First-Principle Studies of the Vibrational Properties of Carbonates under Pressure.

Using the density functional theory with the hybrid functional B3LYP and the basis of localized orbitals of the CRYSTAL17 program code, the dependences of the wavenumbers of normal long-wave vibrations on the (GPa) pressure (cm) = + (/)· + (/)· and structural parameters (Å) (: , , , , ): (cm) = + (/) - ( - ) were calculated. Calculations were made for crystals with the structure of calcite (MgCO, ZnCO, CdCO), dolomite (CaMg(CO), CdMg(CO), CaZn(CO)) and aragonite (SrCO, BaCO, PbCO). A comparison with the experimental data showed that the derivatives can be used to determine the pressures, , , lattice constants and the metal-oxygen, and the carbon-oxygen interatomic distances from the known Δ shifts. It was found that, with the increasing pressure, the lattice constants and distances decrease, and the wavenumbers increase with velocities the more, the higher the is. The exceptions were individual low-frequency lattice modes and out-of-plane vibrations of the -type carbonate ion, for which the dependences are either nonlinear or have negative (positive /) derivatives. The reason for this lies in the properties of chemical bonding and the nature of atomic displacements during these vibrations, which cause a decrease in and an increase in .