Reduced partitioning procedure in configuration interaction studies. II. Excited states

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Abstract
Within the configuration interaction (CI) domain a multidimensional partitioning procedure is employed to provide a high‐order, nonlinear perturbation approach for the treatment of several states of the same symmetry. Two alternative methods are derived, one of which treats the states simultaneously, while the second permits one to focus on a single selected state. In either case, the results are given as a series of converging upper bounds to the full CI energies. The ``selective'' process has been applied the lowest 1Σ+ states of the HeH+ molecular ion to obtain potential curves. In all cases the first‐order solution, which is related to a geometric formula, accounts for about 60% of the energy increment between the full CI and unperturbed result, while an eight‐ or lower‐order solution yields at least 99.9%. Due to the rapid convergence, only small matrices need to be diagonalized to reproduce the full CI eigenvalues.