Efficient Density-Fitted Explicitly Correlated Dispersion and Exchange Dispersion Energies.

The leading-order dispersion and exchange-dispersion terms in symmetry-adapted perturbation theory (SAPT), and , suffer from slow convergence to the complete basis set limit. To alleviate this problem, explicitly correlated variants of these corrections, -F12 and -F12, have been proposed recently. However, the original formalism (M., Kodrycka , 2019, 15, 5965-5986), while highly successful in terms of improving convergence, was not competitive to conventional orbital-based SAPT in terms of computational efficiency due to the need to manipulate several kinds of two-electron integrals. In this work, we eliminate this need by decomposing all types of two-electron integrals using robust density fitting. We demonstrate that the error of the density fitting approximation is negligible when standard auxiliary bases such as aug-cc-pVZ/MP2FIT are employed. The new implementation allowed us to study all complexes in the A24 database in basis sets up to aug-cc-pV5Z, and the -F12 and -F12 values exhibit vastly improved basis set convergence over their conventional counterparts. The well-converged -F12 and -F12 numbers can be substituted for conventional and ones in a calculation of the total SAPT interaction energy at any level (SAPT0, SAPT2+3, ...). We show that the addition of F12 terms does not improve the accuracy of low-level SAPT treatments. However, when the theory errors are minimized in high-level SAPT approaches such as SAPT2+3(CCD)δMP2, the reduction of basis set incompleteness errors thanks to the F12 treatment substantially improves the accuracy of small-basis calculations.