Non-additive Effects of Structural Factors in Pyridine Catalyzed Reactions of Phenyloxirane with N-aroylbenzenesulfonamides

The combined influence of structural factors (Y, Z substituents) on the rate of catalyzed by Z-substituted pyridines reactions of phenyloxirane with Y-substituted N-aroylbenzenesulfonamides in acetonitrile at 293 K was studied. A cross-correlation analysis of the results of a multifactor kinetic experiment was carried out. A polylinear regression, that adequately describes the non-additive effects of substituents Y and Z, was calculated. Due to the interaction of the joint effects of structure, the cross-reaction series exhibits isoparametric properties. The mechanism of the catalytic process has been discussed.


INTRODUCTION
XIRANES have been studied by experimental and theoretical methods for many decades. Oxirane chemistry is still of current interest to researchers (see, e.g., recent publications [1][2][3][4][5] ). Of particular interest are oxirane ring opening reactions in which various internal and external factors are varied simultaneously. To describe these reactions, it is necessary to use the multiparameter relationships, based on the polylinearity principle. [6] Polylinear equations contain cross terms, considering interaction (non-additivity) of the effects of mutually varied factors. Interaction of the effects of two varied factors determines such an intriguing property of the polylinear equations as isoparametricity. This term means that the coefficient of sensitivity to the effect of one of factors in one-parameter correlation becomes zero for the isoparametric value of another factor called the isoparametric point. On passing through the isoparametric point, the inversion of the sign of the corresponding sensitivity coefficient takes place (isoparametricity paradox). As a real phenomenon, isoparametricity is a challenge to traditional concepts in chemistry. The isoparametric points are often experimentally inaccessible since they fall in the region of far extrapolation. This may explain the absence of active interest to investigation of the mysterious isoparametricity phenomenon in various fields of natural sciences.
In reactions of aryloxiranes with arenesulfonic and arenecarboxylic acids the interactions structure-structure and structure-temperature types were clearly manifested, [7][8][9][10] which made it possible to obtain convincing experimental evidence of the isoparametricity phenomenon. Of particular importance is the proof of the physical reality of such an aspect of isoparametricity as the widely discussed enthalpy-entropy compensation effect. [8][9][10] Our recent study [11] showed that in the catalyzed by Z-substituted pyridines reaction of phenyloxirane with such representative of NH acids as N-benzoylbenzenesulfonamide, there was no interaction between the effects of substituents Z and temperature. This reaction turned out to be isoenthalpic with respect to variation of substituents Z (ΔHZ ‡ = const, δZΔH ‡ = 0). The effects of substituents Z were manifested exclusively due to variation of the activation entropy (δZΔG ‡ = -T δZΔS ‡ ). It is of interest to elucidate the O joint effects of the structures of the oxirane substrate, acidic reagent, and catalyst in such reactions.
In this work, we have studied the combined influence of substituents Y and Z on the rate of catalyzed by pyridines Z-Py 3a-3d reactions of phenyloxirane 1 with N-aroylbenzenesulfonamides 2a-2c in acetonitrile at 293 K (Scheme 1). The results of a multifactor kinetic experiment were subjected to cross-correlation analysis, the isoparametric properties of the cross-reaction series were examined, the mechanism of the catalytic process was discussed.

EXPERIMENTAL
Chemically pure grade acetonitrile was dried and distilled over P2O5 and then over CaH2. Commercial phenyloxirane 1 (Merck, content of the main substance no less than 98%) and chemically pure grade pyridines 3a-3d were vacuumdistilled. Acidic reagents 2a-2c (mixed imides of benzenesulfonic and arenecarboxylic acids) were synthesized and purified as described in work. [12] The reaction products (Scheme 1) were primary alcohols, 2-(N-aroyl-N-benzenesulfonyl)amino-2-phenylethanols. [13] The reaction rate was measured as a decrease in the amount of acids 2, as was described in our earlier work. [14] The kinetics of the reactions were studied at more than tenfold excess of the oxirane substrate (S) with respect to initial concentrations of the acidic reagent (NH): [S]0 >> [NH]0 = 0.477 -1.91 mol dm -3 ; in turn, the concentration of pyridines ranged within m = 0.0116 -0.0860 mol dm -3 . Under those conditions, the reactions had a common third order: the first order for each of the reagents and the catalyst, so that the rate of the process at the constant concentration of the catalyst m was described by the following equation: The observed pseudo-first order rate constants k1 (s -1 ) were constant up to 70 -80% conversion of the acidic reagent (the error in measuring k1 was ≤ 5%). The second-order rate constants k2 (mol -1 dm 3 s -1 ) were obtained as k2 = k1 / [S]0. Numerical values of the effective catalytic third-order rate constants kYZ (mol -2 dm 6 s -1 ) were calculated from four kinetic runs at different concentrations m using the k2 = kYZ m linear equation (correlation coefficient r ≥ 0.998).
The accuracy of determining the kinetic and correlation parameters was estimated in term of the standard deviation S, which was determined by a statistical method from n experimental data points. Statistical data processing was carried out for the confidence level of 0.95.

