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This brief investigates the diradical character, which is one of the ground-state chemical indices for bond weakness or electron correlation and which allows researchers to explore the origins of the electron-correlation-driven physico-chemical phenomena concerned with electronic, optical and magnetic properties as well as to control them in the broad fields of physics and chemistry. It then provides the theoretical fundamentals of ground and excited electronic structures of symmetric and asymmetric open-shell molecular systems by using model molecular systems. Moreover, it presents the theoretical design guidelines for a new class of open-shell singlet molecular systems for nonlinear optics (NLO) and singlet fission.