In our previous works, a basic approach is to calculate the parameters of model systems containing an anionic complex with an outer sphere (OS) cationic shell. For similar systems nM⁺⋅[NbF₇], nM⁺⋅[CrCl₆] (n = 1 – n_max) and others (system I), it has been demonstrated that the most thermodynamically stable compositions have some intermediate number of OS cations n < n_max, where n_max is the maximal number of OS cations held by a given complex. In another our papers, an approach was proposed for estimating the stability of particles with different composition of the second coordination sphere of complexes in more complex model systems –M⁺₃Cr(3)Cl₆+18MCl and M²⁺Ti(4)F₆+12MCl₂, where M²⁺ - Mg, Ca, Sr, Ba (system II).

The aim of this study is the quantum-chemical substantiation of the existence stable particles in alkali halide melts of formed by a titanium halide complex and an OS cationic shell of a certain composition in a model system M²⁺∙[Ti(3)F₆]^3-+12MCl₂.

The geometry optimization of structures was performed with the Firefly program package, partially based on the source code of the GAMESS(US) program, by the density functional theory DFT/UHF method with the use of the B3LYP hybrid functional. For the F and Cl atom quasi-relativistic basis set Stuttgart RLC ECP was used; for Ti, Ca, Sr and Ba – Stuttgart RSC 1997 ECP basis set and for Mg – CRENBL ECP. In all cases, the search for the optimized geometry was accompanied by control calculation of vibrational frequencies, and, thus, all the data reported correspond to true minimum of the potential energy surface (there are no imaginary frequencies).

Different from system type I, in the system II it was possible direct calculation of the interaction energy between particle and rest part of the model system. If the interaction energy between the OS shell and titanium complexes exceeds the energy of its interaction with the rest environment, there are presence in the system of such dynamic equilibrium, which ensures the existence of sufficiently stable complex particles of a certain OS composition.

The analysis of interactions in systems I and II on the example of Ti(3) complexes showed that there are discrepancies between the composition of the most stable complex particles in these systems. Allowance for the interaction of the particle "complex plus OS shell" with the surrounding ions gives a much more accurate estimate of the composition of the electroactive particles. Thus, using the model system of nM²⁺ +Ti(3)F₆ for example, it was shown that the calculation parameters of this system may be used just as the initial assessment.