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We recently introduced a low-cost quantum chemistry method for computing intermolecular interactions, combining a monomer-based self-consistent field calculation (the “explicit polarization” method, XPol) with pairwise-additive symmetry adapted perturbation theory (SAPT). The method uses Kohn-Sham (KS) orbitals in the SAPT formalism but replaces the SAPT dispersion and exchange-dispersion terms with empirical potentials (“+ D”), and we called this method XPol+ SAPT (KS)+ D. Here, we report a second-generation version of this approach, XPol+ SAPT (KS)+ D2 or XSAPT (KS)+ D2 for short, in which we have modified the form of the empirical atom–atom dispersion potentials. Accurate binding energies are obtained for benchmark databases of dimer binding energies, and potential energy curves are captured accurately for a variety of challenging systems. We suggest that using different asymptotic corrections …