The pursuit of advanced energy storage technologies has positioned lithium-ion batteries (LIBs) as the dominant solution for portable electronics and electric vehicles, owing to their high energy density and extended cycle life. However, the growing demand for large-scale energy storage systems faces significant challenges due to the relative scarcity, uneven geographical distribution, and rising cost of lithium resources. In this context, sodium-ion batteries (SIBs) have emerged as a compelling alternative. Sodium is abundant, low-cost, and shares similar electrochemical intercalation chemistry with lithium. Nevertheless, the larger ionic radius of Na+ (1.02 Å) compared to Li+ (0.76 Å) often leads to sluggish kinetics, substantial volume expansion, and structural degradation in conventional anode materials, severely limiting their capacity and cycling stability. Therefore, the rational design and discovery of novel anode materials capable of efficiently accommodating sodium ions are crucial for unlocking the full potential of sodium-ion battery technology.
Two-dimensional (2D) materials have garnered tremendous attention in this quest due to their large specific surface area, short ion diffusion pathways, and tunable electronic properties. Among them, a class of 2D transition metal carbides, distinct from conventional MXenes, has shown particular promise. These materials feature stable carbon dimers (C2) exposed on the surface, which offer high electron affinity and strong interaction sites for metal ions. Previous theoretical studies have highlighted exceptional Li+ storage capabilities in structures like TiC2 and VC2. More recently, ZrC2 was predicted to be an outstanding anode for sodium-ion batteries, boasting a high theoretical capacity and an ultra-low diffusion barrier. This compelling evidence motivates a deeper investigation into other members of this material family for sodium-ion battery applications.
In this work, we focus on the two-dimensional VC2 monolayer, specifically its thermodynamically stable β-phase. Using first-principles calculations based on density functional theory (DFT), we systematically evaluate its potential as an anode material for sodium-ion batteries. Our investigation encompasses a comprehensive analysis of its structural stability, electronic properties, sodium adsorption characteristics, diffusion kinetics, and key electrochemical performance metrics such as theoretical capacity and open-circuit voltage. The primary goal is to provide a fundamental understanding of the sodium storage mechanism in VC2 and to assess its viability as a high-performance component in next-generation sodium-ion battery systems.
1. Computational Methodology
All calculations in this study were performed using first-principles methods based on Density Functional Theory (DFT) as implemented in the Quantum ESPRESSO simulation package. The exchange-correlation interactions were treated within the generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) functional. To accurately describe the electronic structure, we employed a plane-wave basis set with a kinetic energy cutoff of 40 Ry. The charge density was expanded with a cutoff of 320 Ry. The Brillouin zone was sampled using a 7×7×1 Monkhorst-Pack k-point grid for structural optimization and electronic property calculations. A vacuum space of approximately 20 Å in the z-direction was introduced to eliminate periodic interactions between adjacent layers.
Geometry optimizations were conducted until the forces on all atoms were less than 0.001 Ry/Bohr and the total energy change was below 10-4 Ry. The climbing-image nudged elastic band (CI-NEB) method was used to determine the minimum energy path (MEP) and the corresponding energy barrier for sodium ion diffusion on the VC2 surface.
To evaluate the strength of sodium interaction with the VC2 monolayer, the adsorption energy ($E_{\text{ad}}$) per sodium atom is calculated as:
$$E_{\text{ad}} = E_{\text{Na@VC}_2} – E_{\text{VC}_2} – E_{\text{Na}}$$
where $E_{\text{Na@VC}_2}$ is the total energy of the VC2 monolayer with an adsorbed Na atom, $E_{\text{VC}_2}$ is the energy of the pristine monolayer, and $E_{\text{Na}}$ is the energy per atom in bulk sodium metal. A negative value indicates a stable adsorption configuration.
For multilayer sodium adsorption, the average adsorption energy for the n-th layer ($E_{\text{ave-layer}}^{(n)}$) is defined as:
$$E_{\text{ave-layer}}^{(n)} = \frac{E_{2n\text{Na@VC}_2} – E_{2(n-1)\text{Na@VC}_2} – 2E_{\text{Na}}}{2}$$
Here, $E_{2n\text{Na@VC}_2}$ and $E_{2(n-1)\text{Na@VC}_2}$ are the total energies of the system with 2n and 2(n-1) sodium atoms adsorbed on both sides of the monolayer, respectively. The overall average adsorption energy for a configuration with N sodium atoms ($E_{\text{ave-total}}$) is:
$$E_{\text{ave-total}} = \frac{E_{N\text{Na@VC}_2} – E_{\text{VC}_2} – N E_{\text{Na}}}{N}$$
The theoretical specific capacity ($C_m$) is a critical metric for any sodium-ion battery anode material and is calculated using the formula:
$$C_m = \frac{nF}{M_{\text{VC}_2}}$$
where $n$ is the maximum number of adsorbed Na atoms per formula unit, $F$ is Faraday’s constant (26898 mAh/mol), and $M_{\text{VC}_2}$ is the molar mass of the VC2 monolayer.
