Alleviating the stability-energy density dilemma via electron-donor-mediated orbital symmetry regulation in sodium phosphate cathodes

Abstract

Manganese-based sodium super ionic conductor-type cathode materials, leveraging the multielectron redox activity of manganese, represent a promising pathway toward high-energy-density sodium-ion batteries (SIBs). However, the unavoidable generation of Mn³⁺(3d⁴) species during charge-discharge processes, characterized by asymmetric e_g orbital occupancy, triggers octahedral symmetry breaking. This inherent electronic structural instability creates a fundamental contradiction between achieving high energy density and ensuring long cycle life that remains inherently difficult to reconcile. Here, we report an electron-donor–mediated (EDM) mechanism that suppresses Mn³⁺-induced octahedral distortion while preserving high-spin functionality. As electron-donating Fe³⁺ and V³⁺ are incorporated, Mn³⁺ 3d electrons undergo partial delocalization. This electronic redistribution promotes orbital interactions between neighboring transition metal sites through the transition metal-oxygen framework, driving the e_g orbitals toward a more symmetric occupation and suppressing octahedral distortion. The EDM-modified cathode demonstrates a high energy density of 492.06 Wh kg⁻¹. It delivers 178.8 mAh g⁻¹ at 0.1 C and retains 80.2% of its capacity over 2000 cycles at 10 C, paving a novel pathway toward next-generation high-performance SIBs cathode materials.

INTRODUCTION

The urgent demand for sustainable, high-performance sodium-ion batteries has propelled manganese-based NASICON cathode materials into the research spotlight (1, 2). These materials integrate a three-dimensional (3D) open framework facilitating rapid sodium-ion conduction, manganese-enabled high operating voltage, and favorable economic viability (3, 4). Their path to achieving high energy density hinges critically on fully harnessing the multielectron redox reactions of Mn²⁺/Mn³⁺/Mn⁴⁺ (5). However, this advantage carries an inherent bottleneck: Activating this reaction process inevitably generates the Mn³⁺ (3d⁴) intermediate state (6). This state has intrinsic electronic asymmetry, with asymmetric e_g orbital occupancy directly inducing local symmetry breaking in the coordinating octahedra, subsequently triggering detrimental structural evolution and capacity decay under high operating voltages (7, 8). The central challenge is therefore to regulate orbital instability without sacrificing the multielectron redox activity required for high energy density. In the ideal state, Mn²⁺ ions (t_2g³e_g²) adopt a symmetric high-spin configuration, and the MnO₆ octahedra remain structurally intact and lattice-stable (Fig. 1A). During electrochemical cycling, Mn²⁺ is converted to Mn³⁺ (t_2g³e_g¹). The resulting asymmetric e_g occupancy and the associated high-spin orbital splitting drive an elongation of the MnO₆ octahedra along specific axes (Fig. 1B), consistent with predictions from Jahn-Teller theory for nonlinear systems with degenerate ground states, where geometric distortion lowers energy and eliminates orbital degeneracy (9). These localized distortions introduce internal strain and accumulate stress, thereby exacerbating lattice distortion, undermining structural stability, and promoting charge localization. In addition, Mn ion readily engages in coupled reactions with electrolyte species (10). This interaction drives its migration toward the interphase and its dissolution into the interfacial region. The above mechanisms—specifically the electronic structural evolution, lattice destabilization, and interfacial side reactions—significantly undermine the structural integrity of cathode materials. This structural integrity serves as a critical determinant of battery cycle life and overall electrochemical performance. Consequently, while activating manganese’s multielectron redox processes holds promise for enhancing energy density, this process inevitably induces structural degradation. Achieving synergistic optimization between high energy density and long-term cycling stability thus remains a persistent challenge.

Fig. 1. Mechanism of Mn³⁺-induced instability and stabilization via EDM orbital interactions.

(A) Ideal state of the Mn-rich NASICON framework. (B) Mn³⁺ causes asymmetric electron distribution and octahedral elongation. (C) Existing strategies partially relieve distortion. Electronic freedom is constrained. (D) EDM promotes electron delocalization between Mn³⁺ and transition metals, stabilizing the structure. (E) EDM stabilizes high-spin Mn³⁺ with symmetric orbital occupancy.

Thus far, several strategies have been proposed to mitigate the local structural instability associated with Mn³⁺. Microstructural design has been adopted, including nanosizing, hollow structures and conductive coatings (11–13). These measures relieve accumulated distortion and improve ion and electron transport. Elemental doping has also been used to tune the orbital-splitting energy (14, 15). Although these approaches improve cycling stability, they primarily mitigate the structural consequences of distortion rather than directly regulating its orbital origin. Therefore, achieving greater structural stability requires precise control of orbital energy levels and the spatial distribution of electrons. In this direction, electron-spin polarization (ESP) has shown distinctive promise in dopant regulation (Fig. 1C) (16–18). By aligning electron spins along defined orientations, ESP enables fine control of transition-metal spin states and offers a new way to reveal how spin-state tuning relates to orbital reconfiguration. To this end, recent studies have induced Mn³⁺ to switch from a high-spin state (t_2g³e_g¹) to a low-spin state (t_2g⁴e_g⁰) (19–21). This transition reduces the asymmetric occupation of the e_g orbital and achieves the more symmetric pattern of orbital filling. It slows the build-up of distortion and improves lattice stability on the local scale. However, this strategy still has inherent limitations. The spin-state transition is constrained by a substantial energy barrier, and the resulting low-spin configuration suppresses hopping-active electronic states. Consequently, although lattice distortion can be mitigated, the participation of Mn in multielectron redox reactions is reduced, ultimately compromising the achievable energy density.

