*3.3. Quantum Chemical Calculations*

All E and K forms of 3HF, 3HFW, and 3HF/γ-CD inclusion complexes in Form I and Form II in the S<sup>0</sup> and S<sup>1</sup> states were studied by PBE0 and TD-PBE0 methods, respectively with def2-SVP basis set by using Gaussian 16, Revision C.01 [56]. The solvation effect was taken into account by means of the non-equilibrium implementation of the conductor polarized continuum model (C-PCM) framework [65,66], so-called PCM-LR [67]. To confirm that the optimized structures (E, K, E\*, and K\*) are located at the local minimum, no imaginary frequency from vibrational calculations was found for all optimized structures both in S<sup>0</sup> and S<sup>1</sup> states. A hydrogen-bonded strength was determined by the important distance parameters involving ESIntraPT and ESInterPT processes namely the covalent O–H bond of 3HF and a water molecule, the intraHB between proton donor and proton acceptor of 3HF, and the interHBs between 3HF and a water molecule for the case study of water assisted effect. The strength of all intraHB and interHBs was further confirmed by the red-shift values of the O–H stretching vibrational frequencies between the S<sup>0</sup> and S<sup>1</sup> states from the simulated IR spectra, together with the topology analysis at bond critical point (BCP) from quantum theory of atoms in molecules (QTAIM) performed by Multiwfn [68], which was employed in previous studies [69–71]. The electronic spectra and frontier MOs were also calculated. Additionally, the absorption and emission spectra of all complexes were simulated to investigate the photophysical properties.
