In this chapter we discuss the utilization of ab initio calculations of IR and VCD spectra for the analysis of experimental IR and VCD spectra. The ab initio options are Hartree-Fock (HF) theory and density functional theory (DFT). In both cases, the choice of the basis set is also an option. In the case of DFT, the choice of the density functional is also an option. The evaluation of the reliability of ab initio calculations of IR and VCD spectra is most easily carried out by comparison of the predicted spectra to the experimental spectra of conformationally rigid molecules, since the spectra of conformationally exible molecules are more complex. In this chapter we compare ab initio calculated IR and VCD spectra to the experimental IR and VCD spectra of the conformationally rigid chiral molecules, camphor, α-pinene, and methyloxirane. These three molecules have been used in testing the accuracies of VCD calculations, using the Stephens theory of VCD, many times [1-19]. The results dene the relative reliabilities of the HF and DFT methods, and of multiple basis sets and density functionals, and thence the optimum choices for the prediction of IR and VCD spectra of maximum accuracy.