1 Introduction

Lithium-ion batteries (LIBs) are widely used due to their high energy density [1] and long cycle life, making them ideal for portable electronics, electric vehicles, and aerospace applications. However, LIBs face challenges such as limited lithium availability, high material costs (e.g., cobalt and nickel), safety risks due to thermal runaway, and environmental concerns from mining and recycling. Additionally, LIBs exhibit performance limitations under extreme conditions and high current rates. Sodium-ion batteries (SIBs) offer a promising alternative, leveraging sodium’s abundance, lower cost, and compatibility with aluminum current collectors [2]. SIBs also benefit from faster ion diffusion and lower operating voltages, reducing energy loss during charge/discharge cycles [3]. While magnesium-ion batteries (MIBs) have gained interest due to their higher volumetric capacity and cycling stability [4], SIBs remain more practical due to their simpler ion transport mechanisms and broader range of electrode materials [5, 6]. Sodium containing metal-organic frameworks (MOFs) have emerged as potential electrode materials for SIBs due to their tunable porosity, high surface area, and structural flexibility [7, 8]. The ability to design and synthesize MOFs with specific structural and electronic properties makes them particularly attractive for energy storage applications [9]. Sodium-based MOFs not only facilitate sodium ion transport through their highly porous frameworks but also offer significant advantages in terms of chemical and thermal stability [10, 11]. One of the most critical challenges in developing MOFs for SIBs is achieving efficient sodium storage and de-intercalation while maintaining structural integrity over prolonged cycles. The inherent design flexibility of MOFs enables the incorporation of functional metal centers and organic linkers that can stabilize sodium ions within the framework, enhancing both capacity and cycle life [12, 13]. Moreover, doping strategies, such as substituting metal ions or modifying organic linkers, have been employed to optimize the electronic conductivity and sodium mobility of these materials [14]. Sodium-containing MOFs also exhibit unique redox properties that can be harnessed to improve the energy density and rate performance of SIBs. For example, the use of MOFs with multivalent metal centers allows for multiple redox reactions during cycling, thereby increasing the theoretical capacity [15]. Additionally, the ability to modify the framework topology and pore size provides control over the ion diffusion pathways, further enhancing electrochemical performance [15]. Recent studies have highlighted the importance of understanding the sodium-ion de-intercalation mechanisms in MOFs to address challenges such as voltage fade and capacity retention [15]. Among them, MOF UAX-1 ([ZnNa(m-BDC)₂], m-BDC = 1,3-benzene-dicarboxylate) (Fig. 1) [16] has shown promise as a cathode material, offering stable sodium intercalation and de-intercalation behavior. To further enhance its properties, this study investigates the effects of doping UAX-1 with Mg, Y, S, Co, Cs, and Si. These elements were selected based on their potential to improve electrochemical performance, including stability, redox activity, and electronic conductivity. Using density functional theory (DFT) [17] calculations via the full-potential linearized augmented plane wave (FPLAPW) method, we analyze the impact of dopants on electronic structure and sodium de-intercalation voltage. This approach provides direct insights into voltage predictions and structural stability, addressing key limitations of MOF-based SIB cathodes. By systematically evaluating dopant effects, this study contributes to the advancement of MOFs as high-performance electrode materials for next-generation sodium-ion batteries [18,19,20].