Based on these insights, we propose an electron-donor–mediated (EDM) mechanism that stabilizes the redox-active Mn³⁺ state rather than suppressing it, thereby enabling high energy density while maintaining structural stability in Mn-based NASICON cathodes. The mechanism establishes intersite orbital interactions between the electron-donor sites and Mn³⁺ within the transition metal-oxygen framework, which regulate the local electronic environment of Mn³⁺ at the orbital level (Fig. 1, D and E). This interaction promotes partial electron delocalization and a more balanced orbital symmetry, effectively suppressing Mn³⁺-induced octahedral distortion and stabilizing the lattice. As a result, the distortion-prone Mn³⁺ electronic configuration becomes electronically stabilized without reducing its redox participation. We used Na₃MnTi(PO₄)₃ (denoted as P-MT) as a model system and introduced 3d transition-metal ions (Fe³⁺ and V³⁺) as electron-donating centers for comparison (denoted as EDM-MT), thereby constructing EDM sites capable of supplying d electrons. Density functional theory (DFT) calculations, together with x-ray absorption spectroscopy (XAS) measurements, support electronic interactions between the electron-donor transition-metal states and Mn³⁺, accompanied by redistribution of the local electronic environment. These results further support the proposed EDM-mediated orbital regulation and associated electron redistribution. The modified cathode simultaneously enhances both structural stability and energy density. The EDM-MT demonstrates a high energy density of 492.06 Wh kg⁻¹ and delivers 178.8 mAh g⁻¹ at 0.1 C. It retains 80.2% of its capacity after 2000 cycles at 10 C. The EDM-MT electrode also forms a more stable cathode-electrolyte interphase (CEI), which helps mitigate Mn³⁺ dissolution and interfacial degradation. The COMSOL simulations further reveal more uniform stress distribution and more coordinated Na⁺ migration during insertion and extraction. These results are consistent with improved lattice stability following EDM regulation. This study shows that EDM orbital interactions effectively reconcile the trade-off between structural stability and energy density, enabling the design of stable, high-performance Mn-based sodium phosphate cathodes.

RESULTS

Electron delocalization driven by EDM

To verify the orbital interactions mediated by electron donors, DFT + U calculations were carried out on P-MT and EDM-MT to account for the strong correlation of transition-metal 3d electrons. The spin-resolved density of states (DOS) reveals a more pronounced spin polarization in EDM-MT (Fig. 2A and fig. S1). The spin-split peaks below the Fermi level become sharper, while the asymmetry in the 0- to 4-eV region is more pronounced. This indicates the enhanced orbital coupling between transition-metal centers. The enhanced states near the Fermi level further indicate a redistribution of transition metal–derived electronic states in EDM-MT. The projected DOS (PDOS) results in Fig. 2B and figs. S2 and S3 further support this observation. In P-MT, Mn 3d orbitals dominate the electronic states near the Fermi level and exhibit clear spin splitting. In EDM-MT, the splitting becomes more evident, accompanied by a higher density of nonbonding electrons and a stronger magnetic response. Mn ions in both structures reside in octahedral coordination, where the 3d orbitals split into the lower-energy t_2g (d_xy, d_yz, and d_xz) and higher-energy e_g (d_z², d_x²-y²) levels. Figure 2C and fig. S4 provide the PDOS of Mn 3d states. In P-MT, the e_g-related orbital components (d_z²-like and d_x²-y²-like contributions) exhibit different intensities near the Fermi level, with a relatively higher contribution from the d_z² component. In EDM-MT, these e_g-related components show a more balanced distribution with reduced intensity variation near the Fermi level. This result suggests a redistribution of Mn 3d electronic states and a reduced orbital asymmetry after EDM regulation. Meanwhile, the reduced Ti 3d splitting implies a more symmetric Ti–O environment in EDM-MT (figs. S5 and S6). As shown in Fig. 2D, the DOS overlap among Mn, Fe, and V states in the energy range of −4 to 0 eV indicates electronic interactions between neighboring transition metal states, suggesting electron redistribution and orbital complementation across the metal centers. Bader charge analysis further reveals a net electron enrichment at the Mn sites after Fe/V incorporation (tables S1 and S2). The average Bader electron population of Mn increases by 0.0574 e per Mn in EDM-MT, providing quantitative support for the electron-donor–mediated redistribution inferred from the orbital-resolved DOS. Figure 2E presents the calculated magnetic moments of the transition metals. Mn retains ∼4.6 μB in both systems, with a notably tighter distribution in EDM-MT, implying a more symmetric local environment and stabilized electronic state. Ti moments diminish to nearly zero, suggesting stabilization of Ti⁴⁺. V adopts a high-spin configuration, while Fe shows an antiparallel moment relative to Mn, indicative of antiferromagnetic coupling. Collectively, Fe and V increase magnetic complexity and reinforce the electronic stability of the Mn-centered network. Last, the calculated Mn–O bond lengths (tables S3 and S4) show a slight variation in EDM-MT due to local electronic redistribution. ICOHP analysis (Fig. 2F) reveals a subtle adjustment in Mn–O bonding character, reflecting a more balanced electronic environment driven by partial electron delocalization between Mn and Fe/V centers, which mitigates orbital overlocalization and strengthens lattice stability.

