Theoretical calculations are given which show the existence of strongly bound doubly excited states. These states show significant decreases in Re and increases in ωe compared to the ground state. Examples include B2 and B2 +, but the discussion is general and may lead to the discovery of many such states.

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Journal Chemical Physics Letters
Wright, J.S, & Bruna, P.J. (Pablo J.). (1989). Strongly bound doubly excited states of diatomic molecules. Chemical Physics Letters, 156(5), 533–535. doi:10.1016/S0009-2614(89)87324-5