Frontier-orbital analysis

Use frontier orbital analysis to decide whether the dimeriza... 

Frontier orbital analysis is a powerful theory that aids our understanding of a great number of organic reactions Its early development is attributed to Professor Kenichi Fukui of Kyoto University Japan The application of frontier orbital methods to Diels-Alder reactions represents one part of what organic chemists refer to as the Woodward-Hoffmann rules a beautifully simple analysis of organic reactions by Professor R B Woodward of Harvard University and Professor Roald Hoffmann of Cornell University Professors Fukui and Hoffmann were corecipients of the 1981 Nobel Prize m chemistry for their work... 

The modes of reaction of several 5-aminoimidazoles (96) with the reagents (135-142) are summarized in Table V. The variation of product structure with reagent is clearly discemable. The preference for C- or N-addition has been interpreted in terms of a frontier orbital analysis of the reactants [92JCS(P1)2779, 92JCS(P1)2789] (see Section VI,C). The... 

Scheme 1.5 represents case f, that is, an anion-radical belonging to the borderline between moderately and completely delocalized species. Its optical spectra, along with frontier orbital analysis, testifies that in this anion-radical there is a positive overlap between C-N bonds and the psendo-geminal carbons of the opposite rings, as shown by the dashed lines in the strnctnre of Scheme 1.5 (Nelsen et al. 2005). Taken together, the experimental results considered provide direct evidence for the throngh-bond mechanism of electron transfer in these paracyclophane systems.

Use frontier orbital analysis to decide whether the dimeriza-tion of 1,3-butadiene shown here is symmetry allowed or forbidden. 

At first sight, radical reactions seem to be ideally adapted to frontier orbital analysis. They are usually exothermic, so their transition states resemble the reagents. Therefore, the starting material frontier orbitals should provide us with a very good approximation. Furthermore, radicals are soft reagents, whose reaction partners are often neutral molecules. Frontier control is dominant in such reactions. 

Another indicator in favor of a living polymerization is a linear increase of number average molar masses (Mn) on monomer conversion. Hsieh et al. reported on linear plots for the dependence of inherent viscosities on monomer conversion. These plots were highly Unear and Hsieh et al. assigned the term quasi-living to these polymerizations [134,139]. Kwag et al. attributed the living character of Nd-catalyzed diene polymerizations to the ionic character of the Nd allyl bond and the stable oxidation state of Nd. In addition, theoretical frontier orbital analysis confirmed these results [653]. 

The proposed mechanism of Dole et al. is shown in Figure 9-1142 and has been confirmed by Gioia et al.66,67 They calculated the optimized structure by DFT and performed frontier orbital analysis. From their analysis, they proposed that H2 reacts... 

A side-by-side comparison of orbital interactions in discrete molecules and a molecule with a surface is revealing. Diagram 53 is a typical molecular interaction diagram, 54 a molecule-surface one. Even though a molecule is, in general, a many-level system, let s assume, in the spirit of a frontier orbital analysis, that a small set of frontier orbitals dominates. This is why the squiggly lines symbolizing interaction go to the HOMO and LUMO of each component. 

A frontier orbital analysis of the ene reaction is shown in Fig. 8.62. It displays many features of the [3,3]-sigmatropic shift. Thus, the hydrogen atom transfer from an allylic site to a double bond is seen to be symmetry allowed with respect to the HOMO of an... 

The frontier orbital analysis of electrocyclic reactions focuses on the HOMO of the open-chain polyene. 

In cycloaddition reactions, frontier orbital analysis considers the interaction of the HOMO of one component and the LUMO of the other. 

Example 6.25. Frontier orbital analysis of sigmatropic 11,3] and [1,5] hydrogen shifts. 

Because of the principle of microscopic reversibility it is appropriate to consider frontier orbital analysis of the reaction in either direction. The Hammond postulate dictates that the more exothermic the reaction the more the transition state will reflect the starting geometry, and frontier orbital analysis of reactant orbitals is expected to be a better predictor of relative transition state orbital interactions than for an endothermic or a less exothermic process. Conversely, frontier orbital analysis of product orbitals in exothermic reactions would be a poorer predictor of transition state energy. 

