Black dye (BD), isomer 1 ([Ru(II)(H3-tctpy)(NCS)3](-1), where H3-tctpy = 4,4',4' '-tricarboxy-2,2':6,2' '-terpyridine) is known to be an excellent sensitizer for dye-sensitized solar cells and exhibits a very good near-IR photo response, compared to other ruthenium dyes. Because isothiocyanate is a linear ambidentate ligand, BD has three other linkage isomers, [Ru(H3-tctpy)(NCS)2(SCN)](-1), isomer 2 and 2', and [Ru(H3-tctpy))(SCN)3](-1), isomer 3. In this study, we have calculated the geometry of BD and its isomers by DFT. Further, we have analyzed the bonding in these isomers using NBO methods. TDDFT calculations combined with scalar relativistic zero-order regular approximations (SR-ZORA) have been carried out to simulate the absorption spectra. Calculations have been performed for the isomers both in vacuo and in solvent (ethanol). The inclusion of the solvent is found to be important to obtain spectra in good agreement with the experiment. The first absorption bands are dominated by the metal-to-ligand charge transfer (MLCT) and ligand-to-ligand charge transfer (LLCT).