The methods of density functional theory in the generalized gradient approximation PBE with dispersion correction D3 and the basis of localized orbitals of the CRYSTAL program code were used to calculate the crystal, electronic and vibrational structure of belousovite and its synthetic analogues AZn(SO_4)X (A= K, Rb, Cs, Tl; X= Cl, Br, I). Dependences of lattice constants, interatomic spacing on average radius of cations A and anions X are determined. Density distribution of electronic states is calculated, and their nature is determined. It is shown that structural features of crystals manifest themselves in infrared absorption spectra, where individual bands in region 1120-1170 and 940-970 cm^-1 correspond to oscillations of atoms of sulfur and oxygen [SO₄] with different spacings S-O. Oscillations of atoms Zn-O occur in region of wavenumbers 350 cm^-1, and Zn-X - from 310 cm^-1 and below. Vibrational modes for A-O atoms have low intensity, and their wavenumbers are in region below 150 cm^-1. The obtained patterns can be used to interpret experimental spectra and identify belousovite, its synthetic analogues and their mixed compositions. Keywords: density functional theory, synthetic crystals, crystal structure, density of states, chemical bonding, vibrational spectra, infrared absorption.

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