Isotopic substitution in theory

High precision isotope ratio mass spectrometry permits reliable measurement of the small changes in isotopic distributions which occur in the reactions of molecules with natural abundance incorporations, especially for experiments with isotopes of carbon, nitrogen or oxygen [35]. An alternative of growing importance is the use of NMR spectroscopy to monitor similar changes for 13C and deuterium at natural abundance [36]. 

As microscopic systems, these oscillators have a zero-point energy (ZPE) equal to hvc aii and the difference in zero-point energies for a particular vibration in isotopomers depends upon vibrational frequencies. These, in turn, depend on the force constant (the same for 

In this semi-classical treatment, effects of isotopic substitution on equilibria and rates in chemical reactions reflect the changes in zero-point energy differences between (i) reactants (R) and products (P) - equilibrium isotope effects (EIE), or (ii) between reactants (R) and transition structures (TS) - kinetic isotope effects (KIE). In both cases, these changes reflect changes of force constants at the isotopically substituted site. When bonds are broken and made at the isotopic atom, the effects are described as primary, otherwise they are described as secondary. 

The ratio of rate constants (the KIE) for the reaction of light and heavy isotopomers is given by Equation 9.17  

A full calculation of a kinetic isotope effect requires estimates of force constants in the transition structure. These are available from ab initio PE calculations, but also from an empirical method based on the bond energy bond order (BEBO) assumption [38], which often provides more useful qualitative feedback for the experimentalist than high-level methods (see Chapter 7). 

---