Time-local and time-nonlocal theories are used in combination with optical spectroscopy to characterize the water-soluble chlorophyll binding protein complex (WSCP) from cauliflower. The recombinant cauliflower WSCP complexes reconstituted with either chlorophyll b (Chl b) or Chl a/Chl b mixtures are characterized by absorption spectroscopy at 77 and 298 K and circular dichroism at 298 K. On the basis of the analysis of these spectra and spectra reported for recombinant WSCP reconstituted with Chl a only (Hughes, J. L.; Razeghifard, R.; Logue, M.; Oakley, A.; Wydrzynski, T.; Krausz, E. J. Am. Chem. Soc. U.S.A. 2006, 128, 3649), the "open-sandwich" model proposed for the structure of the pigment dimer is refined. Our calculations show that, for a reasonable description of the data, a reduction of the angle between pigment planes from 60 degrees of the original model to about 30 degrees is required when exciton relaxation-induced lifetime broadening is included in the analysis of optical spectra. The temperature dependence of the absorption spectrum is found to provide a unique test for the two non-Markovian theories of optical spectra. Based on our data and the 1.7 K spectra of Hughes et al. (2006), the time-local partial ordering prescription theory is shown to describe the experimental results over the whole temperature range between 1.7 K and room temperature, whereas the alternative time-nonlocal chronological ordering prescription theory fails at high temperatures. Modified-Redfield theory predicts sub-100 fs exciton relaxation times for the homodimers and a 450 fs time constant in the heterodimers. Whereas the simpler Redfield theory gives a similar time constant for the homodimers, the one for the heterodimers deviates strongly in the two theories. The difference is explained by multivibrational quanta transitions in the protein which are neglected in Redfield theory.