*2.4. O–H Stretching and Topology Analysis*

In general, the strength of the intraHBs and interHBs in the S<sup>1</sup> state could be revealed based on monitoring the red-shift of vibrational modes involving the hydrogen-bonded formation and the topology analysis at bond critical points (BCPs) using the QTAIM method. The calculated IR spectra of all studied compounds in the conjunct vibrational regions of the O–H stretching modes related with PT process both in the S<sup>0</sup> and S<sup>1</sup> states are listed in Table 2. These O–H stretching modes can be classified into the O1–H1 stretching mode of 3HF and Ow–Hw stretching mode of a water molecule.

For 3HF, the O1–H1 stretching vibrational mode of 3HF is located at 3544 cm−<sup>1</sup> and 3003 cm−<sup>1</sup> for the S<sup>0</sup> and S<sup>1</sup> states, respectively, giving a large red-shift of 541 cm−<sup>1</sup> . Moreover, the large red-shift of the O1–H1 stretching vibrational mode is also observed for Form I (367 cm−<sup>1</sup> ) and Form II (244 cm−<sup>1</sup> ). Therefore, the strength of the O2· · · H1 intraHB for these compounds is increased in the S<sup>1</sup> state providing ESIntraPT process.

For the compounds with a water molecule, the O1–H1 stretching vibrational modes of 3HFW, Form I-W, and Form II-W are located around 2967–3129 cm−<sup>1</sup> in the S<sup>0</sup> state. Note that these vibrational modes changed to be around 2575–2599 cm−<sup>1</sup> in the S<sup>1</sup> state,

which evidently demonstrates that the red-shift is induced by the strengthening of the O1–H1· · · Ow interHB after photoexcitation. Similarly, the Ow–Hw stretching modes of these compounds are also red-shifted. In addition, the red-shift value of 3HFW and Form II-W is larger than that of Form I-W, indicating that the O1–H1· · · Ow and Ow– Hw· · · O2 intermolecular hydrogen-bonded strength of 3HFW and Form II-W in the S<sup>1</sup> state is stronger than that of Form I-W. Overall, these results show that O–H stretching vibrational frequencies shift to lower frequencies in the S<sup>1</sup> state compared with the S<sup>0</sup> state, which confirms that the hydrogen bonding interaction is stronger in the S<sup>1</sup> state.


**Table 2.** A summary of the values of the O1–H1 and the Ow–Hw stretching vibrational modes of enol form for all compounds in both S<sup>0</sup> and S<sup>1</sup> states and their spectral shifts (∆*υ* in cm−<sup>1</sup> ).

A topology analysis of the electron density was used to further determine the strength of the intraHB and interHBs in the excited-state structures (E\* form) of all compounds. The following parameters at BCPs were analyzed: the electron density *ρ*(r), the potential energy density V(r), the Laplacian of the electron density <sup>∇</sup>2*ρ*(r), the Lagrangian kinetic energy G(r), the Hamiltonian kinetic energy density H(r), and the electron delocalization index (DI) between the proton acceptor and transferred proton, which are an O2· · · H1 intraHB, and the Ow· · · H1 and O2· · · Hw interHBs for all studied compounds. Additionally, the hydrogen-bonded energy (EHB) can be calculated by using the Espinosa's equation: *EHB* = <sup>1</sup> 2 |*V*(*rBCP*)|. These results are summarized in Table S1 in the Supplementary Materials. From Table S1, EHB of O2· · · H1 intraHB of 3HF (0.0224 a.u.) is the highest among the compounds without a water molecule. Then, EHB is slightly decreased for Form I (0.0175 a.u.) and Form II (0.0111 a.u.). These results indicate that the intraHB of isolated 3HF is stronger than that the inclusion complexes. Nevertheless, this intraHB of all compounds can facilitate ESIntraPT processes. For the compounds with a water molecule, EHB of Ow· · · H1 and O2· · · Hw of 3HFW/Form II-W are 0.0696/0.0649 and 0.0306/0.0317 a.u., respectively. The Ow· · · H1 interHB of 3HFW/Form II-W is stronger than the O2· · · Hw interHB, indicating that the proton might transfer via a water molecule from O1–H1 bondbreaking before Ow–Hw bond-breaking. However, only EHB of Ow· · · H1 of Form I-W is obviously dropped (0.0253 a.u.). The result implies that the ESInterPT process might occur in 3HFW/Form II-W better than Form I-W. Overall, it can be observed that the intraHB and interHBs are strengthened in the S<sup>1</sup> state confirmed by the shorter distances of important bonds involving in the ESPT process, the red-shift observed by IR vibrational spectral calculations, and a high value of EHB from topology analysis of the electron density.
