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Unconventional Aspects of Coupled-Cluster Theory

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Recent Progress in Coupled Cluster Methods

Part of the book series: Challenges and Advances in Computational Chemistry and Physics ((COCH,volume 11))

Abstract

The formalism ofQuantum chemistry in Fock space is used to analyse coupled-cluster (CC) theory for a closed-shell state. A main aspect is the challenge of generally accepted wisdom. The theoretical background of CC theory is the separation theorem in Fock space. This applies to systems that are separable in a localized representation. In three main parts (a) the traditional coupled cluster (TCC) method, based on a non-unitary similarity transformation of the Hamiltonian, (b) variational coupled cluster (VCC) in intermediate normalization, and (c) unitary coupled cluster (UCC) approaches are analyzed. The infinite summation of diagrams from many-body perturbation theory (MBPT) is studied. It is stressed that higher-order non-linear (multi-commutator) terms are dominated bydiagonal EPV contributions with repeated hole labels, that lead to anindividual normalization of the pair functions, familiar from thecoupled electron pair approximation (CEPA). This concept is generalizable to clusters of higher particle rank. An estimation of the difference between TCC and VCC is presented. The most promising reformulation of CC theory appears to be in terms of UCC, for which a closed summation of the bulk contributions is derived.

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Acknowledgements

The author thanks R. Ahlrichs, K. Jankowski, B. Jeziorski, W. Liu, D. Mukherjee, F. Neese, J. Noga, and V. Staemmler, for valuable comments on this manuscript. He is particularly grateful to F. Neese for a starting cooperation on this topic.

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  1. Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, D-44780, Bochum, Germany

    Werner Kutzelnigg

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  1. ASCR Praha J. Heyrovsky Inst. Physical Chemistry, Praha 8, Czech Republic

    Petr Cársky

  2. Dept. Applied Mathematics, University of Waterloo Fac. Mathematics, Waterloo, Ontario, Canada

    Josef Paldus

  3. ASCR Praha J. Heyrovsky Inst. Physical Chemistry, Praha 8, Czech Republic

    Jirí Pittner

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Kutzelnigg, W. (2010). Unconventional Aspects of Coupled-Cluster Theory. In: Cársky, P., Paldus, J., Pittner, J. (eds) Recent Progress in Coupled Cluster Methods. Challenges and Advances in Computational Chemistry and Physics, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2885-3_12

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