Cyclobutadiene resonance energy

The rectangular structure is calculated to be strongly destabilized (antiaromatic) with respect to a polyene model. With 6-3IG calculations, for example, cyclobutadiene is found to have a negative resonance energy of—54.7 kcal/mol, relative to 1,3-butadiene. In addition, 30.7 kcal of strain is found, giving a total destabilization of 85.4 kcal/mol. G2 and MP4/G-31(d,p) calculations arrive at an antiaromatic destabilization energy of about 42kcal/mol. ... 

Since a calculation of the resonance energy of benzene by the valence bond method shows that the greater part of it is a result of the resonance between the two Kekule structures shown, we might suppose that its homologs would also have significant resonance stabilization energies. Such conclusions are at variance with experimental fact, however, since cyclobutadiene appears to be too unstable to have any permanent existence, and cyclooctatetraene exists as a nonplanar tetraolefin, having no resonance stabilization of the sort considered. 

Table 4 shows Bo values calculated for hexagons and squares using Kollmar s method.157 Comparison of entries 1—4 to entries 5—8 reveals that the benzene analogues, with the 4/V+ 2 electrons, have considerably larger Bo values than the 4 TV analogues of square cyclobutadiene. This trend is related to the accepted view that cyclic delocalization of 47V + 2 electrons possesses a higher resonance energy than cyclic delocalization of 47V electrons. 

Benzene and other aromatics alike are stable molecules, while cyclobutadiene and other antiaromatic molecules are unstable molecules.27-76 Similarly, allylic species are stable intermediates and possess significant rotational barriers. It may appear as a contradiction that, for example, the tr-component of benzene can be distortive but it still endows the molecule with special stability or that the distortive jr-component of allyl radical can lead to a rotational barrier. We would like to show in this section that these stability patterns derive from the vertical resonance energy which is expressed as a special stability because for most experimental probes (in eluding substitution reactions) the o-frame restricts the molecule to small distortion167 in which the vertical resonance energy is still appreciable, as shown schematically in Figure 5. 

Figure 7. Hess cycle used to relate the Dewar resonance energy of cyclobutadiene, DRE(cb), to the vertical resonance energy, Bq (calculated in this study111). All energies are given in kcal/mol.

The very delicate ji a-balance poses an opportunity to study delocalized antiaromatic species and to gain new insight into the resonance energy of antiaromatics and its manifestations, e.g., in the magnetic properties. The calculations of van Wiillen and Kut-zelnigg185 show that AU, cyclobutadiene has a positive... 

For cyclobutadiene, keeping the K0 term as necessary to describe the background exerted by a skeleton, the average of the two Kekule structures is K0-Ja-Jb. Correspondingly, for benzene, confined also to Kekule structures, the non-resonant part can be conventionally defined as K0-3Ja/2-3Jb/2. In this way we estimate a resonance stabilization for benzene of — 8.56 kcal/mol, comparable with the CASVB calculation [22] giving — 7.4 kcal/mol. Here one should note that with respect to the adopted definition and the method of estimation, the resonance energy is disputed in a very large interval (— 5 to — 95 kcal/mol) [23]. The representation in... 

Fig. 4. The hypothetical non-resonant energy in cyclobutadiene and benzene and the corresponding resonance stabilization (in kilocalories per mole) obtained with the help of fitted spin Hamiltonian parameters (as function of bond altering distortion).

More sophisticated calculations indicate that cyclic An systems like cyclobutadiene (where planar cyclooctatetraene, for example, is buckled by steric factors and is simply an ordinary polyene) are actually destabilized by n electronic effects their resonance energy is not just zero, as predicted by the SHM, but less than zero. Such systems are antiaromatic [17, 46]. 

What is the result of using as a reference system for calculating the resonance energy of cyclobutadiene, not two ethene molecules, but 1,3-butadiene What does this have to do with antiaromaticity Is there any way to decide if one reference system is better than another ... 

One can apply this method to other conjugated systems as well. In this manner, the resonance energy is the difference between the variational energies of the full state and the reference VB structure. As such, the resonance energy itself is variational. Tests of these variational resonance energies show that they reproduce experimentally determined values, for example, for benzene and cyclobutadiene (5). 

More recently, Mo and Wu [51] used this type of description for benzene and cyclobutadiene as well. They also optimised the geometries of these molecules and of the ones with localised bonds. In their calculation of resonance- and stabilisation energies, they took another set of structures for the description of the cyclohexatriene, which leads again to a different definition of the resonance energy. 

Resonating Generalised Valence Bond (GVB) calculations were performed on cyclobutadiene by Voter and Goddard [54], They find a resonance energy of -22 kcal/mol for this molecule. According to them its geometry cannot easily be predicted, and is determined by the interaction between resonance and bond strain. 

Finally, we can just use one structure, which for C6H6 gives the elusive cyclohexatriene (D3h symmetry) (fig. 6). Of course, for cyclobutadiene, nothing out of the ordinary is observed and the normal 1,3-cyclobutadiene results. The difference in energy with the two-structure calculation gives the theoretical resonance energy (TRE) [51]. 

The viewpoint expressed by Glendening et al. [62] is that the resonance between the structures is the key factor for delocalisation. We find this as well. When there is no resonance in cyclobutadiene (and benzene), the molecule becomes asymmetric. Just resonance is not enough, however. Both benzene and square cyclobutadiene have large resonance energies. 

Optimized bond lengths and (7 cc) resonance energies (RE) in benzene and cyclobutadiene... 

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