Ab initio density functional theory (DFT) is used to analyze the vibrational unpolarized absorption and circular dichroism spectra (below 1500 cm(-1)) of seven derivatives of 6,8-dioxabicyclo[3.2.1]octane. Two are methyl derivatives, two are methyl-d(3) derivatives, and three are dimethyl derivatives. DFT calculations use hybrid functionals (B3LYP and B3PW91), the 6-31G* basis set, and, in predicting circular dichroism spectra, GIAO basis sets. The two functionals give qualitatively similar spectra. Comparison of predicted and experimental spectra permits assignment of the majority of the fundamentals of the seven molecules (excluding C-H stretching modes). Vibrational circular dichroism intensities are in good overall agreement with experiment, consistent with previously assigned absolute configurations. Spectra are also predicted using the Hartree-Fock/self-consistent field (HF/SCF) and MP2 methodologies. MP2 spectra are similar in accuracy to DFT spectra. HF/SCF spectra are of much lower accuracy and are in poor agreement with experiment.