In this work, we have reported the electronic structure, spin state, and optical properties of a new class of transition-metal (TM) dinuclear molecules (TM = Cr, Mn, Fe, Co, and Ni). The stability of these molecules has been analyzed from the vibration spectra obtained by using density functional theory (DFT) calculations. The ground-state spin configuration of the tetra-coordinated TM atom in each molecule has been predicted from the relative total energy differences in different spin states of the molecule. The DFT + U method has been used to investigate the precise ground-state spin configuration of each molecule. We further performed time-dependent DFT calculations to study the optical properties of these molecules. The planar geometric structure remains intact in most of the cases; hence, these molecules are expected to be well adsorbed and self-assembled on metal substrates. In addition, the optical characterization of these molecules indicates that the absorption spectra have a large peak in the blue-light wavelength range; therefore, it could be suitable for advanced optoelectronic device applications. Our work promotes further computational and experimental studies on TM dinuclear molecules in the field of molecular spintronics and optoelectronics.