A eHealth System for Atrial Fibrillation Monitoring

Electronic band gaps from quantum Monte Carlo methods

“…Molecular hydrogen was placed in the C2/c-24 structure [43] at two different densities (r s = 1.38 and r s = 1.34), roughly corresponding to pressures of 234GPa and 285 GPa, respectively. Energies and structure factors were obtained from Reptation Quantum Monte Carlo calculations using the BOPIMC code [44]. For carbon and silicon, Diffusion Monte Carlo calculations have been performed with the QMCPACK code [45] at the experimentally measured zero pressure valence densities, r s = 1.318 and r s = 2.005, respectively.…”

Benchmarking vdW‐DF first‐principles predictions against Coupled Electron–Ion Monte Carlo for high‐pressure liquid hydrogen

“…In this paper, we use Metropolis Monte Carlo sampling for the nuclear degrees of freedom and, since the focus is on the accuracy of the potential energy surface, we limit our discussion to classical protons. The electronic energies used in the Metropolis sampling arise either from ground-state QMC in the CEIMC [1,8] or from ground-state DFT with the vdW-DF approximation.…”

“…When solving the electronic problem with QMC, energy and forces have statistical noise, which must be taken into account to avoid bias in the sampling. In CEIMC, the noise over electronic energy is accounted for with the penalty method [8,17] Equation of state along the two isotherms investigated. The upper panels report the pressure versus r s from coupled electron-ion Monte Carlo (CEIMC) (blue circles) and from DFTMC with N p = 54 (red squares).…”

“…, a positive term, hence a penalty in the acceptance coming from the noise, can be replaced, to first approximation, by the estimate of the variance of the energy difference. [8,17] We do not report new CEIMC calculations but use past calculations as a reference. Details about these calculations are reported in refs [10,15,18].…”

“…At the same time, the simple electronic structure of hydrogen makes it the ideal candidate for developing new first-principles methods based on more fundamental many-body theories such as those based on quantum Monte Carlo (QMC) techniques. Two similar methods have appeared in the last decade and were applied to study compressed hydrogen: the Coupled Electron-Ion Monte Carlo (CEIMC) [2,[8][9][10] and the quantum Monte Carlo molecular dynamics (QMCMD). [11,12] They are both based on solving the electronic problem by ground-state QMC methods but differ in the way they sample the nuclear configuration space.…”