Single-determinant-based symmetry-adapted perturbation theory without single-exchange approximation

Abstract

It is shown that the exchange-dispersion energy contribution of symmetry-adapted intermolecular perturbation theory (SAPT) can be evaluated without invoking the single-exchange approximation in the case of single-determinant ground-state references. A succinct expression is derived which allows for efficient implementation. Making use of the corresponding exchange-induction contribution, obtained recently, this enables DFT-SAPT calculations, i.e., SAPT based on a density-functional theory description of the monomers, without an expansion in orders of the intermonomer overlap S. The approach is used to test the quality of the S ² or single-exchange approximation for the systems He₂, Ar₂, N₂–Ne, H₂O–Ar, (H₂O)₂ and LiF, i.e., van der Waals and hydrogen-bridged complexes as well as an ionic molecule. While employing the S ² approximation for the exchange-dispersion contribution is found to have minor impact on total SAPT interaction energies, its use to evaluate the exchange-induction contribution significantly affects the quality of the repulsive branches of the potential energy curves for the interacting partners. Adding appropriate Hartree–Fock level estimates of higher-order induction plus exchange-induction energies, however, restores good agreement with complete basis set limit coupled-cluster results.

Keywords:

• intermolecular interactions
• symmetry-adapted perturbation theory
• single-exchange approximation
• overlap expansion
• exchange-induction energy
• exchange-dispersion energy

Notes

^a2.39, 3.03, 2.70, 2.85, 1.36 and 0.91 Å for He₂, Ar₂, N₂–Ne, H₂O–Ar, (H₂O)₂ and LiF, respectively.

^acf. Table IV.

^bcf. Table V, best estimates.

1. Note that the coupled-perturbed HF or DFT coefficients required for E ⁽²⁾ _ind can be obtained iteratively with N ⁴ effort, while the N ⁶ scaling mentioned in Ref. [30] refers to a general matrix inversion approach.