Frontier-controlled 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. 

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. 

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

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 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. 

Another difficulty exists. It has been found that in the gas phase or in dipolar aprotic solutions, small anions (cations) have higher HOMO s (lower LUMO s) than the larger one. It follows that interaction between two hard ions is then favoured by both charge control and frontier control. Therefore, the equivalences suggested by Klopman ... 

Note that a frontier interaction such as HOMO(l)-LUMO(2) automatically implies electron transfer from molecule (1) to molecule (2), so that electrostatic factors are already partially taken into account in frontier control. 

Care must be taken in generalizing gas-phase computational results, which tend to overemphasize charge control while underemphasizing frontier control. Indeed, in the absence of solvent, coulombic forces, which vary as the inverse square of the distance, are stronger at large distances than frontier interactions, which diminish exponentially with the separation. The reaction then becomes charge controlled with an early transition state in which the reagents may still be in their most stable conformations. The role of the conformational effect is then somewhat overstated. This is especially true in older calculations in which O or Cl were replaced by F and Na+ and K+ were modeled by Li+. 

When — E 0 interaction between frontier orbitals (HOMO and LUMO) is important and a frontier-controlled reaction involving electron transfer occurs. A totai may then be written as... 

The proximity of the diffusion limit also inhibits a detailed discussion of the data in Table 7, but a significant difference to the substituent effects discussed in Section III.D.4 is obvious. Whereas the reactivities of terminal alkenes, dienes, and styrenes toward AnPhCH correlate with the stabilities of the new carbenium ions and not with the ionization potentials of the 7r-nucleophiles [69], the situation is different for the reactions of enol ethers with (p-ClC6H4)2CH+ [136]. In this reaction series, methyl groups at the position of electrophilic attack activate the enol ether double bonds more than methyl groups at the new carbocationic center, i.e., the relative activation free enthalpies are not controlled any longer by the stabilities of the intermediate carbocations but by the ionization potentials of the enol ethers (Fig. 20). An interpretation of the correlation in Fig. 20 has not yet been given, but one can alternatively discuss early transition states which are controlled by frontier orbital interactions or the involvement of outer sphere electron transfer processes [220]. 

The high selectivity for the synclinal transition structure in these models may also arise from frontier orbital interactions. Anh and Thanh have suggested that the stereochemical outcome of an aldol reaction may be controlled by the overlap between the frontier molecular orbitals [23aJ. This same cycloaddition-like transition structure was first used by Mulzer to explain the high selectivity observed in... 

The static quantum chemical indexes of the reactivity may be used for description of kinetics of double exchange reactions which occur through the transition state with high charges separation [17. If a barrier height of the surface reaction is controlled by frontier orbitals interaction, then the following correlation may be fulfilled ... 

The size of the reagent is not the only controlling factor since a change in the hardness of the nucleophile implies a modification of its valence orbitals and also of its HOMO energy level (Scheme 29) (160). When the level is high (i.e., in a hard nucleophile), frontier-orbital interaction is predominant. When the level is low (i.e., in a soft nucleophile), the relative importance of the nucleophile HOMO-substrate superjacent MO (161) interaction is increased. The structure of the latter is shown below (Scheme 30) for the Si-F bond. The big lobe of the Si hybrid orbital points to the rear in the superjacent MO, which therefore favors inversion of configuration. 

The tendency of particular site to be involved in frontier-controlled [33] interactions, where frontier orbital densities play important roles, is given by a local softness parameter. Local softness (T) is defined as [64] ... 

In order to understand the importance of frontier orbitals in chemical reactivity, Berkowitz [213] studied the frontier-controlled reactions within the purview of density functional theory. It is evident that the directional characteristics of frontier orbitals determine the extent of charge transfer, and soft-soft interactions are frontier-con-trolled. A somewhat similar analysis showed that charge transfer would be facilitated at a place where the difference in local softness of two partners is large [87], It may be noted that Fukui function is obtainable from local softness but the reverse is not true. On the other hand, local hardness suffers from the drawback of ambiguity [87], which allows one to even consider it to be equal to global hardness without disturbing their... 

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