Scalable Electron Correlation Methods. 5. Parallel Perturbative Triples Correction for Explicitly Correlated Local Coupled Cluster with Pair Natural Orbitals.

A well-parallelized perturbative triples correction implementation for the pair natural orbital based coupled cluster method PNO-LCCSD(T)-F12 is presented. A composite approach is adopted in addressing the coupling due to off-diagonal Fock matrix elements, in which the local triples amplitudes are iteratively solved using small domains of triples natural orbitals, and a semicanonical (T0) domain correction with larger domains is applied to reduce the domain errors. This treatment adds only about 20% to the computational cost of (T0) calculations with large domains, and the errors due to the use of small domains in the iterations are very small. In addition, a two-step triple list selection method is applied: First, an initial triple list is generated using LCCSD-F12 pair energy criteria, and the (T0) triples energies are computed using small domains. Second, this list is reduced by neglecting triples with small energy contributions, and the final calculation with large domains is only carried out for the reduced list. The cost of the (T) calculation scales asymptotically linear with the molecular size and shows excellent parallelization efficiency up to hundreds of CPU cores. The convergence of the (T) contribution to the relative energies of large molecular systems is carefully tested, and for most of the cases the results obtained with our default thresholds agree within ∼0.5 kcal mol-1 with those computed with very tight thresholds. For all tested molecular systems where canonical calculations are still feasible, the PNO-LCCSD(T)-F12 relative energies also agree within 0.5 kcal mol-1 with the canonical CCSD(T)-F12 results using the same F12 treatment. The (T) calculation generally takes 3-5 times the cost of the preceding PNO-LCCSD-F12 calculation, primarily due to the large number of triples required in obtaining accurate relative energies. We find that for large molecular systems the triple selection criteria used in previous local triples methods are insufficient, and a much larger number of triples are required than it was assumed so far. Still, using a commodity computer cluster, the PNO-LCCSD(T)-F12 calculation of molecules with ∼100 atoms using augmented triple-ζ basis sets can be carried out in a few hours of elapsed time.