Fig. 2. Electronic structure and crystallographic characterization of EDM-MT and P-MT electrodes.

(A) TDOS for EDM-MT and P-MT. (B) Mn 3d PDOS for P-MT and EDM-MT. (C) PDOS of Mn 3d orbitals in EDM-MT showing t_2g and e_g contributions. (D) Element-resolved PDOS of Mn, Fe, and V in EDM-MT. (E) Calculated magnetic moments of transition metal ions. (F) ICOHP analysis of Mn–O bonds. (G) XRD pattern and Rietveld refinement of EDM-MT.

Spin state and structural optimization

To experimentally validate the theoretical predictions, EDM-MT and P-MT were synthesized via a sol-gel method. XRD patterns show no detectable crystalline impurities in either sample (fig. S7). Further Rietveld refinement shows EDM-MT crystallizes in a rhombohedral NASICON-type structure (space group R-3c), consistent with the theoretical prediction. The refined lattice parameters (a = b = 8.8615 Å, c = 21.7269 Å, and V = 1477.6 ų) and low residuals support the high structural integrity and phase purity of the sample (Fig. 2G and table S5). The morphology of the materials was characterized by scanning electron microscopy (figs. S8 and S9). P-MT consists of irregular micron-scale secondary particles with noticeable aggregation, whereas EDM-MT exhibits smaller and more uniformly distributed particles formed by aggregated nanosized grains. High-resolution transmission electron microscopy (HRTEM) images of EDM-MT (fig. S10) show clear and ordered lattice fringes with an interplanar spacing of 0.31 nm, corresponding to the (024) plane. The corresponding fast Fourier transform pattern shows distinct diffraction spots, consistent with a well-ordered crystalline lattice. Elemental energy-dispersive x-ray mapping performed by TEM shows the uniform distribution of all constituent elements in both P-MT and EDM-MT (figs. S11 and S12). The carbon contents of the as-synthesized P-MT and EDM-MT powders were quantified using carbon, hydrogen, and nitrogen (CHN) elemental analysis (fig. S13).

Magnetic measurements were performed using a vibrating sample magnetometer (VSM) to investigate the spin-electron configurations of the transition metal centers. As shown in Fig. 3A and fig. S14, both P-MT and EDM-MT exhibit linear M-H responses without detectable hysteresis, consistent with paramagnetic behavior at room temperature. Compared with P-MT, EDM-MT exhibits a slightly steeper slope, consistent with its larger effective magnetic moment (μ_eff = 5.93μ_B) determined from Curie-Weiss fitting (22). This enhancement reflects the modified magnetic environment of the transition metal centers after EDM regulation, which involves the combined contributions from Mn, Fe, and V species. These electronic interactions may contribute to partial electron redistribution and a modified spin environment within the MnO6 framework. Electron paramagnetic resonance (EPR) spectra (Fig. 3B) provide additional information regarding the spin environment and electronic interactions within the transition metal framework. Both samples exhibit a dominant resonance at g ≈ 2.02, which is close to the free-electron value and is associated with transition metal–related paramagnetic centers and electronic interactions. This behavior is consistent with enhanced Mn-O covalency and strengthened intersite orbital interactions within the transition metal-oxygen framework. In EDM-MT, an additional weak resonance emerges at g ≈ 4.20, characteristic of high-spin Fe³⁺ centers located in low-symmetry fields with significant zero-field splitting. The presence of this feature indicates electronic interactions between Fe and the surrounding transition metal environment. The increased intensity and broadened linewidth suggest enhanced spin interactions among transition metal centers, providing additional support for the electronically modified transition metal environment predicted by DFT. To further elucidate the local electronic and coordination structures, XAS measurements were performed. The Mn K-edge x-ray absorption near-edge structure (XANES) spectra (Fig. 3C) of P-MT and EDM-MT lie between those of MnO and Mn₂O₃, indicating mixed-valence Mn^2+/3+ states in both samples. The absorption edge of EDM-MT is slightly shifted toward higher energy compared with that of P-MT, suggesting a modest increase in the Mn³⁺ fraction, consistent with charge redistribution governed by the EDM process. The Ti K-edge XANES spectra of both samples remain nearly unchanged, closely resembling that of Ti⁴⁺ (Fig. 3D). Extended x-ray absorption fine structure (EXAFS) analysis was performed to determine the local coordination environment of Mn in P-MT and EDM-MT. The Fourier-transformed k²χ(k) spectra (Fig. 3E) exhibit two dominant peaks corresponding to Mn–O and Mn–O–Fe scattering paths. In both samples, the first shell at ∼1.5 Å is attributed to Mn–O coordination. For EDM-MT, the Mn-O peak shifts slightly toward a longer distance (from 1.50 to 1.56 Å), suggesting a moderate relaxation of the Mn–O bond resulting from enhanced electron delocalization. The second-shell feature near ∼2.6 Å can be well reproduced using a Mn–O–Fe scattering path, suggesting the presence of Fe-associated local structural correlation around Mn sites. The Fe-associated second-shell contribution supports a local structural correlation between Mn and Fe sites within the transition metal framework. It should be noted that the radial distance obtained from FT-EXAFS is phase-uncorrected and therefore appears shorter than the corresponding crystallographic interatomic distance (23, 24). The presence of this Mn–O–Fe scattering contribution reflects the local structural correlation between Mn and Fe induced by EDM interactions. Fitting results of the EXAFS spectrum (Fig. 3F and fig. S15) further support the presence of Fe atoms in the second coordination shell around Mn (25, 26). The k²χ(k) oscillations of P-MT and EDM-MT exhibit similar periodicity, while the variation in oscillation amplitude reflects changes in the local coordination environment and structural disorder after EDM regulation (figs. S16 and S17). To further probe the Mn 3d electronic structure, Mn L-edge XAS measurements were performed. As shown in fig. S18, the L₃ edge consists of a dominant t_2g-related feature together with an e_g-related shoulder. Compared with P-MT, EDM-MT exhibits a reduced t_2g spectral intensity and a higher relative e_g/t_2g spectral ratio, indicating redistribution of Mn 3d electrons toward a more balanced orbital electronic configuration. Moreover, the lower L₃/L₂ branching ratio suggests a more stabilized local Mn electronic structure, which is consistent with a more symmetric distribution of Mn 3d electrons. The Ti K-edge EXAFS spectra and fitting results (figs. S19 to S22) reveal an intensified and left-shifted Ti–O peak for EDM-MT, indicating a contracted coordination environment and a structural response to EDM interactions. Wavelet transform (WT) analyses (Fig. 3, G and H, and fig. S23) elucidate the local structural evolution driven by EDM interactions. P-MT shows a single Mn-O signal at k ≈ 4 Å⁻¹ and R ≈ 1.5 Å, whereas EDM-MT displays an additional feature at k ≈ 3.8 Å⁻¹ and R ≈ 2.6 Å, assigned to a Mn-Fe scattering contribution in the second coordination shell. In contrast, metallic Mn exhibits a characteristic Mn-Mn signal at k ≈ 6 Å⁻¹ and R ≈ 2.3 Å, thereby ruling out the possibility that the new feature originates from Mn–Mn scattering. Spectral fitting (table S6) reveals the presence of Fe atoms in the second coordination shell around Mn, with a fitted distance of ≈3.27 Å and a coordination number of 1.98 in EDM-MT, accompanied by a slight decrease in the Mn-O coordination number. These results indicate an Fe-associated second-shell environment around Mn, providing local structural context for the EDM-induced electronic redistribution. Ti K-edge WT maps (figs. S24 and S25) display prominent Ti–O and Ti–O–Ti features for both P-MT and EDM-MT, consistent with TiO₂, indicating that Ti retains its octahedral coordination. Spectral fitting (table S7) reveals nearly unchanged Ti–O bonding parameters, indicating that the Ti environment remains structurally stable during the EDM process. The refined parameters show only moderate correlations, with no near-unity correlation coefficients (table S8), supporting the stability of the EXAFS fitting results.

