Rr-electron energy

As we have seen, the important zero energy difference which measures aromatic reactivity contains a term involving rr-electron energies, and rvith the transition state model there will also be a contribution from... 

For example, the ir-eiectron energy change in the dimerization of benzyl is taken as a twofold difference in the rr-electron energies of benzene and benzyl. With the SCF data, a double value of the valence state ionization potential of carbon [I in eq. (25)] has to be added to this difference. The entries of Table XII show that in all equilibria considered, a dimer is favored. 

Until now, the overwhelming majority of disproportionations of larger molecules studied have concerned conjugated systems. Since all respective oxidation levels possess the same number of a bonds, consideration can be restricted to rr-electron energies. In solution, however, solvation energy should be taken into account. 

This means calculating the rr-electron energies of all four entities and assuming that the differences in the cr-bond energies cancel between the two reactions. The result of this rather simple calculation is that attack of Br on benzene is thermodynamically less favorable than on 1,3,5-hexatriene by about 1.0/3. If /3 is 19 kcal mole-1, this is clearly a sizable energy difference, and we can conclude that the simple MO method does indeed account for the fact that benzene is attacked by Br far less readily than is 1,3,5-hexatriene. 

Figure 4. rr-Electron energy of vicinal relative to antipodal N4P4Me4(CH2R)2 (CHr),. asa function of the perturbation Aa , induced by R( 6). The residual n-charge on the ylidic carbon atoms is marked on the curve. 

Gust D, Moore TA (1991) Photosynthetic Model Systems. 159 103-152 Gutman I (1992) Topological Properties of Benzenoid Systems. 162 1-28 Gutman I (1992) Total rr-Electron Energy of Benzenoid Hydrocarbons. 162 29-64 Guyon P-M, Gislason EA (1989) Use of Synchrotron Radiation to Study-Selected Ion-Molecule Reactions. 151 161 -178... 

The integral formulas for total rr-electron energy were invented by Coulson [2, 3, 6], Later, they were extensively elaborated (see [13], pp. 139-147). Their real usefulness in structure-property analysis became evident only after they were combined with the results of graph spectral theory [13, 18, 65, 66]. 

GutmanI (1992) Total rr-Electron Energy of Benzenoid Hydrocarbons. 162 29-64 Guyon P-M, Gislason EA (1989) Use of Synchrotron Radiation to Study-Selected Ion-Molecule... 

Simple Hiickel calculations on benzene, in contrast, place all the t electrons in bonding MOs. The rr-electron energy of the benzene molecule is calculated by... 

One approach to evaluation of the aromaticity of a molecule is to determine the extent of thermodynamic stabilization. Attempts to describe stabilization of a given aromatic molecule in terms of simple HMO calculations have centered on the delocalization energy. The total rr-electron energy of a molecule is expressed in terms of the energy parameters a and 6 that are used in HMO calculations. This energy value can be compared to that for a hypothetical localized version of the same molecule. The HMO energy for the tt electrons of benzene is 6a + 86. The same quantity for... 

The Hiickel rr-electron energy E, is related to the tt bond orders and ir-electron charges q, in fact (Problem 16.20),... 

If, based on sound calculations or experiments, the ring has lower rr-electron energy, then the ring is aromatic. 

The actual calculations and experiments used in determining rr-electron energies are beyond our scope, but we can study four examples that illustrate how this approach has been used. 

Cyclobutadiene For cyclobutadiene we consider the change in rr-electron energy for the following hypothetical transformation ... 

Here calculations and experiments indicate that a planar cyclooctatetraene would have higher rr-electron energy than the open-chain octatetraene. Therefore, a planar form of cyclooctatetraene would, if it existed, be antiaromatic. As we saw earlier, cyclooctatetraene is not planar and behaves like a simple cyclic polyene. 

Calculations indicate that the rr-electron energy decreases for the hypothetical transformation from the allyl cation to the cyclopropenyl cation below. What does this indicate about the possible aromaticity of the cyclopropenyl cation... 

STRATEGY AND ANSWER Because the rr-electron energy of the cyclic cation is less than that of the aUyl cation, we can conclude that the cyclopropenyl cation would be aromatic. (See Practice Problem 14.9 for more information on this cation.)... 

There are two tt electrons in this MO, and the total Hiickel 7r-electron energy for ethylene is 2a -I- 2)8. For butadiene the total Hiickel rr-electron energy is... 

If butadiene had two isolated double bonds, its rr-electron energy would be twice that of ethylene, namely, 4a -I- 4)8. The effect of delocalization is to change the butadiene TT-electron energy by... 

These workers found that the Huckel rr-electron energies of noncyclic conjugated polyenes could be accurately calculated as == 2 , where % is the number of... 

For the radical and the anion, we place one or two additional electrons, respectively, into the nonbonding orbital, tt2. The total rr-electron energy of each system is lower (more favorable) than that expected from three noninteracting p orbitals— because tti is greatly stabilized and filled with two electrons in all cases, whereas the antibonding level, tts, stays empty throughout. 

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