We will classify all exceptional Dehn surgeries on 2-bridge knots according to whether they produce reducible, toroidal, or Seifert fibered manifolds.

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Raman spectra of binary sodium silicates in various components were calculated by the self-consistent field molecular orbital ab initio calculation quantum chemical (QC) method with several polysilicon-oxygen tetrahedral model clusters with both 6-31G and 6-31G(d) basis sets being applied. Relevant pure anion clusters were also be calculated in order to determine the cation effect by comparison with the available sodium series. High and intermediate Raman-active wavenumber ranges were especially considered. The symmetric stretching vibrational wavenumber of non-bridging oxygen (NBO) in the high-wavenumber range and its Raman scattering cross-section were deduced and analyzed. Several synthesized binary sodium silicate crystals were measured for comparison. The correlation between the vibrational Raman shift and the microscopic environment of the silicon-oxygen tetrahedron (SiOT) was found based on interior stress of configuration or superstructure, which depends on the connecting topology of adjacent SiOTs. A newly established empirical stress index of a tetrahedron (SIT) was introduced to elucidate the above relationship. A new notation of SiOT accompanied by superstructure information was proposed and used to describe the practical and delicate types of SiOT in various states of binary sodium silicates. The Raman scattering cross-section of the symmetric stretching vibration of NBO shows a roughly decreasing relationship with SIT or the Raman shift in the high-wavenumber range only under the circumstance of equivalent linkage between SiOTs, and Raman optical activity (ROA) enhancement ofQ 3 species occurs with Q 4 species as its nearest neighbor, which indicates the electronic coupling between them. It was also demonstrated that the Si-O b -Si bending vibrational Raman shift in the intermediate wavenumber range shows a monotonic decreasing relationship with the value of the Si-O b -Si angle while other minor impacting factors remains unknown. This work offers basic information on the superstructure of binary sodium silicates and its relationship with characteristic vibrational Raman spectra, which can be widely applied in qualitative and quantitative studies of the microstructure of silicates.

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