Frontier molecular orbital theory reactions

The BDE theory does not explain all observed experimental results. Addition reactions are not adequately handled at all, mosdy owing to steric and electronic effects in the transition state. Thus it is important to consider both the reactivities of the radical and the intended coreactant or environment in any attempt to predict the course of a radical reaction (18). AppHcation of frontier molecular orbital theory may be more appropriate to explain certain reactions (19). 

An interpretation based on frontier molecular orbital theory of the regiochemistry of Diels Alder and 1,3-dipolar cycloaddition reactions of the triazepine 3 is available.343 2,4,6-Trimethyl-benzonitrile oxide, for example, yields initially the adduct 6.344... 

According to frontier molecular orbital theory (FMO), the reactivity, regio-chemistry and stereochemistry of the Diels-Alder reaction are controlled by the suprafacial in phase interaction of the highest occupied molecular orbital (HOMO) of one component and the lowest unoccupied molecular orbital (LUMO) of the other. [17e, 41-43, 64] These orbitals are the closest in energy Scheme 1.14 illustrates the two dominant orbital interactions of a symmetry-allowed Diels-Alder cycloaddition. 

The period 1930-1980s may be the golden age for the growth of qualitative theories and conceptual models. As is well known, the frontier molecular orbital theory [1-3], Woodward-Hoffmann rules [4, 5], and the resonance theory [6] have equipped chemists well for rationalizing and predicting pericyclic reaction mechanisms or molecular properties with fundamental concepts such as orbital symmetry and hybridization. Remarkable advances in aeative synthesis and fine characterization during recent years appeal for new conceptual models. 

Houk, K.N. "Application of Frontier Molecular Orbital Theory to Pericyclic Reactions", in "Pericyclic Reactions", A.P. 

The Diels-Alder reaction (47t 2ir cycloaddition) is by far the best studied reaction of dienes from both theoretical and experimental viewpoints. Frontier molecular orbital theory predicts three types of Diels-Alder reaction. Structural effects on rate constants show the existence of two types of reaction ... 

These relations highlight the fact that the formalism of DFT-based chemical reactivity built by Parr and coworkers, captures the essence of the pre DFT formulation of reactivity under frontier molecular orbital theory (FMO). Berkowitz showed that similar to FMO, DFT could also explain the orientation or stereoselectivity of a reaction [12]. In addition, DFT-based reactivity parameters are augmented by more global terms expressed in the softness. 

A fundamental understanding of the mechanistic and stereochemical aspects of the Diels-Alder reaction was unfolded during the 1970s. Several theoretical approaches are available nowadays from which Fukui s Frontier Molecular Orbital theory (FMO theory) is most frequently used because of its simplicity49- 53. 

The above work has also led to the prediction that the so-called -effect for nucleophiles containing a heteroatom adjacent to the reaction centre should display normal behaviour in the gas phase (Wolfe et al., 1981a,b, 1982). This prediction has been corroborated by recent experimental determinations that show little variation of reactivity between HOO- and HO (DePuy et al., 1983), contrary to what is predicted by the application of frontier molecular orbital theory (Fleming, 1976). 

By Frontier Molecular Orbital theory several important predictions can be made 1. There will be a preferred chair transition-state for the reaction ... 

Richard Bader was among the earliest of workers to realize the importance of electron density in providing an understanding of chemistry. Early on he was led to formulate the first symmetry rule governing a chemical reaction in answer to the question of how the electron density changes in response to a motion of the nuclei. This rule, termed the pseudo- or second-order Jahn-Teller effect, provides the theoretical underpinnings of frontier molecular orbital theory and is still widely used in discussions of reaction mechanisms and molecular geometries. 

The Fukui function or frontier function was introduced by Parr and Yang in 1984 [144], They generously gave it a name associated with the pioneer of frontier molecular orbital theory, who emphasized the roles of the HOMO and LUMO in chemical reactions. In a reaction a change in electron number clearly involves removing electrons from or adding electrons to the HOMO or LUMO, respectively, i.e. the frontier orbitals whose importance was emphasized by Fukui.4 The mathematical expression (below) of the function defines it as the sensitivity of the electron density at various points in a species to a change in the number of electrons in the species. If electrons are added or removed, how much is the electron density... 

Cycloadditions that involve two unsymmetric reactants can lead to regioisomers. The regioselectivity of these adducts can be predicted with a high degree of success through the use of frontier molecular orbital theory.22 25 The ortho product (this nomenclature follows the analogy of disubstituted aromatic systems) is usually the preferred isomer from 1-substituted dienes, whereas 2-substituted dienes provide the para isomer as the major adduct. However, when a Lewis acid is used as a catalyst in the reaction, the ratio of these isomers can alter dramatically and, occasionally, can be reversed.22... 

Charge-transfer interactions between frontier molecular orbitals are clearly not the only factors which determine the relative stabilities of various transition states, in spite of the fact that frontier orbital theory has been remarkably successful in accounting for relative reactivities and regioselectivities in various reactions. For example, frontier molecular orbital theory is based on orbital shapes and energies present in the isolated molecules, and these are expected to change upon the approach of one molecule to another. 

Two studies on the mechanism of this type of [4 + 2] cycloaddition which have led to very di erent interpretations have appeared. Mock and Nugent suggested that the Diels-Alder reactions of N-sulfi-nyl-p-toluenesulfonamide are stepwise, ionic processes. On the other hand, Hanson and Stockbum prefer a concerted, pericyclic mechanism in accord with frontier molecular orbital theory. Both proposals satisfactorily rationalize the observed regioselectivity of these reactions. 

The variations of periselectivity exhibited in the cycloadditions of fulvenes to dienes have been rationalized by rqjplication of frontier molecular orbital theory. The fulvene orbitals of interest in these reactions are depicted in Figure 2. - The controlling orbitals in the reaction of fulvene with an... 

To rigorously predict the regiochemistry of Diels-Alder reactions, one has to apply frontier molecular orbital theory. 

Houk, K. N. Frontier molecular orbital theory of cycloaddition reactions. Acc. Chem. Res. 1975, 8, 361-369. 

Because of the early transition states in fast radical reactions, frontier molecular orbitals theory can be utilized for these reactions. 

A related method to interpret the diastereofecial selectivities of the reactions of double bonds has been proposed by Dannenberg and coworkers [8, 13, 14,]. Tins method also relies on the 7t frontier orbitals of non symmetrical molecules, and proposes breaking the symmetry of the n or it orbitals due to polarization induced by the substituents. Application of frontier molecular orbital theory, taking into account only the substrate MOs, gives a qualitative trend of stereoselection in a number of nucleophilic (reductions of carbonyl compounds) and electrophilic reactions. 

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