Atomic Orbital Implementation of Extended Symmetry-Adapted Perturbation Theory (XSAPT) and Benchmark Calculations for Large Supramolecular Complexes.

We report an implementation of extended symmetry-adapted perturbation theory (XSAPT) in the atomic orbital basis, extending this method to systems where the monomers are large. In our "XSAPT(KS)" approach, monomers are described using range-separated Kohn-Sham (KS) density functional theory (DFT), with correct asymptotic behavior set by tuning the range-separation parameter ω in a monomer-specific way. This is accomplished either by conventional ionization potential (IP)-based tuning, in which ω is adjusted to satisfy the condition ε(ω) = -IP(ω), or else using a "global density-dependent" (GDD) condition, in which ω is fixed based on the size of the exchange hole. The latter procedure affords better results for both total interaction energies and energy components, when used in conjunction with our third-generation pairwise atom-atom dispersion potential (+ aiD3). Three-body (triatomic) dispersion terms are found to be important when the monomers are large, and we incorporate these by means of an Axilrod-Teller-Muto term, E, which reduces errors in supramolecular interaction energies by about a factor of 2. The XSAPT(KS) + aiD3 + E(ω) approach affords mean absolute errors as low as 1.2 and 4.2 kcal/mol, respectively, for the L7 and S12L benchmark test sets of large dimers. Such errors are comparable to those afforded by far more expensive methods, such as DFT-SAPT, and the closely related second-order perturbation theory with coupled dispersion (MP2C). We also survey the performance of various other quantum-chemical methods for these data sets and identify several semiempirical and DFT-based approaches whose accuracy approaches that of MP2C, at dramatically reduced cost.