Predictions of the unpolarized vibrational absorption and vibrational circular dichroism (VCD) spectra of the chiral molecule 6,8-dioxabicyclo[3.2.1]octane (1) are reported. Harmonic force fields and atomic polar tensors are obtained using the density functional theory (DFT), MP2 and SCF methodologies, and the 3-21G and 6-31G* basis sets. Three functionals, LSDA, BLYP, and B3LYP, are used in DFT calculations. Atomic axial tensors are obtained using the Distribution Origin gauge; distributed atomic axial tensors are calculated using gauge-invariant atomic orbitals (GIAOs) at the SCF level of approximation. The quality of the predicted spectra is highly dependent on the methodology and the basis set is employed. Spectra calculated using 6-31G* MP2 and DFT/B3LYP force fields are very similar and in excellent agreement with experimental spectra. 6-31G* SCF, DFT/LSDA and DFT/BLYP calculations are in significantly worse agreement with experiment, as are 3-21G MP2 and DFT/B3LYP calculations. When both accuracy and computational effort are considered, at this time, predictions of vibrational absorption and VCD spectra of molecules comparable to 1 in size are optimally performed using 6-31G* or equivalent basis sets and (i) harmonic force fields and atomic polar tensors calculated via DFT and a hybrid density functional; (ii) Distributed Origin gauge atomic axial tensors; and (iii) SCF GIAO-based distributed atomic axial tensors.