Frontier orbitals interactions

Other reactions are controlled kinetically, and the most stable product is not the major one observed. In these cases, you must look at the reactant side of the reaction coordinate to discover factors determining the outcome. Klopman and Salem developed an analysis of reactivity in terms of two factors an electrostatic interaction approximated by atomic charges and a Frontier orbital interaction. Fleming s book provides an excellent introduction to these ideas. 

Fig. 11.12. Frontier orbital interactions in Diels-Alder reactions.

Fig. 12.5. Frontier orbital interactions between different combinations of substituted radicals and aikenes.

Cycloaddition reactions also have important applications for acyclic chalcogen-nitrogen species. Extensive studies have been carried out on the cycloaddition chemistry of [NSa]" which, unlike [NOa]", undergoes quantitative, cycloaddition reactions with unsaturated molecules such as alkenes, alkynes and nitriles (Section 5.3.2). ° The frontier orbital interactions involved in the cycloaddition of [NSa]" and alkynes are illustrated in Fig. 4.13. The HOMO ( Tn) and LUMO ( r ) of the sulfur-nitrogen species are of the correct symmetry to interact with the LUMO (tt ) and HOMO (tt) of a typical alkyne, respectively. Although both... 

In certain cases, multiple frontier orbital interactions must be considered. This is particularly true of cycloaddition reactions, such as the Diels-Alder reaction between 1,3-butadiene and ethene. 

The key feature of this reaction is that the reactants combine in a way that allows two bonds to form simultaneously. This implies two different sites of satisfactory frontier orbital interaction (the two new bonds that form are sufficiently far apart that they do not interact with each other during the reaction). If we focus exclusively on the interactions of the terminal carbons in each molecule, then several different frontier orbital combinations can be imagined. 

In all three frontier orbital combinations shown above, the upper orbital components are the same sign, and their overlap is positive. In the two cases on the left, the lower orbital components also lead to positive overlap. Thus, the upper and lower interactions reinforce, and the total frontier orbital interaction is non-zero. Electron movement (chemical reaction) can occur. The right-most case is different. Here the lower orbital components lead to negative overlap (the orbitals have opposite signs at the interacting sites), and the total overlap is zero. No electron movement and no chemical reaction can occur in this case. 

As it happens, the frontier orbital interactions in the Diels-Alder cycloaddition shown above are like those found in the middle drawing, i.e., the upper and lower interactions reinforce and the reaction proceeds. The cycloaddition of two ethene molecules (shown below), however, involves a frontier orbital interaction like the one on the right, so this reaction does not occur. 

Fig. 8.1 Frontier-orbital interaction for carbo-Diels-Alder reactions, (a) The interaction of a dienophile with a low-energy LUMO, in the absence and presence of a Lewis acid (LA),...

Frontier-orbital Interactions for 1,3-Dipolar Cycloaddition Reactions of Nitrones... 

The chemical reactions through cyclic transition states are controlled by the symmetry of the frontier orbitals [11]. At the symmetrical (Cs) six-membered ring transition state of Diels-Alder reaction between butadiene and ethylene, the HOMO of butadiene and the LUMO of ethylene (Scheme 18) are antisymmetric with respect to the reflection in the mirror plane (Scheme 24). The symmetry allows the frontier orbitals to have the same signs of the overlap integrals between the p-or-bital components at both reaction sites. The simultaneous interactions at the both sites promotes the frontier orbital interaction more than the interaction at one site of an acyclic transition state. This is also the case with interaction between the HOMO of ethylene and the LUMO of butadiene. The Diels-Alder reactions occur through the cyclic transition states in a concerted and stereospecific manner with retention of configuration of the reactants. 

Scheme 24 The symmetry-allowed frontier orbital interaction for the Diels-Alder reactions...

Scheme 25a,b The symmetry-forbidden (a) and -free (b) frontier orbital interactions for the dimerization of ethylenes... 

The frontier orbital interaction is forbidden by the symmetry for the dimerization of ethylenes throngh the rectangular transition state. The HOMO is symmetric and the LUMO is antisymmetric (Scheme 25a). The overlap integrals have the opposite signs at the reaction sites. The overlap between the frontier orbitals is zero even if each overlap between the atomic p-orbitals increases. It follows that the dimerization cannot occur throngh the fonr-membered ring transition states in a concerted and stereospecfic manner. 

