Implementation of the locally renormalized CCSD(T) approaches for arbitrary reference function

Several new variants of the locally-renormalized coupled-cluster (CC) approaches that account for the effect of triples (LR-CCSD(T)) have been formulated and implemented for arbitrary reference states using the TENSOR CONTRACTION ENGINE functionality, enabling the automatic generation of an efficient parallel code. Deeply rooted in the recently derived numerator-denominator-connected (NDC) expansion for the ground-state energy [K. Kowalski and P. Piecuch, J. Chem. Phys. 122, 074107 (2005)], LR-CCSD (T) approximations use, in analogy to the completely renormalized CCSD(T) (CR-CCSD(T)) approach, the three-body moments in constructing the noniterative corrections to the energies obtained in CC calculations with singles and doubles (CCSD). In contrast to the CR-CCSD(T) method, the LR-CCSD(T) approaches discussed in this paper employ local denominators, which assure the additive separability of the energies in the noninteracting system limit when the localized occupied spin-orbitals are employed in the CCSD and LR-CCSD(T) calculations. As clearly demonstrated on several challenging examples, including breaking the bonds of the F-2, N-2, and CN molecules, the LR-CCSD(T) approaches are capable of providing a highly accurate description of the entire potential-energy surface (PES), while maintaining the characteristic N-7 scaling of the ubiquitous CCSD(T) approach. Moreover, as illustrated numerically for the ozone molecule, the (LR-CCSD(T)) approaches yield highly competitive values for a number of equilibrium properties including bond lengths, angles, and harmonic frequencies. c 2005 American Institute of Physics.