The properties of a low molecular weight organic dye, namely 4-naphtoyloxy-1-methoxy-2,2,6,6-tetramethylpiperidine, covalently bound to an apolar polyolefin are investigated by means of a multi-level approach, combining classical molecular dynamics simulations, based on an purposely parameterized force fields, and quantum mechanical calculations, based on density functional theory (DFT) and its time-dependent extension (TD-DFT). The structure and dynamics of the dye in its embedding medium is analyzed and discussed in the light of the entangling effect of the surrounding polymer, also by comparing it to the results obtained for a different environment, i.e. toluene solution. The influence on photophysical properties of long lived cages, found in the polymeric embedding is eventually investigated in terms of slow and fast dye's internal dynamics, by comparing computed IR and UV spectra with their experimental counterparts.