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Frontiers in Batteries and Electrochemistry ·

Volume 5 - 2026 | https://doi.org/10.3389/fbael.2026.1845442

First-principles study of electrolyte components stability and orientation on MoS 2 surfaces: implications for SEI formation in sodium-ion batteries

  • Luis A. Selis1,2
  • Utkarsh Vijay3
  • Diego E. Galvez-Aranda4*corresponding author
  1. 1Facultad de Ciencias, Universidad Nacional de Ingeniería, Lima, Peru
  2. 2Facultad de Ingeniería Eléctrica y Electrónica, Universidad Nacional de Ingeniería, Lima, Peru
  3. 3Independent Researcher, Kolkata, India
  4. 4Chemical Engineering Department, Texas A&M University, College Station, TX, United States
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Abstract

The interfacial stability between electrolyte components and electrode materials plays a crucial role in the formation of the solid electrolyte interphase (SEI) in sodium-ion batteries. In this work, density functional theory (DFT) calculations are used to investigate the interface behavior and electronic interactions of five common electrolyte anions (PF 6 −, BF 4 −, ClO 4 −, FSI − and TFSI −) on MoS 2 surfaces. To capture the influence of electrochemical conditions, the surface is analyzed under three different Na concentrations corresponding to 0%, 50%, and 90% electrode degree of sodiation. Multiple interface orientations are considered for each molecule to evaluate interaction energies, charge redistribution, electron localization function, work function, and electronic structure modifications at the interface. The results reveal distinct interaction mechanisms depending on the anion and sodium content. BF 4 − exhibits strong interaction at low Na concentration, which weakens significantly upon sodiation. ClO 4 − shows a reduction in interaction strength despite relatively similar charge redistribution, accompanied by changes in electron localization associated with Na. In contrast, PF 6 − does not form a stable interface configuration and undergoes reorientation with increasing Na, favoring interactions with intercalated Na rather than the MoS 2 surface. TFSI − exhibits a strong dependence on molecular orientation, with more stable configurations associated with oxygen coordination. These findings provide atomistic insight into the evolution of interfacial interactions in sodiated MoS 2 and their possible implications for SEI formation in sodium-ion batteries.

Keywords

1 Introduction

Energy storage systems play a fundamental role in storing renewable energy and supplying it during periods when generation is low or unavailable (Jafarian et al., 2024). Rechargeable batteries are considered one of the most efficient technologies for converting electrical energy into chemical energy (Goodenough and Park, 2013), enabling the repeated generation of clean electricity from stored materials. Currently, the most widely used rechargeable batteries include lithium-ion batteries (LIBs), sodium-ion batteries (SIBs), and potassium-ion batteries (KIBs) (Mamun, 2026; Lee et al., 2025). The performance of these batteries is largely determined by the active materials used in the cathode and anode (Selis and Seminario, 2019; Selis and Seminario, 2018). LIBs have attracted considerable attention because of their high energy density and operating voltage (Selis et al., 2025; Titirici et al., 2024; Galvez‐Aranda et al., 2024; Galvez-Aranda and Seminario, 2022). However, the high cost of lithium salts and the limited availability of terrestrial lithium resources have encouraged the search for alternative battery technologies. Consequently, LIBs are not always the most suitable option for large-scale energy storage applications (Wu et al., 2011). In contrast, the high abundance of sodium in the Earth’s crust and its relatively low cost make (SIBs) a promising alternative to LIBs (Barik and Pal, 2019). As a result, SIBs have emerged as attractive candidates for energy storage systems, offering competitive energy density and favorable electrochemical properties (Sharma et al., 2026; Bahari et al., 2021). Nevertheless, the larger ionic radius (1.02 Å for Na+ compared to 0.76 Å for Li+), higher reduction potential (−2.71 V for Na+ and −3.04 V for Li+), and slower reaction kinetics of Na+ make the identification of suitable electrode materials for SIBs more challenging (Cen et al., 2025; Jia et al., 2024).

Two-dimensional (2D) transition metal sulfides (TMCs) possess a graphene-like layered structure and have attracted considerable attention in recent years. Owing to their high theoretical capacity and good reversibility, they are regarded as promising anode materials for SIBs (Xiao et al., 2022). Molybdenum Disulfide (MoS2) is valued for its natural abundance, straightforward synthesis, and stability under ambient conditions. It can adopt several structural phases, which influence its physical and chemical properties (Shivani and Sriram, 2025). These variations make MoS2 a promising anode material for SIBs, with a high theoretical capacity of approximately 670 mAh/g (Yang et al., 2018; Shivani and Sriram, 2026). As a representative member of the Transition Metal Dichalcogenide (TMDC) family, MoS2 also features relatively large interlayer spacing, which facilitates ion intercalation processes relevant for battery applications. Despite these advances, the interaction between sodiated MoS2 surfaces and electrolyte species, particularly anions, as well as its evolution with the state of charge, remains insufficiently understood at the atomic scale. In particular, the role of the anion chemical composition and the distribution of electrostatic potential in determining preferred interface configurations and interfacial stability has not been fully clarified.

