Determining the Recruiting Rate of Spontaneously Blinking Rhodamines by Density Functional Calculations

A recruiting rate (<i>k</i>_rc) of 0.1-5 s^-1 has been proposed as the criterion for super-resolution spontaneously blinking rhodamines. Accurate prediction of the recruiting rate (<i>k</i>_rc) of rhodamines is very important for developing spontaneously blinking rhodamines. However, as far as we know, there is no reliable theoretical method to predict the <i>k</i>_rc. Herein, we meticulously investigated the effect of intermolecular hydrogen bonds on the spirocyclization reactions of rhodamines. Moreover, a theoretical descriptor (Δ<i>E</i>_C-T) was proposed to reliably assess the <i>k</i>_rc. Δ<i>E</i>_C-T quantified the ring-opening energy barrier of spirocyclization reactions. A robust linear correlation was established between theoretical Δ<i>E</i>_C-T values and experimentally <i>k</i>_rc values. Based on this correlation, we designed and screened five spontaneously blinking sulfonamide rhodamine dyes with optimized <i>k</i>_rc values. We expected that these findings could enable the targeted design of spontaneously blinking rhodamines.