## 3 Results and Discussion
### Metal Release
In equistoichiometric NMC, Ni should oxidize from \(\rm Ni^{2+}/Ni^{3+}\) between \(\rm Li_{1.00}\)\(\rightarrow\)\(\rm Li_{0.66}\) and then oxidize to \(\rm Ni^{4+}\) over the next third of delithiation. Because there are only oxidation events occurring for a third of the metal atoms at any given delithiation step, it would be expected that the changes in \(d_{1}\) are smaller in magnitude than those of \(d_{1}\), as can be seen in Figure 5a. To monitor the changes in metal oxidation states, we carried out state-by-state, atom-projected density of states (PDOS) analysis, with the results plotted in Figure 6. Additionally, shown in Figure 6 are schematic d-orbital crystal field diagrams, showing how the d states of the Ni are split into three lower energy \(t_{\rm 2g}\) orbitals and two higher energy \(e_{\rm g}\) orbitals. The crystal field diagrams aid in the interpretation of the DFT calculated PDOS in assigning the oxidation state of the lattice Ni as a function of \(\rm Li_{x}\). We first focused on Ni over \(\rm Li_{x}\) values, starting from \(\rm Li_{1.00}\) down to \(\rm Li_{0.44}\). The plots in Figure 6 show the PDOS of the d-states for Ni as a function of \(\rm Li_{x}\), with spin-down density plotted in green and spin-up in blue. At \(\rm Li_{1.00}\), we observe Ni in the 2+ state where the electronic densities in the figure match the electron field split diagram of a 2+ (d\({}^{8}\)) configuration. All the d-orbitals are filled with spin-down electrons, causing all the spin-down density to fall below the Fermi energy (\(\rm E_{F}\)) (dashed purple line) and there is a split in the spin-up density with more being located below \(\rm E_{F}\) giving a d\({}^{8}\) configuration. As \(\rm Li_{x}\) decreases, we observe a change in the spin-down density where some of the density moves up across \(\rm E_{F}\), indicating that there are unoccupied \(\rm e_{g}\) orbitals. A similar PDOS analysis was performed for Co and Mn, which  
Figure 4: (**a**) \(\Delta G_{1}\) changes for Ni (black), Co (blue), and Mn (red) with respect to lithiation state. \(\Delta G_{1}\) values are plotted with the lowest \(\Delta G_{1}\) value referenced to zero and \(\sigma\) is shown with error bars. (**b**) To observe how much each metal changes individually, the initial \(M-\)OH. showed that these metals maintained the oxidation states (3+ and 4+, respectively) seen in the pristine NMC (See Figure S3). It is expected that, if Li\({}_{\text{x}}\) was lowered beyond 0.33, the changes in the oxidation state of Co would result as seen in cyclic voltammetry studies of the material [1]. While the above analyses show that trends in \(\Delta G_{1}\) can be interpreted in terms of slab geometry (\(d\)) and electronic structure (PDOS, oxidation state), it is the case that the level of system complexity hinders efforts to delineate the principal factors governing metal release. To this end, we employed RFT machine learning to build a model for \(\Delta G_{1}\) based on descriptors. The initial descriptor testing is shown in the Supplementary Materials (Figure S2), which led to the selection of the four descriptors that are transferable when extending to other systems beyond Li\({}_{\text{x}}\) in NMC. The RFT model is built using two descriptors to track changes in the oxidation state, both derived from the starting (defect-free) slab. First, we used empirical bond-valence sums, referred to as BV, which are determined using the DFT optimized geometries and bond-valence parameters from the literature [43]. Briefly, in bond-valence theory, each bond between pairs of atoms contributes to BV. Bond-valence models are constructed such that the value of BV for a given atom should equal the magnitude nominal charge. Thus, in pristine NMC with Li\({}_{\text{x}}\) = 1.00, the  
Figure 5: (a) O–\(M\)–O (\(d_{1}\)) and O–Li–O layer spacings (\(d_{2}\)) tracked across the charge cycle. (b) Layered NMC structural model indicating O–\(M\)–O layer in black and O–Li–O layer in blue.