Kinetic isotope effect quantum mechanical tunneling

HYDROGEN TUNNELING KINETIC ISOTOPE EFFECT QUANTUM MECHANICAL TUNNELING TURBIDITY... 

QUANTUM MECHANICAL TUNNELING CHEMICAL KINETICS HYDROGEN TUNNELING KINETIC ISOTOPE EFFECTS QUANTUM REQUIREMENT QUANTUM YIELD QUANTUM YIELD FLUQRESCENCE ACTINOMETER Quasi-axial,... 

Abstract Some of the successes and several of the inadequacies of transition state theory (TST) as applied to kinetic isotope effects are briefly discussed. Corrections for quantum mechanical tunneling are introduced. The bulk of the chapter, however, deals with the more sophisticated approach known as variational transition state theory (VTST). 

Complications that arise with this simple reaction are twofold. First, because of the low mass of the hydrogen atom its movement frequently exhibits non-classical behavior, in particular quantum-mechanical tunneling, which contributes significantly to the observed kinetic isotope effect, and in fact dominates at low temperature (Section 6.3). Secondly, in reaction 10.2 protium rather than deuterium transfer may occur ... 

Alhambra and co-workers adopted a QM/MM strategy to better understand quantum mechanical effects, and particularly the influence of tunneling, on the observed primary kinetic isotope effect of 3.3 in this system (that is, the reaction proceeds 3.3 times more slowly when the hydrogen isotope at C-2 is deuterium instead of protium). In order to carry out their analysis they combined fully classical MD trajectories with QM/MM modeling and analysis using variational transition-state theory. Kinetic isotope effects (KIEs), tunneling, and variational transition state theory are discussed in detail in Chapter 15 - we will not explore these topics in any particular depth in this case study, but will focus primarily on the QM/MM protocol. 

The enzyme-product complexes of the yeast enzyme dissociate rapidly so that the chemical steps are rate-determining.31 This permits the measurement of kinetic isotope effects on the chemical steps of this reaction from the steady state kinetics. It is found that the oxidation of deuterated alcohols RCD2OH and the reduction of benzaldehydes by deuterated NADH (i.e., NADD) are significantly slower than the reactions with the normal isotope (kn/kD = 3 to 5).21,31 This shows that hydride (or deuteride) transfer occurs in the rate-determining step of the reaction. The rate constants of the hydride transfer steps for the horse liver enzyme have been measured from pre-steady state kinetics and found to give the same isotope effects.32,33 Kinetic and kinetic isotope effect data are reviewed in reference 34 and the effects of quantum mechanical tunneling in reference 35. 

C H bond (HOMO) with the empty orbital (LUMO) of the divalent carbon would necessarily reduce orbital overlap in 27ax and concommitantly suppress the formation of alkene 28. Of course, the conformation of 27 CyD must resemble that of 26 CyD, and also the classical energy barrier to a 1,2-hydride shift cannot be undermined by ultrafast quantum mechanical (QM) tunneling. The latter caveat, however, can probably be neglected at room temperature.122 Indeed, the H/D primary kinetic isotope effect (KIE) for 1,2-H(D) shifts in scaffolded tricyclo[5.3.0.04,8]decan-2-ylidene (38) is quite low (Scheme 7),112 indicating the absence of QM tunneling. Hence, the photolytic Hax/Heq migration preference of 1.2 that was determined for carbene 38 is a dependable benchmark. 

In electrochemical proton transfer, such as may occur as a primary step in the hydrogen evolution reaction (h.e.r.) or as a secondary, followup step in organic electrode reactions or O2 reduction, the possibility exists that nonclassical transfer of the H particle may occur by quantum-mechanical tunneling. In homogeneous proton transfer reactions, the consequences of this possibility were investigated quantitatively by Bernal and Fowler and Bell, while Bawn and Ogden examined the H/D kinetic isotope effect that would arise, albeit on the basis of a primitive model, in electrochemical proton discharge and transfer in the h.e.r. 

Various quantum-mechanical theories have been proposed which allow one to calculate isotopic Arrhenius curves from first principles, where tunneling is included. These theories generally start with an ab initio calculation of the reaction surface and use either quantum or statistical rate theories in order to calculate rate constants and kinetic isotope effects. Among these are the variational transition state theory of Truhlar [15], the instanton approach of Smedarchina et al. 

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