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Ab initio valence force field calculations for quartz

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Abstract

We have derived valence force constants for the tetrahedral SiO4 unit and the inter-tetrahedral SiOSi linkage from previous ab initio molecular orbital calculations on H4SiO4 and H6Si2O7 using a split-valence polarized Gaussian basis set (6-31G*), and used these to calculate the infrared and Raman active vibrational modes of α-quartz. The calculation gives frequencies approximately 15% greater than experiment, as expected from harmonic force constants obtained at this level of Hartree-Fock theory, but the calculation gives the correct distribution of modes within each frequency range. Calculated 28–30 Si and 16–18 O isotope shifts and pressure shifts to 6 GPa are also in reasonable agreement with experiment. We have also used our ab initio force field to calculate the vibrational spectrum for β-quartz. The results suggest either that inclusion of a torsional force constant is important for determining the stability of this high temperature polymorph, or that the β-quartz has a disordered structure with lower symmetry (P62) domains, as suggested by earlier diffraction studies.

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Author notes

  1. Anthony C. Hess

    Present address: Molecular Sciences Research Center, Batelle, Pacific Northwest Laboratories, PO Box 999, Richland, WA, USA

Authors and Affiliations

  1. Department of Chemistry, Arizona State University, 85287, Tempe, AZ, USA

    Paul F. McMillan & Anthony C. Hess

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  1. Paul F. McMillan
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  2. Anthony C. Hess
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McMillan, P.F., Hess, A.C. Ab initio valence force field calculations for quartz. Phys Chem Minerals 17, 97–107 (1990). https://doi.org/10.1007/BF00199660

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