Molecular systems frontier orbital theory

The chemical potential, chemical hardness and sofmess, and reactivity indices have been nsed by a number of workers to assess a priori the reactivity of chemical species from their intrinsic electronic properties. Perhaps one of the most successful and best known methods is the frontier orbital theory of Fukui [1,2]. Developed further by Parr and Yang [3], the method relates the reactivity of a molecule with respect to electrophilic or nucleophilic attack to the charge density arising from the highest occupied molecular orbital or lowest unoccupied molecular orbital, respectively. Parr and coworkers [4,5] were able to use these Fukui indices to deduce the hard and soft (Lewis) acids and bases principle from theoretical principles, providing one of the first applications of electronic structure theory to explain chemical reactivity. In essentially the same form, the Fukui functions (FFs) were used to predict the molecular chemical reactivity of a number of systems including Diels-Alder condensations [6,7], monosubstituted benzenes [8], as well as a number of model compounds [9,10]. Recent applications are too numerous to catalog here but include silylenes [11], pyridinium ions [12], and indoles [13]. 

Frontier Molecular Orbital theory is closely related to various schemes of qualitative orbital theory where interactions between fragment MOs are considered. Ligand field theory, as commonly used in systems involving coordination to metal atoms, can be considered as a special case where only the d-orbitals on the metal and selected orbitals of the ligands are considered. 

This quantity can be viewed as a generalization of Fukui s frontier molecular orbital (MO) concept [25] and plays a key role in linking Frontier MO theory and the HSAB principle. It can be interpreted either as the sensitivity of a system s chemical potential to an external perturbation at a particular point r, or as the change of the electron density p(r) at each point r when the total number of electrons is changed. The former definition has recently been implemented to evaluate this function [26,27] but the derivative of the density with respect to the number of electrons remains by far the most widely used definition. 

The structural requirements of the mesomeric betaines described in Section III endow these molecules with reactive -electron systems whose orbital symmetries are suitable for participation in a variety of pericyclic reactions. In particular, many betaines undergo 1,3-dipolar cycloaddition reactions giving stable adducts. Since these reactions are moderately exothermic, the transition state can be expected to occur early in the reaction and the magnitude of the frontier orbital interactions, as 1,3-dipole and 1,3-dipolarophile approach, can be expected to influence the energy of the transition state—and therefore the reaction rate and the structure of the product. This is the essence of frontier molecular orbital (EMO) theory, several accounts of which have been published. 16.317 application of the FMO method to the pericyclic reactions of mesomeric betaines has met with considerable success. The following section describes how the reactivity, electroselectivity, and regioselectivity of these molecules have been rationalized. 

Frontier Molecular Orbital Theory can be used to describe qualitatively the trajectory of a nucleophile when it attacks a jt centre. Two sets of first-order interactions are considered. Firstly the stabilizing interaction of the HOMO of the nucleophile with the LUMO (jt and a orbitals) of the jt system and secondly the destabilizing interaction of the HOMO of the nucleophile with the HOMO (jt and a molecular orbitals) of the jt system, as shown in Figure 6. 

Scheme 3-5). Ohya-Nishiguchi et al. (1980) noted that such a large localized spin density is very rare in a ir-electron system of purine s size and should have important application to its chemical reactivity. Reactions such as protonation should take place preferentially at position 6. This was deduced from the result of molecular orbital calculations (Nakajima Pullman 1959). According to Fukui s frontier electron theory (Fukui et al. 1952), such areaction should take place at the position where the frontier electron density is the largest. The calculations clearly indicate that the large electron density is at position 6. Scheme 3-5 describes the protonation of the purine anion radical (Yao Musha 1974). Protonation indeed takes place at position 6. After that, the radical center appears at the cyclic nitrogen in the vicinal 1 position.

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... 

Three levels of explanation have been advanced to account for the patterns of reactivity encompassed by the Woodward-Hoffmann rules. The first draws attention to the frequency with which pericyclic reactions have a transition structure with (An + 2) electrons in a cyclic conjugated system, which can be seen as being aromatic. The second makes the point that the interaction of the appropriate frontier orbitals matches the observed stereochemistry. The third is to use orbital and state correlation diagrams in a compellingly satisfying treatment for those cases with identifiable elements of symmetry. Molecular orbital theory is the basis for all these related explanations. 

By definition, the Fukui function represents the change in electron density due to addition or removal of electrons from the system. Recalling results from the frontier molecular orbital theory, where the magnitude of the highest-occupied and lowest-unoccupied molecular orbitals are used to discern the propensity of a molecular site to attack by electron acceptors and electron donors, respectively, we deduce that the... 

This alternation of chemical behavior, 67t-system versus 47t-system, thermal versus photochemical, has at its core the quantum effeas that dictate the symmetries of molecular orbitals. In 1964, Roald Hoffmann (1937- ) was 27, had completed his Ph.D. at Harvard two years earlier, and was in the second year of an appointment as a Harvard junior fellow. The renowned Woodward (who would win the Nobel Prize in chemistry in 1965) discussed his observations on electrocyclic reactions with Hoffmann. Although Kenichi Fukui had developed frontier molecular orbital theory more than a decade earlier and many related theoretical ideas were percolating in the chemical community, it was Woodward and Hoffmann who published, in 1965, their intellectual synthesis as a book titled The Conservation of Orbital Symmetry. Their theory explained a broad spectrum of concerted reactions and made bold predictions that were later verified. 

Although sophisticated electronic structure methods may be able to accurately predict a molecular structure or the outcome of a chemical reaction, the results are often hard to rationalize. Generalizing the results to other similar systems therefore becomes difficult. Qualitative theories, on the other hand, are unable to provide accurate results but they may be useful for gaining insight, for example why a certain reaction is favoured over another. They also provide a link to many concepts used by experimentalists. Frontier molecular orbital theory considers the interaction of the orbitals of the reactants and attempts to predict relative reactivities by second-order perturbation theory. It may also be considered as a simplified version of the Fukui function, which considered how easily the total electron density can be distorted. The Woodward-Hoffmann rules allow a rationalization of the stereochemistry of certain types of reactions, while the more general qualitative orbital interaction model can often rationalize the preference for certain molecular structures over other possible arrangements. 

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