About

Professor David Ceperley is a founder professor in physics at the University of Illinois Urbana-Champaign, with a research focus on the electronic structure of condensed matter. His work involves developing computational methods for condensed matter starting from the fundamental many-body equations, primarily utilizing quantum Monte Carlo simulations. These methods are used to find exact properties of many-body systems and are applied to diverse solids and liquids, including studies of electron fluids, high-pressure hydrogen metallization, and cold atom systems. His significant contributions include calculations of the energy of the electron gas, which provide essential input for electronic structure calculations, and pioneering the development and application of path integral Monte Carlo methods for quantum systems at finite temperature, such as superfluid helium and hydrogen under extreme conditions. Professor Ceperley's academic background includes a BS in physics from the University of Michigan and a Ph.D. in physics from Cornell University. He has worked at the University of Paris, Rutgers University, Lawrence Berkeley National Laboratory, and Lawrence Livermore National Laboratory before joining the University of Illinois in 1987. His research has earned him numerous honors, including election to the US National Academy of Sciences, fellowship in the American Physical Society, and membership in the American Academy of Arts and Sciences. His work broadly contributes to the understanding of quantum many-body systems and the development of computational techniques in condensed matter physics.

Research topics

• Physics
• Materials science
• Quantum mechanics
• Thermodynamics
• Statistics
• Condensed matter physics
• Mathematical analysis
• Mathematics
• Atomic physics
• Statistical physics

Selected publications

• Melting curves of atomic hydrogen and deuterium calculated using path-integral Monte Carlo

  Physical review. B./Physical review. B · 2025-03-06 · 4 citations

  articleOpen accessSenior author

  We calculate the melting lines of atomic hydrogen and deuterium up to 900 GPa with path-integral Monte Carlo using a machine-learned interatomic potential. We improve upon previous simulations of melting by treating the electrons with reptation quantum Monte Carlo, and by performing solid and liquid simulations using isothermal-isobaric path-integral Monte Carlo. The resulting melting line for atomic hydrogen is higher than previous estimates. There is a small but resolvable decrease in the melting temperature as pressure is increased, which can be attributed to quantum effects.

  PublisherOA PDFDOI

• Liquid-liquid phase transition of hydrogen and its critical point: Analysis from <i>ab initio</i> simulation and a machine-learned potential

  Physical review. E · 2025-04-21 · 7 citations

  articleOpen accessSenior author

  We simulate high-pressure hydrogen in its liquid phase close to molecular dissociation using a machine-learned interatomic potential. The model is trained with density functional theory forces and energies, with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. We show that an accurate NequIP model, an E(3)-equivariant neural network potential, accurately reproduces the phase transition present in PBE. Moreover, the computational efficiency of this model allows for substantially longer molecular-dynamics trajectories, enabling us to perform a finite-size scaling analysis to distinguish between a crossover and a true first-order phase transition. We locate the critical point of this transition, the liquid-liquid phase transition, at 1200-1300 K and 155-160 GPa, a temperature lower than most previous estimates and close to the melting transition.

  PublisherOA PDFDOI

• High temperature melting of dense molecular hydrogen from machine-learning interatomic potentials trained on quantum Monte Carlo

  The Journal of Chemical Physics · 2025-02-05 · 8 citations

  articleOpen accessSenior author

  We present results and discuss methods for computing the melting temperature of dense molecular hydrogen using a machine learned model trained on quantum Monte Carlo data. In this newly trained model, we emphasize the importance of accurate total energies in the training. We integrate a two phase method for estimating the melting temperature with estimates from the Clausius-Clapeyron relation to provide a more accurate melting curve from the model. We make detailed predictions of the melting temperature, solid and liquid volumes, latent heat, and internal energy from 50 to 180 GPa for both classical hydrogen and quantum hydrogen. At pressures of roughly 173 GPa and 1635 K, we observe molecular dissociation in the liquid phase. We compare with previous simulations and experimental measurements.

  PublisherOA PDFDOI

• Electronic excitation spectra of molecular hydrogen in phase I from quantum Monte Carlo and many-body perturbation methods

  Physical review. B./Physical review. B · 2024-06-11 · 2 citations

  articleOpen access

  The electronic excitations in solid molecular hydrogen at room temperature for pressures varying from 5 to 90 GPa are calculated using quantum Monte Carlo methods and many-body perturbation theory. A crossover from a wide-gap insulator to a semiconductor is observed, showing the changing nature of the excitations from localized molecular (left inset figure) to delocalized (right inset figure) excitations. These findings are in agreement with experimental results, demonstrating the capability of accurately predicting band gaps in many-body systems with strong zero point and thermal effects.

  PublisherOA PDFDOI

• High temperature melting of dense molecular hydrogen from machine-learning interatomic potentials trained on quantum Monte Carlo

  arXiv (Cornell University) · 2024-11-23

  preprintOpen accessSenior author

  We present results and discuss methods for computing the melting temperature of dense molecular hydrogen using a machine learned model trained on quantum Monte Carlo data. In this newly trained model, we emphasize the importance of accurate total energies in the training. We integrate a two phase method for estimating the melting temperature with estimates from the Clausius-Clapeyron relation to provide a more accurate melting curve from the model. We make detailed predictions of the melting temperature, solid and liquid volumes, latent heat and internal energy from 50 GPa to 180 GPa for both classical hydrogen and quantum hydrogen. At pressures of roughly 173 GPa and 1635K, we observe molecular dissociation in the liquid phase. We compare with previous simulations and experimental measurements.

