Ab Initio Thermodynamic and Thermophysical Properties of Sodium Metasilicate, Na2SiO3, and Their Electron-Density and Electron-Pair-Density Counterparts

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Abstract
Thermodynamic and thermophysical properties of Na2SiO3 in the Cmc21 structural state are computed ab initio using the hybrid B3LYP density functional method. The static properties at the athermal limit are first evaluated through a symmetry-preserving relaxation procedure. The thermodynamic properties that depend on vibrational frequencies, viz., heat capacities, thermal expansion, thermal derivative of the bulk modulus, thermal correction to internal energy, enthalpy, and Gibbs free energy, are then computed in the framework of quasi-harmonic approximation. Acoustic branches are computed by solving the Christoffel determinant and are assumed to follow sine wave dispersion when traveling within the Brillouin zone. The procedure generates several thermo-physical properties of interest in materials science and geophysics (transverse and longitudinal wave velocities, shear modulus, Young modulus, Poisson ratio) all consistent with experimentally determined properties. A representative cluster is then abstracted from the cell and a detailed electron localization/delocalization analysis is performed on it, in the ground state geometry, and on deformed states imposed by two peculiar mixed asymmetric stretching/bending modes affecting the silicate chain that, according to literature data, have anomalous mode Grüneisen parameters. A Bader analysis reveals an intriguing feature associated with these deformations: an increase in the covalence of the Si–O bond that strengthens the linkage opposing the weakening induced by thermal stress. Finally, on the same cluster, the Ramsey contributions to the JNM coupling are evaluated by the gauge-independent atomic orbital method. The calculated isotropic chemical shifts of both 23Na and 29Si are again in substantial agreement with observations.

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