Skip to main content

David Ceperley

Followers

36

Following

11

Co-authors

10

Public Views

University of Edinburgh

Vincent Hiribarren

King's College London

Armando Marques-Guedes

UNL - New University of Lisbon

Centre National de la Recherche Scientifique / French National Centre for Scientific Research

SOAS University of London

Bar-Ilan University

Eugénio Costa Almeida

ISCTE - University Institute of Lisbon (ISCTE-IUL)

Sciences Po Bordeaux

Centre National de la Recherche Scientifique / French National Centre for Scientific Research

University of California, San Francisco

Interests

Uploads

Papers by David Ceperley

Molecular-Atomic Transition along the Deuterium Hugoniot Curve with Coupled Electron-Ion Monte Carlo Simulations

Physical review letters, Jan 24, 2015

We have performed simulations of the principal deuterium Hugoniot curve using coupled electron-io... more We have performed simulations of the principal deuterium Hugoniot curve using coupled electron-ion Monte Carlo calculations. Using highly accurate quantum Monte Carlo methods for the electrons, we study the region of maximum compression along the Hugoniot, where the system undergoes a continuous transition from a molecular fluid to a monatomic fluid. We include all relevant physical corrections so that a direct comparison to experiment can be made. Around 50 GPa we find a maximum compression of 4.85. This compression is approximately 5.5% higher than previous theoretical predictions and 15% higher than the most accurate experimental data. Thus first-principles simulations encompassing the most advanced techniques are in disagreement with the results of the best experiments.

SPRNG: A SCALABLE LIBRARY FOR PSEUDORANDOM NUMBER GENERATION

Recent Advances in Numerical Methods and Applications II, 1999

In this article we outline some methods for parallel pseudorandom number generation. We will focu... more In this article we outline some methods for parallel pseudorandom number generation. We will focus on methods based on parameterization, meaning that we will not consider splitting methods. We describe parameterized versions of the following pseudorandom number generators: (i) linear congruential generators, (ii) shift-register generators, and (iii) lagged-Fibonacci generators. We brie y describe the methods, detail some advantages and disadvantages of each method and recount results from number theory that impact our understanding of their quality i n parallel applications. Finally, w e present a short description of a scalable library for pseudorandom number generation, called SPRNG. The description contained within this document i s m e a n t only to outline the rationale behind and the capabilities of SPRNG. Much more information, including examples and detailed documentation aimed at helping users with putting and using SPRNG on scalable systems is available at the URL: http://www.ncsa.uiuc.edu/Apps/SPRNG.

Competing Nuclear Quantum Effects and van der Waals Interactions in Water

Water plays a central role in many scientific disciplines, and a number of studies have been perf... more Water plays a central role in many scientific disciplines, and a number of studies have been performed to understand its properties. However, providing an accurate ab initio description is a significant challenge, and because of this, many of water's properties remain elusive. In particular, the description of hydrogen bonding and the importance of van der Waals (vdW) interactions and nuclear quantum effects are still matters of debate. Recent computational advancements have been made that allow for the accurate and efficient modeling of such effects. We present results from path integral molecular dynamics simulations based on density functional theory employing exchange and correlation functionals capable of accounting for vdW interactions (so-called vdW-DF, vdW-DF2, and optB88-vdW). We demonstrate that, contrary to expectation, the interaction between nuclear quantum effects and vdW interactions hardens the structure of water. These results suggest that ad hoc methods to acco...

Computational methods in Coupled Electron-Ion Monte Carlo

In the last few years we have been developing a Monte Carlo simulation method to cope with system... more In the last few years we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer (BO) approximation, the Coupled Electron-Ion Monte Carlo Method (CEIMC). Electronic properties in CEIMC are computed by Quantum Monte Carlo (QMC) rather than by Density Functional Theory (DFT) based techniques. CEIMC can, in principle, overcome

The Coupled Electron-Ion Monte Carlo Method

Lecture Notes in Physics, 2006

Equation of state of the hydrogen plasma by path integral Monte Carlo simulation

by David Ceperley and B. Bernu

Physical review letters, Jan 17, 1994

The equation of state of the hydrogen plasma is calculated by the restricted path integral Monte ... more

Ground state of two-dimensional Yukawa bosons: Applications to vortex melting

Physical review. B, Condensed matter, 1993

... ically re-peated two-dimensional box with an aspect ratio chosen to perfectly accommodate a t... more

