A second problem in my lab dealt with the dynamic behavior of the following diolates. The static structures are asymmetric, but rotation of the o-tolyl group interconverts the enantiomers.

At high temperature (25° C), the average structure exhibits C_s symmetry, and the diolate protons are an AA'BB' pattern. On cooling, however, the lines broaden and separate; each resonance now becomes two identifiable lines. Unfortunately, this sample freezes before the lines sharpen again, but Δν of 33 Hz can be measured at -125° C.

The temperature at which there is a flat portion at the top of the coalescing pair of signals is defined as the colaescence temperature T_c. Provided Δν in known from the low-temperature (slow exchange) limit, the rate constant for interconversion at T_c is given by:

More complex line-shape analysis can be performed to estimate k at other temperatures, but this normally involves iterative curve-fitting. Another variable is the external field frequency; as B₀ changes, Δν will also. Further, choice of different nuclei in the equilibrating group may lead to broader variation in Δν.