The 2H phase of MoS2 has attracted significant attention as an anode material for sodium-ion batteries due to its layered structure and favorable electrochemical properties. Among the different polymorphs of MoS2, the 2H phase is the most widely studied for battery applications because of its structural stability, natural abundance, and experimental accessibility. In contrast, metallic 1T-MoS2, although attractive because of its higher electronic conductivity, is thermodynamically metastable under ambient conditions and tends to revert to the 2H structure (Marinov et al., 2023). Several studies have explored strategies to further enhance its performance, including transition metal doping (Upadhyay and Srivastava, 2024). Other phases, such as the A-phase MoS2 with a narrower band gap (∼0.74 eV), have also been proposed as promising candidates for SIB anodes (Sukhanova et al., 2022), although they have not yet been experimentally synthesized. Therefore, structural modifications of the stable 2H-phase MoS2 remain an effective strategy to further enhance its properties for sodium-ion battery applications (Xiong et al., 2026; Biscaras et al., 2015).

In this work, we investigate the interface of sodium atoms and the interaction with representative electrolyte anions on the 2H-MoS2 surface using density functional theory calculations (Figure 1). Although explicit solvent and reactive decomposition pathways are not included, similar simplified electrode–electrolyte interface models have been widely used in previous DFT studies to investigate interface behavior and early interfacial processes relevant to SEI evolution (Clarke-Hannaford et al., 2021; Bouder et al., 2025). Special emphasis is placed on understanding how anion structure, molecular orientation, and degree of sodiation influence the interfacial electronic response and preferred interaction mechanisms at the MoS2 surface. Several interface configurations are considered to determine the most stable Na interaction sites and their corresponding interaction energies. To represent different stages of sodiation, three Na concentrations (0%, 50%, and 90%) are examined. These systems do not explicitly model electrochemical charging potentials, instead, different Na contents are used as structural models to represent distinct degrees of sodiation of the MoS2 anode while maintaining overall charge neutrality. The associated charge redistribution, electron localization function and modifications in the electronic structure are analyzed to provide atomic-scale insight into the Na storage mechanism in 2H-MoS2, contributing to the evaluation of its potential as an anode material for sodium-ion batteries. Special attention is given to the relationship between molecular electrostatic potential, preferred interaction sites (O vs. F), and interaction strength, in order to elucidate the interfacial mechanisms governing anion stability and SEI formation.

Schematic representation of the computational procedure used to analyze the interaction between electrolyte anion and a 2H-MoS<sub>2</sub>. First, the combined system composed of the 2H-MoS<sub>2</sub> with the intorbed anion is computed. Subsequently, the individual components (the clean 2H-MoS<sub>2</sub> and the free anion) are calculated separately.
Figure 1. Schematic representation of the computational procedure used to analyze the interaction between electrolyte anion and a 2H-MoS2. First, the combined system composed of the 2H-MoS2 with the intorbed anion is computed. Subsequently, the individual components (the clean 2H-MoS2 and the free anion) are calculated separately.

2 Materials and methods

2.1 DFT calculations

All ab initio calculations simulations were performed using the Quantum Espresso (QE) software developed by P. Giannozzi et al. (Giannozzi et al., 2020; Giannozzi et al., 2017; Giannozzi et al., 2009), under the Born−Oppenheimer approximation (Combes et al., 1981), The electronic structure was described using the Perdew−Burke−Ernzerhof (PBE) exchange–correlation functional (Ropo et al., 2008; Perdew et al., 1996). Periodic boundary conditions (PBC) were applied to all simulation cells, employing a plane wave energy cutoff of 40 Ry and 3 × 3 × 3 k-point mesh (27 k-points) within a projector-augmented wave approach (PAW) (Blöchl, 1994). The initial molecular configurations were optimized using GAMESS (Barca et al., 2020). Snapshots of the simulation box were generated using the visualization tools Visual Molecular Dynamics (VMD) (Humphrey et al., 1996), the Open Visualization Tool (OVITO) (Stukowski, 2009), and the Visualization for Electronic and STructural Analysis (VESTA) package (Momma and Izumi, 2008; Momma and Izumi, 2011). All simulations were performed in a periodic box of dimensions 13.380 × 11.064 × 35.045 Å3, containing a MoS2 anode of 48 atoms and a single molecule; in this study, we examined four different molecules (PF 6 −, BF 4 −, TFSI − and ClO 4 −), and multiple molecular orientations approaching the MoS2 anode were optimized (Figure 2).

Simulation setup showing a periodic box of dimensions 13.380 × 11.064 × 35.045 Å<sup>3</sup>, containing a 2H-MoS<sub>2</sub> anode (48–62 atoms) and one anion. Five anions (PF 6 −, BF 4 −, FSI −, TFSI −, and ClO 4 −) were tested, with multiple orientations and degrees of sodiation for each system was optimized as they approached the 2H-MoS<sub>2</sub> anode.
Figure 2. Simulation setup showing a periodic box of dimensions 13.380 × 11.064 × 35.045 Å3, containing a 2H-MoS2 anode (48–62 atoms) and one anion. Five anions (PF 6 −, BF 4 −, FSI −, TFSI −, and ClO 4 −) were tested, with multiple orientations and degrees of sodiation for each system was optimized as they approached the 2H-MoS2 anode.

2.2 Binding energy

The binding energy between anion and the Na+ ion was computed from the total energies obtained after structural relaxations followed by a single point self-consistent field (SCF) calculations in Gaussian and Quantum ESPRESSO. The binding energy is defined as:where E binding is the binding energy, E Na + / anion is the total energy of the paired Na+/anion system, E Na + and E anion correspond to the total energies of the Na+ and anion subsystems. These subsystem energies were obtained within the same supercell and extracted from the relaxed interface geometry rather than from independently optimized structures. More negative binding energy indicates stronger interactions.

