Publications (54)133.04 Total impact
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ABSTRACT: Recent smallcell (< 150atom) quantum molecular dynamics (QMD) simulations for Ta based on density functional theory (DFT) have predicted a hexagonal omega (hexomega) 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 highpolymorphism in Ta with complementary DFTbased model generalized pseudopotential theory (MGPT) multiion interatomic potentials, which allow accurate treatment of much larger system sizes (up to ~ 80000 atoms). We focus on candidate bcc, A15, fcc, hcp, and hexomega phases for the highphase 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 MGPTMD simulations demonstrate that the higherenergy fcc, hcp and hexomega structures are only mechanically stabilized at high temperature by large, sizedependent, anharmonic vibrational effects, with the stability of the hexomega phase also being found to be a sensitive function of its ratio. Both twophase and Zmethod melting techniques have been used in MGPTMD simulations to determine relative phase stability and its size dependence. In the largecell limit, the twophase 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 twophase 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 largecell limit. For the bcc and hexomega structures, however, this is a close upper bound within 5% of the twophase results, although for the A15, fcc, and hcp structures, the Zmelt curves are 2535% higher in temperature than the twophase 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 hexomega 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 MGPTMD bcc and hexomega melt curves are in good agreement with the QMD results, so the QMD prediction is confirmed in the smallcell limit. But in the largecell limit, the MGPTMD hexomega 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 nonbcc Ta phases studied, one requires simulation cells of at least 250500 atoms to be free of size effects impacting mechanical and thermodynamic phase stability.  [Show abstract] [Hide abstract]
ABSTRACT: The manybody diffusion quantum Monte Carlo (DMC) method with twistaveraged boundary conditions is used to calculate the groundstate 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. DMCcalculated defect formation and migration energies agree with available experimental data, except for the nearestneighbor 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. Selfinterstitial 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.  [Show abstract] [Hide abstract]
ABSTRACT: Difficulties can arise in simulating various Hamiltonian operators efficiently in diffusion Monte Carlo (DMC) such as those associated with nonlocal pseudopotentials which require the introduction of an approximate form. The locality approximation and Tmoves are two widely used techniques in fixednode diffusion Monte Carlo (FNDMC) that provide a tractable approach for treating nonlocal pseudopotentials, however their use introduces an uncontrolled approximation. Exact treatment of the nonlocal pseudopotentials in FNDMC 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 nonlocal operators introduce into the Green's function. We then consider the feasibility of running DMC simulations in which the nonlocal pseudopotentials are treated exactly and demonstrate the algorithm on a few molecular systems.  [Show abstract] [Hide abstract]
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 abinitio approaches only valence electrons are taken into account and a pseudopotential is used to mimic the response of the core electrons. Typically an allelectron 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 allelectron manybody 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.  [Show abstract] [Hide abstract]
ABSTRACT: In narrow dband transition metals, electron temperature T(el) can impact the underlying electronic structure for temperatures near and above melt, strongly coupling the ion and electronthermal degrees of freedom and producing T(el)dependent interatomic forces. Starting from the Mermin formulation of density functional theory, we have extended firstprinciples 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 highpressure 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.  [Show abstract] [Hide abstract]
ABSTRACT: We perform releasenode quantum Monte Carlo simulations on the first row diatomic molecules in order to assess how accurately their groundstate energies can be obtained. An analysis of the fermionboson energy difference is shown to be strongly dependent on the nuclear charge, Z, which in turn determines the growth of variance of the releasenode energy. It is possible to use maximum entropy analysis to extrapolate to groundstate 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 groundstate energy of Li(2) (14.9947(1)), Be(2) (29.3367(7)), and B(2)(49.410(2)).  [Show abstract] [Hide abstract]
ABSTRACT: ReleaseNode quantum Monte Carlo (RNQMC) is a method that calculates unbiased groundstate energies of fermionic systems. However, while RNQMC 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 groundstate energy. Direct application of MaxEnt to higher Z elements is, however, not entirely straightforward. We propose strategies for optimizing MaxEnt analysis of short time RNQMC 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.  [Show abstract] [Hide abstract]
ABSTRACT: We use firstprinciples fixednode 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 millielectronvolts 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.  [Show abstract] [Hide abstract]
ABSTRACT: The selfhealing 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 groundstate 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 linearscaling method, in the degrees of freedom of the nodes, that systematically reduces the fermion sign problem.  [Show abstract] [Hide abstract]
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 fixednode 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 freeelectron gas and a handful of other fewelectron 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 DEAC5207NA27344  [Show abstract] [Hide abstract]
ABSTRACT: We develop a formalism and present an algorithm for optimization of the trial wave function used in fixednode diffusion quantum Monte Carlo (DMC) methods. The formalism is based on the DMC mixed estimator of the groundstate 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 fixednode groundstate wave function and (ii) to define a cost function that relates the fixednode groundstate and the noninteracting trial wave functions. We show that (a) locally smoothing out the kink of the fixednode groundstate wave function at the node generates a new trial wave function with better nodal structure and (b) we argue that the noise in the fixednode wave function resulting from finite sampling plays a beneficial role, allowing the nodes to adjust toward the ones of the exact manybody ground state in a simulated annealinglike 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 wavefunction forms such as pfaffians. We test the method in a model system where benchmark configurationinteraction 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 densityfunctionallike 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 KohnSham effective potential from the DMC data.  [Show abstract] [Hide abstract]
