Saddle structure of the three-body Coulomb problem; symmetries of doubly-excited states and propensity rules for transitions

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Abstract
The separable two-centre Coulomb problem is investigated with emphasis on the saddle structure of its potential. A new quasi-degeneracy between molecular orbitals (MO) is identified. The authors demonstrate that the results have threefold relevance for the formation and character of symmetric doubly-excited states: (i) it is shown that all features of Herrick's various multiplet classifications can be explained in terms of MO saddle dynamics; (ii) for the first time quantitative results of resonance energies from the adiabatic MO approach are reported and compared to other theoretical and experimental data; (iii) the propensity rules for radiative and nonradiative transitions are summarized and details of their derivation within the framework of motion in the vicinity of the potential saddle are given.