Ab initio cluster model calculations on the boson peak frequencies of B2O3 glass

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Abstract
We have performed ab initio molecular orbital calculations on the clusters modeling the medium-range ordering (MRO) region of B2O3 glass at the Hartree–Fock (HF)/3-21G and HF/6-31G* levels. Their equilibrium geometries, harmonic vibrational frequencies, and Raman scattering intensities have been calculated. The calculations have reproduced the boson peak frequencies of vitreous B2O3 observed at ≊24 cm−1 and ≊137 cm−1. The normal coordinates have demonstrated that these low-frequency vibrational modes are due to the wavelike motions of atoms within the region composed of one (for the mode at ≊137 cm−1) or two (for the mode at ≊24 cm−1) boroxol ring(s). The results suggest that the boson peak originates from the collective vibrations localized in the MRO region of glasses. We also propose that in glasses there are localized potential surfaces that are defined by the atoms in the medium-range scale. The driving force of the fast β relaxation will be the cooperative motions of atoms at the unstable sites toward the stationary point on the localized potential surface, which occasionally leads to the formation of the MRO region. We then interpret the glass transition phenomena and the strong/fragile differentiation of glasses in terms of the restoring force on the localized potential surface.