1.1 Computational methods: FPLAPW Using GGA in SIESTA

We have employed the Full-Potential Linearized Augmented Plane Wave (FPLAPW) method [21], a highly precise computational approach for solving the Kohn-Sham equation in Density Functional Theory (DFT) [22]. The exchange-correlation energy was described using the Generalized Gradient Approximation (GGA) [23] method, as it offers a good balance between computational efficiency and accuracy for describing the electronic structure of metal-organic frameworks (MOFs). Specifically, the Perdew-Burke-Ernzerhof (PBE) functional [21], a widely used form of GGA, is known to provide reliable predictions for structural, electronic, and thermodynamic properties of materials, particularly those involving transition metals and organic linkers, as in MOF UAX-1 [24]. Additionally, the use of GGA-PBE ensures consistency with prior computational studies on similar MOF systems [24], allowing for meaningful comparisons of the results. While more advanced functionals, such as hybrid or meta-GGA functionals, could improve accuracy further, they are computationally more expensive and were beyond the scope of this study. Therefore, the GGA-PBE functional was deemed suitable for our objectives. as it offers improved accuracy over the Local Density Approximation (LDA) by incorporating the spatial variation of the electron density. Specifically, the Perdew-Burke-Ernzerhof (PBE) functional was used [25]. The PBE functional balances computational efficiency and accuracy, making it well-suited for materials like MOFs with intricate bonding environments. Although SIESTA [25] primarily employs localized atomic orbitals as basis sets, it can emulate the precision of FPLAPW calculations through careful parameter selection. Localized Basis Sets: Numerical atomic orbitals are used to expand wavefunctions, providing an efficient alternative to plane waves. k-Point Sampling: A dense Monkhorst-Pack grid [26, 27] was used for Brillouin zone sampling, ensuring high-resolution energy and density of states calculations [26]. For energy cutoff, a high energy cutoff was set to capture fine details in the electronic structure. Pseudopotentials: Norm-conserving pseudopotentials [21, 27] accurately represent core electrons while treating valence electrons explicitly.

1.2 Computational parameters for Mg-doped MOF (Na-free)

The Na-free supercell was modeled with the following atomic composition: one Mg atom, four H atoms, three C atoms, two O atoms. Periodic boundary conditions were applied to simulate the material’s infinite structure. A plane-wave cutoff energy of 200 Ry was set for the charge density grid. Convergence criteria for calculations were defined as: Energy tolerance: 3 × 10−2 eV; Force tolerance: 5 × 10−3 eV/Å. Full geometry optimization was performed, allowing both atomic positions and cell parameters to relax. Spin-polarized calculations were included to account for possible magnetic effects. A Monkhorst-Pack grid with a 3 × 3 × 3 k-point mesh was used to sample the Brillouin zone effectively. The band structure was calculated with the BandLinesScale set to “pi/a,” indicating scaling by the reciprocal lattice constant a. The high-symmetry points and paths in the Brillouin zone were defined using the following parameters: Start at Γ(0.0,0.0,0.0), proceed to X∣Y(0.5,0.0,0.0) with 40 k-points, return to Γ(0.0,0.0,0.0), move to Z∣R(0.5,0.5,0.5) with 20 k-points, return again to Γ(0.0,0.0,0.0), continue to T|U(0.0,0.5,0.5) with 25 k-points, go back to Γ(0.0,0.0,0.0), finally, transition to V∣Γ(0.5,0.5,0.0) with 50 k-points. This layout ensures a comprehensive exploration of the electronic band structure. The Projected Density of States (PDOS) was calculated to understand the contributions of atomic orbitals and elements to the electronic states near the Fermi level. Parameters used for the PDOS calculation: energy range: −30.00 eV; resolution: 0.200 eV; smoothing points: 2000. This provides a detailed distribution of electronic states and facilitates analysis of the material’s electronic structure. The Local Density of States (LDOS) was calculated for the energy range between − 5.00 eV and 0.00 eV to focus on occupied electronic states near the Fermi energy. The TDOS provides spatial insights into the density of electronic states, especially around specific atoms or regions of the material. The detailed SIESTA Code Parameters used in the calculations is provided in SI1.

1.3 Sodium de-intercalation voltage calculation

$$\left[ {{\text{NaM}}\left( {{\text{m}} - {\text{BDC}}} \right)_{{\text{2}}} } \right]~ \to \left[ {{\text{M}}\left( {{\text{m}} - {\text{BDC}}} \right)_{{\text{2}}} } \right]{\text{ }} + {\text{ xNa}}^{ + } + {\text{ xe}}^{-}$$
$$\Delta {\text{G}}~ = {\text{E}}^{{{\text{tot}}}} - {\text{ PV }} + {\text{ TS}}$$
(1)
$$\Delta {\text{G}}~ = ({\text{E}}_{{{\text{MOF}} - {\text{Na}}}} {-}{\text{ E}}_{{{\text{MOF}}}} - {\text{X }}\mu _{{{\text{Na}}}} )$$
(2)
$${\text{V}}~~ = ~~{{\Delta {\text{G}}} \mathord{\left/ {\vphantom {{\Delta {\text{G}}} {\Delta {\text{X}}}}} \right. \kern-\nulldelimiterspace} {\Delta {\text{X}}}}$$
(3)
Table 1. Calculated Sodium de-Intercalation Voltages for Doped MOF UAX-1
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At T = 0, the PV term is very small and can be neglected. The Gibbs free energy expression incorporating the number of sodium ions transported during de-intercalation can be calculated using Eq. (2). EMOF-Na​ is the total energy of the sodium-intercalated MOF system. EMOF​ is the total energy of the MOF after sodium de-intercalation, µNa ​ is the chemical potential (or energy) of a single sodium atom within a sodium unit cell. The sodium de-intercalation voltage [28] can be calculated through Eq. (3). In this study, x = 6 represents the number of sodium ions within the sodium unit cell. The de-intercalation process involves the transport of Δx = 1 sodium ion. Sodium de-intercalation voltage calculation example on Y-doped MOF:

$$\text{V}= [(-3697.16)-(-3209.82)-(6) ^{*} (-82)]/1=4.66~\text{V}.$$

2 Results

The sodium de-intercalation voltages presented in (Table 1) indicate significant variations among different doped MOFs, highlighting the impact of the metal substitution on electrochemical performance. Among the studied materials, Mg-doped MOF UAX-1 exhibits a moderate sodium de-intercalation voltage of 3.95 V, which is well-balanced between stability and energy efficiency. While Si-doped MOF shows the highest voltage (5.83 V), excessively high de-intercalation voltages can lead to structural instability and increased energy loss during cycling, making it less favorable for practical applications. Conversely, Cs-doped MOF exhibits an exceptionally high de-intercalation voltage of 9.063 V, which is impractically high for efficient sodium-ion battery operation due to the risk of severe framework degradation. The relatively lower voltages of S-doped (3.3 V) and Co-doped (4.02 V) MOFs suggest potential stability but may result in lower energy densities compared to Mg-doped MOF. The balance between structural integrity, sodium mobility, and de-intercalation voltage makes Mg-doped MOF a promising candidate for cathode materials in sodium-ion batteries, as it offers favorable electrochemical stability while maintaining a reasonable operating voltage. This result aligns with previous studies demonstrating that Mg doping enhances sodium-ion diffusion kinetics and prolongs cycling stability [29,30,31]. This observation also aligns with other previous research, where Mg doping in layered oxide cathodes resulted in high average voltages around 3.3 V versus Na/Na⁺, delivering specific capacities of approximately 120 mAh g⁻¹, which remained stable over multiple cycles [32].

Fig. 1
figure 1

MOF UAX-1: (a) Labeled atomic connectivity with measured bond lengths, (b) Scientific illustration of the MOF structure, (c) Asymmetric unit cell with labeled atomic positions, and (d) Layered unit cell representation showcasing metal-linker connectivity. e) both Na (pink) and Mg (yellow) are octahedrally surrounded by oxygen atoms (green)

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The stabilized de-intercalation voltage in Mg-doped MOFs can be attributed to the stabilization of the framework structure and the optimization of the electronic environment, facilitating efficient sodium-ion extraction during the de-intercalation process. These findings underscore the potential of Mg-doped MOFs as promising cathode materials for high-performance sodium-ion batteries.

2.1 Na de-intercalation behavior of doped MOFs and band structure

In the MOF UAX-1, sodium and transition metal (TM) atoms are octahedrally coordinated by six oxygen atoms (Figs. 1e and 2b), resembling the common cathode structure used in sodium-ion batteries. The interaction between metal centers leads to band splitting, which defines the electronic band gap, as illustrated in (Figs. 3, 4, 5, 6, 7 and 8). In addition to the bands arising from metal–metal interactions, additional bands form due to the overlap between oxygen s and p orbitals with the metal s, p, and d orbitals (Fig. 2a). The TM d orbitals dxy, dyz, dxz, dₓ²_y², and dz² split into two subsets under the octahedral crystal field: the e_g orbitals (dₓ²_y² and dz²) and the t2g orbitals (dxy, dyz, dxz). Overlap between TM d and oxygen p orbitals results in the formation of bonding e_g orbitals and antibonding e_g* orbitals. The non-bonding t2g orbitals, which do not significantly overlap with oxygen orbitals, form narrow bands whose width depends on the strength of metal–metal interactions and ultimately define the band gap. Furthermore, orbital overlap between oxygen p and metal s/p orbitals contributes to the formation of t1u and a1g bands, which predominantly exhibit oxygen p character [28].