RESULT AND DISCUSSION
The values of the rate constants kYZ for the catalytic reactions (Scheme 1) are listed in Table 1. For a quantitative assessment of the effects of the substituents Y and Z on the rate the following Hammett-type equations were used: Eq. (1) describes reactions with variable substituents Y and fixed substituents Z, and Eq. (2) describes the effects of variable substituents Z at fixed substituents Y. The Figure  below shows examples of linear dependences according to Eq. (2).
The results of processing kinetic data (Table 1) using Eqs. (1) and (2) are given in Table 2. They show that when passing from one fixed substituent Z (Y) to another, the sensitivity coefficients ρY Z (ρZ Y ) noticeably change. This indicates the interaction of the effects of the substituents Y and Z, which is also confirmed by the statistically significant values of the cross-interaction coefficient, which is equal to the slopes of the dependences (3) and (4).   To quantify the joint effects of substituents Y and Z on the rate of the catalytic process, we used Eq. (5) applicable to the two-parameter variant of polylinearity principle. [6] log kYZ = log kHH + ρY Z=H σY + ρZ Y=H σZ + ρYZσYσZ.
Here, kHH is the rate constant of the standard reaction (Y = Z = H, σY = σZ = 0), ρY Z=H and ρZ Y=H are the sensitivity coefficients of standard reaction series, and ρYZ is the above-mentioned cross-interaction coefficient. By processing the results of the multifactor kinetic experiment (Table 1) using Eq. (5), we obtained the polylinear regression, Eq (6) (R is the multiple correlation coefficient, F is the Fisher test). Regression [Eq. (6)] describes the catalytic reactions to a high degree of accuracy, as is evidenced by its statistical characteristics and the correspondence of the value of cross-interaction coefficient ρYZ to its values in Eqs. (3) and (4). Due to the statistical significance of cross-interaction coefficient (ρYZ = 0.47 ± 0.05), regression, Eq. (6), exhibits the isoparametric properties. Its attributes are isoparametric points with respect to the constants of the substituents Y (σY IP = -ρZ Y=H ρYZ −1 = 1.89) and Z (σZ IP = -ρY Z=H ρYZ −1 = -2.55), as well as the same value of the rate constant kYZ at these points (log kYZ IP = log kHH -ρY Z=H ρZ Y=H ρYZ −1 = -2.93). The experimental achievement of the isoparametric point σZ IP , at which the reaction rate should not depend on substituents Y in imides 2, is not possible due to the deficit of electrondonor substituents Z with σZ = -2.55. The isoparametric point σY IP , where the changes in the structure of substituents Z in pyridines 3 should not affect the reaction rate, also is experimentally unattainable.
The fulfilment of the cross correlations of the kinetic data [Eqs. (3), (4) and (6)] for the studied reactions (Scheme 1) is indicative of a uniform interaction between the effects of substituents Z in pyridines 3 and substituents Y in imides 2 within the framework of a single mechanism of the catalytic process (Scheme 2). The catalytic role of pyridines is to enhance the nucleophilic properties of the acidic reagent Y-NH (imides 2) due to the acid-base interaction in the first equilibrium stage. Among the possible ionic intermediates formed in an acetonitrile medium, imide anion Y-Nand pyridinium cation HPy + -Z should possess the strongest catalytic effect. In the second equilibrium stage, complex A is formed with a hydrogen bond between oxirane 1 and the pyridinium cation HPy + -Z. The oxirane substrate activated in this way undergoes a nucleophilic attack by the imide anion Y-Nwith the formation of transition state B in the third rate-determining stage. This stage proceeds according to the mechanism АNDN with electrophilic assistance from the pyridinium cation HPy + -Z to the С-О bond cleavage in the oxirane ring.
In view of the above considerations, the mechanism of the catalytic action of pyridines presented in Scheme 2 can be characterized as basic with electrophilic assistance.
According to Scheme 2, in the multistage catalytic process the interaction of the effects of substituents Y and Z can occur both in the first stage of the acid-base interaction and in the third stage of the oxirane ring opening. As for the interaction of structure effects in the first stage, it cannot play a dominant role in the catalytic process, because the opposite signs of the cross-interaction coefficient in the studied reaction system (ρYZ = 0.47) and in the process of proton transfer from phenols to pyridines (ρYZ = -0.57). [15] For this reason, the isoparametric points with respect to structural parameters in these crossreaction series differ significantly in nature. They correspond to the maximum of the acid-base interaction in the studied system (σY IP = 1.89, σZ IP = -2.55) and its minimum in the phenols-pyridines system (σY IP = -2.36, σZ IP = 1.89).
In view of the above, we can conclude that in the studied cross-reaction series the interaction of the effects of the substituents Y and Z manifests itself much more intensively in the oxirane ring opening stage than in stage of acid-base interaction.

CONCLUSION
In the presented study we revealed, based on the results a cross-correlation analysis of experimental kinetic data (Table 1), the interaction (non-additivity) of the joint effects of the structural factors (Y, Z substituents) in catalyzed by pyridines 3 reactions of oxirane 1 with NH-acids 2 (Scheme 1). The influence of the cross-varied factors on the rates of catalytic reactions is adequately described by the polylinear regression [Eq. (6)]. Owing to the interaction of the effects of the structural factors the studied crossreaction series exhibits isoparametric properties, the quantitative criteria of which are the cross-interaction coefficient ρYZ = 0.47, and isoparametric points with respect to the constants of the substituents Y (σY IP = 1.89) and Z (σZ IP = -2.55). In accordance with the properties of the isoparametric dependences at the isoparametric point σY IP (σZ IP ) the rate of catalytic reactions should not depend on substituent Z (Y). Both isoparametric points are experimentally unattainable. The positive sign of the crossinteraction coefficient ρYZ indicates the dominant role of the interaction of structural effects in the rate limiting stage of the oxirane ring opening (Scheme 2).