A linear-scaling explicitly correlated local natural orbital CCSD(T) approach

We introduce an integral-direct, linear-scaling, local explicitly correlated (F12) coupled-cluster (CC) singles, doubles, and perturbative triples [CCSD(T)] approach building on our established local natural orbital (LNO) CCSD(T) [J. Chem. Theory Comput. 2018, 14, 4193] and local second-order Møller–Plesset F12 [J. Chem. Theory Comput. 2026, 22, 2946] techniques. By generating and transforming all the required integrals on-the-fly, the algorithm eliminates integral storage requirements, resulting in asymptotically constant memory usage and negligible disk I/O. A key strength of the implementation is the application of the CCSD(F12*) ansatz alongside our (T+) triples correction—currently the most comprehensive scheme incorporating F12 approximations — which delivers rapid basis set convergence. Benchmark tests show that, under default truncation settings, the method recovers over 99.9% of the canonical explicitly correlated CCSD(T) correlation energy, achieving reaction energy errors under 1 kJ/mol. Compared to the complete basis set limit of CCSD(T), the average deviation of reaction energies remains around 1 kJ/mol. Overall, our results demonstrate that combining LNO-CCSD(T) with explicit correlation provides an efficient strategy for high-accuracy calculations on large molecular systems using modest basis sets.