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Li et al. J. Mater. Inf. 2025, 5, 21 https://dx.doi.org/10.20517/jmi.2024.87 Page 9 of 15

Figure 4. Formation energies during charge and discharge, along with the energy above the convex hull (E ) for different compositions
hull
of (A) K AuP, (B) K CuP and (C) K Cu P .
2
3 2
3
2
0.112 eV [Figure 7B], respectively, both of which are significantly lower than the results obtained from the
BVSE analysis [Supplementary Table 1]. This discrepancy arises because the BVSE method does not
account for lattice effects or structural transformations during cation migration . For instance, previous
[32]
+
studies on Li ions have shown that BVSE tends to overestimate the migration barrier compared to DFT by
a significant margin (more than twice) . In contrast, the migration barriers computed by both methods for
[84]
[85]
Mg exhibit close agreement . Additionally, the correlation may be influenced by computational factors
2+
such as the choice of BVSE screening factor, the DFT functional, and the basis set employed in the
calculations. However, the relative values of migration barriers computed for a series of compounds by
BVSE and DFT are consistent, which allows one to use BVSE for the preliminary screening of prospective