Frontier molecular orbital theory relativity

According to frontier molecular orbital theory, the strongest interactions are between those orbitals that have coefficients with similar magnitudes relative to the unperturbed molecules, t.e. the interaction is between the small coefficient on the dienophile and the small coefficient on the diene [16], [17]. 

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. 

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. 

Reactive Enophile in [4 + 2] Cycloadditions. Vinylketenes are not effective as dienes in Diels-Alder reactions because they undergo only [2 + 2] cycloaddition with alkenes, as predicted by frontier molecular orbital theory. However, silylketenes exhibit dramatically different properties from those found for most ketenes. (Trimethylsilyl)vinylketene (1) is a relatively stable isolable compound which does not enter into typical [2 + 2] cy do additions with electron-rich alkenes. Instead, (1) participates in Diels-Alder reactions with a variety of alkenic and alkynic dienophiles. The directing effect of the carhonyl group dominates in controlling the regiochemical course of cycloadditions using this diene. For example, reaction of (1) with methyl propiolate produced methyl 3-(trimethylsilyl)sahcylate with the expected regiochemical orientation. ProtodesUylation of this adduct with trifluoroacetic acid in chloroform (25 °C, 24 h) afforded methyl salicylate in 78% yield (eq 2). 

The basis for these relative reactivity relationships and also the regioselectivity of the Diels-Alder reaction can be interpreted very satisfactorily in terms of frontier molecular orbital theory. The pattern of regioselectivity of the Diels-Alder reaction is summarized in Scheme 10.2. 

Further examination of the results indicated that by invocation of Pearson s Hard-Soft Acid-Base (HSAB) theory (57), the results are consistent with experimental observation. According to Pearson s theory, which has been generalized to include nucleophiles (bases) and electrophiles (acids), interactions between hard reactants are proposed to be dependent on coulombic attraction. The combination of soft reactants, however, is thought to be due to overlap of the lowest unoccupied molecular orbital (LUMO) of the electrophile and the highest occupied molecular orbital (HOMO) of the nucleophile, the so-called frontier molecular orbitals. It was found that, compared to all other positions in the quinone methide, the alpha carbon had the greatest LUMO electron density. It appears, therefore, that the frontier molecular orbital interactions are overriding the unfavorable coulombic conditions. This interpretation also supports the preferential reaction of the sulfhydryl ion over the hydroxide ion in kraft pulping. In comparison to the hydroxide ion, the sulfhydryl is relatively soft, and in Pearson s theory, soft reactants will bond preferentially to soft reactants, while hard acids will favorably combine with hard bases. Since the alpha position is the softest in the entire molecule, as evidenced by the LUMO density, the softer sulfhydryl ion would be more likely to attack this position than the hydroxide. 

Various types of electron-deficient sulfur diimides react as hetero-dienophiles. In general, these cycloadditions occur under conditions similar to those used for AT-sulfinyl compounds. However, fewer types of sulfur diimides have been utilized in this process relative to Af-sulfinyl compounds. Some examples of symmetrical sulfur diimide Diels-Alder reactions are listed in Table l-II. It should again be noted that the orientational selectivity in these cycloadditions is the same as that shown by N-sulfinyl systems (cf. Table l-I). Several examples of cycloadditions with unsymmetrical sulfur diimides are shown in Table l-III. In all cases, these reactions were totally regioselective, and as noted above, reactions occurred at the least electron-deficient nitrogen-sulfur bond. Frontier molecular orbital (FMO) theory has been used to rationalize the regio-selectivity of addition of the cationic sulfur diimide shown in entry... 

The question still remained could a trace amount of bis(p-oxo) species be the oxidizing agent Based on the upper concentration limit of bis(p-oxo) present, (0.0013 1 [Cu 02] [Cu2 (02)] ), its rate of reactivity would have to be > 10 times faster than that of the side-on peroxo in order to coincide with the kinetics observed. This would require the bis(p-oxo) core to be significantly more electrophilic than the side-on peroxo isomer. Frontier molecular orbital (FMO) theory was employed to assess the electrophilic character of the bis(p-oxo) species relative to that of the side-on peroxo isomer. The molecular orbital descriptions (specifically the percentage of ti character) and relative energies of the relevant LUMO s of the side-on peroxo... 

Frontier Molecular Orbital (FMO) theory attempts to predict relative reactivity based on properties of the reactants. It is commonly formulated in term of perturbation theory, where the energy change in the initial stage of a reaction is estimated and extrapolated to the transition state. For a reaction where two different modes of reaction are possible, this may be illustrated as shown in Figure 15.1. 

To summarize how acid-base reactions do work on the basis of molecular orbitals perturbation theory, we have reported on Figure 10.2.1, the relative energies (as perturbed by the field of the other reactant) of the frontier orbitals HOMO and LUMO of a hypothetical species A and of the frontier orbitals of several hypothetical reaction partners B, C, D, E and F. This figure is intended to represent possible variations of donor-acceptor properties in the broadest possible context i.e. not only those species encountered in aqueous solution but also those stabilized by non-aqueous environments. 

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