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Page 4 of 15 Li et al. J. Mater. Inf. 2025, 5, 21 https://dx.doi.org/10.20517/jmi.2024.87

principle of maintaining local bond strength equilibrium, which is essential for understanding ion
movement within a crystal lattice. By considering the Coulombic repulsion between the migrating ion and
[51]
the ions in the crystal framework, the migration energy barriers for the ions are calculated . The migration
+
energy landscape for K was computed using a Cube.file with a resolution of 0.1 and an automatically
determined screening factor (f) .
[52]
To evaluate the dimensionality of the migration map, we determined the migration barrier energy (E ). The
m
most promising candidates for KMC simulations and DFT calculations were selected based on the criterion
that E < 1 eV and the material should exhibit 2D or 3D ionic conductivity. This criterion is important
m
because, although 1D ionic conductors can exhibit high conductivity under certain conditions, their
sensitivity to defects and interfaces limits their practical applications.

KMC simulations
Ionic conductivities and diffusion coefficients were calculated using KMC simulations. For this purpose,
3
supercells with volumes exceeding 10,000 Å were simulated for 1 to 10 million KMC steps at 300 K. The
KMC algorithm, implemented in the command-line version of softBV, utilizes approximate site and
migration energies derived from BVSE analysis. The results were averaged over five different configurations
to ensure statistical reliability. The unit cells were relaxed using the softBV force field. The ionic diffusion
coefficient is a key performance indicator for cathode materials. Compounds with high ionic diffusion
coefficients are characterized by continuous ion transport channels and low migration barriers [53,54] .

DFT calculations
All DFT calculations were performed using the projected augmented wave (PAW) method ,
[56]
[55]
implemented in the Vienna Ab initio Simulation Package (VASP) [57,58] . The Perdew-Burke-Ernzerhof (PBE)
functional in the generalized gradient approximation (GGA) was used to describe the exchange-
[59]
correlation interactions. Structural optimization was carried out using the conjugate gradient method, with
-5
convergence thresholds of 10 eV for energy and 0.03 eV/Å for interatomic forces. A plane-wave energy
cutoff of 520 eV was employed. To correct the self-interaction error and account for strong correlation
effects in localized electrons, Hubbard U corrections were applied, with a U value of 5.2 eV for Cu . The
[60]
Ewald summation method was used to screen the system during the K-ion charging process, leading to
[61]
the generation of various configurations.

The formation energy diagram was constructed to identify the configuration with the lowest energy at
different optimized concentrations. Stable intermediate phases were identified as those on the convex hull,
while other compounds were classified as metastable or unstable. The energy above the hull (E ) for stable
hull
intermediate phases was calculated, and the maximum potassium removal capacity was determined for
those phases with E < 0.1 eV/atom, providing the reversible capacity of the candidate cathode materials.
hull
Ionic migration barriers for K ions were calculated using the nudged elastic band (NEB) method , with
[62]
+
input files generated via the PATHFINDER script (https://pathfinder.batterymaterials.info).
Compounds containing electrochemically active transition metals (Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Nb, Mo,
-1
W) were considered as promising cathode materials. The theoretical capacity (in mAh·g ) was calculated
using :
[63]
(1)