On top of these uncertainties,
the population mix might change up to ±5% so that in extreme
cases (34:36:30 and 44:26:30), the mean values are 96.8 and 142.8
and the standard deviations are 6.9 and 3.3. Using the populations
based on free energies (28:38:34) the arithmetic mean and standard
deviation amount to 71.2 (9.4), and with enthalpies (34:23:43)
to 103.6 (5.5). Interestingly, only using the calculated optical rotation
values, the best match with experiment ([a]D of pure limonene:
122.8; [38]) is obtained with a population mix of 40:30:30,
very close to the mix obtained using experimental carbon chemical
shifts. It remains unclear why Leopold et al. [39] measured a [a]D
value of þ96.6 for the neat compound at 21 C with a 98% purity
assessed by GC.