Predicting oxidation and spin states by high-dimensional neural networks: Applications to lithium manganese oxide spinels

Lithium ion batteries often contain transition metal oxides like Li$_{x}$Mn$_2$O$_4$ ($0\leq x\leq2$). Depending on the Li content different ratios of Mn$^\text{III}$ to Mn$^\text{IV}$ ions are present. In combination with electron hopping the Jahn-Teller distortions of the Mn$^\text{III}$O$_6$ octahedra can give rise to complex phenomena like structural transitions and conductance. While for small model systems oxidation and spin states can be determined using density functional theory (DFT), the investigation of dynamical phenomena by DFT is too demanding. Previously, we have shown that a high-dimensional neural network potential can extend molecular dynamics (MD) simulations of Li$_{x}$Mn$_2$O$_4$ to nanosecond time scales, but these simulations did not provide information about the electronic structure. Here we extend the use of neural networks to the prediction of atomic oxidation and spin states. The resulting high-dimensional neural network is able to predict the spins of the Mn ions with an error of only 0.03 $\hbar$. We find that the Mn e$_\text{g}$ electrons are correctly conserved and that the number of Jahn-Teller distorted Mn$^\text{III}$O$_6$ octahedra is predicted precisely for different Li loadings. A charge ordering transition is observed between 280 and 300 K, which matches resistivity measurements. Moreover, the activation energy of the electron hopping conduction above the phase transition is predicted to be 0.18 eV deviating only 0.02 eV from experiment. This work demonstrates that machine learning is able to provide an accurate representation of both, the geometric and the electronic structure dynamics of Li$_x$Mn$_2$O$_4$, on time and length scales that are not accessible by ab initio MD.