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Fourth-order perturbative extension of the singles-doubles coupled-cluster method

Andrei Derevianko·Erik D. Emmons
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Abstract

Fourth-order many-body corrections to matrix elements for atoms with one valence electron are derived. The obtained diagrams are classified using coupled-cluster-inspired separation into contributions from n-particle excitations from the lowest-order wavefunction. The complete set of fourth-order diagrams involves only connected single, double, and triple excitations and disconnected quadruple excitations. Approximately half of the fourth-order diagrams are not accounted for by the popular coupled-cluster method truncated at single and double excitations (CCSD). Explicit formulae are tabulated for the entire set of fourth-order diagrams missed by the CCSD method and its linearized version, i.e. contributions from connected triple and disconnected quadruple excitations. A partial summation scheme of the derived fourth-order contributions to all orders of perturbation theory is proposed.

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Andrei Derevianko, Erik D. Emmons. 2002-04-18. Fourth-order perturbative extension of the singles-doubles coupled-cluster method. https://doi.org/10.1103/physreva.66.012503

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