A theoretical study of the structure and the vibrational spectra of the P-carotene molecule and its derivatives capsanthin and capsorubin is carried out. We first investigate systematically the theoretical method which provides the best results for P-carotene by performing ab initio calculations at the HF/6-31G(d), SVWN/6-31G(d), PBE0/6-31G(d), BLYP/6-31G(d), B3LYP/6-31G(d), B3LYP/6-31G(d,p), B3LYP/6-311G(d)(d), and B3LYP/6-311G(d,p) levels and by using previous theoretical results available in the literature obtained at the AM1 and BPW91/6-31G(d) levels. The influence of both the level of calculation and the size of the basis set used in the geometry optimization and in the determination of the IR and Raman spectra of this molecule is thus analyzed. It is confirmed that the hybrid functional B3LYP with the basis 6-31G(d) is the method that gives the best results as a whole. By use of this level of calculation, we next optimize the molecular geometries of related molecules of capsanthin and capsorubin, which to the best of our knowledge have only been studied at the semiempirical AM1 level. In addition we calculate the IR and Raman spectra of these molecules at the B3LYP/6-31G(d) level of theory. The results obtained for capsanthin show on the one hand that the double bond of the beta-ionone ring is outside the polyene chain plane, due to the repulsion between the hydrogen atoms of the ring methyl groups and the hydrogen atoms of the polyene chain, and on the other hand that the carbonyl double bond in the other headgroup is very close to planarity with the polyene chain, since in this case such a repulsion does not exist. For the molecule of capsorubin the two carbonyl groups also take the same coplanar orientation relative to the polyene chain. The IR and Raman spectra theoretically computed for these two molecules are finally compared with their experimental spectra and the vibrational normal modes of the main signals are interpreted.