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The Raman scattering, infrared absorption, and reflection spectra of hexagonal non-centrosymmetric BaZnBO3F and BaAlBO3F2 and centrosymmetric BaZn3BO3F2 and BaZnCO3F2 are calculated using the standard procedures of the CRYSTAL package with the basis of localized orbitals and the B3LYP hybrid functional within the framework of the Hartree-Fock conjugate perturbation method. It is shown that the layered structure of crystals manifests itself in the spectra of vibrational modes polarized along and perpendicular to the c axis with wavenumbers for the lattice region formed by displacements of atoms in [BaF]∞ and [MAO3]∞ (M: Zn, Al; A: B, C) layers, for molecular deformation outside and in the plane of anions BO3 and CO3. The quantitative and qualitative composition of the spectra is determined by the symmetry of the crystal lattice. [ABSTRACT FROM AUTHOR]