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 ν vibrations on the P(GPa) pressure ν(cm^-1) = ν₀ + (dv/dP)·P + (d²v/dP²)·P and structural parameters R(Å) (R: a, b, c, R_M-O, R_C-O): ν(cm^-1) = ν₀ + (dv/dR) - (R - R₀) were calculated. Calculations were made for crystals with the structure of calcite (MgCO₃, ZnCO₃, CdCO₃), dolomite (CaMg(CO₃)₂, CdMg(CO₃)₂, CaZn(CO₃)₂) and aragonite (SrCO₃, BaCO₃, PbCO₃). A comparison with the experimental data showed that the derivatives can be used to determine the P pressures, a, b, c lattice constants and the R_M-O metal-oxygen, and the R_C-O carbon-oxygen interatomic distances from the known Δν shifts. It was found that, with the increasing pressure, the lattice constants and distances R decrease, and the wavenumbers increase with velocities the more, the higher the ν₀ is. The exceptions were individual low-frequency lattice modes and out-of-plane vibrations of the v₂-type carbonate ion, for which the dependences are either nonlinear or have negative dv/dP (positive dv/dR) 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 R_M-O and an increase in R_C-O.