A necessary step for considering charge transfer processes by quantum chemistry methods is determination the composition of the most stable particles "samarium complex + outer-sphere shell". The aim of this study was the quantum-chemical substantiation of the existence stable particles in alkali halide melts, which formed by a samarium halide complex and an outer sphere (OS) cationic shell of a certain composition in a model system MX+M₃SmX₆ (X = F, Cl and M = Na, K, Rb, Cs).

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/RHF method with the use of the B3LYP hybrid functional. For the F and Cl atoms a quasi-relativistic basis set Stuttgart RLC ECP (ECP – effective core potential) was used; for K, Rb and Cs – Stuttgart RSC 1997 ECP basis set and for Na – CRENBL ECP; for Sm, the Stuttgart/Cologne group basis set with 4f electrons included in the core was used. In all cases, the search for the optimized geometry was accompanied by control calculation of vibrational frequencies, and, thus, all the reported data correspond to true minimum of the potential energy surface (there are no imaginary frequencies).

The method for determining the composition of electroactive particles in model systems was discussed in detail in our previous works. The main determinable quantity was the energy (ΔE) characterizing the equilibrium:

(AB^ABC)+C^ABC↔A^ABC+(BC^ABC), (1)

where A was the complex particle, B was the outer-sphere shell, C was the remainder of the system, the index ABC means that the corresponding fragment of the complete ABC system in the corresponding geometries was considered. If, ΔE was less than zero, the equilibrium was shifted to the right and the formation of the particle "complex + OS shell" was highly unlikely. Otherwise (ΔE > 0) the "complex + OS shell" particle was stable. The value of ΔE was determined by equation:

∆E = E(B∙C)^ABC - E(A∙B)^ABC (2)

where E(B∙C)^ABC and E(A∙B)^ABC are the interaction energies of the respective fragments.

Based on this method of analysis of the particle composition distribution, the following particles will take part in the charge transfer process: 2M⁺-SmX₆^3-, 3M⁺-SmX₆^3-,
and 4M⁺-SmX₆^3-. Using the calculated value of ΔE, let us estimate the content of each possible composition of the particles "complex + OS shell" in the all studied model systems. In the first approximation, we can assume that the content of particles will be proportional to the energy of its formation. In our case this is the value ΔE. In all studied model systems, the content of 3M⁺-SmX₆^3- particles was higher than that of the others and amounts to 22-28%. The content of 2M⁺-SmX₆^3- and 4M⁺-SmX₆^3- particles was 18-23% and 21-24%, respectively. Thus, the content of the most stable particles with the number of OS cations 2-4 was 63-73%.