Frontier orbital positions HOMO

When you request an orbital, yon can use the cardinal number of the orbital (ordered by energy and starting with number=l) or an offset from either the highest occupied molecular orbital (HOMO) or the lowest unoccupied molecular orbital (LL MO). Offset from the HOMO are negative and from the LUMO are positive. Often these frontier orbitals are the ones of most chemical interest. 

The positively charged allyl cation would be expected to be the electron acceptor in any initial interaction with ethylene. Therefore, to consider this reaction in terms of frontier orbital theory, the question we need to answer is, do the ethylene HOMO and allyl cation LUMO interact favorably as the reactants approach one another The orbitals that are involved are shown in Fig. 1.27. If we analyze a symmetrical approach, which would be necessary for the simultaneous formation of the two new bonds, we see that the symmetries of the two orbitals do not match. Any bonding interaction developing at one end would be canceled by an antibonding interaction at the other end. The conclusion that is drawn from this analysis is that this particular reaction process is not favorable. We would need to consider other modes of approach to analyze the problem more thoroughly, but this analysis indicates that simultaneous (concerted) bond formation between ethylene and an allyl cation to form a cyclopentyl cation is not possible. 

The amplitude of the frontier orbitals determines the selectivity. The most reactive atom in a molecule has the largest amplitude of the frontier orbitals. The frontier orbitals overlap each other to the greatest extent at the sites with the largest amphtudes. Reactions occur on the atoms in the electron donors and acceptors, where the HOMO and LUMO amplitudes are largest, respectively. Electrophiles prefer the a position of naphthalene, an electron donor, with the larger HOMO amplitude (Scheme 21). Nucleophiles attack the carbons of the carbonyl groups, an electron acceptor, with the larger LUMO amplitude (Scheme 7). 

The frontier orbital theory was developed for electrophilic aromatic substitution (Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). Application is successful to the ortho-para orientation (Scheme 23a) for the benzenes substituted with electron donating groups. The ortho and para positions have larger HOMO amplitudes. The meta orientation (Scheme 23b) for the electron accepting groups is under control of both HOMO and the next HOMO [25]. 

Thus we find that the reaction is a syn (suprafacial) addition with respect to both the diene and dienophile. The frontier orbitals involved shows that the reaction occurs by interaction of HOMO and LUMO. So there is no possibility of substituents to change their position. Substituents which are on the same side of the diene or dienophile will be cis on the newly formed ring as is seen between the reaction of dimethyl maleate (a cis dienophile) with 1,3 butadiene. The product formed is cis 4,5 dicarbomethoxy cyclohexane. 

The reactions of electrogenerated cation radicals of diarylsulfldes are mainly orbital-controlled and at this level the electronic structure of their frontier orbitals (HOMO-SOMO) has very interesting synthetic consequences. The 3p orbitals of sulfur are conjugated with only one aromatic ring even if there are two aryls bound to sulfur. Therefore, only one ring can be activated electrochemically. The degree of the charge delocalization in the ArS moiety of a cation radical on the one hand, and the availability of p- and o-positions for the substitution on the other, determine quite different reactivity of such species. 

In homolytic substitution reactions, the 2-position of thiophene is the preferred site of attack. This is easily rationalized in terms of frontier orbital theory (B-76MI31401). Because of symmetry, both HOMO and LUMO of thiophene have the same absolute values for the coefficients (as shown in 216). Thus it is immaterial whether the [SOMO (radical)-HOMO (thiophene)] or the [SOMO (radical)-LUMO (thiophene)] interaction determines the site of attack only the 2-position is the point at which the radical would attack. The same conclusion is iso reached by consideration of product development control (74AHC(16)123). Attack at the 2-position would result in a transition state with an allylic radical, which would be stabilized to a greater extent than the one arising from attack at position 3 (Scheme 57). 

The preference for bridging at the meso positions is dictated by HOMO-LUMO coefficients in the exciplex. At high arene concentrations, the stereochemical preference is diminished. In general, however, the local symmetry of the frontier orbitals determines implicitly the favorable pathway for cycloadditions involving significant charge transfer but without the intervention of radical ions (55). 

Indole and benzofuran combine two problems they are nonalternant and they contain heteroatoms. The indole frontier orbital coefficients in the 8- and 9-positions78 are very similar, 0.491 and 0.493, respectively. The subjacent orbital lies only 0.256/1 below the HOMO, but it has very small coefficients in these positions. The overriding factor seems to be the net charge (—0.12 at position 9, essentially neutral at position 8), which strongly favors attack at position 9. The case of benzofuran is still more complicated. There is a difference between the frontier orbital coefficients at position 8 (0.54) and 9 (0.47), but charge control still prefers the 9-position (—0.10 versus —0.03 units for the 8-position). The experimental results show that the frontier orbital terms dominate. 

In contrast to the [4+2]-additions of butadiene to ethene or acetylene (Figures 15.8 and 15.9), the two HOMO/LUMO interactions stabilize the transition state of the [2+2]- addition of ketenes to alkenes to a very different extent. Equation 15.2 reveals that the larger part of the stabilization is due to the LUMOketene/HOMOethene interaction. This circumstance greatly affects the geometry of the transition state. If there were only this one frontier orbital interaction in the transition state, the carbonyl carbon of the ketene would occupy a position in the transition state that would be perpendicular above the midpoint of the ethene double bond. The Newman projection of the transition state (Figure 15.11) shows that this is almost the case but... 

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