Using the population mix of 39:31:30, the resonances with
differences between the conformers of >1.15 ppm were predicted
and compared to experiment (Table 5). The very good match supports
the view that the populations were accurately determined. All
five resonances differ by less than 1 ppm between experimental
and prediction. The corrected mean absolute error (CMAE) is
0.47 ppm. With the calculated populations (free energies, 28:38:34
and enthalpies 34:23:43) the CMAE is increased to 0.52 and 0.61,
respectively. These values benefit from the internal referencing so
that typical regression formulae based on a variety of compounds
give much larger errors, e.g. 2.07 ppm of a mean unsigned error on
the B3LYP/6e311 þ g(d,p)//6-31g(d) level of theory (van Eikema
Hommes and Clark, 2005) [35].
Depending on the level of theory, calculated populations differ.