforward. We propose strategies for optimizing MaxEnt analysis of short time RN-QMC data and demonstrate their effectiveness in obtaining ground state energies for the first row dimers. Attention is given to the determination of statistical errors in the resulting extrapolations as well as an attempt to characterize the minimum decay time required for unbiased results.
    03/2011;
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    ABSTRACT: The self-healing diffusion Monte Carlo algorithm (SHDMC) is shown to be an accurate and robust method for calculating the ground state of atoms and molecules. By direct comparison with accurate configuration interaction results for the oxygen atom, we show that SHDMC converges systematically towards the ground-state wave function. We present results for the challenging N2 molecule, where the binding energies obtained via both energy minimization and SHDMC are near chemical accuracy (1  kcal/mol). Moreover, we demonstrate that SHDMC is robust enough to find the nodal surface for systems at least as large as C20 starting from random coefficients. SHDMC is a linear-scaling method, in the degrees of freedom of the nodes, that systematically reduces the fermion sign problem.
    Physical Review Letters 05/2010; 104(19):193001. · 7.73 Impact Factor
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    ABSTRACT: Diffusion Monte Carlo (DMC) is one of the most accurate methods for calculating electronic structure and can be applied to systems containing thousands of electrons. Typical applications of DMC utilize the fixed-node approximation, in which the nodes are specified using an input trial wave function. Errors in the locations of the nodes lead to systematic errors in DMC energy estimators. Removing this nodal bias can be done using transient quantum Monte Carlo methods, which have previously been applied to the free-electron gas and a handful of other few-electron systems. The drawback in using transient methods is the significant increase in computational cost. We have studied several quantum systems of varying sizes in order to better understand the scaling properties of various transient methods. We have explored techniques for reducing the computational cost such as cancellation and correlated walkers. We have analyzed our data using Bayesian inference. Prepared by LLNL under Contract DE-AC52-07NA27344
    03/2010;
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    ABSTRACT: Transition metal sites in metal-organic frameworks and in doped carbon structures are actively being studied for their binding properties of molecular hydrogen. We present a study of prototypical metal-organic structures that can be used to bind molecular hydrogen non-covalently. Due to the well known limitations of current density functional theory based descriptions of non-covalent hydrogen bonding we have focused our efforts on a consistent many-body approach based on the fixed-node diffusion Monte Carlo method. Accurate studies of binding energies and the effects of multiple hydrogens in these structures are presented. Prepared by LLNL under Contract DE-AC52-07NA27344
    03/2009;
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    ABSTRACT: We develop a formalism and present an algorithm for optimization of the trial wave function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the ground-state probability density. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project out a multideterminant expansion of the fixed-node ground-state wave function and (ii) to define a cost function that relates the fixed-node ground-state and the noninteracting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixed-node wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust toward the ones of the exact many-body ground state in a simulated annealing-like process. Based on these principles, we propose a method to improve both single determinant and multideterminant expansions of the trial wave function. The method can be generalized to other wave-function forms such as pfaffians. We test the method in a model system where benchmark configuration-interaction calculations can be performed and most components of the Hamiltonian are evaluated analytically. Comparing the DMC calculations with the exact solutions, we find that the trial wave function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave functions orthogonal to the exact ground state. Similarly, the DMC total energy and density converges to the exact solutions for the model. In the optimization process we find an optimal noninteracting nodal potential of density-functional-like form whose existence was predicted in a previous publication [ Phys. Rev. B 77 245110 (2008)]. Tests of the method are extended to a model system with a conventional Coulomb interaction where we show we can obtain the exact Kohn-Sham effective potential from the DMC data.
