In this paper several approaches to compute the one-photon absorption spectrum of the neutral and anionic thioester analogs of the PYP chromophore solvated in either water, chloroform or dimethyl sulfoxide were investigated. All approaches made use of the Polarizable Embedding model potentially combined with the Frenkel exciton model to obtain absorption spectra. First, it was investigated how the different embedding schemes performed when only the chromophore was included in the QM region, i.e. a minimal QM region, and the remaining system was treated with classical models. Here, it was found that representing the solvent using polarizable models in general resulted in spectra comparable to the reference spectrum. It was clear that the low-energy region of the spectrum was more accurately reproduced compared to the high-energy region. The non-polarizable TIP3P water model was on the contrary found have some problems reproducing the reference spectrum both in the low and high energy regions, which was clear when compared to the polarizable water models. Thus, use of minimal quantum regions should in such cases as considered here be performed in combination with the use of a polarizable model for description of the solvent.