E binding = E Na + / anion − E Na + + E anion

2.3 Interaction energy

The interaction energy between the MoS2 anode and the anion was computed from the total energies obtained after structural relaxations followed by a single point self-consistent field (SCF) calculations in Quantum ESPRESSO. The interaction energy is defined as:where E interaction is the interaction energy, E Mo S 2 / anion is the total energy of the relaxed MoS2/anion interphase, E Mo S 2 and E anion correspond to the total energies of the MoS2 and anion sub-systems. These subsystem energies were obtained within the same supercell and extracted from the relaxed interface geometry rather than from independently optimized structures. More negative interaction energy indicates stronger interactions.

E interaction = E Mo S 2 / anion − E Mo S 2 + E anion

2.4 Electron charge density

The electron charge density difference (Δρ) was calculated from the charge densities obtained in the QE simulations. This analysis provides insight into the electron redistribution associated with the formation of the interface. Regions of electron accumulation and depletion were identified by subtracting the electron densities of the isolated MoS2 anode and anion subsystems from that of the combined system. Areas of accumulation indicate charge transfer toward the interface, whereas depletion corresponds to electron loss.

2.5 Bader charge analysis

The distribution of electronic charge was further examined using the Bader charge partitioning scheme, which divides the electron density according to zero-flux surfaces (Tang et al., 2009). This analysis was carried out using the implementation developed by Henkelman et al. (2006).

2.6 Electron localization function

The electron localization function (ELF) was calculated using the charge densities obtained from the QE simulations. ELF is a dimensionless measure of electron localization: values close to 1 indicate strong localization (e.g., covalent bonds or lone pairs), whereas values near 0.5 correspond to delocalized, metallic-like states. Differences in ELF between MoS2 anode, the anions, and their interphase were analyzed and visualized to assess bonding and charge redistribution. The ELF difference follows an analogous approach to charge density difference maps, however, instead of describing charge accumulation or depletion, it highlights changes in electron localization and delocalization induced by bonding.

2.7 Work-function difference

Changes in the work function were analyzed to identify possible electron transfer processes that could populate antibonding states and potentially induce molecular dissociation. For each system, the planar-averaged electrostatic potential along the z-axis, V int (z) was obtained from the interface calculation which consists of the MoS2 slab and the anion. In addition, a single-point calculation was performed after removing the molecule to determine the planar-averaged electrostatic potential of the clean MoS2 anode along the z-axis, V Mo S 2 (z). In both cases, the vacuum level far from the surface was extracted: V vac , int and V vac , Mo S 2. The work functions were then calculated as: where E F Mo S 2 and E F int correspond to the Fermi energy level of the MoS2/anion and MoS2 samples respectively. The work-function shift is defined as:

Φ Mo S 2 = V vac , Mo S 2 − E F Mo S 2

Φ int = V vac , int − E F int

Δ Φ = Φ int − Φ Mo S 2

A negative value of Δ Φ indicates electron accumulation on the vacuum/intorbate side (anode → anion donation), whereas a positive value of Δ Φ would indicate electron depletion on the vacuum side (anion → anode donation).

3 Results

The calculated Na–X binding energies reveal a clear spread in interaction strength across the five anions (Table 1). Binding energies were evaluated using both Gaussian and Quantum ESPRESSO calculations. Although the absolute values differ between the two computational implementations, both methods predict the same qualitative ordering of interaction strengths among the investigated anions. PF 6 − exhibits the weakest interaction with Na+, which indicates a higher degree of charge delocalization, leading to reduced electrostatic attraction. In contrast, BF 4 − and ClO 4 − show the strongest binding, suggesting a more localized charge distribution and stronger Coulombic interaction with sodium. TFSI − and FSI − fall in an intermediate regime, reflecting their balance between charge delocalization and structural flexibility.

TABLE 1. Comparison of Na–anion binding energies and total energies obtained from Gaussian and Quantum ESPRESSO.

SoftwareCounter-ionTotal energy (Ha)Total ion paired NaX energy (Ha)Binding energy Na–X (eV)
GaussianPF 6 −−940.69198−1,102.91278−4.43
BF 4 −−424.53429−586.79026−5.38
TFSI −−1827.26911−1989.51334−5.07
FSI −−1,351.71761−1,513.96269−5.02
ClO 4 −−760.85265−923.10618−5.32
Na+−162.05809--
Quantum espressoPF 6 −−206.212−260.711−2.47
BF 4 −−124.802−179.334−3.36
TFSI −−360.291−414.820−3.27
FSI −−223.151−277.680−3.28
ClO 4 −−122.812−177.343−3.34
Na+−54.409​​

The molecular electrostatic potential (MEP) surface analysis of the five investigated anions (BF 4 −, PF 6 −, ClO 4 −, TFSI −, and FSI −) reveals an overall negative electrostatic potential, as expected from their anionic nature (Figures 3a–e). However, the MEP spatial distribution is highly heterogeneous, with distinct regions of enhanced negativity that are chemically meaningful. Among the high symmetric anions, BF 4 − shows the most pronounced negative regions, followed by ClO 4 − and then PF 6 −, indicating a decreasing tendency for strong electrostatic interactions. In these cases, the negative potential is primarily localized around the terminal atoms (F in BF 4 − and PF 6 −, and O in ClO 4 −), suggesting that these atoms are the most likely interaction sites with positively charged regions on the MoS2 surface (Figures 3f–h).