2.2 Total density of states (TDOS) profiles

Analysis of doped UAX-1 MOFs reveals significant modifications in the electronic structure due to different dopants. As observed in the TDOS plots, the introduction of Mg, S, Co, Cs, Si, and Y affect the distribution of electronic states, particularly near the Fermi level, which is crucial for charge transport and electrochemical performance in sodium-ion batteries (SIBs). The TDOS profiles for Mg-UAX-1 and Co-UAX-1 (Figs. 3b and 4b) show a higher density of states at the conduction band minimum, indicating improved electrical conductivity, which can enhance charge transfer efficiency during cycling [33]. The Cs- and Si-doped MOFs (Figs. 5b and 6b) exhibit a broader energy distribution, suggesting alterations in band gap energy and potential changes in redox activity [34]. Y-UAX-1 (Fig. 7b) exhibits a broader TDOS profile but lacks strong contributions near the Fermi level, limiting its effectiveness in charge transfer. The S-UAX-1TDOS profile (Fig. 8b) exhibits a noticeable shift in energy distribution, which can be attributed to the electronic interactions introduced by sulfur doping. Si and S show more localized conduction states, which could hinder electron mobility and reduce efficiency for SIB applications. Cs presents a fluctuating DOS profile, but its contribution to charge conduction is less significant than Mg. The broad and delocalized conduction band of Mg allows for better charge transport, making it the most suitable candidate for enhancing the electrochemical performance of MOFs in SIBs. The Density of States (DOS) profiles for the Metal-Organic Framework (MOF) with and without sodium (Na) incorporation reveal significant differences in electronic structure. The DOS for Na-free MOF exhibits a more localized electronic state distribution near the Fermi level, whereas the Na-incorporated MOF shows a broader, more delocalized state, particularly in the conduction band region (Figs. 3b, 4, 5, 6, 7 and 8b). This broadening enhances electron mobility, which is beneficial for sodium-ion battery (SIB) applications. The Na-incorporated MOF also presents a higher total DOS near the Fermi level, indicating improved electronic conductivity, a critical factor for efficient charge transfer in SIBs. Therefore, the Na-incorporated MOF demonstrates superior electronic characteristics for SIBs, as it provides better charge carrier transport and increased conductivity compared to the Na-free counterpart [34,35,36].

Fig. 2
figure 2

Schematic representation of the band structure of doped MOF (a) and the doped MOF crystalline structure, Mg-yellow, Na-pink (b)

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2.3 Band structure (BS) profiles

Comparison of the MOF with and without sodium (Na) shows significant differences in electronic properties, which are crucial for sodium-ion battery (SIB) performance. The Na-free MOF profiles (Figs. 3a, 4a, 5, 6, 7 and 8a, respectively) exhibits a wider bandgap, indicating lower intrinsic electronic conductivity, while the Na-incorporated MOF profiles (Figs. 3b, 4b, 5b, 6, 7 and 8b, respectively) show reduced bandgap with more delocalized states near the Fermi level (EF) [37]. This suggests that sodium incorporation enhances charge carrier mobility, which is beneficial for improving battery performance. When comparing Mg band structure profile with sodium (Fig. 3b) with the other five doped profiles (Co, Cs, Si, Y, and S) (Figs. 4b, 5b, 6, 7 and 8b). Mg-doped MOF BS profile (Fig. 3b) demonstrates the most favorable electronic behavior for SIBs. The Mg-doped MOF exhibits a narrower bandgap and more continuous electronic states near the Fermi level, indicating enhanced electronic conductivity. Co and Y-doped MOFs (Figs. 4b and 7b) display more localized (DOS) states, which could hinder charge mobility, while Si and S-doped MOFs (Figs. 6b and 8b) show wider bandgaps, leading to lower electronic conductivity. Cs-doped (Fig. 5b) MOF presents a highly dispersed band structure, but its impact on charge transport is less effective than Mg. The Mg-doped MOF provides the best balance of charge transport and band structure characteristics, making it the most promising candidate for improving SIB performance among the elements analyzed [38].