Fig. 3. Magnetic, local electronic structure, and electrochemical characterization of P-MT and EDM-MT.

(A) M-H curves of P-MT and EDM-MT. (B) EPR spectra. (C and D) Mn and Ti K-edge XANES. (E and F) EXAFS and fitting results. (G and H) Wavelet transform maps of Mn K-edge. (I) Initial charge-discharge profiles.

Electrochemical properties and Na⁺ migration kinetics

To provide evidence that the EDM effectively balances energy density and structural stability, the performance of the EDM-modified material was examined in coin cells using metallic sodium as the counter electrode over a voltage range of 1.5 to 4.3 V (versus Na⁺/Na) at room temperature. At 0.1 C (1 C = 176 mAh g⁻¹), Fig. 3I illustrates that EDM-MT delivers a discharge capacity of 178.8 mAh g⁻¹, higher than P-MT (159.6 mAh g⁻¹), corresponding to an energy density of 492.06 Wh kg⁻¹ versus 443.92 Wh kg⁻¹. The extended discharge plateau and reduced voltage hysteresis contribute to this enhanced energy density. Independent EDM-MT cells exhibit highly consistent Initial charge-discharge profiles, confirming the reproducibility of the electrochemical performance (fig. S26). To evaluate the influence of compositional variation, two control samples with the same Na content, Na_3.5MnTi_0.5Fe_0.5(PO₄)₃ and Na_3.5MnTi_0.5V_0.5(PO₄)₃, were synthesized. Their discharge capacities are 128.38 and 154.62 mAh g⁻¹, respectively, both lower than that of EDM-MT (178.8 mAh g⁻¹) (fig. S27). The result suggests that the improved electrochemical performance is not simply caused by Na-content variation or the introduction of a single Fe or V dopant. The superior performance of EDM-MT is associated with the cooperative effect of Fe and V in the EDM configuration. The redox mechanisms underlying this improvement were then analyzed, and the corresponding profiles are presented in fig. S28. Both electrodes display three distinct redox couples associated with Ti^3+/4+, Mn^2+/3+ (V^3+/4+), and Mn^3+/4+ (V^4+/5+) transitions, highlighting the multielectron redox activity of Mn. The quantitative analysis further reveals the contributions of each redox region: Region I (3.7 to 4.3 V), corresponding to the Mn^3+/4+ (V^4+/5+) couples, contributes 19.7 mAh g⁻¹; region II (2.2 to 3.7 V), associated with Mn^2+/3+ (V^3+/4+) redox, contributes 92.32 mAh g⁻¹; and region III (1.5 to 2.2 V), corresponding to the Ti^3+/4+ couple, contributes 66.78 mAh g⁻¹. For comparison, the corresponding capacities of P-MT in regions I, II, and III are 23.99, 69.56, and 66.13 mAh g⁻¹, respectively. The increased capacity in region II mainly arises from the overlapping Mn^2+/3+ and V^3+/4+ redox processes. Considering that the V content is relatively limited and mainly substitutes for Ti, which is also electrochemically active in P-MT, the capacity enhancement cannot be attributed solely to V redox. Instead, it should be understood as arising from the combined effects of substitution-induced redox activity and the EDM-regulated electronic structure. The EDM regulation enhances the reversibility of the coupled Mn/V redox reactions and stabilizes Mn chemistry during cycling. Notably, EDM-MT exhibits sharper peaks and lower polarization, indicating enhanced redox reversibility that corresponds to its improved discharge performance. These results link the high energy density of EDM-MT to the reversible multielectron redox activity of Mn while retaining structural integrity. The influence of this redox reversibility on rate capability was subsequently evaluated. Figure 4A shows that EDM-MT delivers significantly superior rate performance. Even at 20 C, EDM-MT retains 89.78 mAh g⁻¹ compared with 70.35 mAh g⁻¹ for P-MT, reflecting its improved high-rate kinetics. The galvanostatic charge-discharge profiles (fig. S29) show that EDM-MT maintains well-defined and stable voltage plateaus across all rates, indicating robust structural stability and highly reversible Na⁺ intercalation. In contrast, P-MT shows pronounced plateau collapse, particularly at high rates, reflecting greater polarization and sluggish reaction kinetics. Moreover, the Mn^2+/3+ redox plateau is nearly absent in P-MT, reflecting pronounced structural changes and reduced reversibility. Together, these features point to a more stable local coordination environment in EDM-MT. This stabilization preserves the characteristic redox features and improves the kinetic stability at high rates. Complementarily, Fig. 4B reveals that EDM-MT sustains a higher operating voltage and energy output while maintaining superior efficiency and capacity retention at elevated rates. Overall, EDM-MT delivers consistently improved electrochemical performance across a broad range of operating conditions. The broader comparison in the Ragone plot (Fig. 4C) highlights the notion that EDM-MT