Electrostatic potential distributions for different electrolyte anions and MoS<sub>2</sub> surface at different Na concentrations. **(a–e)** show the electrostatic potential mapped over electronic density of a value: 0.02 e/bohr (Mamun, 2026) for **(a)** PF 6 −, **(b)** BF 4 −, **(c)** TFSI −, **(d)** FSI −, and **(e)** ClO 4 − anions. **(f–h)** present the electrostatic potential of the MoS<sub>2</sub> surface (Top view) at different Na concentrations: **(f)** 0% Na, **(g)** 50% Na, and **(h)** 90% Na.
Figure 3. Electrostatic potential distributions for different electrolyte anions and MoS2 surface at different Na concentrations. (a–e) show the electrostatic potential mapped over electronic density of a value: 0.02 e/bohr (Mamun, 2026) for (a) PF 6 −, (b) BF 4 −, (c) TFSI −, (d) FSI −, and (e) ClO 4 − anions. (f–h) present the electrostatic potential of the MoS2 surface (Top view) at different Na concentrations: (f) 0% Na, (g) 50% Na, and (h) 90% Na.

For the asymmetric anions FSI − and TFSI −, the MEP surfaces display a more complex distribution, with less overall negativity compared to the high symmetric anions (BF 4 −, PF 6 − and ClO 4 −). Importantly, the regions surrounding the oxygen atoms are consistently more negative than those near the fluorine atoms, indicating a stronger propensity for O-centered interactions. This anisotropy suggests that upon approaching the surface, these anions will adopt orientations that favor coordination through oxygen rather than fluorine atoms. When these observations are correlated with the MEP calculated on the MoS2 surface at different degrees of sodiation (0, 50, and 90), a clear interaction pattern emerges. The positive electrostatic potential is predominantly localized on Mo atoms in the neutral state and becomes increasingly concentrated around both Mo and intercalated Na ions at higher Na concentrations. Therefore, for FSI − and TFSI −, the preferential alignment of oxygen atoms toward Mo and Na sites is expected to dominate the interfacial structure.

3.1 Tetrafluoroborate anion (BF 4 −)

The charge density difference maps reveal a localized charge transfer between a fluorine atom of BF 4 − and the MoS2 surface, indicating the formation of a preferred interfacial interaction site. At 0% Na, the charge transfer is maximized, as indicated by the pronounced electron accumulation at the surface, consistent with the ΔELF plots, which shows significant electron delocalization in the same area. These plots suggest partial bond formation and a possible weakening of the B–F bond, and the possible dissociation of F atom driven by the interaction with the MoS2 surface.

At 50% Na, the charge transfer is reduced, accompanied by a considerable decrease in electron charge distribution and delocalization, indicating weaker interactions between BF 4 − and the MoS2 anode. This trend becomes more pronounced at 90% Na, where the charge transfer is further suppressed and the interaction energy becomes positive, as shown in Table 2, thus indicating an unfavorable interaction. This behavior is further supported by the progressive increase in work function (ΔΦ), indicating a reduced electronic perturbation of the MoS2 anode with increasing Na concentration. In these conditions, a secondary and weaker charge redistribution appears between fluorine atoms and the intercalated Na species, as evidenced by subtle Δρ and ΔELF plots (Figure 4), although this contribution remains minor compared to the dominant interaction with the MoS2 anode.

TABLE 2. Charge transfer (Δq *mol*), interaction energy (E *int* ), and work function difference (ΔΦ) for B F 4 − intorbed on the MoS2 surface at varying sodium concentrations (0%, 50%, and 90% Na).

MoleculeOrientation% NaΔq *mol*E *int* (eV)ΔΦ
BF 4 −F-attack00.26−0.87−1.37
500.200.04−1.24
900.100.33−1.01
Charge density difference (Δρ) maps for BF 4 − on a MoS<sub>2</sub> anode at different Na concentrations: **(a)** 0% Na, **(b)** 50% Na, and **(c)** 90% Na. For charge density the negative values (Δρ < 0) are colored cyan and correspond to −0.03 e/volume, and the positive values (Δρ > 0) are colored yellow and correspond to +0.03 e/volume. Electron localization function difference (ΔELF) maps for BF 4 − on a MoS<sub>2</sub> anode at different Na concentrations: **(d)** 0% Na, **(e)** 50% Na, and **(f)** 90% Na. For ΔELF, the cyan surface on the left picture corresponds to a value of −0.8.
Figure 4. Charge density difference (Δρ) maps for BF 4 − on a MoS2 anode at different Na concentrations: (a) 0% Na, (b) 50% Na, and (c) 90% Na. For charge density the negative values (Δρ < 0) are colored cyan and correspond to −0.03 e/volume, and the positive values (Δρ > 0) are colored yellow and correspond to +0.03 e/volume. Electron localization function difference (ΔELF) maps for BF 4 − on a MoS2 anode at different Na concentrations: (d) 0% Na, (e) 50% Na, and (f) 90% Na. For ΔELF, the cyan surface on the left picture corresponds to a value of −0.8.

