This contribution firstly elucidates a structure–property relationship in third-order nonlinear optical molecular systems with singlet diradical characters. It turns out that the second hyperpolarizabilities (γ) of the singlet open-shell molecules with intermediate diradical characters are significantly enhanced as compared with those of closed-shell and pure diradical molecules. The hybrid density functional theory method, i.e. UBHandHLYP, is applied to the calculations of γ of dimer models composed of singlet diradical diphenalenyl molecules, which show a remarkable enhancement of γ per monomer as decreasing the intermolecular distance. The second contribution is concerned with a development of ab initio molecular orbital configuration-interaction-based quantum master equation (QME) approach. This is found to provide both coherent processes, e.g. dynamic polarization and exciton (electron–hole pair) recurrence motion, and incoherent processes, e.g. exciton migration, in molecular systems. Using this approach, the electron/hole dynamics for dynamic polarizabilities α(ω) are examined for several π-conjugated linear chain systems, and the structural dependences of α(ω) are elucidated.