achieves a well-balanced energy-power relationship, delivering both high energy and power densities surpassing those of most reported NASICON-type cathodes (11, 27–32). To further evaluate the contribution of the high-voltage Mn redox process, the electrochemical performance was also assessed within the practical voltage window of 2.5 to 4.3 V (fig. S30). EDM-MT delivers a discharge capacity of 99.45 mAh g⁻¹ with an energy density of 338.85 Wh kg⁻¹, markedly higher than those of P-MT (54.63 and 184.29 Wh kg⁻¹). These results indicate that EDM regulation enhances the utilization of the Mn redox chemistry even within the high-voltage region. To evaluate whether the electrode can effectively balance energy density and structural stability over long-term cycling, long-term performance was evaluated at 10 C, as shown in Fig. 4D. EDM-MT retains 80.2% of its initial capacity after 2000 cycles and maintains 63.9% even after 4000 cycles, whereas P-MT suffers from rapid capacity fading and structural degradation within 3000 cycles. A slight capacity decay during extended cycling is possibly associated with electrolyte consumption and anode-side interfacial side reactions. In addition, Fig. 4E compares EDM-MT with other reported NASICON-type and Mn-rich phosphate cathodes, revealing its outstanding long-term cycling performance (33–39). These results show that EDM regulation enables high energy density to be achieved without compromising long-term cycling performance, effectively balancing the competing demands of capacity and structural stability. To further elucidate the intrinsic reaction kinetics of the electrode, multirate cyclic voltammetry (CV) measurements were conducted within the voltage window of 1.5 to 4.3 V at scan rates ranging from 0.1 to 1.0 mV s⁻¹. Figure S31 indicates that both electrodes display three well-defined pairs of redox peaks, which correspond to the sequential Na⁺ insertion/extraction processes at A1/C1, A2/C2, and A3/C3. With increasing scan rate, the peak currents (i_p) increase proportionally while retaining nearly identical peak shapes, thereby indicating highly reversible Na⁺ intercalation behavior. The EDM-MT electrode exhibits sharper and more symmetric redox peaks with reduced peak separations. These features indicate lower polarization and faster reaction kinetics compared with P-MT. The linear relationship between i_p and ν^1/2 is consistent with diffusion-controlled redox kinetics according to the Randles-Ševčík relation (fig. S32). The apparent Na⁺ diffusion coefficients (D_app,Na+) for the three redox regions (A1-C3) were calculated from the slopes of the linear fits as shown in Fig. 4F. Among these regions, the most pronounced enhancement occurs at the Mn^2+/3+ redox couple (A2/C2), which serves as the primary contributor to the overall capacity. The enhanced Na⁺ transport kinetics in the A2/C2 region arise from the EDM induced modulation of the local electronic environment and lattice dynamics. This modulation enables faster charge compensation and reduces polarization. As a result, the intrinsic reaction reversibility of the EDM-MT electrode is improved. Galvanostatic intermittent titration technique (GITT) measurements were subsequently carried out to evaluate Na⁺ transport, and the corresponding potential responses and diffusion coefficients are shown in Fig. 4G. Throughout both the charge and discharge processes, EDM-MT exhibits smoother potential relaxation and smaller overpotential fluctuations than P-MT, indicating a lower migration barrier for Na⁺ transport. The apparent diffusion coefficients (D_app,Na+) of both materials fall within the range of 10⁻⁹ to 10⁻¹¹ cm² s⁻¹; however, a distinct difference emerges in the high-voltage region. EDM-MT maintains higher and more stable D_app,Na+ values at elevated potentials, whereas P-MT exhibits pronounced fluctuations and repeated drops in D_app,Na+. This suggests that the EDM-MT framework provides more continuous pathways for ion migration, effectively mitigating the structural and electronic limitations that arise at high potentials. To further assess the practical applicability of the EDM strategy, full sodium ion cells were assembled using hard carbon (HC) as the anode. The EDM-MT//HC cell delivers an initial discharge capacity of 162.26 mAh g⁻¹ at 0.1 C and maintains 73.33 mAh g⁻¹ even at 20 C, demonstrating good rate capability under practical configurations. Although the relatively low cutoff voltage window restricts the maximum energy density, the full cell still exhibits stable cycling performance, with a capacity of 85.27 mAh g⁻¹ retained after 300 cycles at 2 C, demonstrating its long-term reliability. The corresponding Ragone analysis further highlights the balanced energy-power characteristics of the full cell (fig. S33) (11, 40–43).