The average open-circuit voltage (OCV) versus Na/Na+ for a specific sodium concentration can be estimated from the following reaction:
$$\text{VC}_2 + n\text{Na} \rightarrow \text{Na}_n\text{VC}_2$$
The voltage is then given by:
$$V_{\text{OCV}} \approx -\frac{E_{\text{Na}_n\text{VC}_2} – E_{\text{VC}_2} – nE_{\text{Na}}}{n e}$$
where $e$ is the elementary charge, and the energies are the DFT total energies at 0 K.
2. Structural and Electronic Properties of Pristine VC2 Monolayer
The optimized VC2 monolayer (β-phase) crystallizes in an orthogonal lattice with the Pmmn space group. The unit cell contains two formula units. The calculated lattice parameters are $a$ = 4.62 Å and $b$ = 3.28 Å. The structure features a unique arrangement where each vanadium (V) atom is coordinated with six carbon atoms. Crucially, carbon atoms form stable C2 dimers with a bond length of 1.34 Å, which are prominently exposed on the surface of the monolayer. The V–C bond lengths are 2.07 Å and 1.99 Å. This configuration, with robust C2 dimers and strong V–C bonding, suggests high structural stability, which is a prerequisite for enduring the repeated sodium insertion/extraction cycles in a sodium-ion battery.
The electronic band structure and projected density of states (PDOS) were calculated to assess the conductive nature of the material, a vital property for an electrode to ensure fast electron transport. The results clearly show that multiple bands cross the Fermi level, indicating metallic behavior. The PDOS analysis reveals that the electronic states near the Fermi level are primarily contributed by the hybridization between V-3d and C-2p orbitals. This strong p-d hybridization not only underpins the structural integrity but also guarantees excellent intrinsic electronic conductivity. High conductivity is essential for achieving good rate performance in a sodium-ion battery, as it minimizes internal resistance during charge and discharge processes.
3. Sodium Adsorption and Storage Capacity
The interaction between sodium atoms and the host material is fundamental to its performance as a sodium-ion battery anode. We first identified the most favorable adsorption site for a single Na atom on a 2×2×1 supercell of VC2. Five high-symmetry sites were considered: above the hollow site of a surface-exposed C2 dimer (Site 1), directly above a surface V atom (Sites 2 & 3 on different sides), and above a C atom of the dimer (Site 5). Site 4, above the bridge of the dimer, was found to be unstable and relaxed to another site.
The calculated adsorption energies and Bader charge transfer are summarized below:
| Adsorption Site | $E_{\text{ad}}$ (eV/atom) | Charge Transfer (|e|) |
|---|---|---|
| Site 1 (Hollow of C2) | -2.37 | 0.79 |
| Site 2 (Top of V) | -2.04 | 0.83 |
| Site 3 (Top of V) | -2.12 | 0.79 |
| Site 5 (Top of C) | -2.34 | 0.79 |
Site 1, located in the hollow center of the C2 dimer, exhibits the strongest adsorption energy of -2.37 eV. This site is surrounded by four carbon atoms, providing an optimal electronic environment for strong ionic interaction with the Na cation. The significant charge transfer (≈0.79 |e|) from Na to the VC2 substrate confirms the ionic nature of the bonding, which is typical for alkali metal adsorption on carbon-containing surfaces. The large negative adsorption energies at all stable sites are highly favorable, as they prevent the clustering of sodium atoms into metallic dendrites, a common failure mode in sodium-ion battery anodes.
To evaluate the maximum sodium storage capability, we investigated multilayer adsorption on both sides of the VC2 sheet using a 1×2×1 supercell. Sodium atoms were sequentially added to the most stable sites (Site 1 for the first layer, etc.). The calculated average adsorption energy for each successive layer remains negative: -2.08 eV (Layer 1), -1.65 eV (Layer 2), -1.30 eV (Layer 3), and -1.22 eV (Layer 4). While the magnitude decreases due to increased Na–Na repulsion at higher concentrations, the consistently negative values indicate that multilayer adsorption is thermodynamically feasible without sodium clustering. This behavior is crucial for achieving high capacity.
The trend of the overall average adsorption energy ($E_{\text{ave-total}}$) as a function of sodium concentration is continuously negative, further confirming the stability of the sodiated phases throughout the charging process of a sodium-ion battery.
At the maximum considered coverage corresponding to a stoichiometry of Na8VC2 in the 1×2×1 supercell, the theoretical specific capacity is calculated as:
$$C_m = \frac{nF}{M_{\text{VC}_2}} = \frac{8 \times 26898 \text{ mAh/mol}}{(50.94 + 2\times12.01) \text{ g/mol}} \approx 715 \text{ mAh/g}$$
This exceptionally high theoretical capacity positions VC2 as a top-tier candidate among two-dimensional anode materials for sodium-ion batteries.
