Three sets of quasi-normal modes (QNMs) considered in this study. Top row: QNMs of a tetrahedral molecule of symmetry T d . From left to right: (symmetric stretch), (asymmetric stretch), (symmetric bending, here and elsewhere referred to as E-bending), and (asymmetric bending, here and elsewhere referred to as umbrella-bending). Arrows indicate the velocity component of interest. Dashed lines in bending modes represent additional projection vectors where a second projection is necessary. Middle row: The QNMs for bridging oxygen Si-O-Si and geminal oxygen O-Si-O parts of Q2-species. From left to right: symmetric stretch, asymmetric stretch and bending. Bottom row: Two ethane-like QNMs of the Si2O7 dimer: symmetric stretch and asymmetric stretch. The structures were drawn using the VMD software package.76
For and , the difference in spectral density is demonstrated caused by using either the silicon atom or the tetrahedral center-of-mass (COM) as projection reference center. Silicon as reference center introduces an artificial high-frequency contribution to (right arrow) as discussed in Sec. ???. The center-of-mass as reference center causes an artificial low-frequency contribution to (left arrow). This frequency overlap results from the silicon atom “cage rattling” motions (grey). Throughout this study the silicon is used as reference center. Spectra are scaled by 1.039.
Spectral density of the four tetrahedral QNMs of the silicate monomer (1000 K and 300 K). For QNM abbreviations see Table II. The full VDOS is plotted for comparison. All spectral densities are scaled by 1.039 (see Sec. IV A). Symbols represent literature data of monomer vibrational frequencies with Raman activity higher than 1% of that of the symmetric stretch near 770 cm−1. Empty diamond: Zotov and Keppler15 (bond polarizability model). Filled diamond: Tossell57 (MP2). Circles: Lasaga and Gibbs24 (Hartree-Fock). Triangles: DeAlmeida and O'Malley25 (Hartree-Fock).
The polymerization-driven frequency shift from 762 cm−1 for Q0-species to 1149 cm−1 for Q4-species. Spectral densities are scaled by 1.039.
The polymerization-driven frequency shift of the asymmetric stretch from Q0- to Q4-species. Spectral densities are scaled by 1.039. Inset: The frequency shift of and with increasing Q n -speciation. Note the cross-over of the and at Q2-species.
The two high-frequency peaks of the Q2 originates from the vibrations of the O-Si-O units of the Q2-species, namely the non-bridging NBO-Si-NBO and the bridging oxygen BO-Si-BO . The peak at 701 cm−1 is an artifact due to transmission of vibrations into Q2 , as discussed in Sec. ???. All spectra are scaled by 1.039.
The single non-bridging oxygen Si-OH stretching for different degrees of polymerization of the tetrahedron. Spectra are scaled by 1.039.
The bridging oxygen for various degrees of polymerization. All spectra are scaled by 1.039. Note the frequency shift with increasing polymerization from 620 cm−1 for Q1-Q1 to about 780 cm−1 for Q1-Q1 and even higher degrees of polymerization.
The bridging oxygen for various degrees of polymerization. All spectra are scaled by 1.039.
The dimer ethane-like and , and two tetrahedral QNMs for comparison. Spectra are scaled by 1.039.
Upper part: Four experimental Raman spectra of the system SiO2-H2O. Lower part: Selected species- and mode-specific frequencies determined in the present study, scaled by 1.039. Spectrum (A): pure SiO2 glass.81 Spectrum (B) and (C): SiO2 with 10 wt.% H2O and 5 wt.% H2O, respectively.81 Spectrum (D): Silica in aqueous solution at 900 °C and 1.4 GPa.15 Note that the intensity shoulder from about 1000 cm−1 is due to the diamond-anvil cell.
Overview of the simulation runs. The calculated pressure is about 0.5 GPa for all bulk cells.
Quasi-normal modes (QNMs) discussed in this study. Other QNMs were also derived, but are not considered further because they are less relevant to Raman band assigments in experimental studies.
Overview over the frequency results of tetrahedral and dimer stretching QNMs. The two monomer symmetric stretch results have been used to derive an averaged scaling factor (SF) of 1.039. For mode abbreviations see Table II. The uncertainty is estimated to be about 10 to 30 cm−1 (see Sec. ???).
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