## 2 Materials and Methods
The combination of CeF\({}_{3}\) and XF complexes (X = Li, Na, K) served as a geometric template for determining the interaction between the Ce ion and alkali metal ions. In this 3D complex, the Ce-F and X-F distances were fixed at 2.3 A while the Ce-X distances varied. In all cases, the energy of non-Coulomb interactions was determined as the difference between the total energy and the energy of Coulomb interactions. The dependence of the non-Coulomb interaction energy on the distance between the ions was approximated by an exponential dependence. [PERSON]'s dispersion corrections D3 [21] were added for accurate accounting of non-covalent interactions. The non-Coulomb contribution was determined by the second term in the expression (1), where the parameters \(B\), \(\rho\), and \(\sigma\) were determined using quantum mechanical DFT calculations and are presented in Table 1. The behavior of cerium ions with an electric charge of +3 in the FLiNaK salt melt is almost completely determined by the Coulomb interaction. The absence of explicit contributions describing the weak dipole-dipole and dipole-quadrupole interactions of cerium with other ions does not significantly change the ion dynamics in the molten salt. This is confirmed by the results of [22], where a similar form of the interaction potential was used for all ions present in pure FLiNaK. To calculate the self-diffusion coefficient, the Einstein relation was used:  
\[D_{\alpha}=\frac{1}{6t}\lim_{t\rightarrow\infty}\left\langle\left|\Delta r_{ \alpha}(t)\right|^{2}\right\rangle, \tag{2}\] \begin{table}
\begin{tabular}{c c c c} \hline
**Cerium** & \(B_{\
u}\)**eV** & \(\rho\), Å & \(\sigma\), Å \\ \hline Ce–Ce & 1.357 & 0.141 & 2.02 \\ Ce–F & 1.618 & 0.3324 & 2.34 \\ Ce–Li & 0.053 & 0.137 & 1.77 \\ Ce–Na & 0.092 & 0.146 & 2.03 \\ Ce–K & 0.078 & 0.168 & 2.39 \\ \hline \end{tabular}
\end{table} 
Table 1: Parameters for interaction of Ce with other components of molten salt. Figure 1: Principal scheme for determining the parameters of the interaction potential between Ce ions and other ions that form the FLiNaK salt mixture. where \(\left\langle\left|\Delta r_{\alpha}(t)\right|^{2}\right\rangle\) is the mean square displacement of the element \(\alpha\) and \(\Delta r_{\alpha}\) is determined for each particle at various times \(t\) and then taking the average. In [23], based on the hydrodynamic model of a particle surrounded by a solvent, an analytical correction was obtained to the effect of the system size on the diffusion coefficient. In this approach, it was assumed that particle diffusion depends not only on the hydrodynamic interaction with the solvent in the nearest environment, but also on periodic images of the particle itself and the solvent. An expression was obtained for the self-diffusion coefficient \(D_{\infty}\) of the particle in an infinite system  
\[D_{\infty}=D_{PBC}^{MD}+\frac{k_{B}T\xi}{6\pi\eta L}, \tag{3}\]  
where \(D_{PBC}^{MD}\) is the self-diffusion coefficient obtained in the MD model with periodic boundary conditions (PBC), \(k_{B}\) is the Boltzmann constant, \(\eta\) is the shear viscosity, \(L\) is an effective simulation cell length, constant \(\xi=2.837297\)[24]. In the case of unequal lengths of edges in an orthogonal cell, we can set \(L=\overline{L}\), where \(\overline{L}\) is the average length of an edge of the cell. We used an orthogonal cell with one side significantly shorter than the other sides for two reasons. First, the initial stacking of the crystals of the constituent components (LiF, NaF, KF and CeF\({}_{3}\)) was carried out in pairs vertically on top of each other. In other words, the larger LiF and KF crystals were placed together at the bottom of the box while the CeF\({}_{3}\) and NaF crystals were located above these crystals. Second, with such a shape of the cell, it was convenient to visually observe the mixing of ions in the system.