Isotope effect of the second kind

In these examples B is a base. The first example is called a secondary isotope effect of the first kind, the next one is a secondary isotope effect of the second kind. The distinction between these is that in the first kind bonds to the isotopic atom have undergone spatial (i.e., structural) change. Halevi has reviewed secondary isotope effects on equilibria and rates. 

Following Streitwieser (13), we will call the type of effect illustrated in (1-6) a secondary isotope effect of the first kind, and those of (1-3) and (1-7) secondary isotope effects of the second kind, the criterion being whether or not bonds to isotopic atoms have undergone spatial reorientation. 

Streitwieser s approximation [Sec. Ill A, Ifb)], now including the additional assumption, certainly valid for secondary isotope effects of the second kind and probably good to a percent or so in those of the ffrst kind, that the ratio of the mass terms can be set equal to unity, leads to ... 

The quantum mechanically sophisticated reader will have realized early in this section that we have been implicity appl dng first-order perturbation theory throughout. The requirement, which seems made to order for secondary isotope effects of the second kind, and probably also holds reasonably well for those of the first kind, is that (SF — F.) should be small relative to the original potential, F. It then follows directly from the theory that SV, the mean value of the perturbation, is the total increment to the energy. Since V, represents the shift of the potential minimum, ( F — F,) is the zero-point vibrational energy difference. Consequently AiF of eq. (III-20) is just the isotope effect on zero-point energy that must be introduced, with opposite sign, into eq. (III-9) for the zero-point effect. 

---