Ab Initio Quantum Simulations of Liquid Water

Some recent efforts at simulating liquid water have employed ``ab initio'' molecular dyna... more Some recent efforts at simulating liquid water have employed ``ab initio'' molecular dynamics (AIMD) methods with forces from a version of density functional theory (DFT) and, in some cases, imaginary-time path integrals (PI) to study quantum effects of the protons. Although AIMD methods have met with many successes, errors introduced by the approximations and choices of simulation parameters are not

Backflow correlations for the electron gas and metallic hydrogen

Physical Review E, 2003

We justify and evaluate backflow-threebody wavefunctions for a two component system of electrons ... more We justify and evaluate backflow-threebody wavefunctions for a two component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use and the analytical form of the backflow function from different points of view. The resulting wavefunctions are used in Variational and Diffusion Monte Carlo calculations of the electron gas and of solid and liquid metallic hydrogen. For the electron gas, the purely analytic backflow and three-body form gives lower energies than those of previous calculations. For bcc hydrogen, analytical and optimized backflow-threebody wavefunctions lead to energies nearly as low as those from using LDA orbitals in the trial wavefunction. However, compared to wavefunctions constructed from density functional solutions, backflow wavefunctions have the advantage of only few parameters to estimate, the ability to include easily and accurately electron-electron correlations, and that they can be directly generalized from the crystal to a disordered liquid of protons.

Proof for an upper bound in fixed-node Monte Carlo for lattice fermions

Physical Review B, 1995

We justify a recently proposed prescription for performing Green Function Monte Carlo calculation... more We justify a recently proposed prescription for performing Green Function Monte Carlo calculations on systems of lattice fermions, by which one is able to avoid the sign problem. We generalize the prescription such that it can also be used for problems with hopping terms of different signs. We prove that the effective Hamiltonian, used in this method, leads to an upper bound for the ground-state energy of the real Hamiltonian, and we illustrate the effectiveness of the method on small systems.

Phase separation in hydrogen-helium mixtures at Mbar pressures

Proceedings of the National Academy of Sciences of the United States of America, Jan 3, 2009

The properties of hydrogen-helium mixtures at Mbar pressures and intermediate temperatures (4000 ... more The properties of hydrogen-helium mixtures at Mbar pressures and intermediate temperatures (4000 to 10000 K) are calculated with first-principles molecular dynamics simulations. We determine the equation of state as a function of density, temperature, and composition and, using thermodynamic integration, we estimate the Gibbs free energy of mixing, thereby determining the temperature, at a given pressure, when helium becomes insoluble in dense metallic hydrogen. These results are directly relevant to models of the interior structure and evolution of Jovian planets. We find that the temperatures for the demixing of helium and hydrogen are sufficiently high to cross the planetary adiabat of Saturn at pressures approximately 5 Mbar; helium is partially miscible throughout a significant portion of the interior of Saturn, and to a lesser extent in Jupiter.

Wave Function Optimization in QMCPACK

Wave function optimization is essential for both the accuracy and efficiency of diffusion, reptat... more Wave function optimization is essential for both the accuracy and efficiency of diffusion, reptation, and variational quantum Monte Carlo (QMC). In this talk we outline the wave function optimization strategy used in the QMC software package QMCPACK developed at the University of Illinois. We use an extension of the linear optimization method originally developed by Umrigar et. al.[1] to optimize

Finite-Size Error in Many-Body Simulations with Long-Range Interactions

Physical Review Letters, 2006

We discuss the origin of the finite size error of the energy in many-body simulation of systems o... more We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from contributions mainly determined by the organized collective oscillations of the interacting system. Finite size corrections, both on kinetic and potential energy, can be calculated within a single simulation. Results are presented for the electron gas and silicon.

The Coupled Electronic-Ionic Monte Carlo Simulation Method

Lecture Notes in Physics, 2002

Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion Monte Carlo or Path ... more Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion Monte Carlo or Path Integral Monte Carlo are the most accurate and general methods for computing total electronic energies. We will review methods we have developed to perform QMC for the electrons coupled to another MC simulation for the ions. In this method, one estimates the Born-Oppenheimer energy E(Z) where Z represents the ionic degrees of freedom. That estimate of the energy is used in a Metropolis simulation of the ionic degrees of freedom. Important aspects of this method are how to deal with the noise, which QMC method and which trial function to use, how to deal with generalized boundary conditions on the wave function so as to reduce the finite size effects. We discuss some advantages of the CEIMC method concerning how the quantum effects of the ionic degrees of freedom can be included and how the boundary conditions can be integrated over. Using these methods, we have performed simulations of liquid H2 and metallic H on a parallel computer.

