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Resonant Raman spectra of a molecule at different spin quantum state have different enhancement, making it possible to identify spin quantum state of single-molecule magnets (SMMs). By using Density Functional Theory, we calculate optimized structures of AFM and FM Single-Molecule Magnet Dimers ([Mn₃]₂) in electronic ground state and excited states. We apply first principle resonant Raman scattering theory and calculate resonant Raman spectra of [Mn₃]₂ in different spin quantum states. We compare the calculated resonant Raman spectra to the nonresonant Raman spectra also calculated from first-principles.