DFT calculation of α-cyclodextrin dimers. Contribution of hydrogen bonds to the energy of formation

The structures and energies of formation of α-cyclodextrin (α-CD) dimers formed according to the "head-to-head" (HH), "head-to-tail" (HT), and "tail-to-tail" (TT) modes, harmonic vibrational frequencies, and intensities of IR bands of the IR transitions were calculated by the DFT/PBE density functional method with full geometry optimization without symmetry restrictions. The spectral data were transformed into spectral patterns. An α-CD molecule can exist in two isomeric forms close in energy, namely, α-CD^- and α-CD⁺, with different directions of the ring intramolecular hydrogen bonds. Among the three α-CD^- dimers, the highest dimerization energy (E _d/kcal mol^-1) belongs to the HH^- (68.9), TT^- (43.4), and HT^- (24.8) dimers. The strength of the α-CD⁺ dimers decreases in the series: TT⁺ (56.7), HT⁺ (49.4), and HH⁺ (42.4). The energies E _H of hydrogen bonds were calculated from the low-frequency shifts of bands of stretching vibrations of the OH groups involved in the formation of these hydrogen bonds. The E _H value for each dimer correlates with E _d. A possibility of formation of intermolecular hydrogen bonds is a driving force of association of α-CD molecules in aqueous solutions.