Using the spin-unrestricted hybrid density functional theory method, we have investigated the intermolecular interaction effects on the longitudinal static second hyperpolarizability (gamma) of open-shell singlet slipped-stack dimers composed of singlet diradical square planar nickel complexes involving o-semiquinonato type ligands, Ni(o-C6H4X2)(2) (Where X = O, NH, S, Se, PH). For comparison, we have also examined the gamma values of a closed-shell singlet slipped-stack dimer composed of closed-shell monomers Ni[o-C6H4S(NH2)](2). It is found that for interplanar distance ranging between 3.0 and 5.0 angstrom the slipped stack dimers with intermediate monomer diradical characters exhibit larger gamma values per monomer(gamma(dimer)/2), than those with large monomer diradical characters or than the closed-shell dimer. These results extend the domain of validity of the relationship found between (gamma) and the diradical character for individual molecules. It also turns out that the ratio R = (gamma(dimer)/2)/gamma(monomer) increases upon decreasing the interplanar distance and that this increase is larger for intermediate diradical character than for the other cases. These phenomena have been analyzed by considering the gamma density distributions of the dimers, demonstrating a significant field-induced third-order charge transfer between the monomers in the case of intermediate diradical character. The present results indicate that open-shell singlet slipped-stack aggregates composed of monomers with intermediate diradical characters constitute another mean for achieving highly efficient and tunable third-order nonlinear optical materials.