*2.5. Frontier MOs Analysis and Simulated Spectra*

To further investigate behaviors of charge distribution and charge transfer in the S<sup>1</sup> state, the frontier MOs of the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) of all studied compounds were analyzed because the main electronic transition is only related with these orbitals in range of 98% (HOMO → LUMO), which is assigned as π to π\* characters, and illustrated in Figure 5. It can be noted that electron density of both HOMO and LUMO is fully localized on the 3HF moieties and no electron density is located on water or γ-CD, indicating that no intramolecular charge transfer within 3HF and no intermolecular charge transfer between 3HF and water

or γ-CD. Moreover, the HOMO and LUMO are localized on different parts of 3HF. For the HOMO orbitals, the electron density is distributed more on P-ring and partially on C-ring of 3HF. Whereas, that of LUMO is distributed completely on the whole molecule of 3HF. For the HOMO orbitals, the electron density is distributed more on P-ring and partially on C-ring of 3HF. Whereas, that of LUMO is distributed completely on the whole molecule of 3HF.

To further investigate behaviors of charge distribution and charge transfer in the S1 state, the frontier MOs of the highest occupied molecular orbitals (HOMO) and the lowest unoccupied molecular orbitals (LUMO) of all studied compounds were analyzed because the main electronic transition is only related with these orbitals in range of 98% (HOMO → LUMO), which is assigned as π to π\* characters, and illustrated in Figure 5. It can be noted that electron density of both HOMO and LUMO is fully localized on the 3HF moieties and no electron density is located on water or γ-CD, indicating that no intramolecular charge transfer within 3HF and no intermolecular charge transfer between 3HF and water or γ-CD. Moreover, the HOMO and LUMO are localized on different parts of 3HF.

*Molecules* **2021**, *26*, x FOR PEER REVIEW 9 of 15

*2.5. Frontier MOs Analysis and Simulated Spectra* 

**Figure 5.** Frontier MOs of all studied compounds. **Figure 5.** Frontier MOs of all studied compounds.

The UV-Vis absorption and emission spectra of all studied compounds were simulated based on their optimized S0 and S1 structures, respectively and then plotted in Figure S3. Furthermore, the absorption band maxima of E form (λabs of E), emission band maxima of E\* (λemis of E\*) and K\* forms (λemis of K\*), the excitation energy (Eex), and the oscillator strength (*f*) as well as the major MOs contribution (%) of the absorption band for all compounds are reported in Table 3. From the detailed information in Table 3, the simulated absorption peaks of the complexes without and with a water molecule are around 341– 345 nm and 350–353 nm, respectively, which are in good agreement with the experimental value of 341 nm for 3HF in water and 340 nm for 3HF in γ-CD [46,47]. Moreover, the predicted maximum wavelength for dual emission spectra of all studied compounds is also consistent with the experimental data [46,47], in which the λemis of E\* in water and in γ-CD are reported at 410 and 404 nm, respectively, while the λemis of K\* in water and in γ-CD are 511 and 538 nm. The deviations from the experimental data around 59–69 nm (0.52– 0.61 eV) indicate that the chosen method at TD-PBE0/def2-SVP level of theory is adequate to describe the electronic spectra and provide the insight understanding of the ESPT pro-The UV-Vis absorption and emission spectra of all studied compounds were simulated based on their optimized S<sup>0</sup> and S<sup>1</sup> structures, respectively and then plotted in Figure S3. Furthermore, the absorption band maxima of E form (λabs of E), emission band maxima of E\* (λemis of E\*) and K\* forms (λemis of K\*), the excitation energy (Eex), and the oscillator strength (*f*) as well as the major MOs contribution (%) of the absorption band for all compounds are reported in Table 3. From the detailed information in Table 3, the simulated absorption peaks of the complexes without and with a water molecule are around 341–345 nm and 350–353 nm, respectively, which are in good agreement with the experimental value of 341 nm for 3HF in water and 340 nm for 3HF in γ-CD [46,47]. Moreover, the predicted maximum wavelength for dual emission spectra of all studied compounds is also consistent with the experimental data [46,47], in which the λemis of E\* in water and in γ-CD are reported at 410 and 404 nm, respectively, while the λemis of K\* in water and in γ-CD are 511 and 538 nm. The deviations from the experimental data around 59–69 nm (0.52–0.61 eV) indicate that the chosen method at TD-PBE0/def2-SVP level of theory is adequate to describe the electronic spectra and provide the insight understanding of the ESPT process.

cess. **Table 3.** UV/Vis absorption band maxima of enol form (λabs of E), emission band maxima of enol (λemis of E) and emission band maxima of keto forms (λemis of K), the excitation energy (Eex), and the oscillator strength (*f*) as well as their major contribution (%) calculated by TD-PBE0/def2-SVP level of theory.


The relative energy of E and K forms of all studied complexes at the S<sup>0</sup> and S<sup>1</sup> states was investigated to explain the ESPT phenomena as illustrated in Table 4. The results show that the E form is more stable than the K form in the S<sup>0</sup> state for all complexes with the energy differences at 6.63–16.85 kcal/mol. Moreover, most of K forms were stabilized in the γ-CD cavity except only Form I. However, in the S<sup>1</sup> state, the K\* form is more stable than

the E\* form for all complexes. It is predicted that both ESIntraPT and ESInterPT processes are favorable in the S<sup>1</sup> state but not in the S<sup>0</sup> state. In case of the complexes without a water molecule (Form I and Form II), K\* of Form II is more stable than Form I. So, the ESIntraPT process of Form II may be more effective than that of Form I, related to the MD results that Form II is favorably more stable. For the complexes with a water molecule, the ESInterPT via interHBs network is feasible to occur in both Form I-W and Form II-W especially Form II-W because of the slightly higher oscillator strength and the lower energy of K\*. In addition, from our previous work, the ESInterPT of 3HFW is hard to occur due to the higher ESInterPT barrier and the rearrangement of a water molecule surrounding 3HF [40]. Therefore, it can be predicted that the encapsulating 3HF into γ-CD assists the disruption of the 3HF-water network in aqueous solution leading to an increment of the fluorescent yield of K\* in aqueous solution from the ESIntraPT process.


**Table 4.** The relative energy and computed energy differences between the E and K forms (∆*E* = *<sup>E</sup>*enol <sup>−</sup> *<sup>E</sup>*keto) in the S<sup>0</sup> and S<sup>1</sup> states for all complexes.
