An exact quantum Monte Carlo calculation of the helium–helium intermolecular potential

Abstract

We report "exact" ab initio calculations of potential energies for the interaction of two helium atoms. The quantum Monte Carlo method used is exact in that it requires no mathematical or physical approximations beyond those of the Schriidinger equation. As in most Monte Carlo methods there is a statistical or sampling error which is readily estimated. For the equilibrium internuclear distance of 5.6 bohr, the calculated electronic energy is-5.807 483 6 f 0.000 000 3 hartrees and the corresponding well depth (e/k) is 11.01 f 0.10 K. The calculated total energies are approximately 0.004 hartrees or 1200 K below the most recent variational calculations of Liu and McLean [J. Chem. Phys. 92, 2348 (1989)]. The calculated interaction energies are in excellent agreement with the interaction energies of Liu and McLean and with a recent experimental/theoretical compromise potential energy curve of Aziz and Slaman [J. Chem. Phys. 94, 8047 (199 1)] which successfully predicts a variety of experimental measurements. The error bars of the "exact" quantum Monte Carlo interaction energies straddle the Liu-McLean and Aziz-Slaman results. The Monte Carlo results support the existence of a bound dimer state.

Electron Correlation Effects in Molecules

“…This surface is illustrated in Figure 2. For the dimer He-He exact quantum Monte Carlo calculations 104 yield energies accurate within (0.000 0003 hartree or (0.10 K at the equilibrium separation of 5.6 bohrs. For the total energy, the quantum Monte Carlo calculations are more accurate than the lowest-energy variational calculations by approximately 1200 K. Nevertheless, the calculated potential energy curvessthe energies relative to separated atomssfor the Monte Carlo and the lowest-energy variational calculations are in excellent agreement with each other and with an experimental-theoretical compromise curve based mostly on experimental data.…”

“…For example, a QMC calculation 102 for the H 3 + molecular ion was the first quantum calculation to achieve an absolute accuracy of 1.0 µhartree for a polyatomic system. In many such cases, [103][104][105][106][107][108][109][110][111] QMC methods can provide solutions of the time-independent Schrödinger equation without systematic error.…”

Extraction of interatomic potentials from structure of liquids

“…The potentials of Aziz et al [4,5,6] seem to be the most popular now. A direct quantum-mechanical calculation of the helium potential was applied by Anderson et al [7]. A perturbation approach for the same problem was utilized by Tang et al [8].…”

Self-scheduling parallel methods for multiple serial codes with application to WOPWOP

“…For example, there are some very important scientific questions in surface chemistry 1 , supercritical fluids 2,3 , quantum Monte Carlo 4 , chemical kinetics 5 , and aeroacoustics 6 that can be tackled using relatively small-scale molecular dynamics or Monte Carlo codes. However, one often needs to run these codes repeatedly to either build up statistical data or vary input parameters.…”