Quantum mechanical calculation of the OH vibrational frequency in crystalline solids

Abstract

The OH vibrational frequency of four crystalline compounds ranging from ionic (brucite, Mg(OH)₂, and portlandite, Ca(OH)₂) to semi-covalent (edingtonite, as representative of free surface OH groups in silica, and acid chabazite, as representative of acid zeolites) has been investigated at quantum mechanical level with the CRYSTAL program using the B3LYP hybrid functional. The OH vibration is calculated in two ways: (i) in the harmonic approximation, by diagonalizing the fully coupled dynamical matrix to yield the harmonic frequency ω _h . (ii) at the anharmonic level, by decoupling the OH stretching mode from the bulk phonons and by numerically solving the one-dimensional Schrödinger equation associated with the OH potential energy to yield the fundamental ω₀₁ and the first overtone ω₀₂ frequencies. The harmonic and anharmonic frequencies differ by more than 150 cm⁻¹. In the cases where direct comparison is possible (brucite, portlandite and edingtonite), the experimental and calculated frequencies differ by less than 10 cm⁻¹; the calculated anharmonicity constant, ω _e x _e  = (2ω₀₁ − ω₀₂)/2, is systematically smaller than the experimental value by about 10 cm⁻¹. The effect of the computational parameters on the computed frequencies is explored, with particular attention to the grid used for the construction of the DFT exchange and correlation contribution to the Hamiltonian and the accuracy in the geometry optimisation.

Acknowledgements

Computer support from the CINECA supercomputing centre is kindly acknowledged.