text: A basic NMR line broadening experiment is to determine the rotational energy barrier of a certain chemical bond. If the bond rotates slowly enough compared to the NMR time scale (e.g., amide bond), two different species can be detected by the NMR spectrometer. Considering that the time scale of NMR spectroscopy is about a few seconds, this technique can be used to examine the kinetics and/or thermodynamics of chemical exchange reactions on the order of seconds.
  In general, the energy barrier to rotate a bond is low enough at room temperature, which means that the rotation is fast, making the two different species indistinguishable. At low temperatures, however, it is harder for a bond to overcome the energy barrier to rotate, resulting in two separate peaks in the spectrum. With these principles, NMR spectra of a molecule with a high rotational barrier should be obtained at several different temperatures (i.e., variable temperature NMR) to distinguish two different peaks at low temperature in slow exchange and to find the temperature at which the two peaks merge.
  Especially at the coalescence temperature (), where the two peaks coalesce, the rate constant of rotation at  and the energy barrier of the rotation can be easily calculated. As increasing the temperature, the exchange reaction get faster, and at a certain temperature, which is , the appearance of the peaks changes from two separate peaks in slow exchange to a single peak in fast exchange. The rate constant  at  can be calculated with the following equation:   , and  are the chemical shift of each species at lower temperatures where they are in slow exchange.
  By using the Eyring equation, the Gibbs free energy of rotation, , can be determined:  (Eyring equation) is gas constant,  is the Boltzmann constant, and  is the Planck constant.