HMO Reaction Indices

In this section, we discuss some applications of the HMO method to reactivities of conjugated molecules. The reactions of conjugated molecules that have received most of this theoretical treatment are  

For any of these reactions, we imagine there to be a path of least energy connecting reactants with products. For the two distinct reaction positions, 1 and 2 on naphthalene, the activation energies e may differ, as indicated in Fig. 8-27. 

The problem is somehow to relate the differences in e (inferred from relative rate data) to a number based on quantum chemical calculations. To do this in a sensible way requires that we have some idea of the detailed way in which the reaction proceeds-we have to know what the reaction coordinate is. In some cases, this is fairly well known. For electrophilic aromatic substitution reactions, evidence suggests that a 

For attack by a neutral radical, electrostatic attraction and charge polarization should not be significant factors. The radical bonds to the site of attack to produce a more-or-less tetrahedrally bonded carbon. This again leads to an interruption of the tt system, but now it is not temporary as it was in the substitution reactions. 

Based on these simple pictures, a number of MO quantities, often referred to as reaction indices, have been proposed as indicators of preferred sites for reaction. It is useful to divide these into two categories-those purporting to relate to early stages of the reaction, and those specifically related to the intermediate stage. 

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The orbital requirements for radical attack on any polyene are given in Table 6. If H3, HC2 and Cl8 (see Walsh diagram, Fig. 2) can be taken as models, then three-center transition states will be linear. If, however, cyclic transition states can be formed, HMO theory indicates a preference for them (Fig. 1). Unfortunately, attempted radical displacements have not been observed, simply because the radicals take other reaction paths (Pryor, 1966). The transition states may have been linear, but for abstraction from rather than displacement on carbon (Bujake et al., 1961). If the radical and molecule generated in these cases remain in... 

Attempts have also been made338 346 to find a theoretical explanation of the stereo or positional selectivity in the first stage of the heterodiene synthesis, especially in the interaction between 5-ethoxy-4-methyloxazole and asymmetric dienophiles, e.g., /9-acetylacrylic acid and its ethyl ester. ir-Electron density calculations for the diene and dienophile molecules by the HMO method indicate the formation of the 4-acetylpyridine derivative (187) from ethyl /3-acetylacrylate, while the opposite orientation would be expected in the reaction with the free acid, giving a substituted 5-acetylpyridine as the main product. Indeed, 5-ethoxy-4-methyloxazole on condensation with ethyl /3-acetylacrylate affords only 187, while in the condensation with /3-acetylacrylic acid, only 2-methyl-3-hydroxy-5-acetylpyridine (188) is isolated.338 348... 

Chemical reactivity has been discussed mainly at the HMO level. Reaction indices such as superdelocalizabilities and localization energies suggest that nucleophilic attack should take place exclusively at the a-carbon. HMO calculations for p-localization energy suggest that intermediate (90) may be formed by the photo-oxidation of (89). The reactivity of (91) (electrophilic and nucleophilic substitution) and of 4-p-substituted derivatives of (88) (basicity) are discussed in refs. 170 and 171 respectively. 

At elevated temperatures (250-400°C) bromine reacts with thiazole in the vapor phase on pumice to afford 2-bromothiazole when equimolecu-lar quantities of reactants are mixed, and a low yield of a dibromothiazole (the 2,5-isomer) when 2 moles of bromine are used (388-390). This preferential orientation to the 2-position has been interpreted as an indication of the free-radical nature of the reaction (343), a conclusion that is in agreement with the free-valence distribution calculated in the early application of the HMO method to thiazole (Scheme 67) (6,117). 

HMO-treatment reveals a closed-shell system for the dianion of 6, thus indicating stabilization for isoelectronic cycl[2,2,2]azines with an additional nitrogen atom in a peripheral position, e.g., 7. Compounds of this type can be prepared by cycloaddition reactions. 

As rate constants of reactions of benzenoid hydrocarbons can be related to differences in energy of reactants and products (or intermediates) Hess-Schaad resonance energy differences can also be used as reactivity indices. Hess-Schaad resonance energies are defined as the difference between HMO ji energy and the additive contribution obtained by summing individual bond energies [42, 43]. Correlations of Hess-Schaad resonance energies with other HMO parameters have been discussed [44, 45],... 

Muetterties and Schunn (1966) suggest that certain boron hydride structures, e.g. 26 and 22 or 23 (C, symmetry, when X=Y), might be used as models for electrophilic substitution. In general, if 21 or 22 were the preferred C3 transition states or intermediates, the reaction would go with retention. Note that these are the analogs of the two-electron three-center species A3 discussed earlier by HMO theory. If, however, X, Y, and R were permuted, there would be several stereochemical possibilities, two of which are indicated in Table 7. To decide what kind of geometry is assumed in SE2 transition states, which are pentacoordinated and electron- and orbital-deficient, calculations on model species are needed to establish preferred geometries. 

The results of the refined MO calculations (tt-SCF MO without and with Cl, open-shell tt-SCF MO, tt-UHF, or CNDO/2 Cl methods) differ depending on the approximations used. In some cases, the tt-SCF MO Cl method gives results quite similar for both states to those obtained by tt-HMO method for the first excited state. These results [spin densities, bond orders Pge, and free valences on the C(5)-C(6) bond] all correlate with the greater tendency to photodimerization of uracil and thymine compared with cytosine and do not indicate which of the excited states is involved in the reaction. On the other hand, Danilov et using the tt-SCF MO CI as well as the open-shell tt-SCF... 

The electrocyclization reaction of 27 to produce 22 also represents a highly selective transformation. Application of orbital symmetry argue-ments 14> indicates that either 22 or 28 may be formed by a disrotatory cyclization reaction. HMO calculations do not allow for a choice between... 

As indicated in the previous section, there are comparatively few known examples of compounds containing fully conjugated rings and very few reactions at a conjugated ring have been reported for any of these compounds. The pyrrolotriazole (28) undergoes electrophilic substitution reactions at C-10, as predicted by simple HMO calculations (Section 8.03.2) <85JCR(S)363>. 

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