Complete sets of harmonic, semidiagonal cubic as well as diagonal cubic and quartic force constants are reported for the internal coordinates of terminal, ≣SiOH, and bridging, ≣SiOH·Al≣, surface hydroxyls on silica and zeolites. They are obtained by numerical differentiation of analytically calculated gradients of the energy (SCF approximation, 6-31 G* basis set). A GF vibrational analysis is performed and after making a nonlinear transformation of the force constants into normal coordinates the anharmonicity constants are evaluated by perturbation theory. Comparison is made with the D 2 OH + ion and the DOH molecule. The calculated anharmonicities of the OH bonds in the systems studied are remarkably constant and vary between -76 and -84 cm -1 , only in agreement with the values observed for DOH (-83 cm -1 ) and surface silanols, ≣SiOH (-90 ± 15 cm -1 ).
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Mix et al. (1988) studied this question.