2.4 Zoomed-in band structure of Na-free MOF

Cs-Na free MOF (Fig. 1S) shows valence band (E < 0 eV) consists of π-bands from the benzene linker, which facilitate charge mobility, while deeper valence states contain σ-bands from C–O and C–C interactions that stabilize the framework. The t₂g bands, originating from Cs d-orbitals, lie below the Fermi level and contribute to the valence band. The conduction band (E > 0 eV) features e_g states, primarily from Cs d-orbitals, which influence electronic transitions. The presence of Na (Fig. 5b) modifies the band structure by lowering the conduction band minimum (CBM) and slightly compressing the bandgap, enhancing conductivity. The absence of Na (Figs. 1S and 5a) increases the bandgap by shifting both the valence band maximum (VBM) and the conduction band minimum (CBM) upwards, reducing intrinsic conductivity but potentially improving optical absorption in the UV range. This shift results from changes in charge distribution and electrostatic interactions between Cs, Na, and the carboxylate linkers. The electronic structure is primarily influenced by Cs 6s and 5p orbitals, while the fully filled 4d orbitals remain core-like and do not actively participate in the band structure near the Fermi level. Overall, Na incorporation fine-tunes the MOF’s electronic and optical properties by modulating band alignment, making it adaptable for applications such as semiconductors, optoelectronics, or catalysis. The band structure of Y-1,3-benzene dicarboxylate MOF (Figs. 2S and 7a), following the removal of Na from Y-Na-1,3-dicarboxylate MOF (Fig. 7b), reveals distinct electronic transitions governed by the coordination environment of Y ions and the π-conjugated organic linker. The electronic states near the Fermi level (E_F) are categorized as follows: (i) t₂g bands, originating from Y(III) d-orbitals, are positioned below the Fermi level and contribute to charge transport; (ii) e_g bands, found above E_F, require external excitation for charge transfer, influencing optical and catalytic behavior; (iii) π-bands, from the benzene ring, facilitate electronic delocalization and mobility; and (iv) σ-bands, deeper in the valence region, arise from strong C–O and C–C interactions, ensuring structural stability. Compared to the Y-Na MOF, the Na-free Y-MOF exhibits an upward shift in the conduction band minimum (CBM) and a fine-tuned valence band maximum (VBM), potentially improving its electronic and catalytic properties. The band structure confirms both occupied valence bands (E < 0 eV) and unoccupied conduction bands (E > 0 eV), characteristic of a semiconducting material where electron transitions between π or t₂g states to e_g or π* orbitals influence conductivity and optical response. Na-free Mg-1,3-benzene-dicarboxylate MOF band structure, (Fig. 9), reveals distinct electronic states across the energy spectrum. The Fermi level (E_F) is set at 0 eV, with valence bands (E < 0 eV) and conduction bands (E > 0 eV) clearly separated. Below the Fermi level, t₂g bands (black) emerge from the d-orbitals of Mg(II), contributing to electronic stability and minimal conductivity. The π-bands (purple), derived from the conjugated benzene dicarboxylate linker, also reside near the Fermi level, supporting electron delocalization and charge transport. At deeper energy levels (E < −4 eV), the σ-bands (red and blue) dominate, arising from strong C–O and C–C bonding interactions that reinforce structural integrity. Above the Fermi level, the e_g bands (green) represent antibonding Mg d-states, requiring external excitation for electron transitions, while unoccupied π* bands (magenta) facilitate optical absorption and charge mobility. The relatively wide band gap suggests semiconducting behavior, indicating that the MOF’s electronic and catalytic properties can be tuned by external stimuli or doping modifications. The Na-free Mg-1,3-dicarboxylate MOF exhibits significant advantages over Cs- and Y-based MOFs due to its superior band structure characteristics, electronic transitions, and chemical stability. The Mg-based MOF features a larger band gap, enhancing stability and reducing charge recombination, which is crucial for photocatalysis and electronic devices.

Fig. 3
figure 3

Band Structure (BS) and Total Density of States (TDOS) profiles for Mg-UAX-1(a) without Na and (b) with Na

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Fig. 4
figure 4

Band Structure (BS) and Total Density of States (TDOS) profiles for Co-UAX-1(a) without Na and (b) with Na

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Fig. 5
figure 5

Band Structure (BS) and Total Density of States (TDOS) profiles for Cs-UAX-1(a) without Na and (b) with Na

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Fig. 6
figure 6

Band Structure (BS) and Total Density of States (TDOS) profiles for Si-UAX-1(a) without Na and (b) with Na

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Fig. 7
figure 7

Band Structure (BS) and Total Density of States (TDOS) profiles for Y-UAX-1(a) without Na and (b) with Na

