Frequency upshift in BO₂ and CO₂⁺ upon electronic excitation: A twin-state model rationalization

The twin-state model, previously shown to provide a simple physical rationalization for the frequency upshift (exaltation) of the Kekulé mode in benzene upon S₀ to S₁ electronic excitation, is extended to the case of the BO₂ radical and the CO₂ ⁺ radical cation. In the case of BO₂/CO₂ ⁺, the ground and excited states are degenerate, yet the model applies to the degenerate two-state system as well. In contrast with a pseudo-Jahn-Teller model, the twin-state one can predict which frequency is exalted and also which pair of electronic states are coupled, thus explaining the specificity of the phenomenon. The frequency exaltation is a spectroscopic manifestation of the resonance between the pair of VB structures describing twin states. In analogy with the case of benzene, it is predicted that the ν₃ asymmetric stretch fundamental will be a dominant peak in the two-photon absorption spectrum of BO₂ and CO₂⁺.