energy? Theoretical researchers have developed the proper modes for radiative decay rates and nonradiative decay rates based on the thermal vibration correlation function (TVCF) formalism, and precisely calculated the quantum yields in both solution state and aggregate state and finally revealed the quantum origins of the RIM mechanism [7].
Studies of the transition process between two electronic states relate to the quantum dynamics. The fluorescence and phosphorescence processes usually occur in the timescale from nanoseconds to milliseconds, while the internal conversion and intersystem crossing often occur in picoseconds or a shorter timescale. However, the current excited‐state dynamic simulation can only deal with the process occurring within picoseconds, which is much faster than the luminescence process. Hence, theoreticians usually evaluate the luminescence quantum efficiency by employing the decay rate formalism based on the Fermi golden rule [3]. The luminescence quantum yield ΦF can be defined as ΦF = kr + knr, in which kr stands for the radiative decay rate and knr stands for the nonradiative decay rate. The kr can be calculated with integration of multiple theories even for polyatomic molecular systems. The problem to evaluate the quantum yield is to precisely calculate the nonradiative decay rates, which contain more factors related to complicated molecular motion modes [3].
Traditional target molecules for the photophysical research always own highly rigid π‐electron structure with large conjugation, which makes the effect of molecular motions less notable, whereas most AIEgens possess highly flexible molecular structures, allowing the high freedom of motion in the isolated state, which facilitates the nonradiative pathways to a large extent through diverse decay modes. Peng et al. have proved that calculation of internal conversion rates considering the Duschinsky rotation effect (DRE) leads to more accurate quantitative evaluation of the nonradiative decay process for the 1,2,3,4‐tetraphenylbutadiene (TPBD) with AIE property since DRE describes the coupling among the multiple modes of molecular motions [7e]. Such mode mixing also significantly contributes to the nonradiative dissipation of excited‐state energy as well as the intrinsic multiple molecular motions. On the other hand, the evaluation of the temperature‐dependent luminescence behaviors of TPBD considering DRE produces more reliable results that are much closer to the experimental observation [7e].
Furthermore, for the fluorescence process, the nonradiative decay pathways are governed by the nonadiabatic coupling (NAC), which can be divided into nonadiabatic electronic coupling (NAEC) and EVC [7e]. The NAEC deciphers the electronic part that contributes to the nonradiative decay, and the EVC relates to the interaction between the electronic and the nuclear motions. The reorganization energy (RE) can be applied to evaluate the intensity of EVC and can offer detailed information on the structure–property relationship [17]. Through investigating NAEC and EVC, researchers have revealed the quantum origins of the energy‐consuming mechanism from molecular motions. Taking HPS as the research model, its fluorescence quantum yield is only 0.30% in the dilute solution, whereas it can reach 78% in the solid film, which is 260 times as high as that in the solution. Zhang et al. have calculated the electronic structures of HPS in both isolated state and crystal state, using the combined quantum mechanics and molecular mechanics (QM/MM) method to explore the detailed working mechanism of HPS from quantum view [7a].
During the vibrational relaxation in the excited state, large conformational reorganization occurs, which mainly relates to the torsion of phenyl rotors on the 2,5‐positions of the silole ring due to their high mobility in the isolated state. However, the optimized HPS in the crystal shows only minor conformational reorganization during the relaxation with almost no change in the dihedral angles of phenyl rings, which proves the RIM features in the solid state. Further, NAC analysis reveals that the distribution and total values of NAEC have no notable change before and after the aggregation occurs (Figure 1.5), indicating that the NAEC is insensitive to the aggregate environment. Nevertheless, the EVC analysis shows that many low‐frequency motion modes (ω < 200 cm−1) of HPS exist in the isolated state, and they are mainly recognized as the torsion of phenyl rotors. The RE of these low‐frequency modes is 197 meV, which occupies 40% of the total RE of the whole system. Afterwards, the RE of low‐frequency modes significantly decreases to 84 meV in the crystal, occupying 21% of the total value. Due to the large suppression of EVC, the calculated knr decreases with four orders in magnitude from the isolated state to the crystal state. Hence, the emission efficiency of HPS can be boosted in the crystal state due to the restricted EVC.
Theoretically, the large EVC of most AIEgens is the main cause for their low emission efficiency in the isolated state, which originates from the nature of the conformational flexibility and high freedom of molecular motions of the AIEgens. Tang and coworkers have studied the substituent effect on the AIE behaviors of a series of stilbene derivatives, as presented in Figure 1.6, and verified the influence from freedom of molecular motions on the excited‐state properties [17b]. Three methyl groups can be attached to 2,4,5‐positions or 2,4,6‐positions of each phenyl rings of the stilbene, which leads to opposite photophysical behaviors. The 2,4,5‐TMe‐DPE shows aggregation‐caused quenching effect, whereas the 2,4,6‐TMe‐DPE shows the typical AIE behavior. The first question that arises is which factors make the 2,4,5‐substituted derivative highly emissive with ΦF of 13.4% but the 2,4,6‐substituted counterpart almost nonemissive with ΦF as 0.6% in the dilute solution. The quantum simulations in the ground state show that 2,4,5‐TMe‐DPE owns a more planar conjugation plane, while 2,4,6‐TMe‐DPE is more twisted. The calculated rotation barrier shows that 2,4,6‐TMe‐DPE undergoes lower barrier to rotate along the coordinate of twisting, but it suffers higher barrier to move along the coordinate of planarization, which reveals that methyl groups in 4,6‐positions can produce strong steric hindrance to prevent the coplanarization between phenyl rings and the double bond, but such steric hindrance can cause preliminary twisting of phenyl rings and reduce the conjugation degree, which leads to the easier torsional motions of the phenyl rings in 2,4,6‐TMe‐DPE. From the ultrafast spectroscopy measurement, the lifetime of excited‐state species of 2,4,6‐TMe‐DPE is only 2.1 ps, much shorter than that of 2,4,5‐TMe‐DPE (263 ps), which indicates that the 2,4,6‐TMe‐DPE is less conjugated and possesses higher motion ability, so it can undergo much faster excited‐state decay process.
Figure 1.5 (a) Chemical structures and the overlap of the S1,min conformation and the S0,min conformation in the gas and the solid state of HPS. (b) Diagonal elements Rkk of the nonadiabatic electronic coupling matrix versus normal mode index in the gas and the solid state. (c) Reorganization energy versus normal mode wave numbers in the gas state and (d) the solid state.
Source: Adapted from Ref. [7a] with permission from American Chemical Society.
