Linear-Scaling Systematic Molecular Fragmentation Approach for High-Level Coupled-Cluster Methods: Coupled-Cluster Meets Macromolecules

The coupled-cluster (CC) singles and doubles with perturbative triples [CCSD(T)] method is frequently referred to as the “gold standard" of modern computational chemistry. However, the high computational cost of CCSD(T) [O(N7)], where N is the number of basis functions, limits its applications to small-sized chemical systems. To address this problem, efficient implementations of linear-scaling coupled-cluster methods, which employ the systematic molecular fragmentation (SMF) approach, are reported. In this study: (1) to achieve exact linear-scaling and to obtain a pure ab inito approach, we revise the handling of nonbonded interactions in the SMF approach (2) a new fragmentation algorithm, which yields smaller sized fragments; hence, better fits high-level CC methods is introduced (3) the new SMF approach is integrated with the high-level CC methods, denoted by LSSMF-CC, for the first time. Performances of the LSSMF-CC approaches, such as LSSMF-CCSD(T), are compared with their canonical versions for a set of alkane molecules, CnH2n+2 (n=6–10), which includes 142 molecules. Our results demonstrate that the LSSMF approach introduces negligible errors compared with the canonical methods, mean absolute errors (MAEs) are between 0.20–0.59 kcal mol-1 for LSSMF-CCSD(T). To further assess the accuracy of the LSSMF-CCSD(T) approach, we also consider several polyethylene (PE) models. For the PE set, the error of LSSMF-CCSD(T)/cc-pVDZ with respect to the experimental polymerization energies per unit are between 0.08–0.63 kcal/mol. To illustrate the efficiency and applicability of the LSSMF-CCSD(T) approach, we consider an alkane molecule with 10004 atoms. For this molecule, the LSSMF-CCSD(T)/cc-pVTZ energy computation on a Linux cluster with 100 nodes, 4 cores and 5 GB of memory are provided to each node, is performed just in ∼ 24 hours. As far as we know, this computation is an application of the CCSD(T) method on the largest chemical system to date. Overall, we conclude that (1) the LSSMF-CCSD(T) method can be reliably used for large scale chemical systems, where the canonical methods are not computationally affordable (2) the LSSMF-CCSD(T) method is very promising for accurate computation of energies in macromolecular systems (3) we believe that our study is a significant milestone in developing CC methods for large-scale chemical systems.