Incorporation of hydrostatic pressure into models of hydrogen tunneling highlights a role for pressure-modulated promoting vibrations

Hydrostatic pressure offers an alternative to temperature as an experimental probe of hydrogen-transfer reactions. H tunneling reactions have been shown to exhibit kinetic isotope effects (KIEs) that are sensitive to pressure, and environmentally coupled H tunneling reactions, those reactions in which H transfer is coupled to atomic fluctuations (a promoting vibration) along the reaction coordinate, often have quite temperature-dependent KIEs. We present here a theoretical treatment of the combined effect of temperature and pressure on environmentally coupled H tunneling reactions. We develop a generalized expression for the KIE, which can be used as a simple fitting function for combined experimental temperature- and pressure-dependent KIE data sets. With this expression, we are able to extract information about the pressure dependence of both the apparent tunneling distance and the frequency of the promoting vibration. The KIE expression is tested on two data sets {the reduction of chloranil by leuco crystal violet Isaacs, N. S., Javaid, K., and Rannala, E. (1998) J. Chem. Soc., Perkin Trans. 2, 709-711] and the reduction of morphinone reductase by NADH Hay, S., Sutcliffe, M. J., and Scrutton, N. S. (2007) Proc. Natl. Acad. Sci. U.S.A. 104, 507-512]} and suggests that hydrostatic pressure is a sensitive probe of nuclear quantum mechanical effects in H-transfer reactions.