Symmetry-adapted coupled-pair approach to the many-electron correlation problem. III. Approximate coupled-pair approaches for the Be atom

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Abstract
Various approximations to the orthogonally spin- and orbital-symmetry-adapted coupled-pair many-electron theory (CPMET) are suggested and discussed. These approximations include methods of the well-known coupled-electron-pair-approximation (CEPA) type and methods consisting of truncating the number of pair clusters considered in the nonlinear part of the CPMET. To enable assessment of the reliability of our approximate approaches in the presence of quasidegeneracy effects, calculations of the correlation energy are performed for the Be-atom ground state.