Using Time-Dependent Density Functional Theory, we have assessed the structural, energetic and spectroscopic properties of a hybrid diarylethene-dihydroazulene multi-addressable switch synthesized by Mrozek et al. [Chem. Commun., 1999, 1487-1488]. All possible closed/open structures have been considered and the different activation barriers along each reaction path have been evaluated. The determination of the energetic profiles allowed us to pinpoint the thermally possible reactions. To simulate the electronic absorption spectra of this compact two-way four-state hybrid compound, we relied on a PCM-TD-DFT approach combined with a molecular orbital analysis. Key insights are reached and the experimental photochromic properties of this multi-component switch are rationalised. From a more methodological point of view, this work also shows that range-separated hybrid functionals (CAM-B3LYP and ωB97XD) allow to reproduce the measured spectroscopic features with a remarkable accuracy.