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In crystals, electrons and holes do not behave like free particles. Their response to external forces such as electric fields depends on the curvature of the energy bands near a specific k-point (typically the Γ-point).
This behavior is described using the concept of effective mass, which allows us to treat charge carriers as free particles with a modified mass that accounts for the influence of the crystal lattice.
The magnitude of the effective mass indicates how easily charge carriers move:
If the effective mass is not the same in all directions, the material is said to be anisotropic. This means that charge carriers will move more easily in the direction with a small effective mass and more slowly in directions with a large effective mass. For example, the material will conduct well along the x-axis if the effective mass is small in that direction but show poor conductivity along the y- or z-axis where the effective mass is much larger.
In battery applications, the effective mass provides deeper insight into the electronic properties of a material.
If the effective mass is small, it suggests high mobility, making the material suitable as an electrode for fast charge transport.
If the effective mass is large, carriers move slowly, which may be ideal for solid-state electrolytes where ionic movement dominates and blocking electron flow is beneficial.
The band structure of a material describes how electron energy levels vary with momentum across the crystal. It determines whether electrons can move freely or whether they are restricted.
Band structures are central in identifying whether a material is a conductor, semiconductor, or insulator.
Band structure helps evaluate how easily charge carriers move through a material:
In electrodes, we need materials with small or no band gaps and dispersive conduction bands to ensure fast electron transport.
In contrast, electrolytes or solid-state separators should ideally exhibit large band gaps to prevent electronic leakage while allowing ionic transport, preserving electrochemical integrity.
Moreover, band alignment at interfaces (e.g., between cathode and electrolyte) governs charge transfer efficiency and stability during battery cycling.
PDOS reveals which atoms and orbitals contribute to the electronic states near the Fermi level, where redox activity and charge transfer occur. It decomposes the total electronic density of states into atomic and orbital components.
This atomic-level insight is crucial for battery applications — it helps predict if a material can conduct electrons, host redox reactions, or block electronic leakage.
In pristine MOFs, PDOS near EF may be minimal — indicating insulating or semiconducting behavior. But when a guest molecule (e.g., Li, Na, Zn) is introduced, it can:
These changes explain why guest-loaded MOFs often outperform their pristine counterparts in electrochemical cycling:contentReference[oaicite:0]{index=0}:contentReference[oaicite:1]{index=1}.
By computing and analyzing PDOS, we can:
NEB calculations reveal how ions move through a material by mapping the minimum energy path between two stable positions. This helps estimate how quickly ions such as Li⁺ or Na⁺ diffuse through MOFs, electrodes, or solid electrolytes.
It is an essential method for evaluating ionic conductivity and transport properties in battery materials.
The diffusivity
The methodology involves identifying active sites via charge analysis, inserting guest ions,
and constructing intermediate structures between configurations. These structures are used in NEB to extract
the migration barrier
Diffusivity is then estimated using the above equation. GFN-xTB was used to ensure scalability across thousands of MOFs, and directions with the lowest effective mass were chosen to reflect realistic transport pathways.
Theoretical capacity quantifies the maximum amount of electrical charge a material can store per unit mass assuming complete and reversible redox activity. It is commonly expressed in milliampere-hours per gram (mAh·g⁻¹).
In this work, the number of guest ions inserted into each MOF without structural overlap was used to calculate the theoretical capacity. This parameter enabled a comparative evaluation of charge-storage capability across thousands of frameworks and guest species. Capacity values serve as a critical metric in identifying high-performance materials for both anode and cathode roles in next-generation battery chemistries.
The open-circuit voltage corresponds to the maximum electrochemical potential difference between the electrodes of a battery when no external current is flowing. It is fundamentally governed by the thermodynamics of redox reactions occurring at the electrode interfaces.
In this study, the OCV was computed for each MOF–guest pair based on sequential guest insertion energies. This enabled rapid classification of MOFs as candidate anode materials (lower voltage), cathode materials (higher voltage), or inactive hosts. The OCV, when evaluated across various metal-ion systems (Li, Na, Mg, Zn, Al), provides crucial insight into redox activity and potential compatibility.