Motion, primary-secondary coupled

Mixed Labeling Experiments as Probes for Tunneling and Primary-Secondary Coupled Motion... 

In 1983, Huskey and Schowen tested the coupled-motion hypothesis and showed it to be inadequate in its purest form to account for the results. If, however, tunneling along the reaction coordinate were included along with coupled motion, then not only was the exaltation of the secondary isotope effects explained but also several other unusual feamres of the data as well. Fig. 4 shows the model used and the results. The calculated equilibrium isotope effect for the NCMH model (the models employed are defined in Fig. 4) was 1.069 (this value fails to agree with the measured value of 1.13 because of the general simplicity of the model and particularly defects in the force field). If the coupled-motion hypothesis were correct, then sufficient coupling, as measured by the secondary/primary reaction-coordinate amplimde ratio should generate secondary isotope effects that... 

These studies had therefore found the tunneling phenomenon, with coupled motion, as the explanation for failures of these systems to conform to the expectations that the kinetic secondary isotope effects would be bounded by unity and the equilibrium effect and that the primary and secondary effects would obey the Rule of the Geometric Mean (Chart 3), as well as being consistent with the unusual temperature dependences for isotope effects that were predicted by Bell for cases involving tunneling. 

Thus the primary and secondary isotope eifects are all within the semiclassical limits and their relationship is in full accord with the semiclassical Swain-Schaad relationship. There is no indication from the magnitudes of the secondary isotope elfects in particular of any coupling between motion at the secondary center and the reaction-coordinate for hydride transfer. Thus the sole evidence taken to indicate tunneling is the rigorous temperature-independence of the primary isotope elfects. 

These data led to the model already described several times above. The enzyme executes a search for a tunneling sub-state, apparently 13 kcaFmol in energy above the principal state from this state the hydrogen atom tunnels with no further vibrational excitation. Probably motion of the secondary center is coupled into the tunneling coordinate. The result is large, temperature-independent primary and secondary isotope effects in the context of an isotope-independent activation energy. 

The observation of exalted secondary isotope effects, i.e., those that are substantially beyond the semiclassical limits of unity and the equilibrium isotope effect. These observations require coupling between the motion at the primary center and motion at the secondary center in the transition-state reaction coordinate, and in addition that tunneling is occurring along the reaction coordinate. 

The present reduced density operator treatment allows for a general description of fluctuation and dissipation phenomena in an extended atomic system displaying both fast and slow motions, for a general case where the medium is evolving over time. It involves transient time-correlation functions of an active medium where its density operator depends on time. The treatment is based on a partition of the total system into coupled primary and secondary regions each with both electronic and atomic degrees of freedom, and can therefore be applied to many-atom systems as they arise in adsorbates or biomolecular systems. 

Let us consider the photolysis of DBK on NaX as a standard system (Table 3). Under a vacuum or in an argon atmosphere, the major product is 1,2-diphenyl ethane (DPE) which results from diffusional separation of the primary radical pair, followed by decarbonylation and random coupling of the benzyl radicals produced in the secondary radical pair. These results, along with isotopic labelling experiments, show that diffusional motion of primary and secondary radical pairs is fast compared to coupling or decarbonylation reactions of the primary or the secondary radical pairs. The results for... 

---