Linear Free Energy Relationship and Kinetic Isotope Effects as Measures for the Transition State Variation. A Computational Study

Linear free energy relationship (LFER) and kinetic isotope effects (KIEs) are frequently used experimental means to study reaction mechanisms, in particular the nature of transition states (TSs). Density functional theory (B3LYP/6-311+G**) calculations were carried out on a model reaction, acid-catalyzed ionization of phenylethyl alcohol, to analyze how experimentally observable properties, such as nonlinearity in the Hammett and Brønsted relations and variation in KIE, are related to a variation of the transition state structure and the mechanism. Several conclusions and insights were obtained:  (1) Linear Hammett plots with a dual parameter treatment may not be evidence for an invariable TS structure for a series of reactions. (2) Variations of KIEs indeed reflect the variations of TS structures. (3) Nonlinear Brønsted plots cannot always be taken as evidence for a stepwise mechanism. (4) A TS structure in the gas phase may change much more easily than a TS structure in solution.