A valence-universal coupled-cluster single- and double-excitation method for atoms. I. Theory and application to the C2+ ion

Abstract

A valence-universal coupled-cluster theory accounting for one- and two-electron excitation is formulated in a special form for applications to atomic systems, i.e. in terms of radial cluster amplitudes labelled by configurational indices (VU-CCSD/R method). The method is based on the general algebraic formulation for open shell systems developed by Jeziorski and Paldus (1989). The algebraic formulation is supplemented by a diagrammatic one. The completeness of the model spaces is postulated, and the wave operator is represented in Lindgren's normal ordered exponential form. Various approximations to the VU-CCSD/R method are considered. A general computer program has been developed, and extensive pilot calculations have been performed for the C2+ ion and, as a result of using a VU approach, for the C4+ and C3+. Among the states considered special attention is paid to the quasi-degenerate 2s2 1S and 2p2 1S ones. It is found that in the present formulation the number of unknowns in the equations for the cluster amplitudes is reduced by a factor of 20. The present energies are the most accurate obtained so far by a multi-reference CCSD method for a realistic (non-model) system, which make them useful for reliability studies of various MR-CC formulations. It is found that proceeding from the single-reference to the multi-reference formulation results in a change of the ground-state correlation energy by more than 1%. The impact of the choice of orbital sets on the accuracy of the results is also addressed.