Linear-Scaling Coupled Cluster with Perturbative Triple Excitations: The Divide-Expand-Consolidate CCSD(T) Model.

We propose a reformulation of the traditional (T) triples correction to the coupled cluster singles and doubles (CCSD) energy in terms of local Hartree-Fock (HF) orbitals such that its structural form aligns with our recently developed linear-scaling divide-expand-consolidate (DEC) coupled cluster family of local correlation methods. In a DEC-CCSD(T) calculation, a basis of local occupied and virtual HF orbitals is used to partition the correlated calculation on the full system into a number of independent atomic fragment and pair fragment calculations, each performed within a truncated set of the complete orbital space. In return, this leads to a massively parallel algorithm for the evaluation of the DEC-CCSD(T) correlation energy, which formally scales linearly with the size of the full system and has a tunable precision with respect to a conventional CCSD(T) calculation via a single energy-based input threshold. The theoretical developments are supported by proof of concept DEC-CCSD(T) calculations on a series of medium-sized molecular systems.