Overall, these results indicate a transition from a strongly surface-dominated interaction at 0% Na to a weakened and partially redistributed interaction at higher Na concentrations (50% and 90% Na), where the presence of intercalated Na perturbs the interface environment without fully stabilizing the BF 4 − molecule.

3.2 Perchlorate anion (ClO 4 −)

The charge density difference (Δρ) maps show a similar pattern across all sodium concentrations, indicating that the overall charge redistribution between ClO 4 − and the MoS2 surface remains relatively unchanged with increasing Na content (Figure 5). This observation is consistent with the relatively small variation in the charge transfer values reported in Table 3. At 0% Na, the interaction is strongest, as shown by the highly negative interaction energy (−2.55 eV), indicating a stable interaction with the surface.

Charge density difference (Δρ) maps for ClO 4 − on a MoS<sub>2</sub> anode at different Na concentrations: **(a)** 0% Na, **(b)** 50% Na, and **(c)** 90% Na. For charge density the negative values (Δρ < 0) are colored cyan and correspond to −0.03 e/volume, and the positive values (Δρ > 0) are colored yellow and correspond to +0.03 e/volume. Electron localization function difference (ΔELF) maps for ClO 4 − on a MoS<sub>2</sub> anode at different Na concentrations: **(d)** 0% Na, **(e)** 50% Na, and **(f)** 90% Na. For ΔELF, the cyan surface on the left picture corresponds to a value of −0.8.
Figure 5. Charge density difference (Δρ) maps for ClO 4 − on a MoS2 anode at different Na concentrations: (a) 0% Na, (b) 50% Na, and (c) 90% Na. For charge density the negative values (Δρ < 0) are colored cyan and correspond to −0.03 e/volume, and the positive values (Δρ > 0) are colored yellow and correspond to +0.03 e/volume. Electron localization function difference (ΔELF) maps for ClO 4 − on a MoS2 anode at different Na concentrations: (d) 0% Na, (e) 50% Na, and (f) 90% Na. For ΔELF, the cyan surface on the left picture corresponds to a value of −0.8.

TABLE 3. Charge transfer (Δq *mol*), interaction energy (E *int* ), and work function difference (ΔΦ) for Cl O 4 − intorbed on the MoS2 surface at varying sodium concentrations (0%, 50%, and 90% Na).

MoleculeOrientation% NaΔq *mol*E *int* (eV)ΔΦ
ClO 4 −O-attack00.10−2.55−1.24
500.16−1.34−1.39
900.15−1.09−1.38

At higher sodium concentrations (50% and 90% Na), the interaction energy becomes progressively less negative, revealing a clear weakening of the ClO 4 −–MoS2 interaction. Despite this, the Δρ maps do not show significant changes, suggesting that the reduction in interaction strength is not directly associated with a decrease in the total charge transfer. In contrast, the ΔELF plots exhibit an increase in electron localization with increasing Na content in the anode, particularly in regions associated with intercalated Na atoms rather than directly on the MoS2 (Figure 5). This indicates a redistribution of electronic density toward regions related with Na, pointing to the emergence of secondary interactions involving the intercalated Na species.

The work function difference (ΔΦ) shows a slight shift toward more negative values with increasing Na concentration, indicating a modest increase in the electronic perturbation of the anode surface. These results suggest that while the total charge transfer remains nearly constant, the spatial distribution of electrons is significantly altered in the presence of Na, leading to a weakening of the surface interaction and a partial shift toward electronic effects related to Na.

3.3 Hexafluorophosphate anion (PF 6 −)

The charge density difference (Δρ) maps show comparable features across all sodium concentrations, indicating that the overall charge redistribution remains limited despite changes in the interface environment. At 0% Na, the anion adopts a tilted configuration relative to the MoS2 anode surface, with a P–F bond oriented at an angle, suggesting a non-preferential interaction with the substrate (Figure 6).

Charge density difference (Δρ) maps for PF 6 − on a MoS<sub>2</sub> anode at different Na concentrations: **(a)** 0% Na, **(b)** 50% Na, and **(c)** 90% Na. For charge density the negative values (Δρ < 0) are colored cyan and correspond to −0.03 e/volume, and the positive values (Δρ > 0) are colored yellow and correspond to +0.03 e/volume. Electron localization function difference (ΔELF) maps for PF 6 − on a MoS<sub>2</sub> anode at different Na concentrations: **(d)** 0% Na, **(e)** 50% Na, and **(f)** 90% Na. For ΔELF, the cyan surface on the left picture corresponds to a value of −0.8.
Figure 6. Charge density difference (Δρ) maps for PF 6 − on a MoS2 anode at different Na concentrations: (a) 0% Na, (b) 50% Na, and (c) 90% Na. For charge density the negative values (Δρ < 0) are colored cyan and correspond to −0.03 e/volume, and the positive values (Δρ > 0) are colored yellow and correspond to +0.03 e/volume. Electron localization function difference (ΔELF) maps for PF 6 − on a MoS2 anode at different Na concentrations: (d) 0% Na, (e) 50% Na, and (f) 90% Na. For ΔELF, the cyan surface on the left picture corresponds to a value of −0.8.

As the sodium concentration increases, PF 6 − progressively reorients toward a more vertical configuration with respect to the surface. At 50% and 90% Na, this reorientation is accompanied by a tendency of Na atoms to approach the F atoms, indicating the emergence of Na–F interactions. This structural change reduces the direct interaction with the MoS2 surface, in agreement with the increasingly positive interaction energies shown in Table 4.

