HOMO coefficients

Similarly, the reaction of an electrophile will involve the HOMO of the reactant, i.e. the reaction should occm preferentially on the atom having the largest HOMO coefficient. The coefficients for fman shown in Figure 15.3 indicate that electrophilic substitution preferentially should occur at the 2-position, again in agreement with experimental results." ... 

Figure 12 Ladder H HOMO coefficients for conformers of Si31 Me64 with cisoid (C) or gauche (G) kinks in an all-transoid chain (amplitude shown by bar length and sign by fill).228 Adapted with permission from Schepers, T. Michl, J. J. Phys. Org. Chem. 2002, 15, 490-498. 2002 John Wiley and Sons Ltd.

The observed preferential electrophilic attack on carbon D of C70 under Friedel-Crafts conditions (CHC13/A1C13) is consistent with the large HOMO coefficient of this carbon (Figure 13). This is in contrast to the fact that nucleophilic addition (7,35-38) and cycloaddition (38-40) to C70 favor carbons A and B, which are most pyramidalized and have large LUMO coefficients (Figure 13). 

In the [4 + 2] cycloadditions discussed so far, the enol ether double bond of alkoxyallenes is exclusively attacked by the heterodienes, resulting in products bearing the alkoxy group at C-6of the heterocycles. This regioselective behavior is expected for [4+2] cycloadditions with inverse electron demand considering the HOMO coefficients of methoxyallene 145 [100]. In contrast, all known intramolecular Diels-Alder reactions of allenyl ether intermediates occur at the terminal C=C bond [101], most probably because of geometric restrictions. 

Reich and coworkers130 demonstrated that the reactions of vinylallenes with unsym-metrical dienophiles proceed predominantly via a transition state in which the largest substituents on both the allene moiety and the olefin are furthest apart. The regiochemistry is governed by these steric interactions, because the HOMO coefficients of the vinylallene at the sites of bond formation are very similar. 

The following rules were used for the determination of the LUMO orbital coefficients from the values determined for the HOMO coefficients [15]. 

The net charges and HOMO coefficients on the O and N(6) of pyrido[2,l-a]phthazinium-7-olate (20) and pyrido[l,2-h]cinnolinium-ll-olate (21) were calculated with the AMI method (92CB929). 

Another QSAR study utilizing 14 flavonoid derivatives in the training set and 5 flavonoid derivatives in the test set was performed by Moon et al. (211) using both multiple linear regression analysis and neural networks. Both statistical methods identified that the Hammett constant a, the HOMO energy, the non-overlap steric volume, the partial charge of C3 carbon atom, and the HOMO -coefficient of C3, C3, and C4 carbon atoms of flavonoids play an important role in inhibitory activity (Eqs. 3-5, Table 5). 

Figure 14.8 Lowest energy VB structures, PM3 calculated lengths of [5,6 - double bonds, HOMO coefficients and energies of different dihydro[60 fullerenes.

Fig. 4. HOMO coefficients of three betaines calculated by the Hiickel method.

As in electrophilic substitution reactions, the reaction occurs preferentially at the position with the highest HOMO coefficient, although the steric factor is also influential [9], as shown in Figure 4. 

Question Substrate B has two reactive sites. Which will be attacked preferentially by A Answer If A is a nucleophile (electrophile), the attack will occur at the site having the largest LUMO (HOMO) coefficient. 

More precisely, a nucleophile will attack the site having the highest LUMO coefficient whereas an electrophile will attack the site having the highest HOMO coefficient. 

The highest HOMO coefficient in a diene will be localized on position 4 if a donor substituent is present at Cv but on position 1 if the donor appears at C2. 

Check that the rule (the nonsubstituted atom has the highest HOMO coefficient in electron-rich and the highest LUMO coefficient in electron-poor dienophiles) is general, using examples in the MO Catalog in the Appendix (enol, propene, acrolein, styrene, acrylonitrile). 

Pentadiene can be used to model ferf-butylbutadiene in Reaction (5.1). The carbonyl group affects the dienophile much more than the methyl, which can then be neglected. The ester function can also be replaced by an aldehyde (verify that ethyl 2-methacrylate can be simulated by either methyl 2-methacrylate, 2-methylacrolein, methyl acrylate or acrolein). In each case, the first-formed bond will link the atom having the highest HOMO coefficient in the diene to the atom having the highest LUMO coefficient in the dienophile. 

The FO explanation is very simple. An electrophile will attack the propene at the site of the highest HOMO coefficient, i.e. the nonsubstituted carbon atom (Exercise 1, p. 32). This is a simple application of rule 3. This rule implies that the transition state FOs are not very different from the FOs of the starting materials, and it probably works best for reactions with early transition states. The main advantage of the FO approach over that based on the stability of the intermediate cations is its generality it applies not only to Markovnikov s rule but also C-substitution of enolates. 

This interpretation is consistent with the nucleophilic properties which are generally associated with the methyl radical. In passing, note that Canadell s rule states that any radical, nucleophilic or electrophilic, reacts with an alkene at the site having the largest HOMO coefficient.62 Canadell and co-workers argue that the three-electron SOMO-HOMO interaction is stabilizing, due to the energetic proximity of these orbitals. See, however, p. 12. 

On the terminal carbon, where the largest HOMO coefficient is localized. This relatively trivial exercise serves to underline that FO theory can also rationalize results usually explained by more classical concepts. 

The arrows indicate the site of the highest HOMO coefficient in each compound. They are also the experimentally preferred sites for attack by electrophiles. The agreement is noteworthy, particularly the different regioselectivities of indole and benzofuran. However, the reasons for this success are different for each case. 

Protonation of pentadienyle anion gives rise to 1,4-pentadiene, instead of the expected conjugated 1,3-pentadiene. Is it really so surprising, when we look at the HOMO coefficients and the charge distribution (STO-3G calculations) ... 

Note that Hiickel calculations give the larger HOMO coefficient at Cr Note also that other factors may intervene to favor this regioselectivity (see p. 109 and Exercise 13 p. 117). 

Shown below are the HOMO coefficients at the a- and y-positions of three enolates. calculated by the AMI and STO-3G methods. STO-3G values are indicated in italics. 

When the nucleophilicities of the two carbons in alkenes differ significantly, the regioselective formation of 1,4-biradicals results. In fact, the regioselective oxetane formation was reported for the PB reaction of both furans [22] and vinyl ethers [23] (Scheme 7.8). Thus, 2-alkoxyoxetanes are formed exclusively during the PB reaction of furan derivatives. In contrast, 3-alkoxyoxetanes were selectively prepared in the PB reaction of vinyl ethers. This dramatic change in regioselectivity can be explained by the difference in the HOMO coefficient. Thus, in a furan ring, the C-2 carbon is known to be more nucleophilic, whereas the (3-carbon is the nucleophilic site in vinyl ethers. 

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