Computational Replication of the Primary Isotope Dependence of

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Computational Replication of the Primary Isotope Dependence of Secondary Kinetic Isotope Effects in Solution Hydride Transfer Reactions: Supporting the Isotopically Different Tunneling Ready State Conformations Mortaza Derakhshani-Molayousefi, Sadra Kashefolgheta, James E. Eilers, and Yun Lu J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b03571 • Publication Date (Web): 27 May 2016 Downloaded from http://pubs.acs.org on June 3, 2016

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The Journal of Physical Chemistry

Computational Replication of the Primary Isotope Dependence of Secondary Kinetic Isotope Effects in Solution Hydride Transfer Reactions: Supporting the Isotopically Different Tunneling Ready State Conformations

Mortaza Derakhshani-Molayouseﬁ,† Sadra Kashefolgheta,†§ James E. Eilers,† Yun Lu†* †Department of Chemistry, Southern Illinois University Edwardsville, Edwardsville, IL 62026 USA; §Department of Theory & Bio-systems, Max Planck Institute of Colloids and Interfaces, Am Mühlenberg 1, 14476 Potsdam Germany [email protected]

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Abstract We recently reported a study of the steric effect on the 1° isotope dependence of 2° KIEs for several hydride transfer reactions in solution (J. Am. Chem. Soc. 2015, 137, 6653). The unusual 2° KIEs decrease as the 1° isotope changes from H to D, and more in the sterically hindered systems. These were explained in terms of a more crowded tunneling ready state (TRS) conformation in D-tunneling, which has a shorter donor-acceptor distance (DAD), than in H-tunneling. In order to examine the isotopic DAD difference explanation, in this paper, following an activated motion-assisted H-tunneling model that requires a shorter DAD in a heavier isotope transfer process, we computed the 2° KIEs at various H/D positions at different DADs (2.9 Å to 3.5 Å) for the hydride transfer reactions from 2propanol to the xanthylium and thioxanthylium ions (Xn+ and TXn+) and their 9-phenyl substituted derivatives (Ph(T)Xn+). The calculated 2° KIEs match the experiments and the calculated DAD effect on the 2° KIEs fits the observed 1° isotope effect on the 2° KIEs. These support the motion-assisted Htunneling model and the isotopically different TRS conformations. Furthermore, it was found that the TRS of the sterically hindered Ph(T)Xn+ system does not possess a longer DAD than that of the (T)Xn+ system. This predicts a no larger 1° KIE in the former system than in the latter. The observed 1° KIE order is, however, contrary to the prediction. This implicates the stronger DAD-compression vibrations coupled to the bulky Ph(T)Xn+ reaction coordinate.


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Introduction Quantum mechanical H-tunneling has been increasingly recognized to be important in chemistry and biology. In this mechanism H particle tunnels through the energy barrier in light of its wave property. Contemporary theories predict that tunneling of a heavier isotope requires a shorter average donoracceptor distance (DAD) than does a lighter isotope, as a result of the less diffused wave packet of the heavier isotope bond vibrations.1-4 These include the activated motion-assisted H-tunneling model that involves heavy atom motions1-6 and the multi-dimensional H-tunneling mechanism within the variational transition state theory7. As a test of the primary (1°) isotopic DAD difference concept, we recently determined the effect of the transferring (in-flight) 1° H/D isotope on the in-place secondary (2°) H/D kinetic isotope effect (KIE) for several hydride transfer reactions in solution.8 The hypothesis is that the decrease in DAD as a result of change from 1° H to D induces a crowded reaction environment that stiffens the nearby 2° isotopic bond vibrations thus decreasing the 2o KIE (known as the steric 2° KIE), and that the pronounced 1o isotope dependence of 2° KIEs should be observed in more sterically hindered systems (Scheme 1). Our hydride transfer reactions were designed to involve various degrees of interactions between a steric factor and the targeted 2° H/D’s. We compared the steric effect on the 1° isotope dependence of 2° KIEs on the bulkier β-CH3/CD3’s and on the less readily sterically accessible “hidden” α-H/D’s. Results show that the β-CH3/CD3 KIEs are more sensitive to the 1° isotope effect than the α-H/D KIEs, especially in the sterically hindered systems, consistent with the hypothesis.

Scheme 1. It is hypothesized that the steric/crowding factors will increase the 1° isotope effect (i.e. the DAD effect) on the 2° KIEs in H-transfer reactions. The 2° KIE at the β-position is expected to be more sensitive than that at the α-position. The ovalshaped area is meant to show the wave packet of the transferring 1° H/D in the tunneling ready states (TRS’s).



