Reactivity index

The reactivity index is the conventional theoretical quantity which is used as a measure of the relative rate of reactions of similar sort occurring in different positions in a molecule or in different molecules. As has already been mentioned in Chap. 2, most reactivity indices have been derived from LCAO MO calculations for unicentric reactions of planar n electron systems 5). The theoretical indices for saturated molecules have also been put to use In the present section the discussion is limited to the indices derived from the theory developed in the preceding sections, since the other reactivity indices are presented in more detail than the frontier-electron theory in the usual textbooks in this field. 

The reactivity indices derived from the theory which has been developed in Chap. 3 are the frontier-electron density, the delocalizability, and the superdelocalizability, as has been mentioned in Chap. 2. These indices usually give predictions which are parallel with the general orientation rule mentioned in Chap. 5. The superdelocalizability is conventionally defined for the w-electron systems on the basis of Eq. (3.21) and q. (3.24) as a dimensionless quantity of a positive value by the following equations  

The Hiickel integrals a and p are those which have appeared in Eq. (4.1). On inspecting the form of Eq. (6.1), the conventional character involved in the definition is obvious. First of all, the problem is the 

Sometimes, a too low-lying LU level of a bare electrophile will immediately rise by the charge transfer from reactant molecules. Similar circumstances will appear in the case of a bare nucleophile. 

For the purpose of comparing the reactivity towards different reagents, however, it may be more or less recommended to take into account the effect of the reagent orbital. In that case we need to go back to Eqs. (3.22) and (3.24). Such a type of modification of superdelocalizability has also been made so,56,67). 

---

The fonn of the classical (equation C3.2.11) or semiclassical (equation C3.2.11) rate equations are energy gap laws . That is, the equations reflect a free energy dependent rate. In contrast with many physical organic reactivity indices, these rates are predicted to increase as -AG grows, and then to drop when -AG exceeds a critical value. In the classical limit, log(/cg.j.) has a parabolic dependence on -AG. Wlren high-frequency chemical bond vibrations couple to the ET process, the dependence on -AG becomes asymmetrical, as mentioned above. 

HOMO and LUMO energies FMO reactivity indices Refractivity Total energy Ionization potential Electron affinity Energy of protonation Orbital populations Frontier orbital densities Superdelocalizabilities... 

A familiar feature of the electronic theory is the classification of substituents, in terms of the inductive and conjugative or resonance effects, which it provides. Examples from substituents discussed in this book are given in table 7.2. The effects upon orientation and reactivity indicated are only the dominant ones, and one of our tasks is to examine in closer detail how descriptions of substituent effects of this kind meet the facts of nitration. In general, such descriptions find wide acceptance, the more so since they are now known to correspond to parallel descriptions in terms of molecular orbital theory ( 7.2.2, 7.2.3). Only in respect of the interpretation to be placed upon the inductive effect is there still serious disagreement. It will be seen that recent results of nitration studies have produced evidence on this point ( 9.1.1). 

The use of q and tt separately as reactivity indices can lead to misleading results. Thus, whilst within the approximations used, the use of either separately leads to the same conclusions regarding electrophilic substitution into halogenobenzenes ( 9.1.4), the orientation of substitution in quinoline ( 9.4.2) cannot be explained even qualitatively using either alone. By taking the two in combination, it can be shown that as the values of Sa are progressively increased to simulate reaction, the differences in SE explain satisfactorily the observed orientation. ... 

Table 1-4 gives some calculated reactivity indices free valence or Wheland atomic localization energies for radical, electrophilic, or nucleophilic substitution. For each set of data the order of decreasing reactivity is indicated. In practice this order is more reliable than the absolute values of the reactivity indices themselves. 

The resonance integral of the 7r-bond between the heteroatom and carbon is another possible parameter in the treatment of heteroatomic molecules. However, for nitrogen compounds more detailed calculations have suggested that this resonance integral is similar to that for a C—C bond and moreover the relative values of the reactivity Indices at different positions are not very sensitive to change in this parameter. 

Theoretical reactivity indices of heteroaromatic systems distinguish reactivity toward electrophilic, nucleophilic and homolytic reactions. 

The significance of frontier electron densities is limited to the orientation of substitution for a given aromatic system, but this approach has been developed to give two more complex reactivity indices termed superdelocalizabilities and Z values, which indicate the relative reactivities of different aromatic systems. 

There are alternatives to the addition-elimination mechanism for nucleophilic substitution of acyl chlorides. Certain acyl chlorides are known to react with alcohols by a dissociative mechanism in which acylium ions are intermediates. This mechanism is observed with aroyl halides having electron-releasing substituents. Other acyl halides show reactivity indicative of mixed or borderline mechanisms. The existence of the SnI-like dissociative mechanism reflects the relative stability of acylium ions. 

