Efficient Density-Fitted Explicitly Correlated Dispersion and Exchange Dispersion Energies

Abstract

The leading-order dispersion and exchange-dispersion terms in symmetry-adapted perturbation theory (SAPT), E disp (20) and E exch−disp (20), suffer from slow convergence to the complete basis set limit. To alleviate this problem, explicitly correlated variants of these corrections, E disp (20)-F12 and E exch−disp (20)-F12, have been proposed recently. However, the original formalism (KodryckaM. M., Kodrycka J. Chem. Theory Comput.20191559655986), 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 disp (20)-F12 and E exch−disp (20)-F12 values exhibit vastly improved basis set convergence over their conventional counterparts. The well-converged E disp (20)-F12 and E exch−disp (20)-F12 numbers can be substituted for conventional E disp (20) and E exch−disp (20) 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.

Overcoming Artificial Multipoles in Intramolecular Symmetry-Adapted Perturbation Theory

“…As expected, the dispersion and exchange-dispersion corrections increase in magnitude as the basis set increases while other, uncorrelated corrections change very little. This observation is in perfect agreement with standard intermolecular SAPT, where the slow basis set convergence of dispersion and exchange-dispersion corrections is well documented and the possible remedies include midbond functions and the explicitly correlated F12 approach . Somewhat disappointingly, the same stable convergence pattern does not apply to the SAO1 link assignment.…”

“…This observation is in perfect agreement with standard intermolecular SAPT, where the slow basis set convergence of dispersion and exchange-dispersion corrections is well documented and the possible remedies include midbond functions 33 and the explicitly correlated F12 approach. 34 Somewhat disappointingly, the same stable convergence pattern does not apply to the SAO1 link assignment. Conversely, Figures 3−6 indicate that the basis set convergence of the ISAPT(SAO1) electrostatic and first-order exchange terms is slow and erratic, and these convergence issues carry on to the total interaction energies.…”

Comprehensive Basis-Set Testing of Extended Symmetry-Adapted Perturbation Theory and Assessment of Mixed-Basis Combinations to Reduce Cost

“…For MP2C and DFT-SAPT, a density fitting approximation is required in order to obtain fifth-order scaling. , This limits DFT-SAPT calculations to dimers with N ≲ 100 atoms . Moreover, the dispersion energy exhibits very slow convergence to the complete basis-set (CBS) limit, sometimes necessitating the use of explicitly correlated techniques. − …”

Dispersion Energy from the Time-Independent Coupled-Cluster Polarization Propagator

“…The calculation of the dispersion energy is a daunting task for two main reasons: it is very sensitive to intramonomer correlation effects, and second, it is slowly convergent with respect to the basis set size. These properties of the dispersion energy make the calculation of the van der Waals interactions difficult: in particular, this is one of the main reasons why the supermolecular calculations of interaction energies are also challenging - the methods used need to include the high-order electronic correlation effects, and the basis sets employed need to be highly saturated and include augmented functions or explicit correlation. , Notably, for many-body electron methods, triply excited configurations are often critical to properly describe the dispersion interaction, which lead to emergence of the CCSD­(T) method as the “gold standard” in calculations of the interaction energies in noncovalent systems.…”