Fig. 4. Electrochemical performance and Na⁺ transport kinetics of P-MT and EDM-MT.

(A) Rate capability. (B) Radar chart comparing overall electrochemical performance. (C) Ragone plot. (D) Long cycling performance at 10 C. (E) Comparison with reported NASICON-type and Mn-rich phosphate cathodes. (F) D_app,Na+ derived from multi-rate CV for three redox regions. (G) GITT profiles and corresponding D_app,Na+ during charge and discharge.

Na-storage mechanism and Mn³⁺ electronic-structure stabilization

In situ XRD was performed over the 2θ range of 18° to 38° to monitor the structural evolution of P-MT and EDM-MT during Na⁺ extraction and insertion (Fig. 5A). The characteristic reflections (104), (113), (024), (211), and (300) display smooth and continuous peak shifts throughout cycling. These continuous peak shifts are characteristic of a predominantly solid-solution reaction pathway over most of the voltage window. The diffraction patterns also show brief two-phase behavior. The (104) reflection near 20.3° undergoes transient splitting, whereas the (211) reflection near 32° shows a reversible merging-separation process. A pronounced contrast emerges between the two materials at full charge. P-MT shows distinct peak distortion and irregular peak trajectories in the circled regions, indicating lattice instability associated with Mn³⁺. In comparison, EDM-MT maintains smooth, reversible, and continuous peak evolution, highlighting a more stable and coherent lattice framework during cycling. This stability reflects the role of EDM in reducing local distortion while preserving the high-spin configuration. The lattice parameters reveal the structural evolution during cycling (Fig. 5, B and C). In both materials, the a axis contracts during Na⁺ extraction and expands on insertion, with P-MT showing a 4.25% change and EDM-MT a slightly smaller 3.93% change. The lattice change arises from the deformation of the corner-sharing MO₆ octahedra and PO₄ tetrahedra that define the lateral dimensions of the NASICON framework. The c axis changes only minimally, indicating the 3D framework remains stable throughout the charge-discharge process. The overall cell volume evolution follows the same trend. P-MT exhibits a maximum cell volume change of 8.3% relative to the initial state, whereas EDM-MT shows a reduced maximum change of 7.65%. Both materials maintain reversible lattice variation, while the smaller amplitude observed in EDM-MT indicates mitigated structural fluctuation during Na⁺ migration. This behavior reflects the role of EDM in moderating local distortions associated with the Mn²⁺/Mn³⁺ transition. Since lattice-parameter variation during repeated sodiation and desodiation inevitably induces internal strain due to transient mismatch between differently sodiated regions, excessive structural fluctuation can lead to heterogeneous strain accumulation and localized stress concentration upon prolonged cycling. The reduced lattice and volume variation in EDM-MT therefore implies a more uniform strain evolution, which is expected to alleviate local stress build-up and decrease the mechanical driving force for microstructural degradation. In situ XRD results and lattice-parameter evolution show that EDM-MT undergoes markedly weaker structural perturbation during Mn oxidation, implying that the local electronic environment of Mn³⁺ is modified in a way that suppresses the instability. As the structural instability is fundamentally governed by the electronic configuration of high-spin Mn³⁺, the electronic structure analysis is required to elucidate the origin of stabilization. To directly probe the local structural evolution of the MnO₆ octahedra, Mn K-edge EXAFS measurements were further performed at the OCV state and after charging to 3.8 V, corresponding predominantly to the Mn²⁺ and Mn³⁺ states, respectively. As shown in fig. S34, the Mn-O coordination environment of EDM-MT changes only slightly during the Mn²⁺/ Mn³⁺ redox process, whereas a more pronounced variation is observed for P-MT. EXAFS fitting further reveals that the Mn–O bond length exhibits a much smaller change in EDM-MT after charging (table S9). The suppressed variation of the local Mn–O coordination environment indicates that the EDM strategy effectively stabilizes the MnO₆ octahedra during Mn³⁺ formation, thereby alleviating local Jahn-Teller distortion. Ex situ x-ray photoelectron spectroscopy (XPS) was used to track the oxidation-state evolution of Mn, Ti, Fe, and V during cycling (figs. S35 to S38). All transition metals show reversible redox behavior, suggesting a cooperative multication charge compensation mechanism throughout Na⁺ extraction/insertion. The highly reversible Mn redox further supports stabilization of the Mn-centered charge-compensation process under EDM regulation. On this basis, spin-polarized DFT calculations were performed on the desodiated models corresponding to the Mn²⁺ → Mn³⁺ oxidation state to examine the changes in DOS and metal-oxygen bonding characteristics. The spin-polarized total density of states D-MT (the desodiated form of P-MT) and D-EDM-MT (the desodiated form of EDM-MT) is shown in Fig. 5D. In the occupied region immediately below the Fermi level, D-MT exhibits higher intensity and more pronounced DOS features, reflecting stronger localization