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Second‑order symmetry‑adapted perturbation theory delivers accurate interaction‑induced dipole surfaces for van‑der‑Waals complexes

November 9, 2026arXiv: 2611.07993v1

A new version of the symmetry‑adapted perturbation theory for properties (propSAPT(2)) has been shown to reproduce the induced dipole moments of weakly bound dimers with near‑percent level accuracy. The method adds analytical second‑order corrections – induction, dispersion and their exchange counterparts – to the first‑order polarisation term calculated from Hartree–Fock monomer references.

In benchmark tests on the He⋯Ar, He⋯H₂, and H₂⋯H₂ dimers, the relative error between propSAPT(2) and finite‑field SAPT (FF‑SAPT) is a median of less than 0.1 % for all three systems, and never rises above 1 % for any geometry or intermolecular distance studied (4–10 Å). These results are illustrated in Figure 1.

Plot showing the relative error between propSAPT(2) and finite‑field SAPT across inter­molecular distances for three weakly bound dimers, all values staying below one percent.
Figure 1. Median relative error < 0.1 % for He⋯Ar, He⋯H₂ and H₂⋯H₂ dimers (4–10 Å).Tyrcha, Bartosz, Stachowiak, Marcin, Patkowski, Konrad, Żuchowski, Piotr S. · ·
arXiv:2611.07993v1 · Figure 1:
CC BY 4.0

Further comparison with high‑level supermolecular CCSD(T) calculations shows agreement within 0.01 % for the H₂ dimer and within 1 % for the He⋯Ar and He⋯H₂ complexes. The propSAPT(2) surfaces also recover the correct asymptotic decay powers: He⋯H₂ displays an R⁻⁴ electrostatic term, and R⁻⁷ induction and dispersion terms; He⋯Ar shows an R⁻⁷ dispersion decay. These long‑range behaviours confirm that the analytical formulation captures the physics of noncovalent interactions. The data supporting these findings are shown in Figure 2.

Graph of local effective decay exponents versus distance for He⋯H₂ and He⋯Ar; the curves approach the expected inverse power‑law slopes at long range.
Figure 2. Long‑range decay exponents: R⁻⁴ electrostatic and R⁻⁷ induction/dispersion for He⋯H₂; R⁻⁷ dispersion for He⋯Ar.Tyrcha, Bartosz, Stachowiak, Marcin, Patkowski, Konrad, Żuchowski, Piotr S. · arXiv:2611.07993v1 · Figure 2: · CC BY 4.0

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Direct calculation of dipole moment surfaces through second-order symmetry-adapted perturbation theory for properties

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Second‑order symmetry‑adapted perturbation theory delivers accurate interaction‑induced dipole surfaces for van‑der‑Waals complexes | arXiv News