Abstract:
Density functional theory methods with the B3LYP hybrid functional and the basis of a linear combination of localized atomic orbitals of the CRYSTAL17 program code were used to study the pressure dependences of the structural and optical properties of double carbonates Na$_2$Ca$_2$(CO$_3$)$_3$, K$_2$Ca$_2$(CO$_3$)$_3$. The parameters of the Birch–Murnaghan equation of state and linear compressibility moduli are determined. The coefficients of generation of the second harmonic, which characterize the nonlinear optical properties of these materials, are determined, and the frequencies and intensities of normal long-wavelength oscillations are calculated, from which the spectra of infrared absorption and Raman scattering of light are plotted by Gaussian expansion. The LO–TO splittings were estimated and the reflection spectra were plotted. It is shown that in the lattice region the spectra differ in the number and intensities of modes, while in the region of intramolecular vibrations of CO$_3^{2-}$ atoms for both compounds they have a qualitatively similar form. For lattice and intramolecular vibrations, with increasing pressure, the rates of increase in wave numbers differ for each type of vibration. For oscillations of the $\nu$4, $\nu$1, $\nu$3 types, the Grüneisen mode parameter is usually equal to 0.2–0.4. For out-of-plane deformations $\nu$2, it is negative in Na$_2$Ca$_2$(CO$_3$)$_3$ and close to zero in K$_2$Ca$_2$(CO$_3$)$_3$.
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