    Physical Review B 01/2009; 79(19). · 3.66 Impact Factor
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    ABSTRACT: We present a method to obtain the fixed node ground state wave function from an importance sampling Diffusion Monte Carlo (DMC) run. The fixed node ground state wave-function is altered to obtain an improved trial wave-function for the next DMC run. The theory behind this approach will be discussed. Two iterative algorithms are presented and validated in a model system by direct comparison with full configuration interaction (CI) wave functions and energies. We find that the trial wave-function is systematically improved. The scalar product of the trial wave-function with the CI result converges to 1 even starting from wave-functions orthogonal to the CI ground state. Similarly, the DMC total energy and density converges to the CI result. In the optimization process we find an optimal non-interacting nodal potential of density-functional-like form. An extension to a model system with full Coulomb interactions demonstrates that we can obtain the exact Kohn-Sham effective potential from the DMC data. Subsequently we apply our method to real molecules such as benzene and find that we can improve the ground state energy as compared with the single determinant result even starting from random wave-functions. Results for other molecular systems and comparison with alternative methods will be presented.
    01/2009;
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    ABSTRACT: We develop a formalism and present an algorithm for optimization of the trial wave-function used in fixed-node diffusion quantum Monte Carlo (DMC) methods. We take advantage of a basic property of the walker configuration distribution generated in a DMC calculation, to (i) project-out a multi-determinant expansion of the fixed-node ground-state wave function and (ii) to define a cost function that relates the fixed-node ground-state and the non-interacting trial wave functions. We show that (a) locally smoothing out the kink of the fixed-node ground-state wave function at the node generates a new trial wave-function with better nodal structure and (b) we argue that the noise in the fixed-node wave-function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust towards the ones of the exact many-body ground state in a simulated annealing-like process. We propose a method to improve both single determinant and multi-determinant expansions of the trial wave-function. We test the method in a model system where benchmark configuration interaction calculations can be performed. Comparing the DMC calculations with the exact solutions, we find that the trial wave-function is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wave-functions orthogonal to the exact ground state. In the optimization process we find an optimal non-interacting nodal potential of density-functional-like form whose existence was predicted earlier[Phys.Rev. B {\bf 77}, 245110 (2008)]. We obtain the exact Kohn-Sham effective potential from the DMC data.
    09/2008;
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    ABSTRACT: We investigate the accuracy of first-principles many-body theories at the nanoscale by comparing the low-energy excitations of the carbon fullerenes C(20), C(24), C(50), C(60), C(70), and C(80) with experiment. Properties are calculated via the GW-Bethe-Salpeter equation and diffusion quantum Monte Carlo methods. We critically compare these theories and assess their accuracy against available photoabsorption and photoelectron spectroscopy data. The first ionization potentials are consistently well reproduced and are similar for all the fullerenes and methods studied. The electron affinities and first triplet excitation energies show substantial method and geometry dependence. These results establish the validity of many-body theories as viable alternative to density-functional theory in describing electronic properties of confined carbon nanostructures. We find a correlation between energy gap and stability of fullerenes. We also find that the electron affinity of fullerenes is very high and size independent, which explains their tendency to form compounds with electron-donor cations.
    The Journal of Chemical Physics 09/2008; 129(8):084311. · 3.12 Impact Factor
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    ABSTRACT: We are developing a scalable parallel and distributed computational framework consisting of methods, algorithms, and integrated software tools for multi-terascle-to-petascale simulations of stress corrosion cracking (SCC) with quantum-level accuracy. We have performed multimillion- to billion-atom molecular dynamics (MD) simulations of deformation, flow, and fracture in amorphous silica with interatomic potentials and forces validated by density functional theory (DFT) calculations. Optimized potentials have been developed to study sulfur embrittlement of nickel with multimillion-to-multibillion atom MD simulations based on DFT and temperature dependent model generalized pseudopotential theory. We have also developed a quasi-continuum method embedded with quantum simulations based on DFT to reach macroscopic length scales and an accelerated molecular dynamics scheme to reach macroscopic time scales in simulations of solid-fluid interfaces that are relevant to SCC. A hybrid MD and mesoscale lattice Boltzmann simulation algorithm is being designed to study fluid flow through cracks.
    Journal of Physics Conference Series 08/2008; 125(1):012060.