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In order to verify the explanation of the 1° isotope dependence of 2° KIEs using the isotopically different TRS conformation concept, theoretical calculation of the DAD effect on the 2° KIEs and examination of whether they match the experiments are needed. In this paper, we carried out such calculations to replicate the observed 2° KIEs in both hydride and deuteride transfers from 2-propanol (2-PrOH) to the xanthylium and thioxanthylium ions (Xn+ and TXn+) and their sterically hindered 9-phenyl substituted derivatives (Ph(T)Xn+) (eqn (1)). The 2° KIEs include those at the β-CH3/CD3 position of the 2propanol and the 9-α-H/D position of the (T)Xn+. The theoretical model followed is the activated motion-assisted H-tunneling model that involves DAD-compression vibrational modes coupled to the reaction coordinate. The DAD effects from 2.9 to 3.5 Å on the 2° KIEs in all four systems were calculated and were compared with the observed 1° isotope effect on 2° KIEs. We will show that calculations match the experiments suggesting that the reactions follow the activated H-tunneling model and the Dtunneling does have a shorter DAD than the H-tunneling. Moreover, we will also compare the resultant TRS DAD order for the (T)Xn+ vs. Ph(T)Xn+ reactions with the order of the observed 1° KIEs in an attempt to evaluate factors (DAD and the DAD-compression vibration frequency) that affect the 1° KIE magnitude within the tunneling model. It has been proposed and debated that in enzymes, vibrations/dynamics of proteins are coupled to the reaction coordinate, compressing the reaction barrier and promoting the enzymatic reactions.9-15 In our work, both 1° and 2° KIE experiments demonstrate the existence of such vibrational modes in the solution reactions as well.


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The Activated Motion-Assisted H-Tunneling Model and the Computation Method There are two activation processes in the activated H-tunneling model, one for which is on the heavy atom reorganization coordinate - thermal energy is needed to mediate the energy of the reactant and product to reach the activated TRS in which the reactant (R-H‡, or R-HTRS) and product (P-H‡, or PHTRS) double potential wells are degenerate; the other for which is the DAD sampling - thermal energy is needed to activate the vibrations so as to sample the DADs at the TRS for efficient wavefunction overlap, i.e. the Frank-Condon (FC) overlap or H-tunneling (Scheme 2).2,5,16 Both processes are mediated by heavy atom thermal motions. Since the wavefunction of the bond vibration of the primary (1°) H possesses longer wavelength than that of the 1° D, their FC overlap is different (more for H than for D) contributing to a 1° kinetic isotope effect (> 1). The D-overlap decreases more rapidly than the Hoverlap with increasing DAD, so the 1o KIE would increase with increasing DAD and thus is a function of the DAD.17,18 While the latter DAD sampling process determines the 1o KIE, the former activation process involves the structural reorganization and is thus 2° isotope sensitive. The 2° KIE is mainly determined by the 2° C-H/D bond vibrational frequency difference in between the ground state and TRS. Generally, steric hindrance suppresses the 2° C-H/D vibrations at the TRS decreasing the 2° KIE.19,20 Due

Scheme 2. The DAD sampling activation process in the activated motion-assisted H-tunneling model. The H tunnels through the barrier in an activated TRS complex in terms of its wave form. Once H wave reaches the FC overlap area from the reactant (R-H) side, it can be found at the product (P-H) side. When the degeneracy of the double potential wells is broken, the H can be locked in the product well generating the product. The rate of the H-tunneling is directly proportional to the integrated FC terms over all the DADs sampled.



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to the H/D wavelength difference, the model requires a shorter DAD in D-tunneling than in Htunneling.2,4 It is then expected that the D-tunneling possesses larger steric hindrance at the TRS and thus the suppressed 2° KIE. Therefore, this model can explain the 1° isotope dependence of 2° KIEs.1,3,4,8 The computation method has been described in our previous publication.21 It is primarily based on the method of Roston and Kohen for modeling the 2° KIEs for the hydride transfer from benzyl alcohol to NAD+ in a yeast alcohol dehydrogenase.3 All geometry optimizations, potential energy surface scans, and frequency calculations were done with the Gaussian09 at the B3LYP/6-31+G(d) level at 60 °C at which the KIEs were determined. To calculate the 2° KIE to fit to the experiment, the structure of the TRS is needed. To search for this structure, the heavy atom skeleton structure was initially optimized with the 1° H atom fixed at the midpoint of the straight line between the “frozen” donor and acceptor carbons at a certain DAD. This is a transition state (TS)-like structure (Note that the real classical TS has shorter DAD, higher energy and different trajectory of the transferring nucleus). The 180o Cdonor-H-Cacceptor bond angle was chosen for the computational simplicity, and the quantum mechanical and molecular mechanical simulations demonstrate that the angle indeed does not substantially deviate from linearity.22,23 As an example, the structure in Figure 1 (A) shows such for the hydride transfer reaction from 2-propanol to PhXn+ at DAD = 3.1 Å. The corresponding C-H vibrational potential energy wells for the reactant (2-propanol) and product (PhXnH) moieties do not have the same energy, but the heavy atom positions are expected to be close to the TRS conformation that requires the double potential wells being degenerate. To yield the degenerate double potential wells, the heavy atom structures of the PhXnH and 2propanol moieties in the TS-like structure (A) need to be adjusted. The H-Cacceptor-Cbenzene angle for the PhXnH moiety and the H-Cdonor-O angle for the alcohol moiety are selected for the purpose, and the rest of the structures are optimized accordingly. The process is finalized until the degenerate double potential wells of the lowest energy are reached, in which the energy difference of the minima of the


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two wells is usually within 0.5 kcal/mol (in most cases,

Computational Replication of the Primary Isotope Dependence of

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