TABLE 4. Charge transfer (Δq *mol*), interaction energy (E *int* ), and work function difference (ΔΦ) for P F 6 − intorbed on the MoS2 surface at varying sodium concentrations (0%, 50%, and 90% Na).

MoleculeOrientation% NaΔq *mol*E *int* (eV)ΔΦ
PF 6 −F-attack00.110.00−0.97
500.130.41−1.26
900.020.44−1.14

The ΔELF maps reflect a redistribution of electron localization that becomes more centered toward the region facing the anode as the molecule adopts a vertical configuration (Figure 6). This is consistent with the increased distance of the remaining F atoms from the surface and the localized interaction of specific F atoms with nearby Na species.

Regarding the work function difference (ΔΦ), it becomes more negative at intermediate Na concentration and slightly recovers at higher Na content, indicating a non-uniform modification of the surface electronic environment. These results suggest that PF 6 − does not form a stable interface configuration on MoS2 anode, and increasing Na content promotes a reorientation of the anion and a shift from direct surface interaction toward Na-related interactions.

3.4 Bis(trifluoromethanesulfonyl)imide anion (TFSI −)

For TFSI −, the interaction with the MoS2 surface strongly depends on the interface orientation, as evidenced by the wide variation in interaction energies and charge transfer values shown in Table 5. At 0% Na, only configurations involving oxygen atoms (O-Attack and 2O-Attack) show a favorable interaction, meanwhile F-dominated configurations remain energetically unfavorable.

TABLE 5. Charge transfer (Δq *mol*), interaction energy (E *int* ), and work function difference (ΔΦ) for TFS I − intorbed on the MoS2 surface at five different orientations and varying sodium concentrations (0%, 50%, and 90% Na).

MoleculeOrientation% NaΔq *mol*E *int* (eV)ΔΦ
TFSI −F-attack00.041.30−0.43
500.001.08−0.37
90−0.011.21−0.36
O-attack00.18−0.49−1.30
500.14−0.16−1.27
900.050.08−1.17
2F-attack0−0.081.240.46
500.12−0.18−1.27
90−0.031.43−0.03
FO-attack00.031.31−0.48
500.000.89−0.59
90−0.011.19−0.38
2O-attack00.19−0.36−1.21
500.15−0.13−1.29
900.000.27−1.17

As the sodium concentration increases, the interfacial behavior becomes highly sensitive to both molecular orientation and Na concentration. The charge density difference maps (Figure 7) reveal that charge redistribution varies significantly across configurations. For F-Attack, the redistribution changes noticeably with Na content, with a reduction in charge transfer at higher sodiation levels, although the ΔELF maps (Figure 8) indicate that electron localization remains appreciable. In the O-Attack configuration, the molecular geometry is relatively preserved, while Na atoms tend to approach the anion, leading to reduced charge transfer but enhanced electron localization, with ΔELF values higher than in the F-Attack case.

Charge density difference (Δρ) maps for TFSI − on a MoS<sub>2</sub> anode at different Na concentrations: **(a,d,g,j,m)** 0% Na, **(b,e,h,k,n)** 50%, and **(c,f,i,l,o)** 90% Na. For charge density the negative values (Δρ < 0) are colored cyan and correspond to –0.03 e/volume, and the positive values (Δρ > 0) are colored yellow and correspond to +0.03 e/volume.
Figure 7. Charge density difference (Δρ) maps for TFSI − on a MoS2 anode at different Na concentrations: (a,d,g,j,m) 0% Na, (b,e,h,k,n) 50%, and (c,f,i,l,o) 90% Na. For charge density the negative values (Δρ < 0) are colored cyan and correspond to –0.03 e/volume, and the positive values (Δρ > 0) are colored yellow and correspond to +0.03 e/volume.
Electron localization function difference (ΔELF) maps for TFSI − on a MoS<sub>2</sub> anode at different Na concentrations: **(a,d,g,j,m)** 0% Na, **(b,e,h,k,n)** 50%, and **(c,f,i,l,o)** 90% Na. For ΔELF, the cyan surface on the left picture corresponds to a value of –0.8.
Figure 8. Electron localization function difference (ΔELF) maps for TFSI − on a MoS2 anode at different Na concentrations: (a,d,g,j,m) 0% Na, (b,e,h,k,n) 50%, and (c,f,i,l,o) 90% Na. For ΔELF, the cyan surface on the left picture corresponds to a value of –0.8.

More pronounced changes are observed for the 2F-Attack configuration, where the interaction becomes comparatively more favorable at 50% Na but becomes energetically unfavorable again at 90% Na as the molecule moves away from the surface, consistent with the reduction in both charge transfer and ΔELF. In contrast, the FO-Attack configuration exhibits more moderate structural changes, with a general decrease in charge transfer and lower ΔELF values as Na concentration increases. The 2O-Attack configuration shows the strongest electron localization among all cases, as observed in Figure 7, with a clear tendency of Na atoms to approach the molecule, indicating reinforced Na–anion interactions.

