The linear and nonlinear optical (L&NLO) properties, the energy difference between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO–LUMO gap), the first excitation energy (Eexc), and four indices for the evaluation of the diradical character (DC) of a series of Ni dithiolene derivatives have been computed by employing density functional theory (DFT). The selected DFT functionals provide reliable results for several properties [e.g., excitation energies and (hyper)polarizabilities]. An Atoms in Molecules analysis has been performed and several related properties have been reported (e.g., the average delocalization index, charge density, and its Laplacian). The selected derivatives with regular structural changes allow us to trace correlations between the (hyper)polarizabilities and some of the computed properties (e.g., Eexc and the DC indices). A small change in the structure may lead to a very large change of the diradical character and the L&NLO properties. Several of the studied derivatives have an exceptionally large second hyperpolarizability. Thus, the considered set of Ni dithiolene derivatives is likely to have applications in the development of photonic devices.