Regular Article

Theoretical Chemistry Accounts

, Volume 127, Issue 3, pp 211-221

First online:

Orbital relaxation and the third-order induction energy in symmetry-adapted perturbation theory

  • Konrad PatkowskiAffiliated withDepartment of Physics and Astronomy, University of Delaware Email author 
  • , Krzysztof SzalewiczAffiliated withDepartment of Physics and Astronomy, University of Delaware
  • , Bogumil JeziorskiAffiliated withFaculty of Chemistry, University of Warsaw

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Theoretical investigations of the induction interaction between closed-shell molecules which fully account for the orbital relaxation effects are presented. Explicit expressions for the third-order induction energy in terms of molecular integrals and orbital energies are given and implemented within the sapt2008 program for symmetry-adapted perturbation theory (SAPT) calculations. Numerical investigations for the He–He, He–LiH, Ar–Ar, H2–CO, H2O–H2O, and H2O–NH3 model dimers show that the orbital relaxation increases the third-order induction interaction by 15 to 50% at near-equilibrium geometries, with the largest effect observed for complexes involving highly polar monomers. At large intermonomer separations, the relaxed third-order induction energy perfectly recovers the difference \(\delta E^{\rm HF}_{\rm int}\) between the Hartree–Fock interaction energy and the sum of the uncorrelated SAPT contributions through second order in the intermolecular interaction operator. At the near-equilibrium geometries, the sum of the relaxed third-order induction and exchange-induction energies reproduces, however, only a small fraction (6 to 15%) of \(\delta E^{\rm HF}_{\rm int}\) for the nonpolar systems and about 40 to 60% for the polar ones. A comparison of the complete SAPT calculations with the coupled-cluster treatment with single, double, and noniterative triple excitations [CCSD(T)] suggests that the pure SAPT approach with all the available third-order corrections is more accurate for nonpolar systems while for the polar ones the hybrid approach including \(\delta E^{\rm HF}_{\rm int}\) gives better results.


Intermolecular interactions Symmetry-adapted perturbation theory Induction energy