Resonance energy butadiene

To calculate the resonance energy of butadiene, we first compute the value of that the molecule would have if the four ir electrons were localized into 1, 2— and 3,4— double bonds. Such localization has the effect of making Pz3 0. The determinant is then 

Verify that the roots of the determinant for localized butadiene are x = 1, 1. 

The two lowest x-electron orbitals of localized butadiene are seen to have the energy a + p while the two highest orbitals have the energy a p. These are, of course, just the orbital energies expected for two isolated ethylene molecules. We expect the four ir electrons to go into the lowest orbitals as follows  

The delocalization or resonance energy DE of delocalized butadiene equals (4a + 4.4720p) - (4a + 4 ) = 0.4728. The resonance energy calculated in this way comes out in units 

Calculate the resonance energy in units of p for butadiene using numerical values of P such as are appropriate for the bond 4istances involved (seep. 33 ). Use the reported 1.37 A for the 1,2— and 3,4—bonds and 1.47 A for the 2, 3—bond in the delocalized molecule. Use 1.34 A for the 1,2— and 3,4-bonds in the localized form. 

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Another molecular orbital approach is to calculate the energy of a model in which the tt bonds are constrained to be localized double bonds by the definition of the wave function. The calculated energy of this model can then be compared with the computed energy of the molecule in which delocalization is permitted. By this definition, butadiene has a resonance stabilization of about 9.3 kcal/mol, while benzene has a resonance energy of about 56 kcal/mol. To compare this value with that obtained with the polyene reference, one must subtract a correction for the butadiene resonance energy (3 x 9.3), which gives a value of about 28 kcal/mol as the resonance stabilization of benzene. 

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. ... 

On the other hand, to apply Dewar s approach within the QMRE scheme, it would be necessary to normalize resonance energies, calculated in terms of the above model, with respect to butadiene in accordance with... 

Since the Dewar resonance energy differs from REs derived for a hypothetical reference system with regard to the bond energy ascribed to a C—C single bond, RE values can be normalized by using the RE value of 1,3-butadiene (or appropriate butadiene derivatives) according to equation 987 ... 

In addition, there is also the question of how to use suitable reference molecules to obtain normalized RE values which correspond to Dewar resonance energies. In the case of cyclopropyl homoconjugation, butadiene is clearly the wrong reference molecule to consider the two C—C single bonds a adjacent to the fusion bond/(see Scheme 10). The... 

Because the benzene resonance energy is much higher than that of an isolated double bond, the oxidation of an ethylenedithiolate to the butadiene-like dithione is easier to accomplish than the oxidation of a benzenedithiolate to the corresponding dithio-or /io-benzoquinone there is a difference in stability between the dianionic ligands (44) and (46) relative to the dithioketone forms (45) and (47) derived from them by a two-electron oxidation. 

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 ... 

In butadiene resonance occurs between the ordinary structure GH2=GH—GH=GH2 and other structures involving only one double bond, viz—GHg—CH=GH—GH,— and also, but to a lesser extent, +GHg—GH=CH— CH. The sum of the energies of the bonds in the ordinary structure is 778 4 kcals and the experimental heat of formation is 782 3 kcals the difference, which is the resonance energy is 4 I kcals. For i-methylbutadiene GH2—GH—GH=GHGH3, 616 kcals, for... 

A comparison of the resonance energies of structures involving triple and double bonds may be made by considering diacetylene, vinylacetylene and butadiene. Their resonance structures are as follows ... 

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