The Uses of Frontier Orbitals

Frontier orbital theory also provides the basic framework for analysis of the effect that the symmetiy of orbitals has upon reactivity. One of the basic tenets of MO theory is that the symmetries of two orbitals must match to permit a strong interaction between them. This symmetry requirement, when used in the context of frontier orbital theory, can be a very powerful tool for predicting reactivity. As an example, let us examine the approach of an allyl cation and an ethylene molecule and ask whether the following reaction is likely to occur. 

To circumvent problems associated with the link atoms different approaches have been developed in which localized orbitals are added to model the bond between the QM and MM regions. Warshel and Levitt [17] were the first to suggest the use of localized orbitals in QM/MM studies. In the local self-consistent field (LSCF) method the QM/MM frontier bond is described with a strictly localized orbital, also called a frozen orbital [43]. These frozen orbitals are parameterized by use of small model molecules and are kept constant in the SCF calculation. The frozen orbitals, and the localized orbital methods in general, must be parameterized for each quantum mechanical model (i.e. energy-calculation method and basis set) to achieve reliable treatment of the boundary [34]. This restriction is partly circumvented in the generalized hybrid orbital (GHO) method [44], In this method, which is an extension of the LSCF method, the boundary MM atom is described by four hybrid orbitals. The three hybrid orbitals that would be attached to other MM atoms are fixed. The remaining hybrid orbital, which represents the bond to a QM atom, participates in the SCF calculation of the QM part. In contrast with LSCF approach the added flexibility of the optimized hybrid orbital means that no specific parameterization of this orbital is needed for each new system. 

The structure and energy of a series of ions generated from penta-cyclo[3.3.1.13,7.01 3.05 7]decane (7) has been explored by using HF, MP2 and DFT methods to estimate enthalpy changes of isodesmic disproportionation reactions and by considering the reorganization of frontier orbitals as a consequence of addition or removal of electrons from the neutral molecule.8 The dication (72+), which is considered to be Three-dimensionally homoaromatic , is stable relative to a localized structure with similar features but is highly unstable compared to the radical cation (7+i)- hi contrast, the dianion (72 ) is unstable relative to the radical anion (T) and shows no evidence of electron delocalization. 

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... 

By mentioning the thermodynamic a-effect in the last section, we have again strayed from the main concern of this book—chemical reactions—into an area beyond its scope, namely the static properties of a molecule. Nevertheless, it is a large and growing area of study, and since it is in fact closely related to the general subject of frontier orbital theory, further digression on the subject will not be inappropriate. The interactions of orbitals within a molecule account for many features of chemical structure, much as the interactions of frontier orbitals account for many features of chemical reactivity. Just as frontier orbital theory is especially successful when it is used to compare the relative reactivity of two closely related systems, so its application to structural problems is most successful when the energies of two closely related molecules are to be compared. Here are two examples. 

Chapter 2 covers kinetics, which provides useful information about reaction mechanisms, and allows us to distinguish between possible mechanisms in many cases. Elementary reactions do not involve intermediates, but go through a transition state. Although this transition state cannot be isolated, it can be studied in various ways which provide insights into the reaction mechanism, and this forms the subject matter of Chapter 3. This is followed by three chapters on the most important intermediates in organic chemistry anions, radicals and cations. A final chapter on molecular reactions concerns thermal and photochemical processes. The concepts of frontier orbitals and the aromatic transition state allow us to predict which reactions are allowed and which are forbidden , and provide insights into why most reactions of practical interest involve multi-step processes. 

James McFarland (to William Purcell) There is an air of mysticism in the use of molecular orbital parameters. Do you feel that these parameters relate to biological processes that we are already familiar with or do they perhaps relate to something we don t yet understand about how drugs act If it is the former, would you elaborate on how we might interpret successful correlations with such terms as highest occupied molecular orbital, lowest unoccupied molecular orbital, and frontier orbital ... 

Let us now explore the reactivity of these compounds as dienes (furan, pyrrole, thiophene) with a dienophile (benzyne) in Diels-Alder reactions. One approach that, for a long time, has been widely employed by chemists, is the use of Frontier Molecular Orbital (FMO) [19] energy gap between two of the reactants. According to this theory, the most reactive reactant pair will be the one that has a lower FMO energy gap. The reaction is predicted to be HOMO diene-controlled. If... 

The basic idea of this theory can be suimnarized in the form of a sinq>le rule expressing the condition for an easy course of reaction by the requirement of the maximal positive overlap between the highest occupied molecular orbital HOMO and the lowest unoccupied molecular orbital LUMO. The practical use of this simple rule can be again best demonstrated by concrete exaitq)les. The sinqrlest situation is in the case of cycloadditions where the role of frontier orbitals is played by the HOMO of the first and the LUMO of the second component. In order to demonstrate the practical use of the above simple criterion let us analyze first the well known case of the Diels-Alder reaction. The situation is in this case depicted by the following Scheme. As can be seen from this scheme, the nodal structure of frontier orbitals is in this case favorable for the positive overlap in the regions of newly created bonds so that the reaction is allowed. 

Btamp/e Another example of frontier orbital theory uses the reaction of phenyl-butadiene with phenylethylene. This reaction is a [4 + 2] pericyclic addition to form a six-membered ring. It could proceed with the two phenyl rings close to each other (head to head) or further away from each other (head to tail). 

The problems associated with predicting regioselectivity in quinone Diels-Alder chemistry have been studied, and a mechanistic model based on frontier molecular orbital theory proposed (85). In certain cases of poor regioselectivity, eg, 2-methoxy-5-methyl-l,4-ben2oquinone with alkyl-substituted dienes, the use of Lewis acid catalysts is effective (86). 

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