For hexatriene

The introduction of electron correlation produces the same kind of effects on the CC bond lengths as those observed for butadiene. For hexatriene and octatetraene the inner C=C bonds are predicted to be longer than the outer C=C bonds. This result is in excellent agreement with experimental data corresponding to hexatriene, but differs from the experimental result in the case of octatetraene. This discrepancy has been suggested to be due to an important experimental error in the reported values42. 

There are three inequivalent SCVB orbitals for hexatriene, and these are given in Figs. 15.2, 15.3, and 15.4. The first of these shows a principal peak at the first orbital and a small satellite at the adjacent position. The second is more interesting with the principal peak at the second C atom, but showing a larger satellite at position 1 than at position 3. This is consistent with having essentially a double bond between atoms 1 and 2 or 5 and 6, with single bonds between 2 and 3 and 4 and 5. 

FIGURE 7.10 Covalent resonance structures for hexatriene. (b) Generation of symmetry adapted combinations of R2 and R3. (c) A VB mixing diagram of the symmetry adapted VB combinations yielding the covalent ground and excited states. 

The free-electron model breaks down readily when it is applied to longer polyenes. For hexatriene, we have a = 6 x 1.40 = 840 pm, AE = E4 - E3, and X = 333 nm. Experimentally this triene absorbs at X = 250 nm. For octatetraene, the box length a now becomes 1120 pm, and AE = 5 - 4 with X = 460 nm, compared to the experimental value of 330 pm. Despite this shortcoming, the model does predict that when a conjugated polyene is lengthened, its absorption band wavelength becomes longer as well. 

One possibility is weighting the partitioning with the original polarizabilities [108]. This may work better in the general case, but it is just as arbitrary. What will happen to local (anisotropic) polarizabilities in the condensed phases is hard to estimate without calculations. Some typical model systems can be found in Ref. [24], It is also demonstrated by the work of Augspurger and Dykstra [109] on acetylene clusters where for linear complexes an increase of the axial components of the linear and second hyperpolarizabilities are found, while van Duijnen et al. [110] for parallel clusters of butadienes and Kirtman et al. [Ill] for hexatrienes obtained a decrease in the same properties. These authors also show that well-constructed fully classical electrostatic models are able to reproduce these results. 

This explains why the compound adopts a planar structure but, in order to understand why the bond lengths are slightly different from their expected values or even why they are not all the same as in benzene, we must look at all the molecular orbitals for hexatriene. Before we can do this, we must first study some simpler systems and address the important question of conjugation seriously. 

Similarly, for hexatriene, the Mobius and Hiickel topologies are shown in Fig. 8.50. It is clear that in a [b-rr]-electrons system, the Hiickel topology is aromatic and the reaction is symmetry allowed by disrotation cyclization. 

For hexatriene the HOMO is the 37T, which has its terminal /7-orbitals in phase. The thermal reaction should be disrotatory, and the photochemical reaction conrotatory. 

Ab initio calculations for hexatriene are less numerous than for butadiene due to its larger However, CASpT2 results for hexatriene have shown that the... 

C-Substituted Dienes. For the coefficients of conjugated trienes, we can simply look at Table 4-1 for hexatriene. Both the HOMO and the LUMO are polarized the same way, as shown in Fig. 4-40. 

Comparisons of the activation enthalpy for this reaction to that for geometric isomerization of ethylene and 2-butene led to an estimate of 13 2 kcal/mol for allyl radical resonance energy once correction for hexatriene resonance energy was made. 

Table 14.10 Excitation distributions and bond indices (14.47) for hexatriene (the first part of the table) and for cycloheptatriene (the second part of the table) in the lowest electronic states ...

The secular equation for a linear system may be written as in Equation 3.30, but since the linear molecule has no connection between atoms 1 and N, the matrix is missing p values in the corners. The x matrix has x in the diagonal, surrounded by Ts, while the rest of the matrix elements are equal to zero. For hexatriene (CgHg) with three conjugate double bonds, the secular equation is... 

There is another approach to predicting the stereochemistry of electrocyclic ring closures. One simply looks at the ends of the HOMO to conclude the proper direction for rotation of the bond by creating in-phase interactions during closure. Show that this method also predicts conrotatory closure for butadiene and disrotatory closure for hexatriene. 

---