Intermolecular exchange-induction energies without overlap expansion

An approach to evaluate the second-order exchange-induction energies of symmetry-adapted intermolecular perturbation theory (SAPT) for single-determinant ground-state monomer wavefunctions has been derived. This approach is correct to all orders of the intermonomer overlap, that is, it takes multiple electron exchange between the monomers into account. The resulting formulae can be written in a compact way and implemented efficiently. Here, the method is employed to investigate the performance of the S ²- or single-exchange approximation at the Hartree-Fock-SAPT level. The list of test systems comprises the prototypical van der Waals- and hydrogen-bridge complexes Ne₂, Ar–HF, and (H₂O)₂, but also the systems HeCl^?, NeNa⁺ and Li⁺F^? involving closed-shell ions. It was found that the errors introduced by the S ²-approximation are more pronounced for the second-order exchange-induction energy than for the first-order exchange energy. While these errors tend to be negligible throughout the well region of complexes such as the neon dimer, they start to be significant in the repulsive part of the well regions of systems such as the water dimer, and in particular for the ionic lithium fluoride molecule. The consequences of these findings for the Hartree-Fock level estimate of higher-order induction plus exchange-induction energies, which is frequently employed in SAPT are also discussed.