Twin Excited States of

Twin Excited States of "Siegel-Cyclohexatriene" and of Benzene Derivatives with Expressed Mills-Nixon Effect... 

Figure 16. Calculated (refs 34 and 164a) and experimental geometries (in italics, from ref 32) for the ground state and twin excited state of Siegel-cyclohexatriene. The diagrams at the bottom show the a— -interplay in the two states. The key difference is the attractive jr-curve in the excited state.

Twin Excited States of Cyclobutadiene, Cyclooctatetraene, and Antiaromatic Annulenes... 

Scheme 40. Frequencies of the big Kekule Mode in the Ground and Twin Excited States of Antiaromatic Species (Ref 188)...

VI. Structural Manifestations of Ground State s jr-Distortivity The Twin Excited State... 

This section considers structural manifestations of the ground state s Tr-distortivity by its comparison with the excited state that can be constructed from the same VB structures as the ground state, henceforth called the twin excited state.1-3-37-113-150-188-209... 

Another feature of the resonance mixing, already alluded to, is the sign inversion which is caused by the different nature of the matrix elements that mix the Kekule structures for aromatics and antiaromatics. Thus, in the case of benzene (part a), the ground state is the positive combination of the two Kekule structures, while in cyclobutadiene (part b), the ground state is the negative combination.15116158210 214 Consequently, the twin excited states are the negative and positive linear combin-tions, respectively, for aromatics and antiaromatics.13-15-115-209 212 This relationship of the ground and excited states to the fundamental Kekule structures has been derived early on by the pioneers of VB theory.211-214... 

Figure 14. Experimental and theoretical C—C bond lengths of benzene in the ground state (ref 216a,b) and in the twin excited state (ref 215 refs 164a, 188, and 209).

Let us return to Siegel-cyclohexatriene (30) and inspect the relationship between the geometries of the ground state and the twin excited states. The model in Figure 11a (also eq 11) predicts that an attractive 77-curve, displaced to the left of the a-minimum, will reduce the bond alternation induced by the er-strain. Since the 77-curve of the twin excited state is attractive, this state will lose the bond alternation of the ground state and the benzene nucleus will regain its local D%h symmetry. 

Using the computed VB diagrams in Figure 15, it is apparent that the jr-force constant of benzene is negative in the ground state and positive in the twin excited state, eq 15. 

The frequency exaltation of the Kekule mode is mirrored by the structural manifestations in the twin states, discussed with reference to Figures 16 and 17. Thus, the repulsive jr-curve in the ground state softens the potential and thereby enables the ground-state molecule to distort along the Kekule mode when angular strain is exerted. In contrast, the attractive jr-curve in the twin excited state stiffens the potential and restores the local Deh symmetry of the benzene nucleus. The two physical effects are in perfect harmony and find a natural reflection in the VB model. 

Scheme 37. Kekule Mode that Interchanges the Kekule (Ki, K2) Structures of Naphthalene and Is Predicted To Possess an Exalted Frequency in the Twin Excited State (Ref 3)...

Despite the quantitative difference between aromatics and antiaromatics, the qualitative picture is the same The combination of a, T-distortive ground state and a -attractive excited state along the Kekule modes is manifested in soft potentials in the ground state and steep ones in the twin excited state. This in turn is expressed as exalted frequencies and symmetrized geometries in the twin excited state. 

As a proof of principle, the twin states were characterized for the semibullvalene rearrangement and found to possess virtually identical geometries. As shown in Fig. 6.23, the twin-excited state possesses B2 symmetry as the symmetry of the reaction coordinate of the thermal process. The TS mode, b2, which is imaginary for (A, was shown to be real for (B ) (83). These calculations match the intriguing findings (84,85) in the... 

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