Efficient density-fitted explicitly correlated dispersion and exchange dispersion energies

TL;DR

This paper introduces a density-fitted explicitly correlated approach for dispersion energies in SAPT, significantly improving basis set convergence and computational efficiency compared to previous methods.

Contribution

The authors develop a density fitting implementation of F12 corrections for dispersion energies, enhancing efficiency and accuracy in SAPT calculations.

Findings

F12 corrections greatly improve basis set convergence.

Density fitting introduces negligible error with standard auxiliary bases.

Enhanced accuracy in high-level SAPT calculations with small basis sets.

Abstract

The leading-order dispersion and exchange-dispersion terms in symmetry-adapted perturbation theory (SAPT), $E^{(20)}_{\rm disp}$ and $E^{(20)}_{\rm exch-disp}$, suffer from slow convergence to the complete basis set limit. To alleviate this problem, explicitly correlated variants of these corrections, $E^{(20)}_{\rm disp}$-F12 and $E^{(20)}_{\rm exch-disp}$-F12, have been proposed recently. However, the original formalism (M. Kodrycka et al., J. Chem. Theory Comput. 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-pVXZ/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 $E^{(20)}_{\rm disp}$-F12 and $E^{(20)}_{\rm exch-disp}$-F12 values exhibit vastly improvement basis set convergence over their conventional counterparts. The well-converged $E^{(20)}_{\rm disp}$-F12 and $E^{(20)}_{\rm exch-disp}$-F12 numbers can be substituted for conventional $E^{(20)}_{\rm disp}$ and $E^{(20)}_{\rm exch-disp}$ 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)$\delta$MP2, the reduction of basis set incompleteness errors thanks to the F12 treatment substantially improves the accuracy of small-basis calculations.