Quantum chemistry by random walk. H 2P, H+3 D3h 1A′1, H2 3Σ+u, H4 1Σ+g, Be 1S

Anderson, James B.

doi:10.1063/1.432868

Cited by 541 publications

(138 citation statements)

References 19 publications

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“…In diffusion quantum Monte Carlo 11,12 (DMC) the imaginary-time Schrödinger equation is used to evolve an ensemble of electronic configurations towards the ground state. The fermionic symmetry is maintained by the fixed-node approximation, 13 in which the nodal surface of the wave function is constrained to equal that of a trial wave function. Furthermore, the use of nonlocal pseudopotentials to represent the Ne 8+ cores necessitates the use of the locality approximation, 14 which leads to errors that are second order in the quality of the trial wave function.…”

Section: Vmc and Dmc Methodsmentioning

confidence: 99%

Quantum Monte Carlo, density functional theory, and pair potential studies of solid neon

Drummond

Needs

2006

Phys. Rev. B

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We report quantum Monte Carlo (QMC), plane-wave density-functional theory (DFT), and interatomic pair-potential calculations of the zero-temperature equation of state (EOS) of solid neon. We find that the DFT EOS depends strongly on the choice of exchange-correlation functional, whereas the QMC EOS is extremely close to both the experimental EOS and the EOS obtained using the best semiempirical pair potential in the literature. This suggests that QMC is able to give an accurate treatment of van der Waals forces in real materials, unlike DFT. We calculate the QMC EOS up to very high densities, beyond the range of values for which experimental data are currently available. At high densities the QMC EOS is more accurate than the pair-potential EOS. We generate a different pair potential for neon by a direct evaluation of the QMC energy as a function of the separation of an isolated pair of neon atoms. The resulting pair potential reproduces the EOS more accurately than the equivalent potential generated using the coupled-cluster CCSD(T) method.

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Section: Vmc and Dmc Methodsmentioning

confidence: 99%

Quantum Monte Carlo, density functional theory, and pair potential studies of solid neon

Drummond

Needs

2006

Phys. Rev. B

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“…A fixed-node approximation [47,48] was initially introduced to solve the sign problem for ground-state quantum Monte Carlo calculations. For the finite-temperature PIMC simulation, a restricted-path method was developed [49], where one only integrates over all paths that do not cross the nodes of a trial density matrix, ρ T (R,R ; β), which must be available in analytic form.…”

Section: B Pimc Calculationsmentioning

confidence: 99%

Multiphase equation of state for carbon addressing high pressures and temperatures

et al. 2014

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We present a 5-phase equation of state for elemental carbon which addresses a wide range of density and temperature conditions: 3g/cc < ρ < 20g/cc, 0 K < T < ∞. The phases considered are diamond, BC8, simple cubic, simple hexagonal, and the liquid/plasma state. The solid phase free energies are constrained by density functional theory (DFT) calculations. Vibrational contributions to the free energy of each solid phase are treated within the quasiharmonic framework. The liquid free energy model is constrained by fitting to a combination of DFT molecular dynamics performed over the range 10 000 K < T < 100 000 K, and path integral quantum Monte Carlo calculations for T > 100 000 K (both for ρ between 3 and 12 g/cc, with select higher-ρ DFT calculations as well). The liquid free energy model includes an atom-in-jellium approach to account for the effects of ionization due to temperature and pressure in the plasma state, and an ion-thermal model which includes the approach to the ideal gas limit. The precise manner in which the ideal gas limit is reached is greatly constrained by both the highest-temperature DFT data and the path integral data, forcing us to discard an ion-thermal model we had used previously in favor of a new one. Predictions are made for the principal Hugoniot and the room-temperature isotherm, and comparisons are made to recent experimental results.

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“…Since VMC by itself is not usually accurate enough, the optimised many-electron wave function produced by VMC is then used in diffusion Monte Carlo (DMC) [1,7], which improves the ground-state estimate by performing an evolution in imaginary time. In principle, the ground-state energy would be exact, but to overcome the fermion sign problem we use the standard "fixed-node approximation" [8]. In practice, only the valence electrons are treated explicitly, the interactions between the valence and core electrons being represented by pseudopotentials.…”

Section: Introductionmentioning

confidence: 99%

Quantum Monte Carlo calculations of the structural properties and the B1-B2 phase transition of MgO

et al. 2005

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We report diffusion Monte Carlo (DMC) calculations on MgO in the rock-salt and CsCl structures. The calculations are based on Hartree-Fock pseudopotentials, with the single-particle orbitals entering the correlated wave function being represented by a systematically convergeable cubic-spline basis. Systematic tests are presented on system-size errors using periodically repeating cells of up to over 600 atoms. The equilibrium lattice parameter of the rock-salt structure obtained within DMC is almost identical to the Hartree-Fock result, which is close to the experimental value. The DMC result for the bulk modulus is also in good agreement with the experimental value. The B1-B2 transition pressure (between the rock-salt and CsCl structures) is predicted to be just below 600 GPa, which is beyond the experimentally accessible range, in accord with other predictions based on Hartree-Fock and density functional theories.

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Quantum chemistry by random walk. H 2P, H+3 D3h 1A′1, H2 3Σ+u, H4 1Σ+g, Be 1S

Cited by 541 publications

References 19 publications

Quantum Monte Carlo, density functional theory, and pair potential studies of solid neon

Quantum Monte Carlo, density functional theory, and pair potential studies of solid neon

Multiphase equation of state for carbon addressing high pressures and temperatures

Quantum Monte Carlo calculations of the structural properties and the B1-B2 phase transition of MgO

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