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Approximate evaluation of the effect of three-body cluster operators in the valence-universal coupled-cluster excitation energy calculations for Be and Mg

The atomically oriented valence-universal coupled-cluster (VU-CC/R) method in the intermediate Hamiltonian formulation is used to calculate excitation energies for the beryllium and magnesium atoms. Having the basic VU-CC/R scheme which includes one- and two-particle cluster operators (VU-CCSD/R), the effect of approximate inclusion of the three-body terms in the cluster operator is investigated. The evaluation is based on the perturbative analysis of equations for the three-body part of the cluster operator at one- and two-valence levels. In this way, an explicit consideration of the three-body terms is avoided since they are expressed as functions of the two-body clusters. Our results show that the effect of the three-body clusters seems rather small for the systems under consideration which suggests that discrepancies between calculated and experimental values cannot be exclusively attributed to the truncated character of the cluster operator in the VU-CCSD/R calculation.