The Direct-Product Decomposition Approach for Symmetry Exploitation in Many-Body Methods in Case of Non-Abelian Point Groups

We demonstrate, for the specific case of C3v, how the direct-product decomposition scheme for the treatment of symmetry in coupled-cluster (CC) calculations can be extended to non-Abelian point groups. We show that for the two-electron integrals and CC amplitudes, a block structure can be obtained by resolving the reducible products of two irreducible representations into their irreducible representations. To deal with the necessary re-sorts of the ordering of the two-electron integrals and amplitudes, spin adaptation, and the O(M5) contractions (with M as the number of basis functions) of a CC calculation, we suggest a strategy that uses both the reduced and nonreduced representations of the corresponding quantities and switches back and forth between them. While the reduced representations are the ones used in the O(M6) contractions, the other steps are better carried out in the nonreduced representation. Our pilot implementation of the CC singles and doubles method confirms in test calculations for NH3 and PH3 using different basis sets that significant savings (of more than 20 compared to treatments without symmetry and about 5 compared to treatments using Cs symmetry) are possible and these findings suggest that the exploitation of non-Abelian symmetry would render CC computations on large, highly symmetric molecules possible.