Resonance energy 1,3,5-hexatriene

The precise value of the resonance energy of benzene depends as comparisons with 13 5 cyclohexatriene and (Z) 13 5 hexatriene illustrate on the compound chosen as the reference What is important is that the resonance energy of benzene is quite large SIX to ten times that of a conjugated triene It is this very large increment of resonance energy that places benzene and related compounds m a separate category that we call aromatic... 

Forster (1968) points out that R0 is independent of donor radiative lifetime it only depends on the quantum efficiency of its emission. Thus, transfer from the donor triplet state is not forbidden. The slow rate of transfer is partially offset by its long lifetime. The importance of Eq. (4.4) is that it allows calculation in terms of experimentally measured quantities. For a large class of donor-acceptor pairs in inert solvents, Forster reports Rg values in the range 50-100 A. On the other hand, for scintillators such as PPO (diphenyl-2,5-oxazole), pT (p-terphenyl), and DPH (diphenyl hexatriene) in the solvents benzene, toluene, and p-xylene, Voltz et al. (1966) have reported Rg values in the range 15-20 A. Whatever the value of R0 is, it is clear that a moderate red shift of the acceptor spectrum with respect to that of the donor is favorable for resonant energy transfer. 

Scheme 23. Vertical Resonance Energy of the Reference Structure, B(R), for Benzene and Its Relation to the Vertical Energy of Hexatriene, B(h)...

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. 

In Summary Two of the filled ir molecular orbitals of benzene are lower in energy than are those in 1,3,5-hexatriene. Benzene is therefore stabilized by considerably more resonance energy than is its acyclic analog. A similar orbital structure also stabilizes aromatic transition states. 

The energy change for the formation of the reference structure hexatriene is Benzene is thus aromatic, having a positive resonance energy of 2/y/3p. 

L. Davenport, R. E. Dale, R. H. Bisby, and R. B. Cundall, Transverse location of the fluorescent probe l,6-diphenyl-l,3,5-hexatriene in model lipid bilayer membrane systems by resonance excitation energy transfer, Biochemistry 24, 4097-4108 (1985). 

In order to put the structure of benzene into better perspective, we give a similar calculation of 1,3,5-hexatriene for comparison. Table 15.5 shows the energies for a set of calculations parallel to those in Table 15.2 for benzene. The most obvious difference is the smaller total spread in the energies, about 3. 3 eV rather than the 5.5 eV for benzene, and the SCVB energy is closer to the full n than in benzene. Standard arguments say that there is only a rather small amormt of resonance... 

As an application, let us compare the energies of two isomers of hexatrienes. The linear s-trans conformation can be described as a resonance between the canonical structure 15 and long-bond structures 16-18 (Scheme 3.7), where one short bond is replaced by a long one. On the other hand, the branched isomer is made of only structures 19-21, since it lacks an analogous structure to 18. 

The overall stabilization of the molecule as the result of conjugation is estimated. Remember from the resonance concept in VB theory that conjugation is generally associated with additional stabilization (see Section 1.1.7). In HMO theory this stabilization is expressed as the difference between the energy of the conjugated system and the same number of isolated double bonds. The energy of an isolated double bond in the HMO method is equal to 2a+ 2(3, so for 1,3,5-hexatriene, a stabilization of 0.988(3 is computed. For benzene, the computed stabilization is 2(3 ... 

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