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

conjugation, resulting in the increase of the electric transition dipole moment (μ) from 5.20 to 5.85 Debye (Table 2.1). Hence, upon aggregation, the calculated k_r increases 6 times, while k_ic decreases about 4 orders of magnitude (Table 2.1). The nonradiative decay channels are generated by the coupling between the electrons and thermal vibrations that can be quantified by the molecular reorganization energy for the ith vibrational mode and , which is very sensitive to the surrounding environment. As seen, λ_total for HPS in the solid phase (403 meV) is obviously smaller than that in the gas phase (492 meV). The decrease in λ_total mainly stems from the low‐frequency vibrational modes (see Figure 2.4a), which are assigned to the rotating vibrations of the phenyl rings at the 2,5‐position. Thus, the excited‐state energy dissipation pathways are easily restricted via the decoupling between the electron and low‐frequency out‐of‐plane rotating modes in aggregates (see Figure 2.2b). The corresponding theoretically calculated Φ_F in the gas phase and solid phases is 0.003 and 76% (see Table 2.1), respectively, consistent with experimental results [45]. This well explains the bright emission of HPS in aggregate phase.

Figure 2.2 (a) PES scheme of AIEgens in solution and solid states. (b–g) Overview of vibrational modes involved in the excited‐state nonradiative decay channels, which contribute to AIE.

A similar AIE mechanism is followed by the other siloles, with the degree of π‐conjugation of the 2,5‐substituents increasing from TPS [47], BrTPS [48], HPS [45], BTPES [48] to BFTPS [49] (Figure 2.3). As shown in Table 2.1, as the conjugation increases, ∆E_g in both gas phase and solid state decreases regularly. Simultaneously, the μ value increases drastically due to the electron delocalization. The balance of excitation energy and μ makes k_r to first increase and then levels off as the extension of conjugation from TPS to BFTPS. After aggregation, λ_total for all AIEgens decreases obviously and k_ic decreases by more than 2 orders of magnitude from 9.30 × 10⁵ s⁻¹ for TPS to 1.22 × 10⁸ s⁻¹ for BFTPS. Overall, with the degree of π‐conjugation of the 2,5‐substituent increases, Φ_F in the solid state first increases sharply, then levels off, and finally starts to decrease slightly, as the competition between k_r and k_ic. Similar to the above discussed HPS, the dramatic decrease of k_ic upon aggregation turns the fluorescence on, which is mainly caused by the decoupling of the electron and low‐frequency rotational normal modes (Figure 2.4a) [38].

Figure 2.3 Overview of molecular structures discussed in Sections 2.3 and 2.4.

      2.3.2 Stretching Vibrations of Bonds

Terephthalic acid (TPA) is a representative AIEgen, which could emit both fluorescence and phosphorescence simultaneously [41]. Through a combined QM/MM approach, the photophysical properties of TPA in both gas phase and crystal were investigated to unravel the effect of crystallization on the nature of the molecular excited states. It is found that the nature of S₁ changes from (n,π*) in the gas phase to (π,π*) in crystal because the excitation energy of (n,π*) is increased up to 5.05 eV from 4.81 eV, whereas the (π,π*) state is reduced to 4.76 eV from 4.99 eV due to the strong electrostatic interaction upon aggregation. Accordingly, the oscillator strength of S₁ is largely enhanced to 3.49 × 10⁻² in the crystalline phase from 3.33 × 10⁻⁵ in the gas phase, which recovers the radiative decay from S₁ to S₀. And the resultant k_r is largely increased by 3 orders of magnitude from 3.34 × 10⁴ s⁻¹ in the gas phase to 3.43×10⁷ s⁻¹ in the solid phase.

Table 2.1 Calculated HOMO–LUMO energy gap (∆E_g), electric transition dipole moment (μ), total reorganization energy (λ_total), k_r, k_ic, and Φ_F in gas phase and aggregate phase at room temperature for HPS, TPS, BrTPS, BTPES, and BFTPS, respectively.

	∆Eg (eV)	μ (Debye)	λ total (meV)	k r (s^−1)	k ic (s^−1)	Φ F (%)
In gas phase
HPS [37]	3.59	5.20	492	1.05 × 10^7	3.76 × 10^11	0.003
TPS [38]	3.21	0.58	1120	9.30 × 10^5	1.62 × 10^10	0.01
BrTPS [38]	2.90	1.71	1161	5.55 × 10^6	5.72 × 10^9	0.09
HPS [38]	2.62	5.26	891	4.98 × 10^7	2.53 × 10^10	0.20
BTPES [38]	2.48	6.03	667	6.76 × 10^7	2.66 × 10^10	0.25
BFTPS [38]