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A general-order local coupled-cluster (CC) method is presented which has the potential to provide accurate correlation energies for extended systems. Our method combines the cluster-in-molecule approach of Li and co-workers J. Chem. Phys. 131, 114109 (2009) with the frozen natural orbital (NO) techniques widely used for the cost reduction of correlation methods. The occupied molecular orbitals (MOs) are localized, and for each occupied MO a local subspace of occupied and virtual orbitals is constructed using approximate Møller-Plesset NOs. The CC equations are solved and the correlation energies are calculated in the local subspace for each occupied MO, while the total correlation energy is evaluated as the sum of the individual contributions. The size of the local subspaces and the accuracy of the results can be controlled by varying only one parameter, the threshold for the occupation number of NOs which are included in the subspaces. Though our local CC method in its present form scales as the fifth power of the system size, our benchmark calculations show that it is still competitive for the CC singles and doubles (CCSD) and the CCSD with perturbative triples CCSD(T) approaches. For higher order CC methods, the reduction in computation time is more pronounced, and the new method enables calculations for considerably bigger molecules than before with a reasonable loss in accuracy. We also demonstrate that the independent calculation of the correlation contributions allows for a higher order description of the chemically more important segments of the molecule and a lower level treatment of the rest delivering further significant savings in computer time.
Rolik et al. (Mon,) studied this question.