Quantum Monte Carlo perturbation calculations of interaction energies

A method of evaluating perturbational components of intermolecular interaction energies by using quantum Monte Carlo (QMC) techniques is presented. It is shown how the nth-order Rayleigh-Schr\"odinger (RS) perturbation term may be expressed in a very compact way in terms of suitably defined stochastic autocorrelation functions of the perturbing operator (the intermolecular interaction potential). The resulting formula is very general (not restricted to intermolecular interactions) and corresponds in fact to an alternative way of expressing RS perturbation theory in any order. As concerns the exchange contribution responsible for repulsion at small distances, an approximate expression for the first-order exchange interaction energy (by far the leading component) is given. Both advantages and drawbacks of the proposed QMC approach with respect to more conventional ab initio perturbational treatments are discussed. Some test calculations for the interaction of two helium atoms at small distances are presented. Results are systematically compared to those obtained with ab initio perturbation calculations using large Gaussian basis sets.