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

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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 Schrödinger 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±0.000 000 3 hartrees and the corresponding well depth (ε/k) is 11.01±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 (1991)] 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.