Upper limit of the O-H⋯O hydrogen bond. Ab initio study of the kaolinite structure

Ab initio density-functional (DFT) investigations of the O-H stretching frequencies are performed on the kaolinite structure. Four distinct OH groups form weak hydrogen bonds with O-H⋯O distances between 1.8 and 2.6 Å. The O-H stretching frequencies, calculated as the Fourier transforms of the velocity autocorrelation function, show a quasi-linear dependence on the O-H⋯O distance. Because of the nonspecific character of extremely weak hydrogen bonds, which are at large distances averaged over several similar hydrogen-bond contacts, we anticipate general validity of the frequency vs bond length dependence for all structures with O-H⋯O hydrogen bonds. In hypothetical isolated layer, two O-H groups are free of hydrogen bonds. The extrapolation of their frequencies indicates an upper limit of ∼3.0 Å for the O-H⋯O and ∼4.0 Å for the O⋯O distances. The limiting value of effective hydrogen bond is checked by a detailed study of the geometry parameters of relaxed structures with continuously increased interlayer distance. Discontinuities observed for both the O-H bond length and the O-H⋯O angles reasonably agree with the value extrapolated in the frequency vs bond length dependence. The geometrical parameters r(O-H⋯O) = ∼3.0 Å and r(O⋯O) = ∼4.0 Å can thus serve as criteria in assessing the incorporation of hydroxyl groups in effective hydrogen bonds.