Transition frontier orbitals theory

Thus the reactivity of transition metal-carbene complexes, that is, whether they behave as electrophiles or nucleophiles, is well explained on the basis of the frontier orbital theory. Studies of carbene complexes of ruthenium and osmium, by providing examples with the metal in either of two oxidation states [Ru(II), Os(II) Ru(0), Os(O)], help clarify this picture, and further illustrations of this will be found in the following sections. 

The discussion by Braterman and Cross of reductive elimination from square planar or octahedral complexes is a special case of frontier orbital theory. A transition metal L MR, R2 is taken to lose grcwps R, R2 in a concerted step to give L M + Rj - R2. By the usual book-keeping convention, the electrons in the initial M—R a bonds are assigned to the R groups but this is of course a mere convention of naming and does not affect the argument. The in-phase combination of metal-carbon a bonds correlates... 

In homolytic substitution reactions, the 2-position of thiophene is the preferred site of attack. This is easily rationalized in terms of frontier orbital theory (B-76MI31401). Because of symmetry, both HOMO and LUMO of thiophene have the same absolute values for the coefficients (as shown in 216). Thus it is immaterial whether the [SOMO (radical)-HOMO (thiophene)] or the [SOMO (radical)-LUMO (thiophene)] interaction determines the site of attack only the 2-position is the point at which the radical would attack. The same conclusion is iso reached by consideration of product development control (74AHC(16)123). Attack at the 2-position would result in a transition state with an allylic radical, which would be stabilized to a greater extent than the one arising from attack at position 3 (Scheme 57). 

In contrast, applying frontier orbital theory to unimolecular reactions like electrocyclic reactions and sigmatropic rearrangements is inherently contrived, since we have artificially to treat a single molecule as having separate components, in order to have any frontier orbitals at all. Furthermore, frontier orbital theory does not explain why the barrier to forbidden reactions is so high—whenever it has been measured, the transition structure for the forbidden pathway has been 40 kJ mol-1 or more above that for the allowed pathway. Frontier orbital theory is much better at dealing with small differences in reactivity. 

A secondary orbital interaction has been used to explain other puzzling features of selectivity, but, like frontier orbital theory itself, it has not stood the test of higher levels of theoretical investigation. Although still much cited, it does not appear to be the whole story, yet it remains the only simple explanation. It works for several other cycloadditions too, with the cyclopentadiene+tropone reaction favouring the extended transition structure 2.106 because the frontier orbitals have a repulsive interaction (wavy lines) between C-3, C-4, C-5 and C-6 on the tropone and C-2 and C-3 on the diene in the compressed transition structure 3.55. Similarly, the allyl anion+alkene interaction 3.56 is a model for a 1,3-dipolar cycloaddition, which has no secondary orbital interaction between the HOMO of the anion, with a node on C-2, and the LUMO of the dipolarophile, and only has a favourable interaction between the LUMO of the anion and the HOMO of the dipolarophile 3.57, which might explain the low level or absence of endo selectivity that dipolar cycloadditions show. 

Hence Fukui s method is justified in the transition state, the FOs then being practically degenerate, with increased frontier coefficients at the reaction centers. All the other interactions are an order smaller.6 Unfortunately, transition state orbitals cannot be obtained easily,7 so we generally substitute the MOs of the reagents instead. This supplementary approximation,8 introduced for practical reasons, occasionally gives results which appear to violate the frontier orbital theory. We will examine such cases in more detail later (pp. 62, 76-78). 

Frontier orbital theory must always be used with the utmost caution in structural problems, for two reasons. The first, and main reason, is that frontier interactions are only dominant in the transition state and in structural problems the structures under study are stable ones. Furthermore, if a transition state may be considered with good reasons to be the perturbed initial system, as the bonds undergoing transformation are not completely formed or completely broken, this is no longer true in structural problems. The formal recombination of two fragments to give the final product corresponds to the complete formation of one or several new bonds, an important modification which may not always be treated as a perturbation. That is the second reason. 

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. 

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. 

This book is both a simplified account of frontier orbital theory and a review of its applications in organic chemistry it provides a basic introduction to the subject and a wealth of illustrative examples. Frontier orbital theory looks at how the transition state of an organic reaction is affected by the interaction of the molecular orbitals of the starting materials. It thus complements the more familiar thermodynamic picture of transition states, in which product-like character is seen as influencing the ease and the course of reactions. 

This situation affects all aspects of Chemistry. For example, ths frontier orbital theory of reaction mechanisms (57) stresses the symmetry properties of the highest occupied MO (HOMO) and of the lowest occupied MO (LUMO) of the reacting species in the point group of the transition state. Suppose we are discussing the protonation of ferrocene the question arises, what is the HOMO of the ferrocene molecule Is it the orbital given by Koopmans sequence of eigenvalues, or is it the 2g orbital whose energy on protonation may follow the ionization pattern and be hi er than that of the protonated orbital ... 

In general the rate of addition of a radical to an alkene depends largely on the substituents at the radical center and the alkene. Since the transition states of these exothermic reactions occur very early on the reaction coordinate, the polar effect of the substituents on the reactivity and selectivity can be described using frontier orbital theory . The interaction of the SOMO of the radical with the LUMO and/or HOMO of the carbon-carbon double bond plays a major role in determining the polar effect of the substituents. 

Nucleophilic alkyl radicals, i.e. c-C6Hir or t-Bu% add to activated alkynes 3.0-5.2 times slower than the corresponding substituted alkenes, whereas nucleophiles having lone pairs of electrons attack alkynes markedly faster than alkenes. Application of Frontier Orbital theory indicates early and late transition states for radical nucleophiles and nonradical nucleophiles, respectively. ... 

Dewar MJS (1989) A critique of frontier orbital theory. J Mol Struct (Theochem) 200 301-323 Doering W von E, Roth WR (1962) The overlap of two allyl radicals or a four-centered transition state in the cope rearrangement. Tetrahedron 18 67-74 Barman J (2004) Laws, symmetry, and symmetry breaking invariance, conservation principles, and objectivity. PSA 2002 Presidential Address, Philos Sci 71 1227-1241 Fisher G (2006) The autonomy of models and explanation anomalous molecular rearrangements in early twentieth-century physical organic chemistry. Stud Hist Philos Sci A 37 562-584 Gavroglu K, Simoes A (2012) Neither physics nor chemistry a history of quantum chemistry. MIT Press, Cambridge, MA... 

In summary, symmetry considerations based on frontier orbital theory enable a good understanding of H2 dissociation on transition-metal clusters. For a single atom, electron promotion energy and hybridization are important variables. In diatomics, the relative position of d versus s electrons determines whether the bonding symmetric s orbital built from s-atomic orbitals is occupied. Occupation of this... 

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