@article{cong_wang_simple_2018,
	title = {A simple permutation group approach to spin-free higher-order coupled-cluster methods},
	url = {https://arxiv.org/pdf/1805.00565.pdf},
	abstract = {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.},
	author = {{Cong Wang} and {Gerald Knizia}},
	month = may,
	year = {2018},
	keywords = {quantum chemistry, uses sympy},
}

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