Accurate, efficient and simple forces with Quantum Monte Carlo methods

Physical Review Letters, 2004

Computation of ionic forces using quantum Monte Carlo methods has long been a challenge. We intro... more Computation of ionic forces using quantum Monte Carlo methods has long been a challenge. We introduce a simple procedure, based on known properties of physical electronic densities, to make the variance of the Hellmann-Feynman estimator finite. We obtain very accurate geometries for the molecules H$_2$, LiH, CH$_4$, NH$_3$, H$_2$O and HF, with a Slater-Jastrow trial wave function. Harmonic frequencies for

Path-integral Monte Carlo simulation of helium at negative pressures

Physical Review B, 2000

Path integral Monte Carlo (PIMC) simulations of liquid helium at negative pressure have been carr... more Path integral Monte Carlo (PIMC) simulations of liquid helium at negative pressure have been carried out for a temperature range from the critical temperature to below the superfluid transition. We have calculated the temperature dependence of the spinodal line as well as the pressure dependence of the isothermal sound velocity in the region of the spinodal. We discuss the slope of the superfluid transition line and the shape of the dispersion curve at negative pressures.

Vortices and Impurities in Large ^4He Droplets

Large (1000 atoms) superfluid ^4He droplets, doped with linear chains of HCN molecules, were simu... more Large (1000 atoms) superfluid ^4He droplets, doped with linear chains of HCN molecules, were simulated at T=0.38 K using Path Integral Monte Carlo. The effect of the linear impurities on the density distribution, moment of inertia, superfluid density, and shape deformations of the droplets was calculated. We find that the energy of forming a vortex is reduced by approximately a third when a chain of at least five HCN molecules is added to the droplet. Droplets doped with cyclic isomers of HCN molecules were also investigated. The effects of impurities on the excitation spectrum and vortex stability will be discussed.

Accurate Theoretical Predictions of the Properties of Energetic Materials MURI Publications

Stochastic calculation of interaction energies

The Journal of Physical Chemistry, 1982

A Monte Carlo method by which the properties of a collection of interacting nuclei and electrons ... more A Monte Carlo method by which the properties of a collection of interacting nuclei and electrons might be accurately calculated is briefly outlined. This method allows quantitative determination of the pairwise intermolecular potential and potential surfaces but eliminates the use of these constructs for dense systems. Preliminary results on the electron gas, hydrogen solid, and the molecules Heâ, LiH, Liâ, and HâO are at least as accurate as the best previous work.

Modeling Positron-Electron Correlations in Solids

Materials Science Forum - MATER SCI FORUM, 1997

Molecular-Atomic Transition along the Deuterium Hugoniot Curve with Coupled Electron-Ion Monte Carlo Simulations

Physical review letters, Jan 24, 2015

We have performed simulations of the principal deuterium Hugoniot curve using coupled electron-io... more We have performed simulations of the principal deuterium Hugoniot curve using coupled electron-ion Monte Carlo calculations. Using highly accurate quantum Monte Carlo methods for the electrons, we study the region of maximum compression along the Hugoniot, where the system undergoes a continuous transition from a molecular fluid to a monatomic fluid. We include all relevant physical corrections so that a direct comparison to experiment can be made. Around 50 GPa we find a maximum compression of 4.85. This compression is approximately 5.5% higher than previous theoretical predictions and 15% higher than the most accurate experimental data. Thus first-principles simulations encompassing the most advanced techniques are in disagreement with the results of the best experiments.

SPRNG: A SCALABLE LIBRARY FOR PSEUDORANDOM NUMBER GENERATION

Recent Advances in Numerical Methods and Applications II, 1999

In this article we outline some methods for parallel pseudorandom number generation. We will focu... more In this article we outline some methods for parallel pseudorandom number generation. We will focus on methods based on parameterization, meaning that we will not consider splitting methods. We describe parameterized versions of the following pseudorandom number generators: (i) linear congruential generators, (ii) shift-register generators, and (iii) lagged-Fibonacci generators. We brie y describe the methods, detail some advantages and disadvantages of each method and recount results from number theory that impact our understanding of their quality i n parallel applications. Finally, w e present a short description of a scalable library for pseudorandom number generation, called SPRNG. The description contained within this document i s m e a n t only to outline the rationale behind and the capabilities of SPRNG. Much more information, including examples and detailed documentation aimed at helping users with putting and using SPRNG on scalable systems is available at the URL: http://www.ncsa.uiuc.edu/Apps/SPRNG.