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Fig. 8
figure 8

Band Structure (BS) and Total Density of States (TDOS) profiles for S-UAX-1(a) without Na and (b) with Na

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Table 2 Summary of doped MOF UAX-1 properties, including specific capacity, band gap energy, band gap type, semiconductor classification, mesh-cutoff, K-grid Monkhorst-Pack parameters, and atomic band contributions at specific energy levels
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Fig. 9
figure 9

Zoomed-in band structure (BS) profile of Mg-MOF UAX-1 in the absence of Na, highlighting the valence band maximum (VBM) and conduction band minimum (CBM) relative to the Fermi level

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Its conduction band (CB) is dominated by e_g states of Mg(II), while the valence band (VB) consists of π and t₂g bands, ensuring efficient charge transport. In contrast, the Y-based MOF has a more complex d-electron configuration, which narrows the band gap, increases carrier recombination, and introduces unwanted mid-gap states. The Cs-based MOF, being highly ionic, exhibits weaker π-conjugation, leading to localized electronic states and poor charge mobility. Structurally, the Mg-based MOF benefits from strong Mg–O coordination bonds, resulting in better framework rigidity and thermal stability. In comparison, the Y-based MOF’s larger ionic radius and flexible coordination introduce framework distortions, while the Cs-based MOF lacks strong covalent interactions, making it less robust. Optically, the higher conduction band minimum (CBM) in the Mg-based MOF enhances its photocatalytic efficiency, unlike the Y-based MOF, which has mid-gap defect states that trap charge carriers, and the Cs-based MOF, which lacks efficient π-conjugation. Ultimately, the Mg-1,3-dicarboxylate MOF stands out due to its wider band gap, stronger Mg–O bonding, better π-system delocalization and fewer defect-induced trap states, making it a superior candidate for semiconducting, photocatalytic, and electronic applications.

2.5 Superior Sodium-Ion storage performance of Mg-UAX-1: high specific capacity, enhanced conductivity, and structural stability

The theoretical specific capacity (Q) in mAh/g is calculated using Eq. (4) formula:

$${\text{Q }} = \frac{{{\text{X}}.{\text{F}}}}{{\text{M}}}$$
(4)

X = the number of transferring electrons, F = Faraday constant, and m = molecular mass of the active material. The comparative analysis of various doped UAX-1 MOFs (Table 2) highlights the superior performance of Mg-UAX-1 for sodium-ion batteries (SIBs). Mg-UAX-1 exhibits the highest specific capacity (2659.85 mAh/g) and a low band gap energy (0.0121 eV), indicating excellent electronic conductivity and enhanced sodium-ion storage capability [39]. Si-UAX-1 and S-UAX-1 also demonstrate relatively high capacity of 1784.35 mA/g and 1673.33 mAh/g. respectively, with Si-UAX-1 having an indirect band gap of 2.4431 eV, which may hinder charge transfer efficiency [40]. Co-UAX-1, Y-UAX-1, and Cs-UAX-1 exhibit significantly lower capacities, with Cs-UAX-1 showing the least performance (190.206 mAh/g) and the smallest band gap energy (0.0005 eV), which may lead to instability [40]. The semiconductor nature of these MOFs also varies, with most being p-type, except for Y-UAX-1, which is n-type. The atomic band contribution analysis indicates that Mg-UAX-1 benefits from Mg(3s) contributions at the conduction band, facilitating improved charge transport compared to other elements, where contributions from Si, S, Co, Y, and Cs lead to either larger band gaps (Figs. 3a, 4a, 5a, 6a and 7a, respectively) or reduced electronic conductivity [41]. Consequently, Mg-UAX-1 stands out as the most promising material for SIB applications due to its high capacity, direct band gap, and favorable atomic contributions [42, 43]. Upon sodium de-intercalation, the M-O bond length in MOFs exhibits a noticeable increase due to the reduced electrostatic interaction between the metal center and the surrounding oxygen ligands. This elongation (Fig. 10) reduces sigma overlap between the oxygen-p orbitals and the metal-d, metal-s, and metal-p orbitals, weakening the covalent bonding within the framework. As the orbital interactions diminish, the electronic band structure undergoes modifications, which can increase the band gap. A wider band gap typically reduces electronic conductivity, while defect-induced mid-gap states may enhance it. This structural and electronic transformation highlights the impact of sodium on the electronic properties of MOFs, influencing their conductivity and potential performance in energy storage and catalysis.

