Oscillating reactions isotope effects

Another consequence of Fig. 3 (and of the harmonic oscillator approximation as well) is that the H—X vibration will have a slightly greater maximum amplitude than the D—X vibration. The space required by the hydrogen atom will thus be somewhat greater than that occupied by the deuterium atom. One could then imagine a steric secondary isotope effect in reactions which either increased or decreased crowding of isotopically substituted hydrogens. 

Even for purely adiabatic reactions, the inadequacies of classical MD simulations are well known. The inability to keep zero-point energy in all of the oscillators of a molecule leads to unphysical behavior of classical trajectories after more than about a picosecond of their time evolution." It also means that some important physical organic phenomena, such as isotope effects, which are easily explained in a TST model, cannot be reproduced with classical molecular dynamics. So it is clear that there is much room for improvement of both the computational and experimental methods currently employed by those of us interested in reaction dynamics of organic molecules. Perhaps some of the readers of this book will be provide some of the solutions to these problems. 

D atom. This value would have determined the KIE under one-dimensional tunneling. The potential barrier oscillations independent of the tunneling particle mass lead to a 10 -10 -fold decrease in the isotope effect. Growth of the intermolecular vibration amplitude with temperature causes a decrease of h/ d. whose dependence on T, computed for the reaction between the methyl radical and CH3CN, is shown in Figure 15. At 77 K, the computed value, 5 x 10, is close to the experimental one (> 3.10 ). 

Disregarding the tunnel effects (see Sect. 1.5) and staying within the approximation rigid rotator-harmonic oscillator, one may, for the biomolecular reaction A -h B), calculate the kinetic isotopic effect (ratio between the reaction rate constant of the compound with the light isotope and the rate constant K2 of the compound containing the heavy isotope) from the Bigeleisen equation ... 

Most of the work reported is covered in Section 4.12.5 on oscillating reactions. Anomalous kinetic isotope effects, which lead to values of the... 

In this equation, /Xj i 2 reduced masses of C- S and C- S harmonic oscillators , N is the number of atoms in the molecule under study, 3N-6 is the number of modes of vibration for a non-linear molecule, and 3N-5 for a linear molecule. The expression will be simplified owing to the fact that we wish to calculate the maximum isotope effect when, in the reaction transition state, the C-S bond is practically broken. For this reason, the right term in the bracketed expression of eq. (1.14.16) can be neglected, since we take the C-S bond, isolated from other atoms, as if it were a diatomic molecule, having 3N-5 modes of vibration in the ground state (i.e., one mode of stretching vibration), and 3N-6 modes of vibration in the reaction transition state, i.e., none. 

Hj Dj exchange on, 26 39-43 heteropolyanion-supported, 41 230-231 high MiUer index, 26 12-15,35,36 -H-USY zeoUte, 39 186-187 hydrocarbons adsorption, 38 229-230 reactions of cyclopropane, cyclohexane, and n-heptane, 26 51-53 structural effects, 30 25-26 hydrogen adsorption on, 23 15 hydrogenation, 30 281-282 olefins, in ethanol, 30 352-353 in hydrogenation reaction, 33 101 -iron alloys, 26 75 isomerization, 30 2-3 isotope, NMR properties, 33 213,274 kinetic oscillations, 37 220-228 ball models of densely packed surfaces, 37 221-222... 

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