Local Correlation Calculations Using Standard and Renormalized Coupled-Cluster Methods

Local correlation variants of the coupled-cluster (CC) theory with singles and doubles (CCSD) and CC methods with singles, doubles, and non-iterative triples, including CCSD(T) and the completely renormalized CR-CC(2,3) approach, are developed. The main idea of the resulting CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) methods is the realization of the fact that the total correlation energy of a large system can be obtained as a sum of contributions from the occupied orthonormal localized molecular orbitals and their respective occupied and unoccupied orbital domains. The CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) algorithms are characterized by the linear scaling of the total CPU time with the system size and embarrassing parallelism. By comparing the results of the canonical and CIM-CC calculations for normal alkanes and water clusters, it is demonstrated that the CIM-CCSD, CIM-CCSD(T), and CIM-CR-CC(2,3) approaches recover the corresponding canonical CC correlation energies to within 0.1 {\%} or so, while offering savings in the computer effort by orders of magnitude. By examining the dissociation of dodecane into C$_{11}$H$_{23}$ and CH$_{3}$ and several lowest-energy structures of the (H$_{2}$O)$_{n}$ clusters, it is shown that the CIM-CC methods accurately reproduce the relative energetics of the corresponding canonical CC calculations.