Consistently, the work function difference (ΔΦ) reported in Table 5 varies across configurations and Na concentrations without following a single trend, reflecting the complex and configuration-dependent nature of the interfacial electronic response. These results indicate that TFSI − exhibits multiple competing interaction mechanisms, where both molecular orientation and effects related with Na atoms govern the interface behavior rather than a single dominant interaction with the MoS2 anode.

3.5 Bis(fluorosulfonyl) imideanion (FSI −)

Similarty to TFSI −, for FSI −, the interaction with the MoS2 surface strongly depends on the interface orientation. Three initial interface configurations were investigated: the 3O attack, 2O–F attack, and 2F attack orientations. All interaction energies and charge transfer values are shown in Table 6.

TABLE 6. Charge transfer (Δq *mol*), interaction energy (E *int* ), and work function difference (ΔΦ) for FS I − intorbed on the MoS2 surface at five different orientations and varying sodium concentrations (0%, 50%, and 90% Na).

MoleculeOrientation% LiΔq *mol*E *int* (eV)ΔΦ
FSI3O-attack00.19−0.16−1.16
500.08−0.23−1.27
900.010.01−1.14
2O-F-Attack00.21−0.58−1.32
500.160.34−1.22
90−1.29−8.64−0.67
2F-attack00.23−0.90−1.34
500.080.15−1.32
90−1.54−9.06−0.18

For the 3O attack configuration, the optimized structures remain molecularly intact over the entire range of Na % states. However, the amount of charge transferred from the substrate to the intorbate gradually decreases as the Na concentration on the MoS2 surface increases. Regarding the interface energies values of −0.16, −0.23, and 0.01 eV for the 0, 50, and 90% Na, respectively, indicate that interface becomes progressively less favorable at high Na concentrations. In contrast, work function difference (ΔΦ) remains nearly unchanged, fluctuating only slightly between −1.14 and −1.16, suggesting that the interfacial dipole is only weakly affected by Na decoration despite the reduction in charge transfer.

A markedly different behavior is observed for the 2O–F attack and 2F attack orientations. First, both configurations converge to similar optimized structures showing similar trends in charge transfer, interface energy and ΔΦ values. In both cases, at 90% Na, the S–F bond within the FSI anion dissociates with the F atom forming a bond with a surface Na atom. This reaction is reflected by the substantial increase in charge transfer, reaching −1.29 e and −1.54 e for the 2O–F attack and 2F attack configurations, respectively (Table 6). Similarly, the interface energies exhibit a pronounced increase in magnitude, consistent with the transition from molecular interface to a dissociative interface mechanism.

The electron density difference (ED) maps provide direct evidence of this interfacial reaction, revealing an extensive redistribution of electron density between the MoS2 surface and the dissociated FSI anion for the 90% Na systems in both the 2O–F attack and 2F attack configurations (Figure 9). These findings are further supported by the electron localization function (ELF) analysis (Figure 10), which shows a pronounced accumulation of localized electron density at the interface, particularly around the newly formed Na–F bond.

Charge density difference (Δρ) maps for FSI − on a MoS<sub>2</sub> anode at different Na concentrations: **(a,d,g)** 0% Na, **(b,e,h)** 50%, and **(c,f,i)** 90% Na. For charge density the negative values (Δρ < 0) are colored cyan and correspond to –0.03 e/volume, and the positive values (Δρ > 0) are colored yellow and correspond to +0.03 e/volume.
Figure 9. Charge density difference (Δρ) maps for FSI − on a MoS2 anode at different Na concentrations: (a,d,g) 0% Na, (b,e,h) 50%, and (c,f,i) 90% Na. For charge density the negative values (Δρ < 0) are colored cyan and correspond to –0.03 e/volume, and the positive values (Δρ > 0) are colored yellow and correspond to +0.03 e/volume.
Electron localization function difference (ΔELF) maps for FSI − on a MoS<sub>2</sub> anode at different Na concentrations: **(a,d,g)** 0% Na, **(b,e,h)** 50%, and **(c,f,i)** 90% Na. For ΔELF, the cyan surface on the left picture corresponds to a value of –0.8.
Figure 10. Electron localization function difference (ΔELF) maps for FSI − on a MoS2 anode at different Na concentrations: (a,d,g) 0% Na, (b,e,h) 50%, and (c,f,i) 90% Na. For ΔELF, the cyan surface on the left picture corresponds to a value of –0.8.

4 Discussion

The results reveal that the interfacial behavior between electrolyte anions and the MoS2 anode is strongly dependent on both the Na concentration and the molecular structure of the anion. This behavior agrees with the intrinsic Na–anion interaction strengths and the molecular electrostatic potential (MEP) distributions, which determine the preferred interaction sites. A general trend is observed in which increasing sodium concentration weakens the direct interaction between the anions and the MoS2 surface, as reflected by less favorable interaction energies and reduced charge transfer in most cases. This phenomenon is accompanied by a progressive redistribution of electronic density, where Na atoms begin to play a more active role in interfacial interaction.

The trends observed in this work are consistent with previous first-principles studies on sodiated MoS2 anodes, which have shown that increasing Na concentration significantly modifies the electronic structure of the anode and its electrochemical behavior (Sharma et al., 2026). Consistent with these findings, our calculations demonstrate that the degree of sodiation also plays a critical role in governing the interaction between the electrode and electrolyte species. While previous DFT studies primarily focused on Na interface and the electronic properties of sodiated MoS2, the present work extends this understanding by systematically comparing the interface behavior of five representative electrolyte anions at different degrees of sodiation. This comparative analysis provides additional atomistic insight into how electrode sodiation and electrolyte chemistry jointly influence the evolution of the electrode/electrolyte interface.