  PublisherOA PDFDOI

• The liquid-liquid phase transition of hydrogen and its critical point: Analysis from ab initio simulation and a machine-learned potential

  arXiv (Cornell University) · 2024-12-19

  preprintOpen accessSenior author

  We simulate high-pressure hydrogen in its liquid phase close to molecular dissociation using a machine-learned interatomic potential. The model is trained with density functional theory (DFT) forces and energies, with the Perdew-Burke-Ernzerhof (PBE) exchange-correlation functional. We show that an accurate NequIP model, an E(3)-equivariant neural network potential, accurately reproduces the phase transition present in PBE. Moreover, the computational efficiency of this model allows for substantially longer molecular dynamics trajectories, enabling us to perform a finite-size scaling (FSS) analysis to distinguish between a crossover and a true first-order phase transition. We locate the critical point of this transition, the liquid-liquid phase transition (LLPT), at 1200-1300 K and 155-160 GPa, a temperature lower than most previous estimates and close to the melting transition.

  PublisherOA PDFDOI

• First principles simulations of dense hydrogen

  arXiv (Cornell University) · 2024-05-17 · 1 citations

  preprintOpen access

  Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g. planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data. rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange-correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principle PIMC and DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions.

  PublisherOA PDFDOI

• Training models using forces computed by stochastic electronic structure methods

  Electronic Structure · 2024-02-29 · 10 citations

  articleOpen access1st authorCorresponding

  Abstract Quantum Monte Carlo (QMC) can play a very important role in generating accurate data needed for constructing potential energy surfaces. We argue that QMC has advantages in terms of a smaller systematic bias and an ability to cover phase space more completely. The stochastic noise can ease the training of the machine learning model. We discuss how stochastic errors affect the generation of effective models by analyzing the errors within a linear least squares procedure, finding that there is an advantage to having many relatively imprecise data points for constructing models. We then analyze the effect of noise on a model of many-body silicon finding that noise in some situations improves the resulting model. We then study the effect of QMC noise on two machine learning models of dense hydrogen used in a recent study of its phase diagram. The noise enables us to estimate the errors in the model. We conclude with a discussion of future research problems.

  PublisherOA PDFDOI

• Toward first principles-based simulations of dense hydrogen

  Physics of Plasmas · 2024-11-01 · 73 citations

  articleOpen access

  Accurate knowledge of the properties of hydrogen at high compression is crucial for astrophysics (e.g., planetary and stellar interiors, brown dwarfs, atmosphere of compact stars) and laboratory experiments, including inertial confinement fusion. There exists experimental data for the equation of state, conductivity, and Thomson scattering spectra. However, the analysis of the measurements at extreme pressures and temperatures typically involves additional model assumptions, which makes it difficult to assess the accuracy of the experimental data rigorously. On the other hand, theory and modeling have produced extensive collections of data. They originate from a very large variety of models and simulations including path integral Monte Carlo (PIMC) simulations, density functional theory (DFT), chemical models, machine-learned models, and combinations thereof. At the same time, each of these methods has fundamental limitations (fermion sign problem in PIMC, approximate exchange–correlation functionals of DFT, inconsistent interaction energy contributions in chemical models, etc.), so for some parameter ranges accurate predictions are difficult. Recently, a number of breakthroughs in first principles PIMC as well as in DFT simulations were achieved which are discussed in this review. Here we use these results to benchmark different simulation methods. We present an update of the hydrogen phase diagram at high pressures, the expected phase transitions, and thermodynamic properties including the equation of state and momentum distribution. Furthermore, we discuss available dynamic results for warm dense hydrogen, including the conductivity, dynamic structure factor, plasmon dispersion, imaginary-time structure, and density response functions. We conclude by outlining strategies to combine different simulations to achieve accurate theoretical predictions that are based on first principles.

  PublisherOA PDFDOI

• Melting of atomic hydrogen and deuterium with path-integral Monte Carlo

  arXiv (Cornell University) · 2024-09-28 · 1 citations

  preprintOpen accessSenior author

  We calculate the melting line of atomic hydrogen and deuterium up to 900 GPa with path-integral Monte Carlo using a machine-learned interatomic potential. We improve upon previous simulations of melting by treating the electrons with reptation quantum Monte Carlo, and by performing solid and liquid simulations using isothermal-isobaric path-integral Monte Carlo. The resulting melting line for atomic hydrogen is higher than previous estimates. There is a small but resolvable decrease in the melting temperature as pressure is increased, which can be attributed to quantum effects.

  PublisherOA PDFDOI

Recent grants

• Computational Methods for Electronic Structure

  NSF · $540k · 2004–2008

• CMG COLLABORATIVE RESEARCH: Quantum Monte Carlo Calculations of Deep Earth Materials

  NSF · $230k · 2010–2014

• ITR: Materials Computation Center

  NSF · $4.0M · 2003–2012

• Collaborative Research: Petascale Simulations of Quantum Systems by Stochastic Methods: Tools and Applications

  NSF · $480k · 2009–2013

Frequent coauthors

• Carlo Pierleoni

  164 shared

• Markus Holzmann

  Centre National de la Recherche Scientifique

  112 shared

• Richard M. Martin

  69 shared

• B. Bernu

  Sorbonne Université

  47 shared

• Miguel A. Morales

  44 shared

• M. H. Kalos

  Lawrence Livermore National Laboratory

  36 shared

• Nandini Trivedi

  32 shared

• Lucia Reining

  Commissariat à l'Énergie Atomique et aux Énergies Alternatives

  29 shared

Education

• PhD, Physics

  Cornell University

  1976

Awards & honors

• Berni J. Alder CECAM Prize (2016)
• Member, International Academy of Quantum Molecular Sciences…
• Blue Waters Professor (2014)
• Center for Advanced Studies Professor (2009)
• Founder Professor of Engineering (2006)