The possibility that ion clusters of different species are formed during dissolution of LiAsF6 in a low- or high-molecular-weight solvent has been studied. The Hessian matrix of clusters has been calculated by the numerical and analytical differentiation of their full energy in the MO LCAO approximation using the Roothaan - Hartree - Fock method and the PC GAMESS software package. It was found that stable ion clusters are represented by ion pairs Li+[AsF6]- with the bi- or tridentate coordination of the cation relative to the octahedral anion, triple ions [AsF6]-Li+[AsF6]- and Li+[AsF6]-Li+ with the bi- or tridentate coordination, ion dimers {Li+[AsF6] -}2 with the bidentate coordination, and also ion trimers {Li+[AsF6]-}3 and ion tetramers {Li+[AsF6]-}4 shaped as symmetric ring structures with the unidentate coordination. The frequencies and intensities of IR absorption bands of different species of ion clusters in the gaseous phase and nonaqueous solutions (acetone, ethanol, nitromethane, and tetrahydrofurane) have been calculated. This presents a basis for identification of ion particles during IR spectroscopic measurements in electrolyte solutions containing LiAsF6.