A direct product decomposition approach for symmetry exploitation in many-body methods. I. Energy calculations

An analysis of the matrix contractions involved in many-body perturbation theory and coupled-cluster calculations leads to a convenient strategy for exploiting point group symmetry, by which the number of floating point operations can be reduced by as much as a factor of h2, where h is the order of the molecular point group. Contrary to a statement in the literature, the significant reduction in computation time realized in coupled-cluster calculations which exploit symmetry is not due to nonlinearities in the equations. Rather, the savings of the fully vectorizable direct product decomposition (DPD) method outlined here is associated with individual (linear) contractions, and is therefore applicable to both linear and nonlinear coupled-cluster models, as well as many body perturbation theory. In addition to the large reduction in floating point operations made possible by exploiting symmetry, core memory requirements are also reduced by a factor of ≊h2. Implementation of the method for both open and closed shells is reported. Computer timings and hardware requirements are given for several representative chemical systems. Finally, the DPD method is applied to the calculation of the equilibrium geometry, totally symmetric harmonic force field and vertical ionization potentials of the cubane molecule at the coupled-cluster singles and doubles (CCSD) level.