Competing Nuclear Quantum Effects and van der Waals Interactions in Water

Water plays a central role in many scientific disciplines, and a number of studies have been perf... more Water plays a central role in many scientific disciplines, and a number of studies have been performed to understand its properties. However, providing an accurate ab initio description is a significant challenge, and because of this, many of water's properties remain elusive. In particular, the description of hydrogen bonding and the importance of van der Waals (vdW) interactions and nuclear quantum effects are still matters of debate. Recent computational advancements have been made that allow for the accurate and efficient modeling of such effects. We present results from path integral molecular dynamics simulations based on density functional theory employing exchange and correlation functionals capable of accounting for vdW interactions (so-called vdW-DF, vdW-DF2, and optB88-vdW). We demonstrate that, contrary to expectation, the interaction between nuclear quantum effects and vdW interactions hardens the structure of water. These results suggest that ad hoc methods to acco...

Computational methods in Coupled Electron-Ion Monte Carlo

In the last few years we have been developing a Monte Carlo simulation method to cope with system... more In the last few years we have been developing a Monte Carlo simulation method to cope with systems of many electrons and ions in the Born-Oppenheimer (BO) approximation, the Coupled Electron-Ion Monte Carlo Method (CEIMC). Electronic properties in CEIMC are computed by Quantum Monte Carlo (QMC) rather than by Density Functional Theory (DFT) based techniques. CEIMC can, in principle, overcome

The Coupled Electron-Ion Monte Carlo Method

Lecture Notes in Physics, 2006

Equation of state of the hydrogen plasma by path integral Monte Carlo simulation

by David Ceperley and B. Bernu

Physical review letters, Jan 17, 1994

The equation of state of the hydrogen plasma is calculated by the restricted path integral Monte ... more

Ground state of two-dimensional Yukawa bosons: Applications to vortex melting

Physical review. B, Condensed matter, 1993

... ically re-peated two-dimensional box with an aspect ratio chosen to perfectly accommodate a t... more

Ab Initio Quantum Simulations of Liquid Water

Some recent efforts at simulating liquid water have employed ``ab initio'' molecular dyna... more Some recent efforts at simulating liquid water have employed ``ab initio'' molecular dynamics (AIMD) methods with forces from a version of density functional theory (DFT) and, in some cases, imaginary-time path integrals (PI) to study quantum effects of the protons. Although AIMD methods have met with many successes, errors introduced by the approximations and choices of simulation parameters are not

Backflow correlations for the electron gas and metallic hydrogen

Physical Review E, 2003

We justify and evaluate backflow-threebody wavefunctions for a two component system of electrons ... more We justify and evaluate backflow-threebody wavefunctions for a two component system of electrons and protons. Based on the generalized Feynman-Kacs formula, many-body perturbation theory, and band structure calculations, we analyze the use and the analytical form of the backflow function from different points of view. The resulting wavefunctions are used in Variational and Diffusion Monte Carlo calculations of the electron gas and of solid and liquid metallic hydrogen. For the electron gas, the purely analytic backflow and three-body form gives lower energies than those of previous calculations. For bcc hydrogen, analytical and optimized backflow-threebody wavefunctions lead to energies nearly as low as those from using LDA orbitals in the trial wavefunction. However, compared to wavefunctions constructed from density functional solutions, backflow wavefunctions have the advantage of only few parameters to estimate, the ability to include easily and accurately electron-electron correlations, and that they can be directly generalized from the crystal to a disordered liquid of protons.

Proof for an upper bound in fixed-node Monte Carlo for lattice fermions

Physical Review B, 1995

We justify a recently proposed prescription for performing Green Function Monte Carlo calculation... more We justify a recently proposed prescription for performing Green Function Monte Carlo calculations on systems of lattice fermions, by which one is able to avoid the sign problem. We generalize the prescription such that it can also be used for problems with hopping terms of different signs. We prove that the effective Hamiltonian, used in this method, leads to an upper bound for the ground-state energy of the real Hamiltonian, and we illustrate the effectiveness of the method on small systems.

Phase separation in hydrogen-helium mixtures at Mbar pressures

Proceedings of the National Academy of Sciences of the United States of America, Jan 3, 2009

The properties of hydrogen-helium mixtures at Mbar pressures and intermediate temperatures (4000 ... more The properties of hydrogen-helium mixtures at Mbar pressures and intermediate temperatures (4000 to 10000 K) are calculated with first-principles molecular dynamics simulations. We determine the equation of state as a function of density, temperature, and composition and, using thermodynamic integration, we estimate the Gibbs free energy of mixing, thereby determining the temperature, at a given pressure, when helium becomes insoluble in dense metallic hydrogen. These results are directly relevant to models of the interior structure and evolution of Jovian planets. We find that the temperatures for the demixing of helium and hydrogen are sufficiently high to cross the planetary adiabat of Saturn at pressures approximately 5 Mbar; helium is partially miscible throughout a significant portion of the interior of Saturn, and to a lesser extent in Jupiter.

