SparseMaps-A systematic infrastructure for reduced scaling electronic structure methods. V. Linear scaling explicitly correlated coupled-cluster method with pair natural orbitals.

In this work, we present a linear scaling formulation of the coupled-cluster singles and doubles with perturbative inclusion of triples (CCSD(T)) and explicitly correlated geminals. The linear scaling implementation of all post-mean-field steps utilizes the SparseMaps formalism [P. Pinski et al., J. Chem. Phys. 143, 034108 (2015)]. Even for conservative truncation levels, the method rapidly reaches near-linear complexity in realistic basis sets, e.g., an effective scaling exponent of 1.49 was obtained for n-alkanes with up to 200 carbon atoms in a def2-TZVP basis set. The robustness of the method is benchmarked against the massively parallel implementation of the conventional explicitly correlated coupled-cluster for a 20-water cluster; the total dissociation energy of the cluster (∼186 kcal/mol) is affected by the reduced scaling approximations by only ∼0.4 kcal/mol. The reduced scaling explicitly correlated CCSD(T) method is used to examine the binding energies of several systems in the L7 benchmark data set of noncovalent interactions.

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