## 2 Computational Methods
This approach is derived from the work of [PERSON] and [PERSON], which details this method further [40]. Here, DFT was used to calculate the total energies of all product and reactant terms in Equation (2). The DFT total energies  
Figure 2: The release of a \(M\)-OH unit from the Li(Ni\({}_{1/3}\)Mn\({}_{1/3}\)Co\({}_{1/3}\))O\({}_{2}\) cathode surface is modeled in three steps. Initially, the cathode is in its operational conditions and is Li terminated (NMC\({}_{\text{Li-term}}\)). Upon exposure to aqueous environments, there is a quick Li/H exchange on the surface, giving NMC\({}_{\text{H-term}}\). The last step involves the release of an \(M-\)OH group, creating a vacancy on the surface (NMC\({}_{M-\text{OH vacancy}}\)). were converted to free energies based on zero-point energy corrections and vibrational contributions to the free energy, as detailed elsewhere [41]. The dataset of \(\Delta G_{1}\) values obtained in this study covered the range of Li\({}_{x}\) for x = 1.00, 0.89, 0.78, 0.67, 0.56, 0.44. This dataset was well suited to then build a random forest tree (RFT) machine learning model. RFT models are a collection of decision trees that individually categorize input values, in our case, \(\Delta G_{1}\), based on descriptors to find relationships between similar release values. RFT averages the predictions of the individual decision trees, which are corrected for any bias that may arise in a single tree. We implemented the RFT model from the \"sci-kit learn\" library and provide an optimization of the RFT model in the Supplementary Materials (Figure S1), where we determined how many trees and layers should be implemented. To predict \(\Delta G_{1}\) values, we tabulated structural descriptors from the (de)lithiated surfaces, before introducing the \(M\)-OH vacancy, related to the oxidation state and magnetic moments of the surface metals. RFT can provide importance values to the descriptors, ranking which features play a larger role in controlling \(\Delta G_{1}\). Using these importance values, we were able to reduce the number of descriptors and consider transferability between different materials; the optimization of the RFT model and descriptor selection are in the Supplementary Materials (Figure S2). The descriptors that were chosen for this model include three parameters of the vacancy site metal: the bond valance sum (BV_vac), magnetic moment (\(\rho_{s}\)) and number of valance electrons (Charge_vac) and another descriptor that considers the spin paring in the lattice, which is the sum of the magnetic moments of the six neighboring metals to the vacancy site, (\(\Sigma\rho_{s}\)). We first considered a small bulk structure with 6 Li atoms. A total of 6 Li atoms resulted in 64 total configurations that could be modeled and could calculate the intercalation voltage in 2 ways: (1) a single pathway where Li is removed from the previously delithiated structure or (2) sample all the configurations to find the lowest energy arrangement at each value of Li\({}_{x}\). Shown in Figure 3 are the voltage curves for the 6 Li atom bulk structure using the 2 approaches, including the results of a published computational study using a 6 lithium atom structure for comparison [1]. Approach 1 involved removing an individual Li atom and using that vacancy structure to generate the next Li vacancy in a stepwise fashion. As shown in Figure 3, this leads to non-monotonic changes in the voltage curve. Ideally, we wanted to reproduce cyclic voltammetry measurements, which show monotonic increases in potential as the materials are oxidized [1; 2; 19; 42], leading us into the results of approach 2. For approach 2, only the lowest energy configuration at each lithium fraction was used, which yields a monotonic voltage curve. Knowing this, to approach the 18-lithium atom supercell surface model, we needed to optimize a range of configurations at each lithium fraction to find the lowest energy configurations.