Handbook of Aggregation-Induced Emission, Volume 1. Группа авторов

material design [2–4]. The compounds with AIE characteristics (AIEgens) have attracted much attention for their wide applications in solid‐state lighting, flat panel display, chemical sensor, cell imaging, and so on in the last 20 years [2]. The luminescent properties in the solid state are often significantly different from the isolated component at the molecular level. It is urgent to reveal the intrinsic AIE mechanism to realize the precise design of more efficient emitters; however, it is a challenging task.

In this rapid expanding field, many endeavors have been devoted to unravel the AIE mechanism through both theory and experimental means. The J‐aggregation was demonstrated to play an important role for the enhanced solid‐state emission of the strong conjugated rigid systems in earlier works [5]. For flexible systems, the restriction of intramolecular rotations (RIR) [6–8] was proposed firstly by comparatively analyzing the molecular steric hindrance‐, temperature‐, and viscosity‐dependent fluorescence intensities through all kinds of experimental measurements. Then, the restriction of intramolecular vibration (RIV) [3] and the restriction of intramolecular motion (RIM) [9] were put forward to explain more universal AIE mechanism through combining experiments and theoretical calculations. In theory, Peng and Shuai et al. developed a thermal vibration correlation function (TVCF) formalism [10–12] based on Fermi’s golden rule (FGR), which could quantitatively evaluate the nonradiative decay rate constants for isolated molecules, nanoaggregates, and crystals. And they proposed the AIE mechanism that the trip‐out of electron–vibration coupling and the demix of vibration modes block the excited‐state nonradiative decay channels in various rigid environments, sharply decreasing the nonradiative rate constants and turning fluorescence on [12–14]. Blancafort et al. proposed the restricted access to a conical interaction mechanism based on the potential energy surface (PES) topology analysis [15, 16] (see Chapter 9). In addition, many other scenarios have been declared, such as hydrogen‐bond‐induced excimer emission [17], vibration‐induced emission [18], the restriction of E/Z isomerization process [19], the blockage of access to dark state via isomerization mechanism [20, 21], and the reversal from dark ¹(n,π*) or ¹(n + σ,π*) to bright ¹(π,π*) excited states for generation of the solid‐state emission [22]. In this chapter, we will focus on introducing the revealed AIE mechanism in which the photophysical behaviors are supposed to occur in the Franck–Condon region without any photoisomerizations or conical intersections in the PESs. The chapter is organized in the following manner. In the second section, we show a short overview of the theoretical methodology and procedure. In the third section, we carefully elaborate on the revealed AIE mechanism at the level of first principle by several representative AIEgens. In the fourth section, we further validate our unraveled AIE mechanism by establishing the relationship between the calculated key photophysical parameters with measurable signals in experiments. Finally, we give a brief conclusion of the currently revealed AIE mechanism and outlook of the development direction theoretically in the future.

2.2 Theoretical Methods

      2.2.1 Radiative and Nonradiative Rate Constants

      The radiative decay rate constant (k_r) and nonradiative decay rate constant (k_nr = k_ic + k_isc) are decisive parameters for the luminescence quantum efficiency, where k_ic and k_isc are nonradiative internal conversion (IC) and intersystem crossing (ISC) rate constants, respectively. In most organic molecules, k_isc can be neglected owing to the small spin−orbit coupling for the π → π* electronic transition; therefore, k_nr ≈ k_ic.

      The k_r was computed by integrating over the whole emission spectrum:

(2.1)

      (2.2)

      where P_iν is the Boltzmann distribution function of the initial state at a certain temperature, Θ is the nuclear vibrational wave function, and is the electric transition dipole moment between two electronic states.

      Based on the FGR, the nonradiative IC constant can be written as [23]:

(2.3)

      where E_iv(E_fu) reflects the electronic and vibrational energies of the initial (final) state, and represents the non‐Born–Oppenheimer coupling.

Based on the Franck–Condon principle, applying Fourier transform of the δ‐function, Equation 2.3 can be written as [24, 25]:

(2.4)

      where is the nonadiabatic electronic coupling and ρ_IC(t, T) is the thermal vibration correlation function (TVCF) [10–12]

      (2.5)

As shown in Equation