Wave Function Optimization in QMCPACK

Wave function optimization is essential for both the accuracy and efficiency of diffusion, reptat... more Wave function optimization is essential for both the accuracy and efficiency of diffusion, reptation, and variational quantum Monte Carlo (QMC). In this talk we outline the wave function optimization strategy used in the QMC software package QMCPACK developed at the University of Illinois. We use an extension of the linear optimization method originally developed by Umrigar et. al.[1] to optimize

Finite-Size Error in Many-Body Simulations with Long-Range Interactions

Physical Review Letters, 2006

We discuss the origin of the finite size error of the energy in many-body simulation of systems o... more We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from contributions mainly determined by the organized collective oscillations of the interacting system. Finite size corrections, both on kinetic and potential energy, can be calculated within a single simulation. Results are presented for the electron gas and silicon.

The Coupled Electronic-Ionic Monte Carlo Simulation Method

Lecture Notes in Physics, 2002

Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion Monte Carlo or Path ... more Quantum Monte Carlo (QMC) methods such as Variational Monte Carlo, Diffusion Monte Carlo or Path Integral Monte Carlo are the most accurate and general methods for computing total electronic energies. We will review methods we have developed to perform QMC for the electrons coupled to another MC simulation for the ions. In this method, one estimates the Born-Oppenheimer energy E(Z) where Z represents the ionic degrees of freedom. That estimate of the energy is used in a Metropolis simulation of the ionic degrees of freedom. Important aspects of this method are how to deal with the noise, which QMC method and which trial function to use, how to deal with generalized boundary conditions on the wave function so as to reduce the finite size effects. We discuss some advantages of the CEIMC method concerning how the quantum effects of the ionic degrees of freedom can be included and how the boundary conditions can be integrated over. Using these methods, we have performed simulations of liquid H2 and metallic H on a parallel computer.

Accurate, efficient and simple forces with Quantum Monte Carlo methods

Physical Review Letters, 2004

Computation of ionic forces using quantum Monte Carlo methods has long been a challenge. We intro... more Computation of ionic forces using quantum Monte Carlo methods has long been a challenge. We introduce a simple procedure, based on known properties of physical electronic densities, to make the variance of the Hellmann-Feynman estimator finite. We obtain very accurate geometries for the molecules H$_2$, LiH, CH$_4$, NH$_3$, H$_2$O and HF, with a Slater-Jastrow trial wave function. Harmonic frequencies for

Path-integral Monte Carlo simulation of helium at negative pressures

Physical Review B, 2000

Path integral Monte Carlo (PIMC) simulations of liquid helium at negative pressure have been carr... more Path integral Monte Carlo (PIMC) simulations of liquid helium at negative pressure have been carried out for a temperature range from the critical temperature to below the superfluid transition. We have calculated the temperature dependence of the spinodal line as well as the pressure dependence of the isothermal sound velocity in the region of the spinodal. We discuss the slope of the superfluid transition line and the shape of the dispersion curve at negative pressures.

Vortices and Impurities in Large ^4He Droplets

Large (1000 atoms) superfluid ^4He droplets, doped with linear chains of HCN molecules, were simu... more Large (1000 atoms) superfluid ^4He droplets, doped with linear chains of HCN molecules, were simulated at T=0.38 K using Path Integral Monte Carlo. The effect of the linear impurities on the density distribution, moment of inertia, superfluid density, and shape deformations of the droplets was calculated. We find that the energy of forming a vortex is reduced by approximately a third when a chain of at least five HCN molecules is added to the droplet. Droplets doped with cyclic isomers of HCN molecules were also investigated. The effects of impurities on the excitation spectrum and vortex stability will be discussed.

Accurate Theoretical Predictions of the Properties of Energetic Materials MURI Publications

Stochastic calculation of interaction energies

The Journal of Physical Chemistry, 1982

A Monte Carlo method by which the properties of a collection of interacting nuclei and electrons ... more A Monte Carlo method by which the properties of a collection of interacting nuclei and electrons might be accurately calculated is briefly outlined. This method allows quantitative determination of the pairwise intermolecular potential and potential surfaces but eliminates the use of these constructs for dense systems. Preliminary results on the electron gas, hydrogen solid, and the molecules Heâ, LiH, Liâ, and HâO are at least as accurate as the best previous work.

Modeling Positron-Electron Correlations in Solids

Materials Science Forum - MATER SCI FORUM, 1997