Isotope vibrational contribution

Recently, this view of secondary a-deuterium KIEs has had to be modified in the light of results obtained from several different theoretical calculations which showed that the Ca—H(D) stretching vibration contribution to the isotope effect was much more important than previously thought. The first indication that the original description of secondary a-deuterium KIEs was incorrect was published by Williams (1984), who used the degenerate displacement of methylammonium ion by ammonia (equation (4)) to model the compression effects in enzymatic methyl transfer (SN2) reactions. 

Table 28. Tunnelling and vibrational contributions to kinetic isotope effects in steps (a) and (d)...

The force constants needed for the calculation of the stretching vibrational contribution to the primary hydrogen isotope effect are... 

These findings are in agreement with theoretical predictions [93—96] (see Vol. 2, pp. 360—361). A maximum isotope effect is expected if the hydrogen ion is approximately one-half transferred in the transition state, and lower isotope effects are expected if the transition state is either more reactant-like (n2 < 0.5, n > 0.5) or more product-like (n2 > 0.5, n < 0.5). In Table 8, experimental isotope effects are compared with calculated nmax values and with calculated stretching vibrational contributions to the isotope effects. The calculations have been done on the basis of the semi-empirical model, as outlined in Sect. 4.1. As expected, calculated n values close to 0.5 correspond to high experimental isotope effects and n values different from 0.5 correspond to low experimental isotope effects. However, the calculated isotope effects exhibit very little dependence on nmax i they are close to the maximum value of the stretching vibrational contribution even for the examples with n = 0.18 and n = 0.12. This is a consequence of the relatively high curvature of the barrier [96], as computed from the semi-empirical model. 

Tn calculations of the vibrational contribution to isotope effects on partition functions for diatomic molecules it is usual to employ the expression... 

TABLE 5.4 Equilibrium Isotope Effect Contributions From Individual Vibrational Modes (cm ) for H2 (D2) Complexation to W(CO)3(PCy3)2(H2) at T 300 K... 

We shall prove below that the isotopic dependence of the vibrational contribution As(v) on the permittivity e(v) is small, unlike the ID of the reorientation contribution 0r(v). It appears that the relaxation time td differs in HW from that in OW, since td strongly depends not only on the structure of liquid water but also on the strength of an individual hydrogen bond (a detailed analysis of dependence of td on water structure is given by Agmon [18]. 

Rotational and translational contributions are essentially independent of the isotopic substitution as they refer to the molecule as a whole and the mass change on isotopic substitution is negligible. There will be one vibrational contribution for each mode and these will depend on isotopic substitution (Eqn. 7). 

When the mass of the tunneling particle is extremely small, it tunnels in the one-dimensional static barrier. With increasing mass, the contribution from the intermolecular vibrations also increases, and this leads to a weaker mass dependence of k, than that predicted by the onedimensional theory. That is why the strong isotope H/D effect is observed along with a weak k m) dependence for heavy transferred particles, as illustrated in fig. 18. It is this circumstance that makes the transfer of heavy reactants (with masses m < 20-30) possible. 

Detailed analysis of isotope effects reveals that there are many other factors that can contribute to the overall effect in addition to the dominant change in bond vibrations. For that reason, it is not possible to quantitatively predict the magnitude of either primary or seconday isotope effects for a given reaction. Furthermore, there is not a sharp numerical division between primary and secondary effects, especially in the range between 1 and 2. 

Fig. 13 Isotopic line splitting of the V3 stretching vibration in single crystalline (see also Fig. 12(a)), after [108, 109], The origin of each absorption band is indicated by an isotopomer present in crystals of natural composition. While the absorption could be fitted by a Lorentzian band profile, the remaining peaks were dominated by the Gaussian contribution in the Voigt band shapes (solid lines below the spectrum). The sum result of fitting the isotopic absorption bands is inserted in the measured spectrum as a solid line...

---