ABSTRACT: Transition metal sites in metalorganic frameworks and in doped carbon structures are actively being studied for their binding properties of molecular hydrogen. We present a study of prototypical metalorganic structures that can be used to bind molecular hydrogen noncovalently. Due to the well known limitations of current density functional theory based descriptions of noncovalent hydrogen bonding we have focused our efforts on a consistent manybody approach based on the fixednode 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 DEAC5207NA27344  [Show abstract] [Hide abstract]
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 wavefunction is altered to obtain an improved trial wavefunction 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 wavefunction is systematically improved. The scalar product of the trial wavefunction with the CI result converges to 1 even starting from wavefunctions 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 noninteracting nodal potential of densityfunctionallike form. An extension to a model system with full Coulomb interactions demonstrates that we can obtain the exact KohnSham 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 wavefunctions. Results for other molecular systems and comparison with alternative methods will be presented.  [Show abstract] [Hide abstract]
ABSTRACT: We develop a formalism and present an algorithm for optimization of the trial wavefunction used in fixednode 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) projectout a multideterminant expansion of the fixednode groundstate wave function and (ii) to define a cost function that relates the fixednode groundstate and the noninteracting trial wave functions. We show that (a) locally smoothing out the kink of the fixednode groundstate wave function at the node generates a new trial wavefunction with better nodal structure and (b) we argue that the noise in the fixednode wavefunction resulting from finite sampling plays a beneficial role, allowing the nodes to adjust towards the ones of the exact manybody ground state in a simulated annealinglike process. We propose a method to improve both single determinant and multideterminant expansions of the trial wavefunction. 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 wavefunction is systematically improved. The overlap of the optimized trial wave function and the exact ground state converges to 100% even starting from wavefunctions orthogonal to the exact ground state. In the optimization process we find an optimal noninteracting nodal potential of densityfunctionallike form whose existence was predicted earlier[Phys.Rev. B {\bf 77}, 245110 (2008)]. We obtain the exact KohnSham effective potential from the DMC data. 
Article: Neutral and charged excitations in carbon fullerenes from firstprinciples manybody theories
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ABSTRACT: We investigate the accuracy of firstprinciples manybody theories at the nanoscale by comparing the lowenergy 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 GWBetheSalpeter 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 manybody theories as viable alternative to densityfunctional 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 electrondonor cations.  [Show abstract] [Hide abstract]
ABSTRACT: Constantvolume 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 αU, bodycenteredcubic (bcc), and liquid phases, using an ab initio planewave pseudopotential method within the generalized gradient approximation of densityfunctional theory. A robust U pseudopotential has been constructed for these simulations that treats the 14 valence and outercore electrons per atom necessary to calculate accurate structural and thermodynamic properties up to 100 GPa. Its validity has been checked by comparing lowtemperature results with experimental data and allelectron fullpotential linearmuffintinorbital 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, bondangle distribution function, electronic density of states, and liquid diffusion coefficient, as well as evidence for shortrange order in the liquid.  [Show abstract] [Hide abstract]
ABSTRACT: Firstprinciples generalized pseudopotential theory (GPT) provides a fundamental basis for bridging the quantumatomistic gap from densityfunctional quantum mechanics to large scale atomistic simulation in metals and alloys. In directionallybonded 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 highpressure 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 felectron actinide metals, and high computational speed. A further advance in progress is the development temperaturedependent MGPT potentials that subsume electronthermal contributions to hightemperature properties. 
Article: BetheSalpeter and Quantum Monte Carlo Calculations of the Optical Properties of Carbon Fullerenes
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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 GWBetheSalpeter Equation (GWBSE) and diffusion Quantum Monte Carlo (QMC) methods. We compare these approaches with time dependent density functional results and with experiment. GWBSE 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. GWBSE 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 DEAC5207NA27344.  [Show abstract] [Hide abstract]
ABSTRACT: Fixednode quantum MonteCarlo (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 fixednode QMC ansatz. In particular, the efficacy / necessity of backflow corrections and multideterminant expansions as a method for optimizing the nodal surface in these systems will be discussed.  [Show abstract] [Hide abstract]
ABSTRACT: HighZ metals constitute a particular challenge for largescale ab initio electronicstructure calculations, as they require high resolution due to the presence of strongly localized states and require many eigenstates to be computed due to the large number of electrons and need to accurately resolve the Fermi surface. Here, we report recent findings on highZ metals, using an efficient massively parallel planewave implementation on some of the largest computational architectures currently available. We discuss the particular architectures employed and methodological advances required to harness them effectively. We present a paircorrelation function for U, calculated using quantum molecular dynamics, and discuss relaxations of Pu atoms in the vicinity of defects in aged and alloyed Pu. We find that the selfirradiation associated with aging has a negligible effect on the compressibility of Pu relative to other factors such as alloying.
Publication Stats
1k  Citations  
133.04  Total Impact Points  
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Institutions

19992012

Lawrence Livermore National Laboratory
 • Condensed Matter and Materials Division
 • Physics Division
Livermore, California, United States


20002001

University of Cambridge
 Department of Physics: Cavendish Laboratory
Cambridge, England, United Kingdom


19971998

Georgia Institute of Technology
 School of Physics
Atlanta, GA, United States