2.6 Projected density of states (PDOS) profiles

The atomic orbital contributions in the PDOS profiles for Mg- and Si-doped MOFs (Figs. 11 and 12) reveal key insights into their electronic structures and sodium storage capabilities. In the Mg-doped MOF, the Mg 3 s orbitals play a significant role in modifying the electronic states near the Fermi level, leading to enhanced charge delocalization. The interaction of Mg with surrounding O and C atoms contributes to a more evenly distributed density of states, particularly in the conduction band. Upon sodium removal, the PDOS of Mg-doped MOF shows minimal disruption, suggesting that Mg stabilizes the framework and maintains efficient charge transport pathways. In contrast, the Si-doped MOF exhibits a stronger contribution from Si 3p orbitals, which interact with the O 2p states. However, this interaction is more localized, leading to a more pronounced shift in the electronic states upon sodium removal. The localization of states in the Si-doped MOF suggests a higher degree of structural and electronic perturbation, which may reduce charge transport efficiency. Additionally, the removal of sodium leads to a significant reduction in the density of states near the Fermi level, indicating a higher voltage requirement for de-intercalation. The atomic orbital contributions in the PDOS profiles for S- and Y- doped MOFs reveal significant differences in their electronic structures and their stability upon sodium de-intercalation. In the S-doped MOF (Fig. 13), the S 3p orbitals play a dominant role in hybridizing with the O 2p states, contributing to the overall electronic density of states near the Fermi level. This hybridization enhances charge delocalization and provides additional electronic pathways for sodium-ion transport. However, upon sodium removal, the PDOS of the S-doped MOF exhibits a noticeable shift, particularly in the conduction band, suggesting a structural and electronic rearrangement. The reduction in density of states near the Fermi level indicates a possible increase in the de-intercalation voltage, which could impact the efficiency of sodium storage and release. In contrast, the Y-doped MOF profile (Fig. 14) shows a significant contribution from the Y 4d orbitals, which strongly interact with surrounding O and C atoms. This interaction creates a more extended electronic structure, improving charge transport across the material. The PDOS of the Y-doped MOF remains relatively stable upon sodium de-intercalation, suggesting that Y doping enhances the robustness of the framework. The reduced disruption in the electronic states upon sodium removal implies a lower energy barrier for sodium diffusion, making Y-doped MOFs a promising candidate for sodium-ion storage applications. In the Co-doped MOF (Fig. 15), the cobalt 3 d orbitals exhibit significant contributions near the Fermi level, particularly in both spin-up and spin-down states, suggesting strong hybridization with surrounding ligands such as oxygen 2p and carbon 2p orbitals. This hybridization enhances electronic conductivity and structural stability. Upon sodium de-intercalation, noticeable shifts occur in the Co 3d states, indicating charge compensation effects and potential changes in the local electronic environment, which could influence ion migration and storage performance. For the Cs-doped MOF (Fig. 16).

Fig. 10
figure 10

Bond distance measurements: (a) Mg-doped MOF UAX-1 (Mg: purple, Na: green), (b) Cs-doped MOF without Na (Cs: violet), and (c) Y-doped MOF without Na (Y: cyan)

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Cesium 6s orbitals have a relatively lower contribution to the total density of states due to the weakly bound nature of Cs in the framework. However, Cs doping influences the surrounding electronic states by modifying the carbon and oxygen orbital interactions. After sodium de-intercalation, the Cs-doped MOF exhibits noticeable changes in the valence band region, with a redistribution of states, particularly in the O 2p and C 2p orbitals, suggesting structural relaxation and potential changes in redox activity. The PDOS profiles for Mg, Si, Y, S, Co, and Cs-doped MOFs reveal distinct atomic orbital contributions that influence their suitability for sodium-ion battery (SIB) applications. Mg-doped MOFs exhibit strong hybridization between Mg 3s orbitals and O 2p/C 2p, resulting in a well-distributed electronic density near the Fermi level, which enhances conductivity and structural stability during sodium de-intercalations.In contrast, Si-doped MOFs show more localized Si 3p states with weaker hybridization, leading to increased electronic confinement and lower charge transport efficiency. Y and S-doped MOFs display notable interactions between transition metal d-orbitals and surrounding ligand states, but their PDOS structures suggest moderate electronic activity with partial charge localization. Co and Cs-doped MOFs exhibit highly spin-polarized PDOS features, with Co showing strong d-orbital contributions but higher state localization, while Cs displays more dispersed but weakly interacting orbitals. Among all the dopants, Mg provides the most continuous and broadened PDOS near the Fermi level, indicating superior charge transport properties, making it the best candidate for SIB applications due to its enhanced electronic conductivity, stability upon sodium de-intercalation, and efficient charge compensation.

