Quantum-Chemical Analysis of the Electron Transfer in the MgTiF6+12MgCl2 Molten System By Frontier Molecular Orbital Method

Abstract

Investigation of the electrochemical charge transfer mechanism in molten salts containing transition metal complexes is a challenging task. Such studies could be facilitated by analysis of the corresponding model systems by quantum-chemical methods. However, in practice, a direct search for the transition state in such systems requires enormous computational time. In this work, we suggest to use an approach that allows us to qualitatively characterize possible variants of electron transfer and, thus, to sharply narrow the search for the transition state. We mean the use of the frontier molecular orbital method. The method is traditionally employed to evaluate the reactivity of species. However, when applied to electrochemical systems, the method can also provide extremely useful information on whether a certain electron transfer mechanisms is possible or impossible In this work, we were interested in the state of the complex TiF6 2- near the cathode surface. For this reason, on one side of the molten system, a flat boundary layer consisting of 17 chlorine and magnesium ions was formed. In general, the boundary ions of chlorine and magnesium are not in the same plane. The mutual displacement of these ions was determined from the computation in the model system C96H24+7MgCl2, where C96H24 is a flat carbon cluster simulating the surface of the cathode; hydrogen atoms close the broken bonds of carbon atoms to prevent artifacts. After optimization of this system, the chlorine anions shifted by 0.3 Å relative to the magnesium cations (Δd) in the direction opposite to the surface of the carbon cluster. The direction of this displacement corresponds to the effect of the electric field on the chlorine anions. Thus, the equilibrium shift Δd is 0.3 Å. The model system MgTiF6+12MgCl2 with such shift value will be considered referent. A systematic study of the influence of the Δd value and the length of Ti-F bonds (Δr) on the lowest unoccupied molecular orbital (LUMO) character showed the following: 1) the group of lower free MOs, the main contribution to which gives the TiF6 2- complex, is destabilized with increasing of Ti-F bond contraction; 2) when the shift Δd increases, this MO group is also destabilized and simultaneously free MOs belonging to the boundary ions become more stable. In particular, when the Ti-F bonds are compressed on Δr = 0.05 Å, the critical value of the shift Δd is 0.6 Å. That is, at Δd ≥ 0.6 Å and Δr = 0.05 Å, LUMO is delocalized between the complex and the bridge cation. At excessively large values of Δd and Δr, LUMO is completely localized on the boundary ions, but this is undesirable. The combination of the parameters Δd = 0.6, 0.7 Å and Δr = 0.05 Å is optimal. At these values, LUMO is delocalized between the complex and the bridge cation and the activation energy (~18 kJ mol-1) is close to the experimental value (21±4 kJ mol-1). An increase in the parameter Δr leads to a rapid increase in the activation energy, a contraction value of 0.05 Å is optimal. An equally important characteristic is the highest occupied molecular orbital (HOMO) type of the structure after electron transfer (ET). Theoretically, there may exist three main types of HOMO for our structures (after ET): 1) HOMO is completely localized on the boundary ions; 2) HOMO is delocalized between the boundary ions and the complex; 3) HOMO is completely localized on the complex. In the first case, probability of electron capture by the complex is very small. After diffusion of the complex into the depth of the melt, electron remains on the boundary ions and then returns to the cathode. In the second case, there is a significant probability of ET to the complex through the bridge cation. In the latter case, the probability of electron capture by the complex is close to 100%, if the complex is in contact with the surface of the electrode.