Symmetry-adapted perturbation theory (SAPT) was applied to the helium dimer for interatomic separations R from 3 to 12 bohrs. The first-order interaction energy and the bulk of the second-order contribution were obtained using Gaussian geminal basis sets and are converged to about 0.1 mK near the minimum and for larger R. The remaining second-order contributions available in the SAPT suite of codes were computed using very large orbital basis sets, up to septuple-zeta quality, augmented by diffuse and midbond functions. The accuracy reached at this level was better than 1 mK in the same region. All the remaining components of the interaction energy were computed using the full configuration interaction method in bases up to sextuple-zeta quality. The latter components, although contributing only 1% near the minimum, have the largest uncertainty of about 10 mK in this region. The total interaction energy at R=5.6 bohrs is -11.000+/-0.011 K. For R< or =6.5 bohrs, the supermolecular (SM) interaction energies computed by us recently turned out to be slightly more accurate. Therefore, we have combined the SM results for R< or =6.5 bohrs with the SAPT results from 7.0 to 12 bohrs to fit analytic functions for the potential and for its error bars. The potential fit uses the best available van der Waals constants C(6) through C(16), including C(11), C(13), and C(15), and is believed to be the best current representation of the Born-Oppenheimer (BO) potential for helium. Using these fits, we found that the BO potential for the helium dimer exhibits the well depth D(e)=11.006+/-0.004 K, the equilibrium distance R(e)=5.608+/-0.012 bohrs, and supports one bound state for (4)He(2) with the dissociation energy D(0)=1.73+/-0.04 mK, and the average interatomic separation R=45.6+/-0.5 A.

Nonrelativistic clamped nuclei interaction energies for a pair of helium atoms have been computed using the Gaussian geminal implementation of the coupled cluster theory with single and double excitations (CCSD). Effects of triple and quadruple excitations were subsequently included employing the conventional orbital approach and very large augmented, correlation-consistent bases extended by sets of bond functions. Up to the coupled cluster doubles (CCD) level, the Gaussian geminal expansions provide nearly an order of magnitude better accuracy than orbital expansions even if the latter results are extrapolated. The recommended values of the helium dimer interaction energy are 292.54 ± 0.04 K, −11.009 ± 0.008 K, and −4.619 ± 0.007 K at the interatomic distances equal to 4.0, 5.6, and 7.0 bohr, respectively. The major contributions to the error estimates come from the orbital parts of the calculations beyond the CCSD level.