How to calculate kH/KD value using proton NMR data?

Calculate kH/KD from NMR

How to calculate kH/KD value using proton NMR data?

The kH/KD value is the ratio of the rate constants for the exchange of a hydrogen atom with deuterium in a molecule. It is possible to estimate this value using proton NMR data by performing a series of experiments at different temperatures.

Here are the steps to calculate the kH/KD value using proton NMR data:

First, obtain two sets of proton NMR spectra of the molecule of interest. The first set should be recorded in a proton solvent, such as CDCl3, while the second set should be recorded in a deuterium solvent, such as DMSO-d6.

Next, compare the chemical shifts of the protons in the two sets of spectra. For each proton, the chemical shift will be different in the proton and deuterium solvents due to the difference in solvent polarity. The difference in chemical shift, denoted Δδ, can be calculated for each proton by subtracting the chemical shift in the deuterium solvent from the chemical shift in the proton solvent.

Plot the values of Δδ against the reciprocal of the absolute temperature (1/T) for each proton. This plot should give a straight line with a slope equal to the ratio kH/KD.

Calculate the slope of the line using linear regression analysis, and this value will give you the kH/KD value for that particular proton.

It is important to note that this method assumes that the exchange of the hydrogen and deuterium atoms is fast compared to the NMR time scale. If the exchange is slow, then the NMR signals will not be in the fast exchange limit, and the kH/KD value cannot be accurately determined using this method.