Inverse isotope dependence

The first order in both the metal hydride and CO2 confirms that 5 and 7 are possible transition states (TSs). The reaction shows an inverse isotope dependence (kii/ d = 0.55) [8]. The activation parameters are reported to be AH = 53.5 kJ/mol and A5 = —138 J/mol K. If the ancillary ligands are changed, one can observe an effect on the reaction rate. This effect can be explained by considering that ancillary ligands may... 

Product analysis by NMR indicated an isotope effect at 118°C of = 2.14, corrected for numbers of H versus D. On lowering the temperature to -12°C, however, it was found that the isotope effect increased to 3.25. Referring to earlier experimental results on the C-H shift in methylchlorocarbene, " the authors cited the normal temperature dependence of the isotope effect as evidence against tunneling in 64. In retrospect, however, as noted above, theoretical support for an atypical inverse temperature dependence in methylchlorocarbene has been refuted. Hence, the involvement of tunneling in 62/64 at ambient temperatures is still an open question. 

Subsequent work confirmed this apparently abnormal behaviour. Deuteriation at remote sites (the S- or e-position) induces small inverse secondary isotope effects in a-cleavages occurring in the ion source, but normal isotope effects in the decomposition of metastable ions in the field-free regions94,95. The time dependence of the isotope effect was also studied by field ionization kinetics, which permit the analysis of fragmentations occurring after lifetimes as short as 10 12 s-1. It was found that the inverse isotope effect favouring loss of the deuteriated radical operates at times shorter than 10 9 s95. 

The issue of isotope effects is further complicated by the recently reported unusual temperature dependences such that either a normal or an inverse isotope effect may be observed for the same reaction depending on the temperature.96 Calculations suggest that significant contributions to the zero-point energy can come from vibrations that do not involve the bonds being made or broken. The transition between the normal and inverse isotope effects occurs because of the inverse enthalpy and normal entropy components that oppose each other and exhibit different temperature dependences. 

The results [538] for Cl + HI and Cl + DI show no isotope dependence on the nature of the average energy disposal (correlation between vibrational and rotational excitation of the HC1 (or DC1) products products formed in high vibrational levels have low rotational excitation, whereas products with low vibrational excitation have higher rotational energies. Preliminary results [538] for Br + HI and Cl + HBr, indicate that 50% of the reaction energy becomes product vibrational energy. 

We now turn to the discussion of isotope effects in hydrogen diffusivity. The classical diffusion theory predicts that the pre-exponential factor Dq in Eq. (26.17) is inversely proportional to the square root of the mass of a diffusing particle, while the activation energy does not depend on this mass. According to these predictions, the diffusion coefficient of D atoms should be s/2 times lower than that of H atoms over the entire temperature range. However, the isotope dependence of hydrogen diffusivity in all metal-hydrogen systems studied so far shows deviations from the predictions of the classical theory. In particular, the measured effec-... 

A second mechanism was also proposed to account for the kinetic dependence on the concentration of CD3COOD (equation 117). In this mechanism, the deuterated acetic acid supplies the which adds to the silver ion-Tz complex in the rate-determining step of the reaction. This slow step also has the appropriate hybridization change from sp to sp at the terminal acetylenic carbon and would lead to the inverse isotope effect that is observed. 

Figure3-15. The non-equilibrium plasma (Ty To) isotopic effect dependence on translational gas temperature To temperature Tq corresponds to the maximum value of the selectivity coefficient of the inverse isotopic effect.

In special cases an inverse temperature dependence of an equilibrium isotope effect increasing at higher temperatures has been observed (Kates, 1978 Walter, 1985). When an equilibrating system, that exhibits a small isotope effect, is separated by only a small energy barrier from a structurally different system and this interchange causes a larger isotope effect, the observed effect will increase at higher temperatures. 

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