2018/05/01 by Cong Wang, Wang, Cong, Gerald Knizia +1
Computer Science · Mathematics · Medicine · #Advanced Neuroimaging Techniques and Applications #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Matrix Theory and Algorithms #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.1805.00565
openalex publication_date 2018/05/01 · openalex created_date 2018/05/07 · openalex updated_date 2026/07/28
We present a general-order spin-free formulation of the single-reference closed-shell coupled-cluster method. We show that the working equations of a fully biorthogonal contravariant projection formulation of the residual equations, as near-universally used in closed-shell CCSD, can also be defined at the CCSDT and CCSDTQ levels, despite singularities in the spin projection manifolds. We describe permutation-group based techniques for obtaining and simplifying the equations encountered in general second-quantization-based methods; this includes a permutation group based approach of evaluating second-quantized matrix elements into tensor contraction networks, and the use of Portugal's double coset canonical representation technique [Int. J. Mod. Phys. C 13, 859 (2002)] for eliminating redundant terms. A computer implementation of our techniques is simple, because no operator-valued symbolic algebra is required. Explicit working equation lists for closed-shell CCSD, CCSDT, and CCSDTQ in the semi-biorthogonal formulation are provided. We also release open-source computer programs for both deriving and numerically evaluating these equations.