I've synthesised a protic and deuterated version of a specific molecule where there are two deuterium atoms in the latter. I then go about and measure the kinetic isotope effect (KIE) for a reaction involving these two molecules. However, in many papers where there are multiple deuteriums per molecule it is common to quote a KIE per deuterium in addition to the observed KIE.
This is usually achieved by taking the nth root of the observed KIE where n= no. of deuteriums (see attachment for example: 10.1039/ b405075d).
My questions are:
- Why the nth root? What is the basis for this? No paper explains why they chose the nth root.
- Should one use the observed KIE or the KIE per deuterium when discussing a mechanistic proposal?