The ab initio variational R-matrix method is combined with generalized quantum-defect theory to calculate quantum defect matrices for ¹Σᵤ⁺ and ¹Πᵤ symmetries of molecular hydrogen. The calculations take account of doubly excited channels and are optimized so as to minimize the dependence of the quantum-defect matrix elements as functions of energy and internuclear distance. The matrices are used to calculate the lowest clamped-nuclei Rydberg potential energy curves as well as doubly excited resonance positions and widths near the first excited state of H₂⁺. The results are in good agreement with previous ab initio results. Owing to their smoothness, the quantum-defect matrices are well suited for rovibronic multichannel quantum-defect applications. This opens up the possibility of a fully ab initio quantitative theoretical description of excited H₂, including ionization and dissociation.
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Telmini et al. (2003) studied this question.