Chemical Bonding Effects and Physical Properties of Noncentrosymmetric Hexagonal Fluorocarbonates ABCO(3)F (A: K, Rb, Cs; B: Mg, Ca, Sr, Zn, Cd)

The present work applied the methods of density functional theory and the van der Waals interaction PBE + D3(BJ) on the basis of localized orbitals of the CRYSTAL17 package. It featured the effect of interactions between structural elements of fluorocarbonates ABCO(3)F (A: K, Rb, Cs; B: Mg, Ca, Sr, Zn, Cd) on their elastic and vibrational properties. The hexagonal structures proved to consist of alternating ···B-CO(3)··· and ···A-F··· layers in planes ab, interconnected along axis c by infinite chains ···F-B-F···, where cations formed polyhedra AO(n)F(3) and BO(m)F(2). The calculations included the band energy structure, the total and partial density of electron states, the energy and band widths of the upper ns- and np-states of alkali and alkaline-earth metals, as well as nd-zinc and nd-cadmium. For hydrostatic compression, we calculated the parameters of the Birch–Murnaghan equation of state and the linear compressibility moduli along the crystal axes and bond lines. We also defined the elastic constants of single crystals to obtain the Voigt–Reuss–Hill approximations for the elastic moduli of polycrystalline materials. The study also revealed the relationship between the elastic properties and the nature of the chemical bond. Hybrid functional B3LYP made it possible to calculate the modes of normal long-wavelength oscillations, which provided the spectra of infrared absorption and Raman scattering. Intramolecular modes ν1 and ν4 with one or two maxima were found to be intense, and their relative positions depended on the lengths of nonequivalent C–O bonds.