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
εHOMO(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, Edisp,3BATM, which
reduces errors in supramolecular interaction energies by about a factor
of 2. The XSAPT­(KS) + aiD3 + Edisp,3BATM(ωGDD) 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.