Chemistry

Yu. A. Zhdanov

Correlation between Taft $\sigma^*$ Constants and Information Entropy in Aromatic Substitution Reactions

(Presented by Academician A. N. Nesmeyanov, February 11, 1965)

Earlier \((^1)\) we showed that information entropy can serve as a measure of specificity in aromatic substitution reactions. In accordance with Shannon’s formula \((^2)\), the information entropy (or distribution entropy) for the products of subsequent substitution of monosubstituted benzenes is determined by the formula:

\[ H_s=-p_o \log p_o - p_m \log p_m - p_n \log p_n, \tag{1} \]

where $p_o$, $p_m$, $p_n$ are the molar fractions of the individual isomers (i.e., $p_o+p_m+p_n=1$)*. Obviously, the quantity $H_s$ expresses a measure of uncertainty in the course of the substitution reaction; its value is maximal when the yields of the isomers are equal and is equal to zero when only one product is formed.

It is of interest to establish a relationship between information entropy and quantitative characteristics of substituents in the benzene nucleus. To this end we compared the value of $H_s$ with Taft’s polar (inductive) constant $\sigma^*$ \((^3)\). Data for the nitration reaction in acetic anhydride at 25° are presented in Table 1. It follows from the data of this table that a decrease in the value of $\sigma^*$ entails an increase in the uncertainty of the course of the reaction. The value of $H_s$ begins to fall when we pass to alkyl substituents that donate electrons to the benzene ring by the inductive mechanism $+I$.

Table 1

By the method of least squares we calculated the correlation between $H_s$ and $\sigma^*$ separately for two groups of substituents: those having positive and negative values of $\sigma^*$. For the first group of substituents it turned out that the quantity $H_s$ is related to $\sigma^*$ by a linear dependence

\[ H_s = 0.4937 - 0.09345\,\sigma^*. \tag{2} \]

* The positions $o$ and $o'$, as well as $m$ and $m'$, are taken as indistinguishable.

The correlation coefficient is \(r = 0.96\). The calculated values of \(H_s\) correlate quite satisfactorily with the experimental data. For alkyls with negative values of \(\sigma^*\), the equation \(H_s = 0.3985 + 0.1765\sigma^*\) was obtained. In this series the correlation is weaker: \(r = 0.7\). In all cases we excluded from the calculation the data for the \(\mathrm{CH_3}\) group \((\sigma^* = 0.0)\), which

Table 2

sharply deviates from both series (in the first series \(\Delta H_s = 0.1389\); in the second \(\Delta H_s = 0.0437\)). This is also evident from Fig. 1, in which nitration is shown by the solid line and chlorination by the dashed line.

A somewhat different picture is observed for the chlorination reaction in acetic acid, as follows from the data in Table 2.

In this table, the presence of two groups of substituents is noteworthy. The first group includes \(\mathrm{NO_2}\), \(\mathrm{CN}\), \(\mathrm{Cl}\), and \(\mathrm{Br}\). As for the nitration reaction, here we observe a linear increase in the value of \(H_s\) as the substituent \(\sigma^*\) decreases. This dependence is well described by the equation

\[ H_s = 0.5923 - 0.0908\sigma^* . \tag{3} \]

In the present case the correlation coefficient is very high, \(r = 0.992\).

The behavior of the second group of substituents—\(\mathrm{NHAc}\), \(\mathrm{OH}\), \(\mathrm{OCH_3}\), \(\mathrm{CH_3}\)—is distinctive. Here \(H_s\) is practically independent of \(\sigma^*\); the process is characterized by approximately constant uncertainty of occurrence for different substituents, while the experimental values of \(H_s\) lie considerably below those calculated by formula (3).

Fig. 1

The regular change in \(H_s\) as a function of the substituent \(\sigma^*\) value in nitration reactions confirms the assumption of a single mechanism for this reaction for various substituted benzenes \((^4)\). This mechanism is associated with the initial formation of the nitronium cation, which attacks the aromatic nucleus, first forming a \(\pi\)-complex (I), and then a \(\sigma\)-complex (II), which subsequently decomposes to the final product:

\[ \mathrm{ R{-}C_6H_5 \xrightarrow{+NO_2} (I) \xrightarrow{} (II) \xrightarrow{-H^+} R{-}C_6H_4{-}NO_2 } \tag{4} \]

For the chlorination of substituted benzenes with \(\mathrm{Cl_2}\), a single mechanism \((^4)\) is usually also considered, which assumes attack of the aromatic nucleus by a chlorine molecule with the participation of a polar solvent (A).

\[ \tag{5} \]

However, on the basis of the data presented, it may be assumed that chlorination proceeds in the benzene ring by two routes. Of these, the first is close to the mechanism of nitration: attention is drawn to the parallel course of the nitration and chlorination plots, which makes it possible, from equations (2) and (3), to write the fairly exact relation

\[ H_s(\text{chlor.}) = H_s(\text{nitr.}) + 0.1. \]

It may be assumed that in this case, under the influence of the strong polar effect of the substituent already present in the benzene ring (high values of \(\sigma^*\)), a \(\pi\)-complex (I) is initially formed, which, under the influence of the electron-donating substituent \(R\), undergoes heterolytic decomposition with formation of the \(\pi\)-complex (I′); the latter, behaving analogously to the \(\pi\)-complex with the nitronium cation, rearranges into a \(\sigma\)-complex with the lesser degree of orientation (larger value of \(H_s\)), the lower the magnitude of \(\sigma^*\).

\[ \tag{6} \]

For chlorination reactions of the second type, mechanism (5) should be considered more probable, in which the decisive role belongs to the electromeric effect \(+E\). This explains the absence of a pronounced dependence of \(H_s\) on variation of \(\sigma^*\) and, at the same time, the high specificity of the process. The existence of two chlorination mechanisms is also indicated by the data on relative substitution rates (5). For reactions of the first type (\(-I\)-effect stronger than the \(+F\)-effect), the values of \(K_R/K_B\) lie in the range \(10^{-2}\)–\(10^{-1}\); for reactions of the second type they reach \(10^6\)–\(10^7\). In this case the \(+E\)-effect of the substituents considerably exceeds their inductive action.

Rostov-on-Don
State University

Received
8 II 1965

CITED LITERATURE

1. Yu. A. Zhdanov, Zh. Fiz. Khim., 39, No. 3 (1965).
2. C. Shannon, Works on Information Theory and Cybernetics, Moscow, 1963.
3. V. A. Palm, Russ. Chem. Rev., 30, 1069 (1961).
4. H. Becker, Einführung in die Elektronentheorie organischchemischen Reaktionen, Berlin, 1961.
5. L. M. Stock, H. C. Brown, Advances in Physical Organic Chemistry, 1, 1963.