Nonapproximated third-order exchange induction energy in symmetry-adapted perturbation theory

The exchange terms in symmetry-adapted perturbation theory (SAPT) are normally calculated within the so-called S2 or single approximation, which approximates all-electron antisymmetrizer by interchanges of at most one electron pair between interacting molecules. This approximation is typically very accurate van der Waals minimum separation and larger intermolecular distances but begins to deteriorate short range. Nonapproximated expressions for second-order SAPT corrections have been derived some time ago Schäffer Jansen [Mol. Phys. 111, 2570 (2013)]. In this work, we extend Jansen’s formalism derive implement a nonapproximated expression third-order exchange-induction correction. Numerical tests on several representative noncovalent databases show that underestimates contributions both second third orders. underestimation similar relative terms, absolute values effects, their near complete cancellation with corresponding induction energies, make errors more severe. worst-case scenario interactions involving ions, breakdown can result qualitatively wrong, attractive character total energies range {as first observed Lao Herbert [J. Chem. A 116, 3042 (2012)]}. As expected, inclusion full energy place its S2-approximated counterpart restores correct, repulsive short-range behavior potential curves computed through order.