We have recently argued [39] that facial selectivity in the Diels-Alder reactions of 5-substituted cyclopenta-1,3-dienes is a reflection of hyperconjugative effects a frontier orbital analysis is shown in Fig. 6-10 [40], The molecule adopts a conformation where the better electron-donating group (C-Me rather than C-X) hinders approach of the dienophile from that face. Overlap of the C-C (T-bond (a better donor than C-X) increases the energy of the diene HOMO. Furthermore overlap of the C-C (T -orbital with the diene LUMO yP reduces the energy of the... 

For axial and equatorial nucleophilic addition to cyclohexanone, the principle of microscopic reversibility dictates that frontier orbital analysis can be considered for addition of the nucleophile to the carbonyl or loss of nucleophile from the product. Since the reaction is considered to be exothermic the frontier orbital interaction that should best represent the transition energy is the orbital interaction of the nucleophile HOMO with the ketone n (LUMO) (Fig. 6-11). 

The second technique which both confirms some of our deductions and provides useful quantitative data for frontier orbital analysis is electron spin resonance spectroscopy9,10 (ESR). This technique detects the odd electron in radicals the interaction of the spin of the electron with the magnetic nuclei (1H, 13C, etc.) gives rise to splitting of the resonance signal, and the degree of splitting is proportional to the electron population at the nucleus. Since we already know that the coefficients of the atomic orbitals, c, are directly related... 

There is some evidence157 that the cycloaddition of the allyl cation (183) to cyclopentadiene (184) takes place with a transition state like 186 rather than 185. This is clearly in agreement with a frontier orbital analysis, provided that we look at the HOMO of the allyl cation and the LUMO of the diene. 

By contrast, C-substituted benzenes are reduced to 3-substituted cyclohexa-1,4-dienes,343 and this too fits nicely into a frontier orbital analysis. We can use biphenyl (430) as an example. The Hiickel coefficients for the SOMO of the radical anion are shown on 431. Since this molecule does not have heteroatoms... 

The C-amino substituents possess reduced reactivity towards electrophiles in comparison with an. annular nitrogen. Reactions which result in exocyclic substitution may be a consequence of primary annular substitution followed by rearrangement (see CHEC-I). A frontier orbital analysis of elec-... 

AJ Duben. Frontier Orbital Analysis of the Bathochromic Shift of Monosubstituted Benzenes. J. Chem. Ed. 62 373-375, 1985. 

These trends agree with the frontier orbital analysis. In particular, the delivery of hydride from carbon breaks a relatively unpolarised bond, making the hydride notably soft, as we saw earlier in its capacity to attack pyridinium salts preferentially at the 4-position. The metal hydrogen bond will be more polarised, and metal hydrides should therefore be harder. Similarly, the delivery of hydride from boron will make it softer than when it is delivered from the more electropositive metal, aluminium. It also seems that, among a,(3-unsaturated carbonyl compounds, the susceptibility to conjugate reduction increases in the sequence ketones < esters < acids < amides but there are too few examples to be sure. 

Another formal treatment of the rearside attack model was proposed by Liotta, Burgess and Eberhardt [31]. These authors extended frontier orbital analysis of the interactions between a nucleophile and a n-electrophile by including the stabilizing two-electron interactions of the nucleophile HOMO with all the unoccupied n and a MO s on the rt-electrophile, as well as the net destabilizing four-electron interactions of the nucleophile HOMO with all the occupied n and a MO s. The analysis... 

Frontier orbital analysis of a [4 -I- 2] cycloaddition reaction shows that overlap of in-phase orbitals to form the two new a bonds requires suprafacial orbital overlap (Figure 29.5). This is tme whether we use the LUMO of the dienophile (a system with one TT bond Figure 29.1) and the HOMO of the diene (a system with two conjugated rr bonds Figure 29.2) or the HOMO of the dienophile and the LUMO of the diene. Now we can understand why Diels-Alder reactions occur with relative ease (Section 8.8). 

---