The linear scaling local correlation approach, termed “cluster-in-molecule” (CIM), is extended to the coupled-cluster (CC) theory with singles and doubles (CCSD) and CC methods with singles, doubles, and noniterative triples, including CCSD(T) and the completely renormalized CR-CC(2,3) approach. The resulting CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) methods are characterized by (i) the linear scaling of the CPU time with the system size, (ii) the use of orthonormal orbitals in the CC subsystem calculations, (iii) the natural parallelism, (iv) the high computational efficiency, enabling calculations for much larger systems and at higher levels of CC theory than previously possible, and (v) the purely noniterative character of local triples corrections. By comparing the results of the canonical and CIM-CC calculations for normal alkanes and water clusters, it is shown that the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) approaches accurately reproduce the corresponding canonical CC correlation and relative energies, while offering savings in the computer effort by orders of magnitude.

An efficient implementation of the “cluster-in-molecule” (CIM) approach is presented for performing local electron correlation calculations in a basis of orthogonal occupied and virtual localized molecular orbitals (LMOs). The main idea of this approach is that significant excitation amplitudes can be approximately obtained by solving the coupled cluster (or Møller-Plesset perturbation theory) equations of a series of “clusters,” each of which contains a subset of occupied and virtual LMOs. In the present implementation, we have proposed a simple approach for constructing virtual LMOs of clusters, and new ways of constructing clusters and extracting the correlation contributions from calculations on clusters, which are more efficient than those suggested in the original work. More importantly, linear scaling of computational time of the CIM approach is achieved by evaluating the transformed two-electron integrals over LMOs using simple truncation techniques in limited operations (independent of the molecular size). With typical thresholds, for a variety of molecules our test calculations demonstrate that more than 99% of the conventional MP2 or coupled cluster with doubles correlation energies can be recovered in the present CIM approach.