Monatshefte für Chemie - Chemical Monthly ( IF 1.7 ) Pub Date : 2021-08-06 , DOI: 10.1007/s00706-021-02804-9 Joaquin F. Perez-Benito 1 , Arnau Clavero-Masana 1
|
Many homologous reaction series present linear correlations between the enthalpy (\(\Delta H_{{ \ne {\text{,i}}}}^{{\text{o}}}\)) and entropy (\(\Delta S_{{ \ne {\text{,i}}}}^{{{\text{ o}}}}\)) of activation (kinetic compensation effect), the slope being the isokinetic temperature of the series (Tiso), so that at T = Tiso, all the reactions of the family share the same value of the rate constant. However, the random errors committed in the laboratory in the determination of \(\Delta H_{{ \ne {\text{,i}}}}^{{\text{o}}}\) and \(\Delta S_{{ \ne {\text{,i}}}}^{{{\text{ o}}}}\) are interrelated, and so tend to produce false isokinetic relationships. As a result, the existence of physically meaningful isokinetic relationships is a topic of lasting controversy. Here, it is shown that both the LFER (linear free energy relationships)-type and isokinetic linear correlations are direct consequences of two other correlations, those of \(\Delta H_{{ \ne {\text{,i}}}}^{{\text{o}}}\) vs. \(\sigma _{{\text{i}}}\) and \(\Delta S_{{ \ne {\text{,i}}}}^{{{\text{ o}}}}\) vs. \(\sigma _{{\text{i}}}\), where the abscissa is the Hammett (or Taft) substituent parameter. A mathematical model has been developed, according to which Tiso can be interpreted as the temperature at which the reaction constant obtained as the slope of the LFER-type straight line takes a zero value (ρ = 0). Moreover, the numerical simulations performed indicated that the \(\log {\text{ }}k_{{{\text{ T}}}}\) vs. \(\sigma _{{\text{i}}}\) and \(\Delta H_{{ \ne {\text{,i}}}}^{{\text{o}}}\) vs. \(\Delta S_{{ \ne {\text{,i}}}}^{{{\text{ o}}}}\) linear plots can be visualized as two faces of the same coin, since, if the kinetic data obey the first with a correlation coefficient high enough, the probability of fulfillment of the second will be very high. Finally, it has been found that values of Tiso and Tδ (the slope of the linear correlation between the enthalpy–entropy deviations) very close to the mean working temperature, as well as correlation coefficients of the \(\Delta H_{{ \ne {\text{,i}}}}^{{\text{o}}}\) vs. \(\Delta S_{{ \ne {\text{,i}}}}^{{{\text{ o}}}}\) linear plots much higher than those corresponding to the \(\Delta H_{{ \ne {\text{,i}}}}^{{\text{o}}}\) vs. \(\sigma _{{\text{i}}}\) and \(\Delta S_{{ \ne {\text{,i}}}}^{{{\text{ o}}}}\) vs. \(\sigma _{{\text{i}}}\) plots, are all indicative of false isokinetic relationships, highly contaminated by the statistical correlation between the enthalpy and entropy experimental errors.
Graphic abstract
中文翻译：
哈米特和等速关系的相互依赖：一种数值模拟方法
许多同源反应系列呈现出焓 ( \(\Delta H_{{ \ne {\text{,i}}}}^{{\text{o}}}\) ) 和熵 ( \(\Delta S_{{ \ne {\text{,i}}}}^{{{\text{ o}}}}\) ) 的激活（动力学补偿效应），斜率是系列的等速温度（T iso )，因此在T = T iso 时，该族的所有反应都具有相同的速率常数值。然而，实验室在确定\(\Delta H_{{ \ne {\text{,i}}}}^{{\text{o}}}\)和\(\Delta S_ {{ \ne {\text{,i}}}}^{{{\text{ o}}}}\)是相互关联的，因此往往会产生错误的等速关系。因此，物理上有意义的等速关系的存在是一个持久争议的话题。在这里，表明 LFER（线性自由能关系）类型和等速线性相关性都是其他两个相关性的直接结果，即\(\Delta H_{{ \ne {\text{,i}}}} ^{{\text{o}}}\) vs. \(\sigma _{{\text{i}}}\)和\(\Delta S_{{ \ne {\text{,i}}}} ^{{{\text{ o}}}}\) vs. \(\sigma _{{\text{i}}}\)，其中横坐标是哈米特（或塔夫脱）取代基参数。已经开发了一个数学模型，根据该模型，T iso可以解释为反应常数作为 LFER 型直线的斜率取零值 ( ρ = 0) 时的温度。此外，所进行的数值模拟表明\(\log {\text{ }}k_{{{\text{ T}}}}\) vs. \(\sigma _{{\text{i}}}\ )和\(\Delta H_{{ \ne {\text{,i}}}}^{{\text{o}}}\)与\(\Delta S_{{ \ne {\text{,i }}}}^{{{\text{ o}}}}\)线性图可以可视化为同一枚硬币的两个面，因为，如果动力学数据服从第一个且相关系数足够高，则第二个的完成度会很高。最后，已经发现T iso和T δ 的值（焓-熵偏差之间线性相关的斜率）非常接近平均工作温度，以及\(\Delta H_{{ \ne {\text{,i}}}}^{的相关系数{\text{o}}}\) vs. \(\Delta S_{{ \ne {\text{,i}}}}^{{{\text{ o}}}}\)线性图远高于那些对应于\(\Delta H_{{ \ne {\text{,i}}}}^{{\text{o}}}\) vs. \(\sigma _{{\text{i}} }\)和\(\Delta S_{{ \ne {\text{,i}}}}^{{{\text{ o}}}}\)与\(\sigma _{{\text{i }}}\)图，都表明错误的等速关系，被焓和熵实验误差之间的统计相关性严重污染。
京公网安备 11010802027423号