Reactions involving monocyclic six-membered heteroaromatic rings have not been studied sufficiently extensively to allow a quantitative treatment of substituent effects. However, comparison with aza-naphthalene reactivities indicates that aza- and polyaza-benzene systems must also be highly selective. 

Our investigations agree with arguments in earlier articles by other authors, namely that empirical reactivity indices provide the best correlation with the goal values of the cationic polymerization (lg krel, DPn, molecular weight). On the other hand, the quantum chemical parameters are often based on such simplified models that quantitative correlations with experimental goal values remain unsatisfactory 84,85>. But HMO calculations for vinyl monomers show, that it is possible to determine intervals of values for quantum chemical parameters which reflect the anionic and cationic polymerizability 72,74) (see part 4.1.1) as well as grades of the reactivity (see part 3.2). 

Table 9. Anionic polymerization ability of vinyl monomers limits of quantum chemical reactivity indices from HMO calculations...

Numerous positive delayed skin tests in patients with contrast medium-induced non-immediate skin reactions have been reported when the patients were tested with the culprit contrast medium [summarized in 1]. In a large European multicenter study, 37% of patients with non-immediate reactions were positive in delayed IDEs and/or patch tests [13]. The majority of the patients also reacted to the culprit contrast medium and also to other, structurally similar RCM. Notably, in more than 30% of those skin test-positive patients a RCM had been administered for the first time. Thus, there is a lack of a sensitization phase. Again it may be hypothesized that these previously non-exposed patients may have already been sensitized. Different patterns of RCM cross-reactivity indicate that several chemical entities could be involved. No positive skin tests have been obtained with other contrast medium excipients, such as ethylenediaminetetraacetic acid (EDTA), and only rarely patients have been found to react to inorganic iodide. 

An alternative route for stabilization of quinone methides by metal coordination involves deprotonation of a ri5-coordinated oxo-dienyl ligand. This approach was introduced by Amouri and coworkers, who showed that treatment of the [Cp Ir(oxo-ri5-dienyl)]+ B1, 22 with a base (i-BuOK was the most effective) resulted in formation of stable Cp Ir(r 4-o-QM) complexes 23 (Scheme 3.14).25 Using the same approach, a series of r 4-o-QM complexes of rhodium was prepared (Scheme 3.14)26 Structural data of these complexes and a comparison of their reactivity indicated that the o-QM ligand is more stabilized by iridium than by rhodium. 

As has already been mentioned in Chap. 2, aromatic substitution was the first object of theoretical treatment of chemical reactivity. The reactivity indices of Chap. 6 have also been first applied to the aromatic substitution. Since existing papers 43> and reviews 44>65> are available for the purpose of verifying the usefulness of the indices, fT and Sr, only a few supplementary remarks are added here. 

Fig. 18 Invariant composition of nitrotoluene isomers obtained from various nitrating agents, with their (varying) reactivities indicated by the substrate selectivity (k/ko for toluene relative to benzene). The nitrating agents are identified by numbers in footnote 49 of ref. 235a. Reproduced with permission from Ref. 235a.

Configuration mixing model a general approach to organic reactivity, 21,99 Conformations of polypeptides, calculations of, 6,103 Conjugated molecules, reactivity indices, in, 4,73... 

The usual reactivity indices, such as elements of the first-order density matrix, are also incapable of distinguishing properly between singlet and triplet behavior. Recently, French authors 139,140) have discussed the problem and shown how electron repulsion terms can be introduced to obtain meaningful results. The particular case of interest to them was excited state basicity, but their arguments have general applicability. In particular, the PMO approach, which loses much of its potential appeal because of its inability to distinguish between singlet and triplet behavior 25,121) coui(j profit considerably from an extension in this direction. 119,122)... 

The number of Sis, present in today s chemical process industry is overwhelming as discussed by Tixier (Tixier et al., 2002). These indicators are categorized in several ways in literature, for example pro-active versus reactive indicators. Many of these categories are not unambiguous. Some authors, like Kletz (Kletz, 1998) define proactive as prior to the operational phase of an installation while other authors, like Rasmussen et al. (Rasmussen et al., 2000), define pro-active as prior to an accident. In this thesis two categories of indicators are used, i.e. pro-active and reactive indicators. Here the definition of Rasmussen (Rasmussen et al., 2000) is adopted, who defined pro-active indicators as indicators before an accident and reactive indicators as indicators after an accident. Moreover, the pro-active indicators are divided into predictive and monitoring indicators. The monitoring indicators use actual events as a measure for the likelihood, while the predictive indicators predict the likelihood. 

---