Tunnelling, zero activation energy

Based on C-H versus C-D zero point vibrational differences, the authors estimated maximum classical kinetic isotope effects of 17, 53, and 260 for h/ d at -30, -100, and -150°C, respectively. In contrast, ratios of 80,1400, and 13,000 were measured experimentally at those temperatures. Based on the temperature dependence of the atom transfers, the difference in activation energies for H- versus D-abstraction was found to be significantly greater than the theoretical difference of 1.3kcal/mol. These results clearly reflected the smaller tunneling probability of the heavier deuterium atom. 

Fortunately, it is relatively simple to estimate from harmonic transition-state theory whether quantum tunneling is important or not. Applying multidimensional transition-state theory, Eq. (6.15), requires finding the vibrational frequencies of the system of interest at energy minimum A (v, V2,. . . , vN) and transition state (vj,. v, , ). Using these frequencies, we can define the zero-point energy corrected activation energy ... 

Hydron atoms readily dissolve into bulk Pd, where they can reside in either the sixfold octahedral or fourfold tetrahedral interstitial sites. Determine the classical and zero-point corrected activation energies for H hopping between octahedral and tetrahedral sites in bulk Pd. In calculating the activation energy, you should allow all atoms in the supercell to relax but, to estimate vibrational frequencies, you can constrain all the metal atoms. Estimate the temperature below which tunneling contributions become important in the hopping of H atoms between these two interstitial sites. 

In the presence of tunneling, the difference in the activation energies for H and D transfer, A a = is greater than the difference in zero-point energies, AZPE,... 

On the other hand, the excimer emission because it is 80% non-correlated with monomer trap emission and because it is effectively quenched in the copolymers even at low temperatures, must largely arise from a mobile precursor. The activation energy for hopping of this precursor is implied to be <10 cm l. This is not unreasonably low(12,17), and indeed, the zero-point energy of the phenyl chromo-phore could in principle allow completely activationless hopping (tunneling) at reasonable rates. Determination of the true situation will require measurements at still lower temperatures, which are now in progress. We note that the polystyrene emission spectrum at 4.2K reported in (Id) indicates a monomer/excitner intensity ratio nearly the same as our 20K spectra. 

What was most striking in the BSAO system was the evidence for deuterium as well as protium tunneling. First, the value of the D/T isotope effect on kcat/ M at 25 °C is greater than the maximum expected value arising from zero-point energy differences. Second, the isotope effect on the Arrhenius pre-factor is well below that which is expected from semi-dassical predictions. Finally, the differences in enthalpy of activation for D vs. T in the primary position well exceed differences predicted from zero point energies. 

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