The frontier orbital interaction can be free from the symmetry restriction. A pair of the reaction sites is close to each other while the other pair of the sites is far from each other (Scheme 25b). This is the geometry of the transition state leading to diradical intermediates. 

The frontier orbital interactions at other than reaction sites can determine the selectivity [14]. The interaction between the HOMO of cyclopentadiene and the LUMO of maleic anhydride is illustrated in Scheme 26. The HOMO of cyclopentadiene has the same phase property as butadiene (Scheme 18). The LUMO of maleic anhydride is an in-phase combined orbital of and transition state for the... 

Scheme 27 Frontier orbital interaction in the radical reactions...

The alkene with the electron donating group has the HOMO (n) raised by the interaction with the occupied orbital of the substiment. The low-lying SOMO (n ) interacts with the HOMO of the alkene more effectively. The frontier orbital interaction is the interaction (Scheme 30b), which is impossible at the four-membered... 

Scheme 2 Change of the frontier orbital interactions with the power of donors and acceptors...

With the power of the donors and acceptors, changes occur in the important frontier orbital interactions (Scheme 2) and in the mechanism of chemical reactions. The continuous change forms a mechanistic spectrum composed of the delocalization band to pseudoexcitation band to the electron transfer band. 

The reactions in this band are controlled by the frontier orbital interactions (Sect... 

The HOMO of alkenes is an out-of-phase combination of the n and 0, orbitals. The amplitude is larger on n. The LUMO of singlet oxygen is %. The frontier orbital interaction occurs most effectively when the alkenes and the singlet oxygen... 

Amplitudes of frontier orbitals are important for regioseletivities of organic reactions (Sect. 3.4 in the Chapter Elements of a Chemical Orbital Theory by Inagaki in this volume). Stabilization by the frontier orbital interaction is greatest when it occurs... 

The most reactive site of the diene part is Cj of the cyclohexadienone ring with the alkoxy gronp. This corresponds to Cj of 2-alkoxybutadiene (Scheme 15), which has the largest HOMO amplitnde. The preferable frontier orbital interactions (Scheme 22) are in agreement with the reversed regioselectivities. 

Scheme 22 Preferable frontier orbital interactions reversing the regioselectivities...

The rationale behind this choice of bond integrals is that the radical stabilizing alpha effect of such radicals are explained not by the usual "resonance form" arguments, but by invoking frontier orbital interactions between the singly occupied molecular orbital of the localized carbon radical and the highest occupied molecular orbital (the non-bonding electrons atomic orbital) of the heteroatom (6). For free radicals the result of the SOMO-HOMO interaction Ts a net "one-half" pi bond (a pi bond plus a one-half... 

It is thus evident that the reaction path is controlled by the frontier-orbital interaction. The position of reaction will be determined by the rule of maximum overlapping of frontier orbitals, that is, HO and LU MO s of the two reacting molecules. Sometimes SO takes the place of HO or LU in radicals or excited molecules. Hence, the general orientation principle would be as follows ... 

The actual rates of thermally-allowed pericyclic reactions vary vastly, and frontier-orbital theory (14, 15, 16) has proven to be the primary basis for quantitative understanding and correlation of the factors responsible. It is therefore of interest to find the dominant frontier orbital interactions for the group transfer reactions hypothesized to occur. 

The charge transfer model suggested to rationalize the correlati on between i oni zati on potenti al and reacti vi ti es of i ron, vanadium, and niobium with dihydrogen fails for other systems. However a model that takes into account the frontier orbital interactions, although highly simplistic, does account for a variety of observations. This model suggests extensions that include... 

Scheme 1.5. Frontier orbital interactions in ji-complexation, hydrometallation, and carbometallation.

Figure 5. Frontier orbital interaction between a transition metal peroxo group and an olefin.

The frontier orbital interaction between the olefin HOMO 7t(C-C) and the orbitals with c (0-0) character in the LUMO group of the metal peroxo moiety controls the activation of 0-0 bond. Electron donating alkyl substituents at the olefin double bond raise the energy of the HOMO, with the epoxidation barrier dropping concomitantly. On the other hand, a base coordinated at the metal center pushes the a (0-0) LUMO to higher energies and thus entails a higher barrier for epoxidation. 

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