## 3 Results
### Elastic Modulus  
The stiffness for 11 SOCs was calculated using the analytical empirical Buckingham potential model for the selected optimized and equilibrated structures. The results, presented in Figure 6, show a substantial decrease in stiffness from 452 GPa for a fully lithiated state to 130 GPa at 16% lithiation. This significant variation highlights the material's sensitivity to changes in the state of charge, as reflected in its mechanical properties. Figure 4: Confusion matrix of predicted versus actual energy per atom values for the trained DeePMD-kit model. Notably, comparisons with similar oxides have shown differences of up to 50% in elastic modulus values [10]. The substantial variation in elastic moduli observed in our results is consistent with the pronounced SOC-dependent changes reported for LiCoO\({}_{2}\) in previous studies [42]. Such large differences have been attributed to lithium concentration-driven changes in Co-O bond strength, evolving cation valence states, and associated structural distortions. This agreement further supports the robustness of our calculated results and highlights the expected mechanical behavior of LCO under varying SOC conditions. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**SOC**} & \multicolumn{2}{c}{**Buckingham Potential**} & \multicolumn{2}{c}{**Deep Potential**} & \multicolumn{2}{c}{**Previous Studies**} \\ \cline{2-9}  & **a (Å)** & **c (Å)** & **a (Å)** & **c (Å)** & **a (Å)** & **c (Å)** & **Reference** \\ \hline  & & & & & 5.631 & 14.054 & [36] & DFT \\  & & & & & 5.629 & 14.052 & [37] & DFT \\  & & & & & 5.652 & 14.207 & [38] & DFT \\
1.00 & 6.01 & 14.21 & 5.62 & 14.00 & 5.680 & 14.160 & [42] & DFT \\  & & & & & 5.583 & 13.593 & [14] & MD \\  & & & & & 2.859 \({}^{*}\) & 14.02 & [43] & DFT \\  & & & & & 2.816 \({}^{*}\) & 14.04 & [44] & NI \({}^{**}\) \\  & & & & & 2.840 \({}^{*}\) & 14.16 & [42] & DFT \\ \hline
0.91 & 5.99 & 14.17 & 5.62 & 14.00 & & & \\
0.83 & 5.97 & 14.11 & 5.63 & 14.01 & & & \\
0.75 & 6.09 & 15.15 & 5.63 & 14.00 & 2.811 \({}^{*}\) & 14.226 & [45] & NPD *** \\
0.66 & 5.93 & 14.76 & 5.63 & 14.00 & 2.811 \({}^{*}\) & 14.286 & [45] & NPD *** \\
0.58 & 5.85 & 13.83 & 5.62 & 14.00 & & & \\
0.50 & 5.77 & 13.64 & 5.62 & 13.99 & 4.865 & 14.420 & [46] & XRD \\
0.41 & 5.84 & 14.53 & 5.62 & 13.99 & & & \\
0.33 & 5.68 & 13.43 & 5.62 & 13.98 & & & \\
0.25 & 5.88 & 14.64 & 5.62 & 13.99 & & & \\
0.16 & 5.78 & 14.39 & 5.63 & 14.01 & & & \\ \hline \hline \end{tabular} \({}^{*}\) Half of the unit cell length in the a-direction. \({}^{**}\) NI: Nanoindentation. \({}^{***}\) NPD: Neutron powder diffraction.  
\end{table} 
Table 4: Lattice parameters of LCO with varying SOC. Figure 5: Variation of lattice constants along the x, y, and z directions as a function of SOC. Results are shown for both Buckingham potential (Buck) and Deep Potential (DP) models. The improved reliability of the DP model compared to the analytical Buckingham model arises from both its data-driven foundation and its ability to generalize across different states of charge. The DP model is trained on a diverse set of DFT-calculated structures that span a wide range of lithium contents and atomic configurations, allowing it to capture subtle changes in bonding environments, local stress fields, and Co\({}^{3+}\)/Co\({}^{4+}\) interactions across the SOC spectrum. In contrast, the Buckingham model relies on fixed formal charges and predefined pairwise parameters, which do not adapt to the evolving electronic structure during delithiation. As shown in Figure 6, the DP model predictions exhibit closer agreement with experimental reference values at multiple SOCs, further supporting its validity. This consistency highlights the DP model's strength not only in reproducing known data but also in reliably interpolating mechanical behavior in regimes where experimental measurements are scarce.