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

Lithium ion batteries often contain transition metal oxides such as Li_xMn₂O₄ (0 ≤ x ≤ 2). Depending on the Li content, different ratios of Mn^III to Mn^IV ions are present. In combination with electron hopping, the Jahn-Teller distortions of the Mn^IIIO₆ octahedra can give rise to complex phenomena such as 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_xMn₂O₄ 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 ℏ. We find that the Mn e_g electrons are correctly conserved and that the number of Jahn-Teller distorted Mn^IIIO₆ octahedra is predicted precisely for different Li loadings. A charge ordering transition is observed between 280 K 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_xMn₂O₄ on time and length scales that are not accessible by ab initio MD.