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Ospadov E, Rothstein SM, Baer R. Quantum Monte Carlo assessment of density functionals for π-electron molecules: ethylene and bifuran. Mol Phys 2018. [DOI: 10.1080/00268976.2018.1517905] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
Affiliation(s)
- Egor Ospadov
- Department of Chemistry, The University of Western Ontario, London, ON, Canada
| | | | - Roi Baer
- Fritz Haber Center for Molecular Dynamics and Institute of Chemistry, The Hebrew University of Jerusalem, Jerusalem 9190401, Israel
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Kim J, Baczewski AT, Beaudet TD, Benali A, Bennett MC, Berrill MA, Blunt NS, Borda EJL, Casula M, Ceperley DM, Chiesa S, Clark BK, Clay RC, Delaney KT, Dewing M, Esler KP, Hao H, Heinonen O, Kent PRC, Krogel JT, Kylänpää I, Li YW, Lopez MG, Luo Y, Malone FD, Martin RM, Mathuriya A, McMinis J, Melton CA, Mitas L, Morales MA, Neuscamman E, Parker WD, Pineda Flores SD, Romero NA, Rubenstein BM, Shea JAR, Shin H, Shulenburger L, Tillack AF, Townsend JP, Tubman NM, Van Der Goetz B, Vincent JE, Yang DC, Yang Y, Zhang S, Zhao L. QMCPACK: an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:195901. [PMID: 29582782 DOI: 10.1088/1361-648x/aab9c3] [Citation(s) in RCA: 74] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.
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Affiliation(s)
- Jeongnim Kim
- Intel Corporation, Hillsboro, OR 987124, United States of America
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Vrbik J, Ospadov E, Rothstein SM. Note: A pure-sampling quantum Monte Carlo algorithm with independent Metropolis. J Chem Phys 2016; 145:026101. [PMID: 27421426 DOI: 10.1063/1.4958340] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Recently, Ospadov and Rothstein published a pure-sampling quantum Monte Carlo algorithm (PSQMC) that features an auxiliary Path Z that connects the midpoints of the current and proposed Paths X and Y, respectively. When sufficiently long, Path Z provides statistical independence of Paths X and Y. Under those conditions, the Metropolis decision used in PSQMC is done without any approximation, i.e., not requiring microscopic reversibility and without having to introduce any G(x → x'; τ) factors into its decision function. This is a unique feature that contrasts with all competing reptation algorithms in the literature. An example illustrates that dependence of Paths X and Y has adverse consequences for pure sampling.
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Affiliation(s)
- Jan Vrbik
- Department of Mathematics, Brock University, St. Catharines, Ontario L2S 3A1, Canada
| | - Egor Ospadov
- Department of Physics, Brock University, St. Catharines, Ontario L2S 3A1, Canada
| | - Stuart M Rothstein
- Department of Physics, Brock University, St. Catharines, Ontario L2S 3A1, Canada
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Holzmann M, Bernu B, Pierleoni C, McMinis J, Ceperley DM, Olevano V, Delle Site L. Momentum distribution of the homogeneous electron gas. PHYSICAL REVIEW LETTERS 2011; 107:110402. [PMID: 22026651 DOI: 10.1103/physrevlett.107.110402] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/18/2011] [Revised: 07/06/2011] [Indexed: 05/31/2023]
Abstract
We calculate the off-diagonal density matrix of the homogeneous electron gas at zero temperature using unbiased reptation Monte Carlo calculations for various densities and extrapolate the momentum distribution and the kinetic and potential energies to the thermodynamic limit. Our results on the renormalization factor allow us to validate approximate G0W0 calculations concerning quasiparticle properties over a broad density region (1≤r(s)≲10) and show that, near the Fermi surface, vertex corrections and self-consistency aspects almost cancel each other out.
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Affiliation(s)
- Markus Holzmann
- Université Grenoble 1/CNRS, LPMMC UMR 5493, Maison des Magistères, 38042 Grenoble, France
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Oblinsky DG, Yuen WK, Rothstein SM. Ground-state properties of the water molecule by reptation quantum Monte Carlo. ACTA ACUST UNITED AC 2010. [DOI: 10.1016/j.theochem.2010.08.040] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Carleo G, Becca F, Moroni S, Baroni S. Reptation quantum Monte Carlo algorithm for lattice Hamiltonians with a directed-update scheme. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:046710. [PMID: 21230415 DOI: 10.1103/physreve.82.046710] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2010] [Revised: 07/16/2010] [Indexed: 05/30/2023]
Abstract
We provide an extension to lattice systems of the reptation quantum Monte Carlo algorithm, originally devised for continuous Hamiltonians. For systems affected by the sign problem, a method to systematically improve upon the so-called fixed-node approximation is also proposed. The generality of the method, which also takes advantage of a canonical worm algorithm scheme to measure off-diagonal observables, makes it applicable to a vast variety of quantum systems and eases the study of their ground-state and excited-state properties. As a case study, we investigate the quantum dynamics of the one-dimensional Heisenberg model and we provide accurate estimates of the ground-state energy of the two-dimensional fermionic Hubbard model.
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Affiliation(s)
- Giuseppe Carleo
- Scuola Internazionale Superiore di Studi Avanzati and Democritos National Simulation Center, Istituto Officina dei Materiali del CNR, Via Bonomea 265, I-34136 Trieste, Italy
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Wu X, Hu X, Dai Y, Du C, Chu S, Hu L, Deng J, Feng Y. Quantum Monte Carlo calculated potential energy curve for the helium dimer. J Chem Phys 2010; 132:204304. [DOI: 10.1063/1.3432250] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Badinski A, Haynes PD, Trail JR, Needs RJ. Methods for calculating forces within quantum Monte Carlo simulations. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2010; 22:074202. [PMID: 21386380 DOI: 10.1088/0953-8984/22/7/074202] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/30/2023]
Abstract
Atomic force calculations within the variational and diffusion quantum Monte Carlo methods are described. The advantages of calculating diffusion quantum Monte Carlo forces with the 'pure' rather than the 'mixed' probability distribution are discussed. An accurate and practical method for calculating forces using the pure distribution is presented and tested for the SiH molecule. The statistics of force estimators are explored and violations of the central limit theorem are found in some cases.
