Reactivity numbers

Reactivity numbers of the most reactive positions have been used to correlate the reactivities in nitration (see below) and other substitutions of a series of polycyclic aromatic hydrocarbons, and they give somewhat better correlations than any of the other commonly used indices of reactivity. The relationship shown below, which was discussed earlier ( 7.1.1),... 

Dewar s treatment of transition state structure, using reactivity numbers, has the logical defect that in the intermediate kinds of transition states for which it provides evidence the electron localisation is only partial. However, in obtaining the values of the reactivity numbers (which are approximate localization energies), the process of localization is considered to be complete thus, values of parameters which strictly are relevant only to the Wheland type of transition state are incorporated into a different model. ... 

Somewhat more involved is the computation of further reactivity indices Wheland s atom localization energy, A6 exact super-delocalizability, S7 various polarizabilities, ir8 Brown s factor, Z° Dewar s reactivity number, Ap10 and the approximate superdelocali-zability, S 7... 

Dewar and Maitlis143 discussed quite successfully the course of nitration in series of pyridine-like heterocycles in terms of the Dewar reactivity numbers. There is a continuing interest in the electronic structure of pyridine65, 144-140 a model of this compound has been studied by the ASP MO LCAO SCF (antisymmetrized products) method in the 77-electron approxition.146 The semi-empirical parameters146 were obtained from the most recent values of ionization potentials and electron affinities, and bicentric repulsion integrals were computed theoretically. 

In cases where the oxirane ring is unsymmetrically substituted, the product structure can be predicted on the basis of attack at the most electrophilic center. This center has the lowest Dewar reactivity number (A/,) as predicted by MO calculations. The following example is illustrative. Benzo[c]phenanthrene 5,6-oxide (31) could give rise to two different zwit-terions (237 and 238). The former has a Dewar reactivity number 1.79 and the... 

In these equations, e represents the relative volume increase due to the feed and Rh the ratio of the heat capacities of both liquid phases. By representing the reactivity number as a function of the exothermicity number (Figure 5.3), different regions are obtained. The region where runaway occurs is clearly delimited by a boundary line. Above this region, for a high reactivity, the reaction is operated in the QFS conditions (Quick onset, Fair conversion and Smooth temperature profile) and leads to a fast reaction with low accumulation and easy temperature control (see Section 7.6). 

Various reactivity indices have been derived for benzenoid hydrocarbons from the following purely topological approaches the Huckel model (HMO), first-order perturbation theory (PMO), the free electron MO model (FEMO), and valence-bond structure resonance theory (VBSRT). Since many of the indices that have been known for a long time (index of free valence Fr, self-atom polarizability ir , superdelocalizability Sr, Brown s index Z, cation localization energy Lr+, Dewar reactivity number Nt, Brown s para-localization energy Lp) have been described in detail by Streitwieser in his well-known volume [23] we will refer here only to some more recent developments. 

The calculus for obtaining reactivity numbers according to the PMO or PMO-F model respectively is outlined in Scheme 2. 

Scheme 2. Calculation of the reactivity number (localization energy) for the 1-position of naphthalene according to the PMO and PMO-F method. (The denominator follows from the normalization condition, i.e. the normalized NBMO coefficients are inversely proportional to the root of the sum of squares of the unnormalized coefficients)...

There are principally two different approaches of correlating experimental rate data of electrophilic substitution with reactivity indices (1) Correlating the index with the rate data of a given reaction, e.g. bromination. For example, a satisfying correlation of Dewar reactivity numbers with the log of rate constants of the bromination of benzene, naphthalene (1- and 2-position), biphenyl (4-position), phenanthrene (9-position), and anthracene (9-position) has been observed [55]. In correlations of this type the reactivity index corresponds to the reactivity constant in the Hammett equation while the slope of the linear correlation corresponds to the reaction constant (see also Sect. 3) (2) correlating the index with experimental a values. 

More recently, correlations of a values with purely topological reactivity indices, vie. structure count ratio and Dewar reactivity number have been extensively studied by v. Szentpaly and Herndon [33, 58], Rather satisfying correlations were obtained the correlation coefficients for obvious reasons (see Sect. 4) being nearly identical for both indices (0.959 and 0.960 respectively, sample size 27). A significant improvement was achieved with Dewar reactivity numbers calculated according to the free electron version of the PMO treatment (correlation coefficient r = 0.973). 

To cast some light on the relative importance of steric effects on the positional reactivities of benzenoid hydrocarbons, correlations of experimental a values of phenanthrene (4), tetrahelicene (5), pentahelicene (<5), and hexahelicene (7) with purely topological reactivity indices (Huckel cation localization energy, Dewar reactivity number and Herndon structure count ratio) have been studied [59],... 

Experimental log k2 values were correlated with Brown para-localization energies, Dewar reactivity numbers, Herndon structure count ratios, Hess-Schaad resonance energy differences, indices of free valence, and second-order perturbation stabilization energies. The latter are based on Fukui s frontier orbital theory [67] which classifies the Diels-Alder reaction of benzenoid hydrocarbons with maleic anhydride as mainly HOMO (aromatic hydrocarbon)-LUMO (maleic anhydride) controlled. However, the corresponding orbital interaction energy given by... 

Correlations of experimental rate constants of benzogenic Diels-Alder reactions with Polansky (butadienoid) character orders [74] and Dewar reactivity numbers [75] have been observed. Herndon structure-count ratios, however, proved to be superior [76]. The standard deviation of the linear correlation between log k2 and structure count ratio is 0.483, i.e. goodness of fit is much less compared to that of plots obtained... 

As the values of the minimum Dewar reactivity number can obviously be connected only with the initial step of the thermal chemistry of benzenoid hydrocarbons it was concluded that the initial step is rate-determining. However, it is also possible that some other factor, connected with the Dewar localization energies for topological reasons, determines the rates of reaction. 

Since /S is negative, substitution should occur more readily the smaller the reactivity number Nt also there should be a linear relation between log k and Nt. Both these relations hold in practice.14-17... 

The similarity between Eqs. (39) and (64) implies that there must be a relationship between free valence number and reactivity number. This is indeed the case, for it can be shown14 at once by first order perturbation theory that... 

Statistical studies indicate13 that the reactivity number provides the best measure of reactivity in AH s at present available. This is surprising in view of the simplicity of the method. The calculations involved in it can be carried out by anyone in a matter of seconds using only pencil and paper. 

A nice example is provided by 10,9-borazarophenanthrene (V). The reactivity numbers for the isoconjugate AH, phenanthrene, are shown in (VI). The lowest numbers are in the 9,1- and 4-positions but the 4-position is sterically hindered. Experiment22 showed that the order of reactivity (nitration in acetic anhydride) for the various positions in phenanthrene was 9 > 1 > 3 4, 2. 

Where Ns is the reactivity number of atomy. But it can be shown19 that... 

There is therefore a correlation between the rate and the reciprocal of the self-polarizability, due to this accidental first-order correspondence between it and the reactivity number. The correlation does not in any way support the physical model on which it was originally based. 

Relative reactivity Number times reactivity Percent chlorination... 

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