Frontier orbital approximation HOMO-LUMO interactions

The frontier orbital approximation recognizes the interaction between the HOMO and LUMO on both reactants as the crucial effect controlling the course of a... 

The 1,3-dipolar cycloaddition of organic azides with nitriles could give rise to two regioisomers. Since organic azides are Type II 1,3-dipoles on the Sustmann classification (approximately equal HOMO-LUMO gaps between the interacting frontier orbital pairs) the reactions could be dipole HOMO or LUMO controled and the regioselectivity should be determined by the orbital coefficients for the dominant HOMO-LUMO interaction. Such systems show U-shaped kinetic curves in their... 

We start with Salem s treatment of the Walden inversion Frontier orbital approximation is assumed the major interaction is supposed to be that between the nucleophile s HOMO and the substrate s LUMO. Now, according to ab initio calculations, the latter is essentially an out-of-phase combination of a carbon hybrid atomic orbital 0c with a leaving group hybrid atomic orbital 0x- In the first approximation, the LUMO wave function may be written as ... 

Anh and Minot (6) reported a rationalization of the stereochemistry at silicon by an extension of Salem s treatment of the Walden inversion (6 ). The frontier-orbital approximation is assumed, i.e., the major interaction during the reaction occurs between the HOMO of the nucleophile and the LUMO of the substrate o-f j-x. The calculated structure of the latter is shown below, with the big lobes of the hydrid AOs pointing toward each other (Scheme 9). 

It is important to note that many metallic properties, such as the Knight shift and the Korringa relationship, are determined by the finite and quasiFermi level local density of states ( p-LDOS). In the approximation most familiar to chemists, what this means is that the highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap in metals is much smaller than the thermal energy kf,T, and the value of the / f-LDOS reflects the frontier orbital contributions in a metallic system [23]. The /ip-LDOS also represents a crucial metal sxudace attribute that can serve as an important conceptual bridge between the delocalized band structure (physics) picture and the localized chemical bonding (chemical) picture of metal-adsorbate interactions. 

The cycloaddition of alkenes and dienes is a very useful method for forming substituted cyclohexenes. This reaction is known as the Diels-Alder reaction The concerted nature of the mechanism was generally accepted and the stereospecificity of the reaction was firmly established before the importance of orbtial symmetry was recognized. In the terminology of orbital symmetry classification, the Diels-Alder reaction is a [AUg + lUg] cycloaddition, an allowed process. The transition state for a concerted reaction requires that the diene adopt the s-cis conformation. The diene and substituted alkene (which is called the dienophile) approach each other in approximately parallel planes. The symmetry properties of the n orbitals permit stabilizing interations between C-1 and C-4 of the diene and the dienophile. Usually, the strongest interaction is between the highest occupied molecular orbital (HOMO) of the diene and the lowest unoccupied molecular orbital (LUMO) of the dienophile. The interaction between the frontier orbitals is depicted in Fig. 6.1. 

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 first term is the screened electrostatic interaction between the donor and acceptor charges Qi and Q2 - assumed to be point charges - at the equilibrium distance Rn in the adduct. The second term accounts for covalent effects. The factor of 2 indicates that two electrons are shared. The c coefficients are the molecular wave-function weights on atoms 1 and 2. The energies Em and E are equal, to a first approximation, to the frontier orbital energies the base HOMO (HOMO = highest occupied molecular orbital) and the acid LUMO (LUMO = lowest unoccupied molecular orbital), i.e. to the base first ionization potential and to the acid electron aflSnity. A typical frontier orbital diagram is shown in Fig. 6.1. 

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