of Mn-derived states upon oxidation to Mn³⁺. By contrast, D-EDM-MT presents the smoother occupied-state distribution and displays a distinct unoccupied peak just above the Fermi level. The reduced localization of occupied states, together with the more defined unoccupied-state contribution, indicates enhanced electronic delocalization around Mn³⁺ in D-EDM-MT. This enhanced delocalization mitigates orbital symmetry breaking associated with Mn³⁺. Figure 5E together with figs. S39 and S40 provides the PDOS of the desodiated models. The PDOS shows the basic splitting is present in both models, but the degree of splitting and the orbital occupancies differ markedly. In D-MT, the e_g-related region, particularly the d_z²-like component, displays a pronounced occupied-state contribution immediately below the Fermi level, while the d_x²-y²–like component shows a relatively different distribution. This indicates an increased asymmetry of e_g-related orbital contributions under Mn oxidation. These features are characteristic of a high-spin d⁴ Mn³⁺ configuration with pronounced orbital asymmetry and a strong propensity for local distortion. They agree with the previously observed Mn─O bond-length anisotropy and the larger local magnetic moments. In contrast, D-EDM-MT exhibits a more balanced distribution of d-orbital–derived states. The d_z²-like and d_x²-y²–like components show closer energetic features and reduced intensity difference near the Fermi level. This redistribution suggests a moderated orbital asymmetry and a more homogeneous local electronic environment. The PDOS results indicate that interactions among neighboring transition metal states enhance d-electron delocalization, preserve the high-spin configuration, and reduce orbital asymmetry, thereby mitigating Mn³⁺-associated distortion. Element PDOS (Fig. 5F) shows that both Fe and V contribute mainly low-energy occupied d states, with Fe displaying the stronger intensity. These donor-derived states further promote intersite electronic coupling and reduce local electronic instability. The MnO₆ octahedron in D-EDM-MT exhibits a notably narrower Mn–O bond-length distribution compared with D-MT (tables S10 and S11), indicating a more uniform local coordination environment. In contrast, D-MT exhibits a much broader Mn–O bond-length span, including pronounced long-short pairs, suggesting pronounced local lattice strain. Ti PDOS changes little in the two models (fig. S41), indicating minimal involvement in the Mn-related electronic rearrangement. The magnetic moments further corroborate the electronic and structural trends described above. As summarized in table S12, Mn sites in D-EDM-MT exhibit systematically larger local magnetic moments than those in D-MT. The higher absolute moments indicate that Mn retains a more robust high-spin configuration after oxidation. The Mn moments in Fig. 5G follow the same trend, with both Mn²⁺ and Mn³⁺ retaining higher values in EDM-MT, consistent with the stabilization of the high-spin state during the Mn^2+/3+ transition. The COHP analysis of the desodiated Mn–O bonds (Fig. 5H) reveals distinct bonding responses in the two structures. D-MT exhibits a more pronounced redistribution of Mn–O bonding states upon desodiation, together with stronger energy-dependent variations near the Fermi level. By contrast, D-EDM-MT shows a more moderate bonding response, consistent with its reduced orbital asymmetry and narrower Mn–O bond-length distribution. The corresponding ICOHP values further indicate that EDM regulation modifies the overall Mn–O bonding interaction rather than simply strengthening the bond, in line with the more homogeneous local coordination environment of D-EDM-MT.

Fig. 5. Structural and electronic evolution of P-MT and EDM-MT.

(A) In situ XRD pattern. (B and C) Lattice parameters (a, c) and cell volume changes during cycling. (D) TDOS of desodiated D-MT and D-EDM-MT. (E) PDOS of Mn d-orbitals in desodiated models. (F) Element-resolved PDOS of Mn, Fe, and V. (G) magnetic moments of Mn²⁺ and Mn³⁺. (H) ICOHP analysis of Mn–O bonds.

Interfacial stability enabled by EDM regulation

To clarify whether the reduced lattice fluctuation in EDM-MT leads to more uniform stress evolution during prolonged cycling, detailed interfacial characterization was performed. By stabilizing the bulk electronic structure and suppressing Mn-centered distortions, the EDM strategy is expected to promote a more ordered and stable interfacial chemistry. To probe this linkage between bulk structural robustness and interfacial evolution, depth-resolved XPS was conducted on electrodes after 200 cycles at 2 C to analyze the chemical composition and spatial distribution of the CEI (Fig. 6A). Peak fitting was performed using a consistent fitting protocol with identical peak assignments and background functions. Minor variations in peak position and full width at half maximum (FWHM) were allowed within physically reasonable ranges to account for local chemical evolution and sputtering-induced effects during depth profiling. The depth-resolved C 1s spectra reveal distinct CEI compositions in the two electrodes. Across all probed depths, EDM-MT consistently exhibits a higher O–C=O fraction than P-MT, indicating a greater contribution from inorganic carbonate species (table S13).