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Affiliation(s)
- A Badinski
- Theory of Condensed Matter Group, Cavendish Laboratory, Cambridge CB3 0HE, UK
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Morales MA, Pierleoni C, Ceperley DM. Equation of state of metallic hydrogen from coupled electron-ion Monte Carlo simulations. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:021202. [PMID: 20365556 DOI: 10.1103/physreve.81.021202] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2009] [Revised: 01/19/2010] [Indexed: 05/29/2023]
Abstract
We present a study of hydrogen at pressures higher than molecular dissociation using the coupled electron-ion Monte Carlo method. These calculations use the accurate reptation quantum Monte Carlo method to estimate the electronic energy and pressure while doing a Monte Carlo simulation of the protons. In addition to presenting simulation results for the equation of state over a large region of the phase diagram, we report the free energy obtained by thermodynamic integration. We find very good agreement with density-functional theory based molecular-dynamics calculations for pressures beyond 600 GPa and densities above rho=1.4 g/cm(3) , both for thermodynamic and structural properties. This agreement provides a strong support to the different approximations employed in the density-functional treatment of the system, specifically the approximate exchange-correlation potential and the use of pseudopotentials for the range of densities considered. We find disagreement with chemical models, which suggests that a reinvestigation of planetary models--previously constructed using the Saumon-Chabrier-Van Horn equations of state--might be needed.
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Affiliation(s)
- Miguel A Morales
- Department of Physics, University of Illinois at Urbana-Champaign, Illinois 61801, USA.
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Lin F, Morales MA, Delaney KT, Pierleoni C, Martin RM, Ceperley DM. Electrical conductivity of high-pressure liquid hydrogen by quantum Monte Carlo methods. PHYSICAL REVIEW LETTERS 2009; 103:256401. [PMID: 20366267 DOI: 10.1103/physrevlett.103.256401] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/11/2009] [Indexed: 05/29/2023]
Abstract
We compute the electrical conductivity for liquid hydrogen at high pressure using Monte Carlo techniques. The method uses coupled electron-ion Monte Carlo simulations to generate configurations of liquid hydrogen. For each configuration, correlated sampling of electrons is performed in order to calculate a set of lowest many-body eigenstates and current-current correlation functions of the system, which are summed over in the many-body Kubo formula to give ac electrical conductivity. The extrapolated dc conductivity at 3000 K for several densities shows a liquid semiconductor to liquid-metal transition at high pressure. Our results are in good agreement with shock-wave data.
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Affiliation(s)
- Fei Lin
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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Badinski A, Needs RJ. Accurate forces in quantum Monte Carlo calculations with nonlocal pseudopotentials. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:036707. [PMID: 17930361 DOI: 10.1103/physreve.76.036707] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/27/2007] [Indexed: 05/25/2023]
Abstract
Calculating accurate forces within variational and diffusion Monte Carlo (VMC and DMC) methods is a very challenging problem. We derive expressions for the contribution to the Hellmann-Feynman force from nonlocal pseudopotentials for use within the VMC and DMC methods. Equilibrium bond lengths and harmonic vibrational frequencies are calculated from the Hellmann-Feynman forces and compared with those obtained from the energies at the Hartree-Fock, VMC, and pure DMC levels. Results for five small molecules show that the equilibrium bond lengths obtained from the force and energy calculations differ by less than 0.007 A at the DMC level.
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Affiliation(s)
- A Badinski
- Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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Wagner LK, Mitas L. Energetics and dipole moment of transition metal monoxides by quantum Monte Carlo. J Chem Phys 2007; 126:034105. [PMID: 17249863 DOI: 10.1063/1.2428294] [Citation(s) in RCA: 58] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The transition metal (TM) oxygen bond appears very prominently throughout chemistry and solid-state physics. Many materials, from biomolecules to ferroelectrics to the components of supernova remnants, contain this bond in some form. Many of these materials' properties depend strongly on fine details of the TM-O bond, which makes accurate calculations of their properties very challenging. Here the authors report on highly accurate first principles calculations of the properties of TM monoxide molecules within fixed-node diffusion Monte Carlo and reptation Monte Carlo.
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Affiliation(s)
- Lucas K Wagner
- Center for High Performance Simulation and Department of Physics, North Carolina State University, Raleigh, North Carolina 27695, USA
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Delaney KT, Pierleoni C, Ceperley DM. Quantum Monte Carlo simulation of the high-pressure molecular-atomic crossover in fluid hydrogen. PHYSICAL REVIEW LETTERS 2006; 97:235702. [PMID: 17280214 DOI: 10.1103/physrevlett.97.235702] [Citation(s) in RCA: 17] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/28/2006] [Indexed: 05/13/2023]
Abstract
A first-order liquid-liquid phase transition in high-pressure hydrogen between molecular and atomic fluid phases has been predicted in computer simulations using ab initio molecular dynamics approaches. However, experiments indicate that molecular dissociation may occur through a continuous crossover rather than a first-order transition. Here we study the nature of molecular dissociation in fluid hydrogen using an alternative simulation technique in which electronic correlation is computed within quantum Monte Carlo methods, the so-called coupled electron-ion Monte Carlo method. We find no evidence for a first-order liquid-liquid phase transition.
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Affiliation(s)
- Kris T Delaney
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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