Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces

Clay, Raymond C.; Holzmann, Markus; Ceperley, David M.; Morales, Miguel A.

doi:10.1103/physrevb.93.035121

Cited by 41 publications

(40 citation statements)

References 52 publications

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“…In our recent work, we have demonstrated that for studying the high‐pressure solid hydrogen phase diagram, the BLYP XC functional is more accurate than most other semi‐local XC functionals. Independent studies of others have confirmed the superior accuracy of the used BLYP XC functional for the description of thermodynamic properties of high‐pressure hydrogen . Geometry and cell optimizations were performed using the Broyden–Fletcher–Goldfarb–Shanno quasi‐Newton algorithm with a convergence thresholds on the total energy and forces of 0.01 mRy and 0.1 mRy/Bohr, respectively, to guarantee convergence of the total energy to better than 1 meV/proton and the pressure to better than 0.1 GPa/proton.…”

Section: Methodsmentioning

confidence: 99%

Nuclear quantum effects induce metallization of dense solid molecular hydrogen

2017

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We present an accurate computational study of the electronic structure and lattice dynamics of solid molecular hydrogen at high pressure. The band-gap energies of the C2/c, Pc, and P63/m structures at pressures of 250, 300, and 350 GPa are calculated using the diffusion quantum Monte Carlo (DMC) method. The atomic configurations are obtained from ab initio path-integral molecular dynamics (PIMD) simulations at 300 K and 300 GPa to investigate the impact of zero-point energy and temperature-induced motion of the protons including anharmonic effects. We find that finite temperature and nuclear quantum effects reduce the band-gaps substantially, leading to metallization of the C2/c and Pc phases via band overlap; the effect on the band-gap of the P63/m structure is less pronounced. Our combined DMC-PIMD simulations predict that there are no excitonic or quasiparticle energy gaps for the C2/c and Pc phases at 300 GPa and 300 K. Our results also indicate a strong correlation between the band-gap energy and vibron modes. This strong coupling induces a band-gap reduction of more than 2.46 eV in high-pressure solid molecular hydrogen. Comparing our DMC-PIMD with experimental results available, we conclude that none of the structures proposed is a good candidate for phases III and IV of solid hydrogen. © 2017 Wiley Periodicals, Inc.

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Section: Methodsmentioning

confidence: 99%

Nuclear quantum effects induce metallization of dense solid molecular hydrogen

2017

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“…For fixed nuclei positions, we have calculated the electronic energy using the QMCPACK [49,50] simulation package based on a single Slater-Jastrow wavefunction with single particle orbitals obtained from Quantum espresso [39] using the PBE functional (see Ref. [47,48] for further details).…”

Section: Hydrogen-helium Mixturesmentioning

confidence: 99%

Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids

et al. 2016

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Concentrating on zero temperature Quantum Monte Carlo calculations of electronic systems, we give a general description of the theory of finite size extrapolations of energies to the thermodynamic limit based on one and two-body correlation functions. We introduce new effective procedures, such as using the potential and wavefunction split-up into long and short range functions to simplify the method and we discuss how to treat backflow wavefunctions. Then we explicitly test the accuracy of our method to correct finite size errors on example hydrogen and helium many-body systems and show that the finite size bias can be drastically reduced for even small systems. PACS numbers:Quantum Monte Carlo (QMC) methods allow us to calculate the energy per particle E N of a finite system containing N particles, with N 10 3 for almost all simulations of electronic systems [1,2]. However, for extended systems, we are often interested in scaling to the thermodynamic limit, E ∞ ; this scaling is one of the major source of bias in Quantum Monte Carlo calculations of electronic structure. In practice, extrapolation is often performed numerically by assuming simple functional forms for E N as a function of 1/N , often inspired by results of approximate theories, such as KohnSham DFT [3][4][5] or from the behavior of approximate many-body calculations, e.g. from RPA calculations [6]. These heuristic extrapolations can be dangerous and introduce a possible systematic bias, as the exact ground state energy, as well as other properties, are in general not a simple analytic function of 1/N . In fact, the scaling function will depend on the electronic state, for example, it will be different in a metal and an insulator, and can depend on the form of the trial wave function underlying the QMC calculation. In addition, within variational approaches, the amount that the variational energy is above the exact energy may depend on the system size because of the values of the variational parameters. This introduces a further source of error in a purely numerical extrapolation. Projection methods can reduce this bias, since they are closer to the true ground state energy, but in practice it can be a difficult problem to ensure a uniform convergence concerning projection time or population size with respect to the system size [7].In this paper we present a general theory for understanding the finite size bias of QMC calculations. Although we concentrate on electronic systems where finite size effects represent one of the major limitations, our approach applies equally well to other quantum systems with different interactions and dimensionality, including bosonic ones. As we will show, the leading order size effects can be understood by looking at the analytical structure of the trial wavefunction [8,9] which is -at least partially -determined by singularities of the Hamiltonian and/or the boundary conditions [10][11][12]. Different types of wavefunction will, in general, have different types of size effects. In particular, we show that backflow...

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“…In DFT simulations, however, a bottleneck is the exchange-correlation (XC) functional for which a variety of options exist, the accuracy of which is often poorly known, what limits the predictive power of the method. This requires tests against independent methods such as quantum Monte Carlo simulations for the electron component [4] or against electronion quantum Monte Carlo [70][71][72]. Also, the use of finite-temperature functionals was shown to be important [73,74] when the XC-contribution is comparable to the thermal energy, see Ref.…”

Section: Introductionmentioning

confidence: 99%

Ab initio simulation of warm dense matter

et al. 2020

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Warm dense matter (WDM) -an exotic state of highly compressed matter -has attracted high interest in recent years in astrophysics and for dense laboratory systems. At the same time, this state is extremely difficult to treat theoretically. This is due to the simultaneous appearance of quantum degeneracy, Coulomb correlations and thermal effects, as well as the overlap of plasma and condensed phases. Recent breakthroughs are due to the successful application of density functional theory (DFT) methods which, however, often lack the necessary accuracy and predictive capability for WDM applications. The situation has changed with the availability of the first ab initio data for the exchange-correlation free energy of the warm dense uniform electron gas (UEG) that were obtained by quantum Monte Carlo (QMC) simulations, for recent reviews, see Dornheim et al., Phys. Plasmas 24, 056303 (2017) and Phys. Rep. 744, 1-86 (2018). In the present article we review recent further progress in QMC simulations of the warm dense UEG: namely, ab initio results for the static local field correction G(q) and for the dynamic structure factor S(q, ω). These data are of key relevance for the comparison with x-ray scattering experiments at free electron laser facilities and for the improvement of theoretical models.In the second part of this paper we discuss simulations of WDM out of equilibrium. The theoretical approaches include Born-Oppenheimer molecular dynamics, quantum kinetic theory, timedependent DFT and hydrodynamics. Here we analyze strengths and limitations of these methods and argue that progress in WDM simulations will require a suitable combination of all methods. A particular role might be played by quantum hydrodynamics, and we concentrate on problems, recent progress, and possible improvements of this method.

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Benchmarking density functionals for hydrogen-helium mixtures with quantum Monte Carlo: Energetics, pressures, and forces

Cited by 41 publications

References 52 publications

Nuclear quantum effects induce metallization of dense solid molecular hydrogen

Nuclear quantum effects induce metallization of dense solid molecular hydrogen

Theory of finite size effects for electronic quantum Monte Carlo calculations of liquids and solids

Ab initio simulation of warm dense matter

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