Energy decomposition of dispersion-corrected density functional theory (DFT-D3 and DFT-D4) in terms of symmetry-adapted perturbation theory components

Symmetry-adapted perturbation theory based on density functional theory [SAPT(DFT)] improves the electrostatic, exchange, and induction components compared to Hartree-Fock-based SAPT. However, the dispersion component of SAPT(DFT) converges slowly with the basis set and is a major computational bottleneck due to the requirement to compute frequency-dependent density susceptibilities. Here, we combine SAPT(DFT) with inexpensive Grimme -D3 and -D4 damped asymptotic dispersion corrections to obtain physically meaningful energy components and accurate interaction energies, even in augmented double-ζ basis sets. However, we find that an "intermolecular" approach to the -D4 correction, rather than a "supermolecular" one, is needed. We also introduce a prescription for obtaining a SAPT partitioning of conventional DFT-D interaction energies, which are quite accurate for a number of functionals and which also avoid the rather costly computation of SAPT(DFT) dispersion. Tests on a set of 4530 van der Waals dimers demonstrate that the latter approach using PBE0-D4 or B3LYP-D4 and the aug-cc-pVDZ basis yields interaction energy mean absolute errors below 0.2 kcal mol-1 vs benchmark values at the coupled-cluster complete-basis-set level [CCSD(T)/CBS], comparable with much more expensive SAPT2+3(CCD)/aug-cc-pVTZ calculations. Meanwhile, replacing dispersion in SAPT(PBE0)/aug-cc-pVDZ with a -D4 correction yields a mean absolute error below 0.3 kcal mol-1 for this test set. Both types of approximations are much faster than SAPT(DFT) or wavefunction-based SAPT computations of similar quality.