An Experimentally Based Family of Potential Energy Surfaces for Hydride Transfer between NAD⁺ Analogues

A family of three-body potential energy surfaces has been constructed to model experimental rate constants, k_ij for hydride transfer between NAD⁺ analogues in a 2-propanol-water solvent at 25 ^°C. The potential energy surfaces are analytical expressions for potential energy as functions of atom and group coordinates. They permit the use of variational transition-state theory (VTST) and large-curvature semiclassical tunneling approximations to calculate reaction rates. In previous work, about 50 experimental rate constants, k_ij, spanning a range of 10¹¹ in equilibrium constant, K_ij, and 10⁶ in k_ij, were fitted to a simplified form of Marcus theory which we now call linearized Marcus theory. With the aid of this formalism and four parameters, all rate constants for hydride transfer under the specified conditions can be reproduced. The average discrepancy between calculated and observed rate constants is a factor of 1.6. Primary kinetic isotope effects (KIEs) were also measured, for a range of K_ij. Structure variation in the donor leads to an increase in the KIE when K_ij is increased, while structure variation in the acceptor leads to a decrease in the KIE when K_ij is increased, both in accord with linearized Marcus theory. The rate constants and KIEs calculated by the VTST-plus-tunneling method were also treated by linearized Marcus theory. The parameters of the potential energy surface were varied to optimize the agreement between computational and experimental isotope effects, and the same four Marcus parameters for both hydride and deuteride transfer. All the relevant qualitative features of the experimental results were reproduced, and the quantitative agreement is satisfactory. The C-H stretching frequencies of the reactants and products are also reproduced. The most probable critical configurations in the VTST-plus-tunneling calculations involve tunneling at heavy-atom separations greater than that of the transition state (corner-cutting tunneling). About 1 kcal mol⁻¹ of the barrier is evaded by tunneling. Tunneling has a major effect on the calculated KIE values and their variation with K_ij, and it has a perceptible effect on the Marcus parameters. Because so many characteristics of the experimental k_ij values are reproduced, we conclude that the potential functions are a reasonable representation of the real potential energy functions governing the hydrogenic motions, at least in the neighborhood of reactants and critical configurations.