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For more than 30 years, nonlinear optical (NLO) properties of molecular systems have been actively studied both theoretically and experimentally due to their potential applications in photonics and optoelectronics. Most of the NLO molecular systems are closed-shell species, while recently open-shell molecular species have been theoretically proposed as a new class of NLO systems, which exhibit larger NLO properties than the traditional closed-shell NLO systems. In particular, the third-order NLO property, the second hyperpolarizability , was found to be strongly correlated to the diradical character , which is a quantum-chemically defined index of effective bond weakness or of electron correlation: the values are enhanced in the intermediate y region as compared to the closed-shell (y = 0) and pure open-shell (y = 1) domains.

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