Correction to Explicitly Correlated Dispersion and Exchange Dispersion Energies in Symmetry-Adapted Perturbation Theory

Efficient Density-Fitted Explicitly Correlated Dispersion and Exchange Dispersion Energies

“…The F12 extensions to E disp (20) and E exch−disp (20) proposed in refs and significantly improve the basis set convergence of these SAPT0 corrections. However, in the original implementations, they are not competitive with conventional E disp (20) and E exch−disp (20) calculations in larger basis sets.…”

“…However, the approach of ref is not very practical as the complete amplitude optimization scales like the eighth power of the system size and sometimes suffers from numerical instabilities. Therefore, our collaborators and we have recently proposed several approximate Ansätze for E disp (20) -F12 including the optimized diagonal Ansatz (ODA, defined precisely in the next section) that scales like N 5 just like conventional E disp (20) , is numerically stable, and produces F12 dispersion energies nearly as accurate as the full F12 amplitude optimization. In the same work, we have employed the F12 dispersion amplitudes (computed using any Ansatz ) in the calculation of an explicitly correlated exchange dispersion energy, E exch−disp (20) -F12 (within the S 2 approximation), substantially improving the convergence of conventional E exch−disp (20) to its CBS limit.…”

“…Both RI and DF have been the essential factors in turning MP2-F12 and approximate CCSD­(T)-F12 − into robust practically useful approaches that combine improved basis set convergence with only a modest increase in the computational cost relative to the parent MP2 and CCSD­(T) methods. On the contrary, our initial implementation of E disp (20) -F12 and E exch−disp (20) -F12 uses RI but not DF; therefore, while the CBS convergence of these SAPT terms is vastly improved, the computational complexity is substantially higher than for the parent E disp (20) and E exch−disp (20) corrections due to the need to compute and transform several types of two-electron integrals. Moreover, these integrals involve not just AO basis indices, but up to two indices running over the RI basis that is typically several times larger than the AO set.…”

“…In this work, we derive and implement efficient expressions for the E disp (20) -F12­(ODA) and E exch−disp (20) -F12­(ODA) explicitly correlated SAPT0 corrections employing robust density fitting , in all two-electron quantities. The initial implementation of the new expressions (just like for the non-DF formulas of ref ) is facilitated by the P si 4N um P y framework that combines the low-level functionality (integrals, HF vectors, ...) of the P si 4 electronic structure program , with the tensor manipulation and linear algebra capabilities of the N um P y library. In the near future, the new DF- E disp (20) -F12­(ODA) and DF- E exch−disp (20) -F12­(ODA) functionality will be implemented in the development version of the P si 4 code itself.…”

“…In the near future, the new DF- E disp (20) -F12­(ODA) and DF- E exch−disp (20) -F12­(ODA) functionality will be implemented in the development version of the P si 4 code itself. The new DF formalism enables us to extend benchmark studies of the explicitly correlated SAPT dispersion and exchange dispersion to substantially larger systems and basis sets, and we first exploit this capability by extending the SAPT-F12 calculations , for the A24 database of noncovalent complexes to larger basis sets, including bases with midbond functions. Then, we investigate the CBS convergence of E disp (20) and E exch−disp (20) , and the effect of its F12 enhancement, on the total SAPT2+, SAPT2+(3), and SAPT2+3 interaction energies, on the same noncovalent databases as the SAPT benchmarking study of ref .…”