Some comments on the use of isotopes in kinetic investigations

This topic, compartmental analysis, is not covered in this volume and the reader is referred to specialized literature (Zierler, 1981, and references therein). Stable isotopes of different weights can also be used for this purpose in conjunction with mass spectrometry. Deuteriiun in particular, because of its large ratio to the atomic weight of hydrogen, is a suitable tracer. 

In some cases replacements of isotopes result in spectral and/or fluores cence changes. An interesting application of deuterium/hydrogen exchange is the study of the mobility of different domains of proteins (Englander Kallenbach, 1983). This approach to the study of protein dynamics has already been referred to in section 5.3. The exchange of isotopes into specific positions (for instance deuterium and/or carbon-13) is also widely used to increase the potentialities of NMR investigations. 

Secondary isotope effects can sometimes be observed when vibrations of the reactive bond are coupled to nearby bonding involving isotopically substituted atoms. They are always very small and require very precise kinetic analysis. Sometimes it is possible to carry out reactions with and without substitution, using a differential technique (for instance using the two cuvettes of a spectrophotometer). The following elementary description of the kinetic isotope effect will provide some insight in terms of the theory of absolute reaction rates. For more profound treatments and references to fundamentals the texts mentioned above must be consulted (see also Westheimer, 1961 Jencks, 1969). 

As an example the discussion here is based on the discrimination between reactivity at a C—H and a C—D bond. There is no discrimination between the electronic, rotational or translational properties of H and D atoms. The vibrational frequencies observed by infrared spectroscopy are near the values of 2900 cm for C—H and 2100 cm for C—D. The zero point energy of vibration e is given by 

The force constant of C—D and C—H bonds are essentially the same and the zero point energy will be inversely proportional to the square root of the mass. Accordingly the zero point energy of C—D should be 1/ /2 times that of C—H, which corresponds very closely to the relative energies calculated from the above infrared frequencies  

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