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.