4. Sodium Diffusion Kinetics
The rate capability of a sodium-ion battery is largely governed by the mobility of Na+ ions within or on the surface of the anode material. We investigated the diffusion pathways for a Na atom migrating between two adjacent optimal Site 1 positions on the VC2 surface using the CI-NEB method. Three symmetric paths were considered:
- Path 1: Via a bridge site over a V atom (Site 2).
- Path 2: Via a top site over a V atom (Site 3).
- Path 3: Via a top site over a C atom (Site 5).
The calculated energy profiles reveal that Path 2, passing through Site 3, presents the lowest energy barrier of only 0.23 eV. Path 1 has a slightly higher barrier of 0.30 eV, while Path 3 is less favorable with a barrier of 0.66 eV. This low diffusion barrier of 0.23 eV suggests that sodium ions can migrate rapidly across the VC2 surface. Fast ion diffusion is key to supporting high charge/discharge rates, enabling the sodium-ion battery to deliver high power when needed, which is a critical advantage for applications like fast-charging electronics and grid frequency regulation.
5. Electrochemical Performance Evaluation
To provide a comprehensive assessment for sodium-ion battery applications, we calculated the average open-circuit voltage (OCV) profile. The voltage, derived from the total energy differences between sodiated phases, gradually decreases from about 2.09 V at very low Na concentration to 1.56 V at the maximum studied coverage (Na8VC2). The average voltage over this range is approximately 1.81 V vs. Na/Na+. This voltage range is suitable for an anode material in a full-cell sodium-ion battery configuration, as it provides a sufficient voltage difference against typical cathode materials while avoiding sodium plating at very low potentials.
The combination of high capacity, low diffusion barrier, appropriate OCV, and strong but not excessive adsorption energy paints a very promising picture. To contextualize the performance of VC2, we compare its predicted properties with other theoretically proposed 2D anode materials for sodium-ion batteries in the table below.
| Material | Na Adsorption Energy (eV) | Theoretical Capacity (mAh/g) | Diffusion Barrier (eV) | Reference/Note |
|---|---|---|---|---|
| VC2 Monolayer | -2.37 | 715 | 0.23 | This work |
| ZrC2 Monolayer | -0.96 | 932 | 0.02 | High capacity, very low barrier |
| Ti3C2 MXene | -0.93 | ~320 | 0.10 | Classic MXene |
| MoS2 Monolayer | -1.10 | 146 | ~0.28 | Widely studied 2D material |
| Phosphorene | -1.65 | 433 | 0.08 | High capacity but poor air stability |
| Boron Phosphide (BP) | -0.90 | 409 | 0.008 | Ultra-low barrier |
| Ca2C Monolayer | -2.84 | 582 | 0.06 | Very strong adsorption |
| g-GeC Monolayer | -1.26 | 633 | 0.06 | Germanium carbide |
As evident from the comparison, the VC2 monolayer offers a balanced and superior set of properties. Its sodium adsorption energy is among the strongest, which is beneficial for safety and preventing dendrite formation. Its theoretical capacity is very high, surpassed in this list only by ZrC2. Its diffusion barrier is low enough to ensure good rate performance, comparable to or better than many other promising candidates. This balance makes it an exceptionally attractive candidate for further investigation in the field of sodium-ion batteries.
6. Conclusion and Outlook
In summary, we have conducted a systematic first-principles investigation into the potential of the two-dimensional VC2 monolayer as an anode material for sodium-ion batteries. Our calculations demonstrate that this material possesses excellent structural stability, inherent metallic conductivity, and a strong affinity for sodium atoms with an optimal adsorption energy. The unique surface-exposed C2 dimer units play a pivotal role in facilitating strong ionic bonding and efficient sodium storage.
The key electrochemical performance metrics predicted for VC2 are outstanding: a high theoretical specific capacity of 715 mAh/g, a low sodium diffusion barrier of 0.23 eV ensuring fast kinetics, and an appropriate average open-circuit voltage of ~1.81 V vs. Na/Na+. The consistently negative average adsorption energy across increasing sodium concentrations confirms the thermodynamic stability of the sodiated phases, which is crucial for the reversible operation and long cycle life of a sodium-ion battery.
These theoretical predictions position the VC2 monolayer as a highly promising anode candidate that could address several challenges faced by current sodium-ion battery technology, particularly in terms of energy density and rate capability. This work contributes to the expanding database of novel 2D materials for energy storage and provides a solid theoretical foundation for subsequent experimental synthesis and testing. Future studies could explore the performance of VC2 under bilayer or multilayer stacking, its behavior in a full-cell configuration with compatible cathodes, and the effects of functional groups or defects on its sodium storage properties. The search for and optimization of such high-performance materials remain essential for advancing the commercialization and application of efficient, low-cost sodium-ion batteries.