Conformational analysis of the chemical shifts for molecules containing diastereotopic methylene protons

Quantum chemistry SCF/GIAO calculations were carried out on a set of compounds containing diastereotopic protons. Five molecules, including recently synthesized 1,3-di(2,3-epoxypropoxy)benzene, containing the chiral or pro-chiral center and the neighboring methylene group, were chosen. The rotational averages (i.e. normalized averages with respect to the rotation about the torsional angle τ with the exponential energy weight at temperature T) calculated individually for each of the methylene protons in 1,3-di(2,3-epoxypropoxy)benzene differ by ca. 0.6 ppm, which is significantly less than the value calculated for the lowest energy conformer. This value turned out to be low enough to guarantee the proper ordering of theoretical chemical shifts, supporting the interpretation of the (1)H NMR spectrum of this important compound. The rotational averages of chemical shifts for methylene protons for a given type of conformer are shown to be essentially equal to the Boltzmann averages (here, the population-weighted averages for the individual conformers representing minima on the E(τ) cross-section). The calculated Boltzmann averages in the representative conformational space may exhibit completely different ordering as compared to the chemical shifts calculated for the lowest-energy conformer. This is especially true in the case of molecules, for which no significant steric effects are present. In this case, only Boltzmann averages account for the experimental pattern of proton signals. In addition, better overall agreement with experiment (lower value of the root-mean-square deviation between calculated and measured chemical shifts) is typically obtained when Boltzmann averages are used.