For smaller and more symmetric anions such as BF 4 − and ClO 4 −, the interaction is initially dominated by the MoS2 surface, with clear charge transfer and electron redistribution at low Na concentration. However, as sodiation increases, this interaction weakens and partial contributions from Na-mediated interactions emerge, although without fully stabilizing the interfacial interaction.

In contrast, PF 6 −, TFSI − and FSI − exhibit a more complex behavior governed by structural reorientation and multiple competing interaction mechanisms. In the case of PF 6 −, increasing Na content induces a transition from a tilted to a vertical configuration, reducing surface interaction and promoting Na–F interactions. For TFSI −, the interfacial interaction highly depends on the molecular orientation, with oxygen-coordinated configurations showing stronger interactions, while fluorine-dominated configurations remain energetically unfavorable. MEP calculations help us to understand this behavior, where oxygen atoms exhibit more negative electrostatic potential than fluorine atoms, making them the preferred interaction sites with positively charged centers (Mo and Na+). In that sense, configurations involving oxygen atoms show more favorable (more negative) interaction energies compared to F-dominated orientations. TFSI − exhibits significant Na-mediated effects, particularly at higher sodiation levels, as evidenced by enhanced electron localization around Na-rich regions. For the FSI, configurations that bring an F atom into direct proximity with surface Na atoms become significantly more reactive at high Na states. In those cases, we observed spontaneous S–F bond dissociation, followed by the formation of a stable Na–F bond at the interface. These findings indicate that the presence of highly sodiated surface regions dramatically lowers the energetic barrier for FSI decomposition, identifying the Na–F interaction as the primary driving force for the initial electrolyte degradation. Analysis of the differences in the work function provides further support to the previous observations, indicating that the electronic response at the interface is not only determined by the transfer of charges but also by the formation of dipoles and the redistribution of charges. In some cases, the difference in the work function is not found to follow a monotonic trend.

The computational models presented in this work should be regarded as an initial framework for identifying interfacial trends and reaction mechanisms prior to more computationally demanding approaches, such as an ab initio molecular dynamics (AIMD) simulation, which can explicitly account for the dynamic behavior of a complete electrolyte environment, including both salt and solvent molecules. Despite their simplified nature, the static DFT calculations presented in this work provide valuable mechanistic insights into the fundamental interactions governing electrolyte decomposition and interfacial stability. Consequently, this approach offers a computationally efficient strategy for the preliminary screening of candidate electrode materials and electrolyte chemistries, enabling the identification of promising systems before undertaking more computational costly simulations.

In that line, our findings suggest that formation and stability of the solid electrolyte interphase (SEI) on MoS2 are strongly associated by the interplay between anion orientation and the degree of sodiation. While low Na concentrations favor direct surface–anion interactions, higher Na content promotes a transition toward Na-mediated interactions and altered electronic environments. It is important to understand the implications for the design of electrolytes, indicating that larger and more flexible anions may lead to more complex and less predictable interfacial behavior compared to smaller, more symmetric species. In particular, the presence of highly electronegative oxygen atoms plays a key role in stabilizing interfacial configurations and enhancing interaction strength. From a practical perspective, these results provide atomistic descriptors that may assist in the screening of electrolyte salts for MoS2-based sodium-ion batteries. The calculated interface energies, preferred molecular orientations, charge redistribution, and work-function changes help identify how different anions interact with the electrode surface at different degrees of sodiation, providing guidance for selecting electrolyte components with distinct interfacial behaviors before experimental validation. Although explicit electrolyte decomposition and SEI growth were not modeled in this work, the present results offer fundamental insight into the early stages of electrode/electrolyte interactions that can support the rational design of future experimental studies.

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Footnotes

Edited by: Artur Tron, Austrian Institute of Technology (AIT), Austria

Reviewed by: Hussam Bouaamlat, Roma Tre University, Italy

Jeetu Babu, National Institute of Technology Calicut, India

Statements

Conflict of interest

The author(s) declared that this work was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Funding

The author(s) declared that financial support was not received for this work and/or its publication.

Data availability

The original contributions presented in the study are included in the article/supplementary material, further inquiries can be directed to the corresponding author.

Author contributions

LS: Validation, Writing – original draft, Formal Analysis, Methodology, Data curation, Investigation, Software. UV: Software, Methodology, Writing – original draft, Investigation. DG-A: Project administration, Supervision, Writing – review and editing, Conceptualization.

Acknowledgements

LS would like to acknowledge the support and valuable scientific discussions provided by the research group Grupo de Investigación en Energía, Computación Científica, Ciberseguridad, Inteligencia Artificial y Automatización (GIEC *3* IA *2* - UNI), of which he is a member, for their productive and insightful exchanges.

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Citation

Selis, L. A., et al. (2026). First-principles study of electrolyte components stability and orientation on MoS 2 surfaces: implications for SEI formation in sodium-ion batteries. Frontiers in Batteries and Electrochemistry, Volume 5. https://doi.org/
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Copyright © 2026 Selis, Vijay and Galvez-Aranda.

License: https://creativecommons.org/licenses/by/4.0/

*Correspondence: Diego E. Galvez-Aranda

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