Benchmark calculations of the doublet <i>S</i>-states of the singly charged carbon ion

We report acurate variational calculations of the five lowest doublet S-states of the C⁺ ion. The wave functions of the six-particle system (five electrons and nucleus) have been expanded in terms of 16000 all-particle explicitly correlated Gaussians whose nonlinear variational parameters were subject to extensive optimization. The motion of the finite-mass nucleus has been explicitly included in the Hamiltonian, while relativistic corrections to the energy levels have been computed in the framework of the perturbation theory. Lowest-order quantum electrodynamics (QED) corrections have also been estimated. The results obtained for the energy levels have enabled the determination of transition frequencies with sub-wavenumber accuracy.