A many-body version of the symmetry-adapted perturbation theory is developed for a direct calculation of intermolecular potentials as a sum of the electrostatic, exchange, induction, and dispersion contributions. Since no multipole expansion is used, the obtained interaction energy components are properly dampened at short distance by the charge-overlap (penetration) effects. The influence of the intramonomer correlation is accounted for by the perturbation expansion in terms of the Mo/ller–Plesset type fluctuation potentials WA and WB for the individual molecules. For the electrostatic and for the dispersion energy, the terms of the zeroth, first, and second order in WA+WB are considered. In this way, the leading three-particle correlation contribution to the dispersion energy is taken into account. As a test of our method, we have performed calculations of the interaction energy for the water and hydrogen fluoride dimers. Both the geometry and the basis set dependence of the interaction energy components have been investigated. For a comparison, we have also computed the supermolecular interaction energies through the full fourth order of the many-body perturbation theory. On the basis of our results, we predict the association energy for (H2O)2 equal to −4.7±0.2 kcal/mol in relatively poor agreement with the experimental value of −5.4±0.7 kcal/mol, but still within the experimental error bars. For (HF)2, the predicted association energy is −4.2±0.2 kcal/mol, while the experimental value (corrected by a theoretical zero-point energy) is −4.9±0.1 kcal/mol.

The second-order pair energies are calculated for the H2O molecule employing explicitly correlated Gaussian-type geminals. The selection of the basis functions is guided by the completeness criteria for Gaussian geminal bases of C2v symmetry and by the recently developed technique [J. Chem. Phys. 100, 1366 (1994)] of crude optimization of nonlinear geminal parameters. Several simplifications have been made in the matrix elements evaluations that substantially reduce the optimization time without sacrificing numerical accuracy. The present results provide the new best upper bound to the second-order correlation energy for the water molecule. These results are compared with those obtained by Kutzelnigg and co-workers using the basis set containing terms linear in the interelectronic distance.

Third-order correlation energies for He, Be, H2, and LiH were calculated using highly accurate first-order pair functions obtained recently by us [J. Chem. Phys. 78, 1420 (1983)] with a novel second-order energy functional and a large basis set of explicitly correlated Gaussian geminals. Since these strong orthogonality projection, no new types of integrals appear as compared to the second-order treatment. Consequently, the third-order calculation does not require much more time than the second-order one. For He and Be atoms, the calculated third-order energies agree very well with the most accurate results obtained using the partial-wave expansion and extrapolation techniques. We estimate that our third-order energies are accurate up to within a fraction of 1%. The sum of the calculated values of the second- and third-order energies represents 97.5%, 90.4%, 94.4%, and 95.0% of the experimental correlation energy for He, Be, H2, and LiH, respectively.