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 omega in a monomer-specific way. This is accomplished either by conventional ionization potential (IP)-based tuning, in which omega is adjusted to satisfy the condition epsilon(HOMO)(omega) = -IP(omega), or else using a global density-dependent (GDD) condition, in which omega 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-disp,3B(ATM), which reduces errors in supramolecular interaction energies by about a factor of 2. The XSAPT(KS) + aiD3 + E-disp,3B(ATM)(omega GDD) 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.