Over the last decades, scientists have designed molecules and materials with unique nonlinear optical (NLO) properties targeting the realization of all-optical computing and signal processing. For many reasons (large response, short response time) organic compounds are of considerable interest. However, suitable materials for practical applications are still missing because the third-order NLO responses and the related molecular second hyperpolarizability (γ) are still too small. Increasing the conjugation length was a first strategy to optimize the third-order nonlinear optical responses while in subsequent approaches appropriate substituents with specific donor and acceptor strengths were selected. More recent strategies consist of varying the shape and dimensionality of the π-electron chromophore and of charging it, for instance by chemical doping. Although these systems are closed-shell molecules, recent studies have demonstrated that open-shell species show potential as materials with high NLO efficiency and in particular, singlet diradical systems with intermediate diradical character (y). For instance, ab initio molecular orbital and density functional theory calculations performed on the p-quinodimethane model showed that γ attains a maximum in the intermediate diradical character region and subsequently that i) π-conjugated diradical systems involving imidazole rings and ii) compounds of the family of thermally stable diphenalenyl diradical systems synthesized display significant enhancements of γ with respect to their analogous closed-shell systems. Then, the dependence of γ value on the spin states makes these compounds attractive for designing multifunctional materials. In this presentation, theoretical aspects on the evaluation and interpretation of the second hyperpolarizabilities of diradical species are discussed.