This dissertation presents a detailed computational investigation into the vibrational properties of quinones involved in solar energy conversion processes in photosynthetic reaction centers. In particular, we focus on the vibrational properties of the ubiquinone molecule that occupies the QA binding site in purple bacterial photosynthetic reaction centers. To provide a foundation upon which to base computational studies of pigments in protein binding sites density functional theory based calculations of the vibrational properties of neutral ubiquinone in the gas phase and in solvent were undertaken. From single point energy calculations it was shown that at least eight ubiquinone conformers, each with slightly different FTIR spectra, could be present in solvent at room temperature. The calculated and experimental spectra for neutral ubiquinone in solution are very different from the spectra associated with ubiquinone in the QA binding in purple bacterial reaction centers. For this reason an ONIOM method was undertaken in which the pigment was treated using density functional theory based methods while the protein was treated using molecular mechanics. The ONIOM calculations not only modeled the experimental QA FTIR difference spectra but also resolved the long standing issue of whether a very strong hydrogen bond exists between the bound ubiquinone and the imidazole nitrogen of a histidine residue (HisM219). To further validate the usefulness of the ONIOM approach experimental isotope edited FTIR spectra obtained using purple bacterial reaction centers with a range of chainless symmetrical quinones incorporated were modeled. Again, the agreement between the calculated and experimental spectra is outstanding. We also modeled the vibrational properties of the ubisemiquinone anion radical both in solvent and in the QA binding site. Vibrational modes of ubisemiquinone display a greater degree of mixing of the various molecular groups of the molecule. Nonetheless the calculated FTIR spectra for ubisemiquinone in solution and in the QA site agree very well with that found experimentally. Vibrational frequencies of ubisemiquinone obtained from ONIOM calculated Raman spectra also agree very well with that found in experimental resonance Raman spectra associated with the ubisemiquinone anion radical in the QA binding site.