Frontier molecular orbital theory chemical reactivity

Simple Approaches to Quantifying Chemical Reactivity 3.4.2.1 Frontier Molecular Orbital Theory... 

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. 

According to the frontier molecular orbital theory (FMO) of chemical reactivity, the formation of a transition state is due to an interaction between the frontier orbitals, such as HOMO and LUMO of reacting species. In general, the important frontier orbitals for a nucleophile reacting with an electrophile are HOMO (nucleophile) and LUMO (electrophile). 

More recently, molecular orbital theory has provided a basis for explaining many other aspects of chemical reactivity besides the allowedness or otherwise of pericyclic reactions. The new work is based on the perturbation treatment of molecular orbital theory, introduced by Coulson and Longuet-Higgins,2 and is most familiar to organic chemists as the frontier orbital theory of Fukui.3 Earlier molecular orbital theories of reactivity concentrated on the product-like character of transition states the concept of localization energy in aromatic substitution is a well-known example. The perturbation theory concentrates instead on the other side of the reaction coordinate. It looks at how the interaction of the molecular orbitals of the starting materials influences the transition state. Both influences on the transition state are obviously important, and it is therefore important to know about both of them, not just the one, if we want a better understanding of transition states, and hence of chemical reactivity. 

A variety of molecular descriptors have been defined and used proceeding from frontier molecular orbital theory (FMO) of chemical reactivity [42]. This theory is based on the concept of the superdelocalizability, an index characterizing the affinity of occupied and unoccupied orbitals in chemical reactions. A distinction has been made between the electrophilic and the nucleophilic superdelocalizability (or acceptor and donor superdelocalizability), respectively. The former describes the interaction of... 

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. 

In view of this, early quantum mechanical approximations still merit interest, as they can provide quantitative data that can be correlated with observations on chemical reactivity. One of the most successful methods for explaining the course of chemical reactions is frontier molecular orbital (FMO) theory [5]. The course of a chemical reaction is rationali2ed on the basis of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO), the frontier orbitals. Both the energy and the orbital coefficients of the HOMO and LUMO of the reactants are taken into account. 

From 1933 85>, several theoretical approaches to the problem of the chemical reactivity of planar conjugated molecules began to appear, mainly by the Huckel molecular orbital theory. These were roughly divided into two groups 36>. The one was called the "static approach 35,37-40)j and the other, the "localization approach 41,42). in 1952, another method which was referred to as the "frontier-electron method was proposed 43> and was conventionally grouped 44> together with other related methods 45 48> as the "delocalization approach". 

Frontier molecular orbital (FMO) theory 62) has provided new insights into chemical reactivity. This, and the simplicity of its application, has led to its widespread use, particularly in the treatment of pericyclic reactions 63). An FMO treatment depends on the energy of the highest occupied (HOMO) and lowest unoccupied molecular... 

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.

We cannot, then, expect this approach to understanding chemical reactivity to explain everything. Most attempts to check the validity of frontier orbital theory computationally indicate that the sum of all the interactions of the filled with the unfilled orbitals swamp the contribution from the frontier orbitals alone. Even though the frontier orbitals make a weighted contribution to the third term of the Salem-Klopman equation, they do not account quantitatively for the many features of chemical reactions for which they seem to provide such an uncannily compelling explanation. Organic chemists, with a theory that they can handle easily, have fallen on frontier orbital theory with relief, and comfort themselves with the suspicion that something deep in the patterns of molecular orbitals must be reflected in the frontier orbitals in some disproportionate way. 

Over the years, different approaches have been developed to reveal chemical bonds. Covalent bonds are intuitively represented using conventional Lewis stractures [19]. Molecular Orbital (MO) theory has been veiy useful and successfiil for the theoretical analysis of chemical reactions and chemical reactivity. The frontier orbital theory [20] and the orbital symmetry rules of Woodward and Hoffman [21] are paradigmatic examples of the possibilities of quantum chemistry within the MO 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]. 

R. McWeeny, Coulson s Valence, 3rd Edn, Oxford University Press, Oxford, 1979 A. Szabo and N. S. Ostlund, Modern Quantum Chemistry, Dover, New York, 1996 N. J. B. Green, Quantum Mechanics 1 Foundations, Oxford University Press, Oxford, 1997 D. A. McQuarrie and J. D. Simon, Physical Chemistry A Molecular Approach, University Science Books, Sausalito, CA, 1997 V. M. S. Gil, Orbitals in Chemistry, Cambridge University Press, Cambridge, 2000 A. Vincent, Molecular Symmetry and Group Theory, 2nd Edn, John Wiley Sons, Ltd, Chichester, 2001 A. Rauk, Orbital Interaction Theory of Organic Chemistry, 2nd Edn, John Wiley Sons, Ltd, New York, 2001 D. O. Hayward, Quantum Mechanics for Chemists, Royal Society of Chemistry, Cambridge, 2002 J. E. House, Fundamentals of Quantum Chemistry, 2nd Edn, Elsevier, Amsterdam, 2004 N. T. Anh, Frontier Orbitals A Practical Manual, John Wiley Sons, Ltd, Chichester, 2007 J. Keeler and P. Wothers, Chemical Structure and Reactivity, Oxford University Press, Oxford, 2008. 

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