A Simple Correction for Nonadditive Dispersion within Extended Symmetry-Adapted Perturbation Theory (XSAPT)

Extended symmetry-adapted perturbation
theory (XSAPT), in conjunction with empirical “+aiD” potentials fit to ab initio dispersion
data, is a low-scaling approach to compute intermolecular interaction
energies in noncovalent clusters. One shortcoming is that the aiD atom–atom dispersion potentials are independent
of the chemical environment of the atoms in question and therefore
neglect nonadditive dispersion effects. These can be significant in
large systems, so to account for them we test a simple correction
to XSAPT­(KS)+aiD, where “KS” indicates
the use of Kohn–Sham orbitals. This correction, which can be
evaluated at fourth-order cost using double-ζ basis sets, is
based on comparing second-order SAPT dispersion with and without a
self-consistent charge embedding for the monomer wave functions. The
correction amounts to ∼1.4 kcal/mol in (H2O)6 but ∼5.5 kcal/mol in (H2O)20. With the nonadditive dispersion correction, XSAPT­(KS)+aiD affords errors of ∼1 kcal/mol for isomers of F–(H2O)10 and (H2O)20,
where the benchmarks are complete-basis CCSD­(T) energies, as well
as for ion–water clusters X­(H2O)n where n ≤ 6 and X = F–, Cl–, SO42–, Li+, Na+, or
K+. We also test the MP2 method and a variety of density-functional
methods that have been specifically recommended for noncovalent interactions.
Among the latter, only ωB97X-V and ωB97M-V can be recommended
for ion–water clusters, as mean errors for other popular approaches
(including ωB97X-D3 and several Minnesota functionals) exceed
1 kcal/mol. Lastly, we examine clathrate-hydrate host/guest complexes
whose mixture of hydrogen bonding and dispersion make them challenging
tests for noncovalent quantum chemistry. Although the B97-D2 functional
performs best for clathrate hydrates and has been previously recommended
in other studies of these inclusion complexes, its performance for
other systems examined here is quite poor. We are unable to find a
functional whose accuracy is ≲1 kcal/mol accuracy for both
clathrate hydrates and ion–water clusters. However, the XSAPT­(KS)+aiD method with the nonadditive dispersion correction can
achieve this, with a mean error for the clathrate hydrates of 0.3
kcal/mol.