Computational replication of the abnormal secondary kinetic isotope effects in a hydride transfer reaction in solution with a motion assisted H-tunneling model

Abstract

We recently reported abnormal secondary deuterium kinetic isotope effects (2° KIEs) for hydride transfer reactions from alcohols to carbocations in acetonitrile (Chem. Comm. 2012, 48, 11337). Experimental 2° KIE values were found to be inflated on the 9-C position in the xanthylium cation but deflated on the β-C position in 2-propanol with respect to the values predicted by the semi-classical transition-state theory. No primary (1°) isotope effect on 2° KIEs was observed. Herein, the KIEs were replicated by the Marcus-like H-tunneling model that requires a longer donor-acceptor distance (DAD) in a lighter isotope transfer process. The 2° KIEs for a range of potential tunneling-ready-states (TRSs) of different DADs were calculated and fitted to the experiments to find the TRS structure. The observed no effect of 1° isotope on 2° KIEs is explained in terms of the less sterically hindered TRS structure so that the change in DAD due to the change in 1° isotope does not significantly affect the reorganization of the 2° isotope and hence the 2° KIE. The effect of 1° isotope on 2° KIEs may be expected to be more pronounced and thus observable in reactions occurring in restrictive environments such as the crowded and relatively rigid active site of enzymes.

Scheme 1. Hydride Transfer Reaction from 2-Propanol to Carbocations

Figure 1

Marcus-like model of H-tunneling. (A) Top, middle, and bottom panels show three stages of the reaction in two designated coordinates: the H position and the positions of the heavy atoms that modulate the potential surfaces (reactant surface is blue and product surface is red) for the transferred H. In the top panel, the heavy atoms are in a position such that the ZPE of the H is lower in the reactant well, so the H-wave function (green) is localized there. In the middle panel, the heavy atoms have rearranged to a TRS (‡), where the ZPE for the transferred H is equal in the reactant and product wells and the H-wave function (including contributions from any motions coupled to the H-position) can tunnel through the barrier. The rate of reaching this tunneling ready state depends on the reaction driving force (ΔG°) and the reorganization energy (λ). In the bottom panel, the heavy atoms have rearranged further, making the ZPE of the product lower than the reactant and thus trapping the transferred H in the product well. (B) At the TRS (middle panel of A) fluctuations of the DAD affect the tunneling probability. The top panel shows a free energy surface for the designated DAD coordinate, indicating the different levels of reactant–product wave function overlap at different DADs. At short enough DAD, the ZPE of the transferred particle may be above the barrier, but this leads to very small 1° KIEs and does not appear to be the case for ADH. The middle panel shows the Boltzmann probability distribution of the system being at any given DAD (magenta), along with the tunneling probabilities of H and D as a function of DAD (orange and purple, respectively). The bottom panel shows the product of the Boltzmann factor and the tunneling probability for each particle, yielding the probability of a reactive trajectory as a function of DAD. Panel B illustrates that the reactive trajectories for H and D go through different average DADs, constituting an isotope effect on TRS structure. In ADH, the difference in average DAD for hydride vs deuteride transfers, which was estimated as 0.2 Å, leads to differences in 2° KIEs when the transferred isotope is different. Figure and caption are reprinted with permission from ref (39). Copyright 2013 American Chemical Society.

Figure 2

(A) Initial optimized TS-like structure with DAD = 3.1 Å and the corresponding asymmetric double-potential wells (left for Acceptor-H vibrations in product XnH; right for Donor-H vibrations in reactant 2-propanol). The structure is in a position close to the TRS (‡) on the heavy atom coordinate in Figure 1A. (B) TRS structure with DAD = 3.1 Å, and the corresponding degenerate double-potential wells. The calculated hybridization states are for the reacting carbons, respectively. Although the transferring hydride is shown in both the donor and acceptor positions (i.e., in (Donor-H)^TRS and (Acceptor-H)^TRS), it is actually delocalized between the two.