12 Search Results

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 onmore » 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.« less

Here, we survey the phase diagram of high-pressure molecular hydrogen with path integral molecular dynamics using a machine-learned interatomic potential trained with quantum Monte Carlo forces and energies. Besides the HCP and C2/c–24 phases, we find two new stable phases both with molecular centers in the Fmmm–4 structure, separated by a molecular orientation transition with temperature. The high temperature isotropic Fmmm–4 phase has a reentrant melting line with a maximum at higher temperature (1450 K at 150 GPa) than previously estimated and crosses the liquid-liquid transition line around 1200 K and 200 GPa.

The synthesis of the high-temperature superconductor LaH₁₀ requires pressures in excess of 100 GPa, wherein it adopts a face-centered cubic structure. Upon decompression, this structure undergoes a distortion, which still supports superconductivity, but with a lower critical temperature. Previous calculations have shown that quantum and anharmonic effects are necessary to stabilize the cubic structure, but have not resolved the low pressure distortion. Using large scale path-integral molecular dynamics enabled by a machine learned potential, we show that a rhombohedral distortion appears at sufficiently low pressures. Here, we also highlight the importance of quantum zero-point motion in stabilizing the cubic structure.

We describe a simple scheme to perform phonon calculations with quantum Monte Carlo (QMC) methods and demonstrate it on metallic hydrogen. Because of the energy and length scales of metallic hydrogen and the statistical noise inherent to QMC methods, the conventional manner of calculating force constants is prohibitively expensive. We show that our alternate approach is nearly 100 times more efficient in resolving the force constants needed to calculate the phonon spectrum in the harmonic approximation. This requires only the calculation of atomic forces, as in the conventional approach, and otherwise little or no programmatic modification.

Berni Julian Alder, one of the leading figures in the invention of molecular dynamics simulations used for a wide array of problems in physics and chemistry, died on September 7th, 2020. His career, spanning more than 65 years, transformed statistical mechanics, many body physics, the study of chemistry and the microscopic dynamics of fluids, by making atomistic computational simulation (in parallel with traditional theory and experiment) a new pathway to unexpected discoveries. Among his many honors, the CECAM prize, recognizing exceptional contributions to the simulation of the microscopic properties of matter is named for him. He was awarded the Nationalmore » Medal of Science by President Obama in 2008.« less

Here, using quantum Monte Carlo (QMC) calculations, we investigate the insulator-metal transition observed in liquid hydrogen at high pressure. Below the critical temperature of the transition from the molecular to the atomic liquid, the fundamental electronic gap closure occurs abruptly, with a small discontinuity reflecting the weak first-order transition in the thermodynamic equation of state. Above the critical temperature, molecular dissociation sets in while the gap is still open. When the gap closes, the decay of the off-diagonal reduced density matrix shows that the liquid enters a gapless, but localized, phase: there is a crossover between the insulating and themore » metallic liquids. Compared to different density functional theory (DFT) functionals, our QMC calculations provide larger values for the fundamental gap and the electronic density of states close to the band edges, indicating that optical properties from DFT potentially benefit from error cancellations.« less

Here, we present coupled electron-ion Monte Carlo results for the principal Hugoniot of deuterium together with an accurate study of the initial reference state of shock-wave experiments. We discuss the influence of nuclear quantum effects, thermal electronic excitations, and the convergence of the potential energy surface by wave-function optimization within variational Monte Carlo and projection quantum Monte Carlo methods. Compared to a previous study, our calculations also include low pressure-temperature (P,T) conditions resulting in close agreement with experimental data, while our revised results at higher (P,T) conditions still predict a more compressible Hugoniot than experimentally observed.

Here, we study the gap closure with pressure of crystalline molecular hydrogen. The gaps are obtained from grand-canonical quantum Monte Carlo methods properly extended to quantum and thermal crystals, simulated by coupled electron ion Monte Carlo methods. Nuclear zero point effects cause a large reduction in the gap (~2 eV). Depending on the structure, the fundamental indirect gap closes between 380 and 530 GPa for ideal crystals and 330–380 GPa for quantum crystals. Beyond this pressure the system enters into a bad metal phase where the density of states at the Fermi level increases with pressure up to ~450–500 GPamore » when the direct gap closes. Our work partially supports the interpretation of recent experiments in high pressure hydrogen.« less

We have measured the momentum distribution and renormalization factor $$Z_{k_F}$$ in liquid and solid lithium by high-resolution Compton scattering. High-resolution data over a wide momentum range exhibit a clear feature of the renormalization and a sharp drop of momentum densities at the Fermi momentum $$k_F$$. In this work, these results are compared with those computed by quantum Monte Carlo simulation performed both on a disordered crystal and a liquid exhibiting very good agreement. Asymptotic behavior of the experimental and theoretical momentum distributions are examined to estimate $$Z_{k_F}$$. The experimentally obtained $$Z_{k_F} = 0.43^{+0.11}_{–0.01}$$ for liquid Li and $$0.54^{+0.11}_{–0.02}$$ for solidmore » Li are in good agreement with theoretical results of 0.54 ± 0.01 and 0.64 ± 0.01, respectively.« less

Optical properties of compressed fluid hydrogen in the region where dissociation and metallization is observed are computed by ab initio methods and compared with recent experimental results. We confirm that at T > 3,000 K, both processes are continuous, while at T < 1,500 K, the first-order phase transition is accompanied by a discontinuity of the dc conductivity and the thermal conductivity, while both the reflectivity and absorption coefficient vary rapidly but continuously. Our results support the recent analysis of National Ignition Facility (NIF) experiments [Celliers PM, et al. (2018) Science 361:677–682], which assigned the inception of metallization to pressuresmore » where the reflectivity is ~0.3. Furthermore, our results also support the conclusion that the temperature plateau seen in laser-heated diamond-anvil cell (DAC) experiments at temperatures higher than 1,500 K corresponds to the onset of optical absorption, not to the phase transition.« less