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.