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    Randolph Q. Hood, L. H. Yang, John A. Moriarty
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    ABSTRACT: Constant-volume quantum molecular dynamics (QMD) simulations of uranium (U) have been carried out over a range of pressures and temperatures that span the experimentally observed solid orthorhombic α-U, body-centered-cubic (bcc), and liquid phases, using an ab initio plane-wave pseudopotential method within the generalized gradient approximation of density-functional theory. A robust U pseudopotential has been constructed for these simulations that treats the 14 valence and outer-core electrons per atom necessary to calculate accurate structural and thermodynamic properties up to 100 GPa. Its validity has been checked by comparing low-temperature results with experimental data and all-electron full-potential linear-muffin-tin-orbital calculations of several different uranium solid structures. Calculated QMD energies and pressures for the equation of state of uranium in the solid and liquid phases are given, along with results for the Grüneisen parameter and the specific heat. We also present results for the radial distribution function, bond-angle distribution function, electronic density of states, and liquid diffusion coefficient, as well as evidence for short-range order in the liquid.
    Physical Review B 06/2008; 78(2):024116. · 3.66 Impact Factor
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    ABSTRACT: First-principles generalized pseudopotential theory (GPT) provides a fundamental basis for bridging the quantum-atomistic gap from density-functional quantum mechanics to large scale atomistic simulation in metals and alloys. In directionally-bonded bcc transition metals, advanced generation model GPT or MGPT potentials based on canonical d bands have been developed for Ta, Mo and V and successfully applied to a wide range of thermodynamic and mechanical properties at both ambient and extreme conditions of pressure and temperature, including high-pressure phase transitions, multiphase equation of state; melting and solidification; thermoelasticity; and the atomistic simulation of point defects, dislocations and grain boundaries needed for the multiscale modeling of plasticity and strength. Recent algorithm improvements have also allowed an MGPT implementation beyond canonical bands to achieve increased accuracy, extension to f-electron actinide metals, and high computational speed. A further advance in progress is the development temperature-dependent MGPT potentials that subsume electron-thermal contributions to high-temperature properties.
    TMS 2008 Annual Meeting Supplemental Proceedings Volume I: Materials Processing and Properties. 03/2008;
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    ABSTRACT: Fixed-node quantum Monte-Carlo (QMC) methods are becoming an increasingly attractive approach for the study of large scale problems in electronic structure. Current challenges lie in efficient application of QMC to large (thousands of electrons) systems and removal or amelioration of the uncontrolled approximations inherent in most practical applications of the method. I will present recent progress and address some of the particular challenges associated with the development of exact potential energy surfaces for weakly interacting closed shell carbon complexes within the fixed-node QMC ansatz. In particular, the efficacy / necessity of backflow corrections and multi-determinant expansions as a method for optimizing the nodal surface in these systems will be discussed.
    03/2008;
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    ABSTRACT: We have calculated the low energy optical excitations of the carbon fullerenes C20, C24, C50, C60, C70, and C80. Properties are calculated via the GW-Bethe-Salpeter Equation (GW-BSE) and diffusion Quantum Monte Carlo (QMC) methods. We compare these approaches with time dependent density functional results and with experiment. GW-BSE and QMC have previously shown good agreement for small molecules, but this is the first study of these methods for these larger yet prototypical nanostructures. The first ionization potentials are consistently well reproduced and are similar for all the fullerenes and methods studied. However, electron affinities and first triplet exciton show substantial method and geometry dependence. GW-BSE yields triplet energies around 1eV below the QMC results. We discuss the possible reasons for these differences. Research at Oak Ridge National Laboratory performed at the Materials Science and Technology Division, sponsored by the Division of Materials Sciences, and at the Center for Nanophase Materials Sciences, sponsored by the Division of Scientific User Facilities, U.S. Department of Energy. Research at Lawrence Livermore National Laboratory was performed under Contract DE-AC52-07NA27344.
    03/2008;

Publication Stats

684 Citations
125.74 Total Impact Points

Institutions

  • 2000–2012
    • Lawrence Livermore National Laboratory
      • Condensed Matter and Materials Division
      Livermore, CA, United States
  • 2008–2010
    • Oak Ridge National Laboratory
      • Materials Science and Technology Division
      Oak Ridge, FL, United States
  • 2000–2001
    • University of Cambridge
      • Department of Physics: Cavendish Laboratory
      Cambridge, England, United Kingdom
  • 1997–1998
    • Georgia Institute of Technology
      • School of Physics
      Atlanta, GA, United States