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The polycyclic p-quinodimethanes are proposed to be the novel candidates of the high-performance nonlinear optical (NLO) materials because of their large third order polarizabilities ( γ). We investigate the switchable NLO responses of a series of polycyclic p-quinodimethanes with redox properties by employing the density functional theory (DFT). The polycyclic p-quinodimethanes are forecasted to exhibit obvious pure diradical characters because of their large y0 index (the y0 index is a value between 0 [closed-shell state] and 1 [pure biradical state]). The γ values of these polycyclic p-quinodimethanes and their corresponding one-electron and two-electron reduced/oxidized species are calculated by the (U)BHandHLYP method. The γ values of polycyclic p-quinodimethanes and their corresponding one-electron reduced species are all positive and significantly different. The large differences of the γ values are due to a change in the transition energy and are related to the different delocalization of the spin density, which demonstrates that the NLO switching is more effective on one-electron reduction reactions. Therefore, the study on these polycyclic p-quinodimethanes provides a guideline for a molecular design of highly efficient NLO switching. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]