In this paper, we present an efficient implementation of general tensor contractions, which is part of a new coupled-cluster program. The tensor contractions, used to evaluate the residuals in each coupled-cluster iteration are particularly important for the performance of the program. We developed a generic procedure, which carries out contractions of two tensors irrespective of their explicit structure. It can handle coupled-cluster-type expressions of arbitrary excitation level. To make the contraction efficient without loosing flexibility, we use a three-step procedure. First, the data contained in the tensors are rearranged into matrices, then a matrix-matrix multiplication is performed, and finally the result is backtransformed to a tensor. The current implementation is significantly more efficient than previous ones capable of treating arbitrary high excitations.

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In this article we report on the coupled-cluster factorization problem. We describe the first implementation that optimizes (i) the contraction order for each term, (ii) the identification of reusable intermediates, (iii) the selection and factoring out of common factors simultaneously, considering all projection levels in a single step. The optimization is achieved by means of a genetic algorithm. Taking a one-term-at-a-time strategy as reference our factorization yields speedups of up to 4 (for intermediate excitation levels, smaller basis sets). We derive a theoretical lower bound for the highest order scaling cost and show that it is met by our implementation. Additionally, we report on the performance of the resulting highly excited coupled-cluster algorithms and find significant improvements with respect to the implementation of Kállay and Surján [J. Chem. Phys. 115, 2945 (2001)] and comparable performance with respect to MOLPRO's handwritten and dedicated open shell coupled cluster with singles and doubles substitutions implementation [P. J. Knowles, C. Hampel, and H.-J. Werner, J. Chem. Phys. 99, 5219 (1993)].

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