The Role of Frontier Orbitals

Important is also the fact that, as a rule, the localization of frontier orbitals at the interacting centers leads to the narrowing of the gap between energy levels of the orbitals and thereby to the enhancement of orbital interactions [3]. If the symmetry (nodal) properties of the frontier MO s of reactants are such that an effective overlapping of the orbitals is impossible, then the mechnism described cannot be realized for the given geometry of approach. This conclusion constitutes the basis for the principle of stereoelectronic selection of appropriate reaction pathways. 

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Reactivity Patterns The Role of Frontier Orbital Theory... 

K. Fukui, The Role of Frontier Orbitals in Chemical Reactions (Nobel Lecture), Angew. Chem. Int. Ed. Engl. 1982, 21, 801-809. 

F.A. La Porta, R.T. Santiago, T.C. Ramalho, M.P. Freitas, and E.F.F. Da Cunha, The role of frontier orbitals in acid-base chemistry of organic amines probed by ab initio and chemometric techniques, Int. J. Quantum Chem. no (2010), pp. 2015-2023. 

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. 

Eukui K (1982) The role of frontier orbitals in chemical reactions. Angew Chem frit Ed Engl 21 801-809... 

As chemists we can pose a simple, focussed question how do the Woodward-Hoffmann rules (WHR) [18] arise from a purely electron density formulation of chemistry The WHR for pericyclic reactions were expressed in terms of orbital symmetries particularly transparent is their expression in terms of the symmetries of frontier orbitals. Since the electron density function lacks the symmetry properties arising from nodes (it lacks phases), it appears at first sight to be incapable of accounting for the stereochemistry and allowedness of pericyclic reactions. In fact, however, Ayers et al. [19] have outlined how the WHR can be reformulated in terms of a mathematical function they call the dual descriptor , which encapsulates the fact that nucleophilic and electrophile regions of molecules are mutually friendly. They do concede that with DFT some processes are harder to describe than others and reassure us that Orbitals certainly have a role to play in the conceptual analysis of molecules . The wavefunction formulation of the WHR can be pictorial and simple, while DFT requires the definition of and calculations with some nonintuitive ( ) density function concepts. But we are still left uncertain whether the successes of wavefunctions arises from their physical reality (do they exist out there ) or whether this successes is merely because their mathematical form reflects an underlying reality - are they merely the shadows in Plato s cave [20]. 

Explain the role of frontier electron orbital configuration on environmental chemistry. 

Water plays different roles that can be rationalized from the perspective of frontier orbital interactions. 

Although the applicability of the frontier orbital theory is very broad indeed, it is nevertheless necessary to be aware of the fact that the nature of this approach is still only approximate so that in certain cases some exceptions cannot be ruled out. The origin of these eventual failures was thoroughly discussed by Dewar in the study [51], where it was demonstrated that the greatest potential weakness of the approach consists in the very assumption attributing the decisive role only to interactions between the HOMO and LUMO orbitals of the individual components. It appears, namely, that this assumption need not be satisfied in all cases, and if this happens, the predictions of frontier orbital theory may fail. The typical example in this respect is, e.g., the addition of electron rich alkenes to ketenes, which is not, as demonstrates the formation of cyclobutanone instead of the expected a-methyleneoxetane,... 

The way the substituents affect the rate of the reaction can be rationalised with the aid of the Frontier Molecular Orbital (FMO) theory. This theory was developed during a study of the role of orbital symmetry in pericyclic reactions by Woodward and Hoffinann and, independently, by Fukui Later, Houk contributed significantly to the understanding of the reactivity and selectivity of these processes. ... 

However, there exists a reason which makes the role of the frontier orbitals in the process of chemical reactions more essential than expected from the expression of D. This can be understood if the change in nuclear configuration along the reaction path is taken into consideration. The discussion of this point will be made with the aid of three principles governing the reaction pathway. 

The value vr is regarded as a measure of the extent to which the electron in the rth AO takes part in the bond formation with other atoms. In contrast with this, pT is the part of population in the rth AO which is living there and responsible for the interaction with outside. Hence, in view of the role of the frontier orbital in the charge-transfer interaction, it is reasonable to take, as the frontier density, the valence-inactive part 7S>. Namely,... 

Apeloig and Kami (13) have also studied the effects of substituents on the reactivity of silenes by the frontier molecular orbital (FMO) approach. They have concluded that, concerning electronic factors, the polarity of the carbon-silicon double bond, and thus the coefficients of the frontier orbitals, play a more important role than the energies of these orbitals in controlling the reactivity of silenes. 

The frontier orbital approach (Fukui et al., 1962, 1954b) has met with considerable success in so far as frontier orbital charges correlate well with experimental data. The performance of these indices is often superior to that of others, with the possible exception of localization energies. It is, however, difficult to give meaning to the correlation since physical interpretations of the role of the frontier electrons in reaction mechanisms are often obscure, and attempts to give substance to Fukui s hypothesis have frequently embodied questionable procedures or models. 

The concept is in many ways attractive, and is based upon less speculative applications of quantum mechanical ideas than those described earlier in this section, but it does not result in any form of chemical bonding in the usual sense either by partial or complete a bonds or tr bonds. It would seem to be, in fact, more appropriate in describing stable Tt complexes as visualized by Mulliken (1950) and Dewar (1951). The role of the frontier orbitals in providing the configuration that... 

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... 

It can be seen from Eq. (53a) that the average over states at the chemical potential of the KS orbital density plays the role of the Fukui frontier-orbital... 

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