Li-S batteries have high theoretical capacity and specific energy density, but suffer from the dissolution of intermediate species, lithium polysulfides, into the electrolyte, leading to capacity fading and eventual battery failure. Research aimed at uncovering the elementary cathode reaction mechanisms during discharge/charge is critical to our ability to overcome this fundamental problem and design more efficient cells. Spectroelectrochemical methods, i.e. the coupling of spectroscopy with electrochemical measurements, has arisen as a powerful approach for studying Li-S reaction mechanism. In particular, Uv-vis spectroscopy has been one of the most useful techniques, because lithium polysulfides chemistry is sensitive to uv-visible light. However, interpretation of these measurements is difficult, due to a lack of fingerprints for each specific lithium polysulfide species, which cannot be easily isolated experimentally. Thus motivated by the need for spectral fingerprints, we simulated the theoretical spectra of each lithium polysulfides in a ether based solvent from first principles. Specifically, we sampled thermodynamically relevant ensemble structures in diglyme from first principal molecular dynamics simulations and calculated the associated absorption spectra using time-dependent density functional theory calculations. Our approach explicitly includes effects due to solvent screening, thermal reorganization and specific atomic interactions, which we show as critical for the unambiguous assignment of peaks in the experimental uv-vis spectrum.