Zero-point energy factors reactions

Thus the secondary and primary deuterium isotope effects determined in this study also indicate that entropy and zero-point energy factors associated with breaking of the C—D bond and migration in the activated complexes are important for the structural isomerization to yield butene-1 and butene-2, and reaction path B (equation 197) must be included in the mechanistic considerations concerning the cyclopropane isomerization. But the higher activation energy for isobutane formation (g = 64.3 kcal mol" ) than that for butene-2 or butene-1 (Q = 62.0 0.6 kcal mol" ) indicates also that the rupture of... 

The MMI (mass moment of inertia), EXC (excitation factor), and ZPE (zero point energy) terms are defined on successive lines of Equation 4.145. For reactions involving heavier isotopes the effects are no longer concentrated in the ZPE term and it is convenient to apply the Teller-Redlich product rule (Section 3.5.1) and eliminate the moments of inertia by using Equations 4.79,4.79a, and 4.141, thus obtaining an equivalent relation... 

Fig. 1 Lewis and Funderburk found that the H/D primary kinetic isotope effects (25 °C in aqueous t-butyl alcohol) for proton abstraction from 2-nitropropane by pyridine derivatives all exceed the maximum isotope effect that could have been derived from the isotopic difference in reactant-state zero-point energies alone (a value around 7). The magnitude of the isotope effect increases with the degree of steric hindrance to reaction presented by the pyridine derivative, the identical results for 2,6-lutidine and 2,4,6-collidine ruling out any role for electronic effects of the substituents. The temperature dependence shown for 2,4,6-collidine is exceedingly anomalous the pre-exponential factor Ahis expected to be near unity but is instead about 1/7, while the value of AH — AH = 3030 cal/mol would have generated an isotope effect at 25 °C of 165 if the pre-exponential factor had indeed been unity.

Having successfully matched the several experimental observables available for the enolase system, Alhambra and co-workers then examine the reaction coordinate to better understand the factors discriminating H from D reactivity. They discover that the TS for the reaction of H is much later than that for reaction of D, because the rapidly increasing zero-point energy of the N-H bond compared to the N-D bond offsets the drop in reaction coordinate potential energy and moves the free-energy bottleneck for H further towards products. 

It is not possible to discuss this complex subject in any detail here. It is necessary, however, to indicate its nature. The major factor involved is the difference in zero point energies of bonds between an element and the various isotopes of another element. For example a C—D bond has a lower zero point energy than a C—H bond. Consequently when proceeding along a reaction co-ordinate from reactants to products over an energy barrier (Fig. 1), rupture of a C—D bond requires a higher activation energy than rupture of a C—H bond. Thus, the kinetic isotope effect manifests itself in a smaller rate constant for C—D bond rupture. 

The expression for the thermal rate constant k(T) is given as a product of two functions an exponential function and a prefactor. The prefactor contains the partition function for the reaction complex, the supermolecule , at the saddle point (with the reaction coordinate omitted) and partition functions for the reactants. The second factor is an exponential with an argument that contains the energy difference between the zero-point energy level of the supermolecule at the saddle point and of the reactants. 

There are several rough experimental values for the decomposition of chemically activated CH4. Some older data on the reaction D + CH3 — CH3D, studied at 25°C. by Taylor and co-workers,38 correspond to (tf) 3 keal. (the zero-point energy difference for C—H and C—D is 2 keal.). These experiments correspond to the low-pressure limit, for which the calculated value in Table XI is kao 1.7 X 1010 sec.-1 at this energy. Marcus14 analyzed these data to obtain ka = 8 X 108 sec.-1 which, if we correct for the presence of a primary and secondary isotope effect due to the D atom, would be ka 1.5 X 109 sec.-1. He estimated a possible error of a factor of 5-10 in these values. We believe that the collision number used by Marcus in the calculation of ka is too low by a factor of 3-5 which would raise the experimental value to >5 X 10 sec.-1. The agreement is adequate, but the desirability of redoing these experiments with improved techniques is evident. 

Q is the usual partition function of the activated complex referred to the minimum in the potential of the normal molecule as the zero of energy, Q is the partition function qf the three rotations and three translations of the normal molecule, Ea IS the activation energy of the reaction as measured from the minimum of the normal molecule potential energy surface to the minimum of the activated complex, 0 is the zero-point energy of the activated complex, and the v( s are the vibrational frequencies, of the normal molecule. Moreover, A the rate of deactivation of active molecules to normal molecules, has been set equal to the collision number Z times an efficiency factor y, assumed to be isotope independent. 

---