3 Conclusion

The findings of this study highlight the significant impact of metal doping on the electrochemical performance of MOF UAX-1 as a cathode material for sodium-ion batteries. Among the investigated dopants, Mg-doped MOF exhibited the most balanced de-intercalation voltage (3.95 V), offering a promising combination of structural stability, sodium mobility, and energy efficiency. While Si and Cs doping resulted in excessively high voltages that could compromise structural integrity, S and Co doping led to moderate voltages but with potential trade-offs in energy density. Density of States (DOS) and band structure analyses further revealed that Mg doping enhances charge transport by stabilizing the electronic structure and promoting conductivity near the Fermi level. The PDOS results confirmed that Mg’s interaction with surrounding atoms facilitates charge delocalization, improving the material’s suitability for long-term cycling stability. Overall, these results suggest that Mg-doped UAX-1 is a strong candidate for advancing sodium-ion battery cathodes, offering an optimal balance of voltage stability, electronic conductivity, and structural robustness. Supplementary material available online at: https://doi.org.10.1007/s43939-025-00328-1.

Fig. 11
figure 11

Projected Density of States (PDOS) profiles for the Mg-doped MOF UAX-1: (a) PDOS of the Mg-doped MOF with Na; (b) PDOS after sodium de-intercalation, indicating changes in electronic states. The left-side panels illustrate the overall projected density of states for the full system, while the right-hand panels show spin-resolved orbital contribution from key atoms and orbitals: C and O 2s and 2p states, H 1s, Mg 3s and 3p orbitals.

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Fig. 12
figure 12

Projected Density of States (PDOS) profiles for the Si-doped MOF UAX-1: (a) PDOS of the Si-doped MOF with Na,; (b) PDOS after sodium de-intercalation, indicating changes in electronic states. The left-side panel illustrate the overall projected density of states for the full system, while the right-hand panels show spin-resolved orbital contribution from key atoms and orbitals: C and O 2s and 2p states, H 1s, Si 3s and 3p orbitals.

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Fig. 13
figure 13

Projected Density of States (PDOS) Profiles for S-doped MOF UAX-1: (a) PDOS of the S-doped MOF with Na; (b) PDOS after Sodium de-Intercalationindicating changes in electronic states. the left-side panel illustrate the overall projected density of states for the full system, while the right-hand panels show spin-resolved orbital contribution from key atoms and orbitals: C and O 2s and 2p states, H 1s, S 3s and 3p orbitals.

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Fig. 14
figure 14

Projected Density of States (PDOS) Profiles for Y-doped MOF UAX-1: (a) PDOS of the Y-doped MOF with Na; (b) PDOS after Sodium de-Intercalation indicating changes in electronic states. the left-side panel illustrate the overall projected density of states for the full system, while the right-hand panels show spin-resolved orbital contribution from key atoms and orbitals: C and O 2s and 2p states, H 1s, Y 5s, 4d orbitals.

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Fig. 15
figure 15

Projected Density of States (PDOS) profiles for Co-doped MOF UAX-1: (a) PDOS of the Co-doped MOF with Na; (b) PDOS after Sodium de-Intercalation indicating changes in electronic states. the left-side panel illustrate the overall projected density of states for the full system, while the right-hand panels show spin-resolved orbital contribution from key atoms and orbitals: C and O 2s and 2p states, H 1s, Co 4s, 3d orbitals.

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Fig. 16
figure 16

Projected Density of States (PDOS) profiles for doped Cs-doped MOF UAX-1: (a) PDOS of the Cs-doped MOF with Na; (b) PDOS after Sodium de-Intercalation indicating changes in electronic states, the left-side panel illustrate the overall projected density of states for the full system, while the right-hand panels show spin-resolved orbital contribution from key atoms and orbitals: C and O 2s and 2p states, H 1s, Cs 6s.

Full size image