Fig. 6. Interfacial characterization in P-MT and EDM-MT.

(A) Depth-profiling XPS spectra of C 1s and F 1s for electrodes after 200 cycles at 2 C. (B) High-resolution TEM images of the CEI, with EDM-MT on top and P-MT on bottom. (C) GPA of strain distribution for the cycled electrode, with EDM-MT on top and P-MT on bottom. (D) AFM topography of cycled electrodes. (E and F) COMSOL simulations of Na⁺ concentration and corresponding local stress.

The similar trend appears in the F 1s region, where Na–F (∼684.5 eV) dominates the EDM-MT CEI at all depths, while the organic C–F component (∼687.2 eV) is nearly absent (table S14). In contrast, P-MT retains a noticeable C–F signal near the surface, indicating the persistence of organic decomposition products. These depth-dependent profiles reveal a more inorganic-rich CEI on EDM-MT, with a higher proportion of inorganic carbonate and Na–F species across the probed depths. Consistently, high-resolution TEM (Fig. 6B) reveals more uniform and compact CEI on EDM-MT, whereas P-MT develops a thicker, more heterogeneous, and structurally disordered interphase. Geometric phase analysis (GPA) (Fig. 6C) further reveals this difference: EDM-MT maintains a low and spatially uniform strain field near the surface even after extended cycling, indicating effective mitigation of interfacial stress and suppression of lattice distortion. In contrast, P-MT exhibits pronounced strain localization, reflecting accumulated mechanical mismatch between the CEI and the bulk arising from repeated elongation and contraction of MnO₆ units. Atomic force microscopy (AFM) (Fig. 6D) was further used to probe the surface topography of the cycled electrodes. EDM-MT shows a comparatively smoother surface after 200 cycles, with both Rq and Ra significantly lower than those of P-MT. By contrast, P-MT exhibits greater surface roughness, consistent with accumulated Mn³⁺-centered lattice distortion and a less uniform CEI formed during cycling. The combination of more uniform Na⁺ distribution and lower lattice strain in EDM-MT translates into a more homogeneous local stress field, explaining the experimentally observed suppression of interfacial damage and crack formation compared with P-MT. To directly quantify transition metal dissolution during cycling, inductively coupled plasma mass spectrometry measurements were performed on the electrolytes collected after 100 cycles at 2 C. The Mn concentration detected in the electrolyte of the P-MT cell reached 9.33 mg liter⁻¹, whereas only 0.47 mg liter⁻¹ was detected for EDM-MT. The substantially reduced Mn dissolution indicates enhanced interfacial stability in EDM-MT during prolonged cycling (fig. S42). To examine the ion transport and stress evolution associated with the experimentally observed structural differences, 3D finite-element simulations were performed using COMSOL Multiphysics. In this model, each electrode particle was approximated as a spherical geometry with a diameter of ∼1 μm, and a constant current density (5 A m⁻²) was applied to simulate Na⁺ insertion under operating conditions. All transport and reaction parameters were adopted from experimentally determined values (table S15). As shown in Fig. 6E, the normalized Na⁺ concentration represented by the state of sodiation remains much more uniformly distributed in EDM-MT at all sodiation levels (20 to 80%), while P-MT develops pronounced concentration gradients. This more homogeneous Na⁺ distribution is accompanied by a substantially more uniform local stress field (Fig. 6F). Although localized stress develops in EDM-MT at high states of sodiation, its overall stress distribution remains substantially more uniform than that of P-MT, which exhibits pronounced stress concentration. The more homogeneous ion-transport and stress evolution in EDM-MT aligns with the experimentally observed improvements in structural integrity and electrochemical stability.

DISCUSSION

In this work, the EDM mechanism provides a new perspective for regulating the electronic structure of Mn-based NASICON cathodes. Rather than relying solely on conventional strategies such as compositional substitution or lattice strain engineering, EDM promotes oxygen-mediated orbital interactions within the transition metal-oxygen framework, enabling partial electron redistribution among Fe/V and Mn sites. This electronic interaction promotes a more balanced distribution of e_g-related orbital contributions of Mn. As a result, the local coordination environment becomes more symmetric, which stabilizes the MnO₆ octahedra and suppresses the accumulation of lattice strain during repeated Na⁺ insertion and extraction. The orbital-level regulation has broader implications for the design of high-energy phosphate cathodes. In many Mn-rich systems, achieving high capacity often requires activating multielectron redox reactions, which inevitably increases structural distortion and mechanical stress. These results show that tuning intersite electronic interactions can mitigate Mn-centered distortion while preserving redox activity, thereby alleviating the trade-off between energy density and structural stability. The resulting homogenization of Na⁺ diffusion and stress distribution suggests that orbital engineering may represent a viable pathway to regulate coupled electrochemical-mechanical behavior in polyanionic frameworks. Nevertheless, several limitations should be considered. The present study mainly focuses on a specific Fe/V-Mn interaction environment, and the universality of the EDM mechanism across other transition metal combinations remains to be systematically explored. The strategy may be extended to other NASICON or polyanionic cathodes and combine EDM regulation with interface engineering or electrolyte optimization to further enhance practical performance. Overall, the EDM concept highlights the importance of orbital-level electronic interactions in stabilizing high-energy Mn-based cathodes. This approach provides a new design principle for balancing energy density, structural stability, and ion transport in sodium-ion battery materials.

MATERIALS AND METHODS

Access to reagents and raw materials

The EDM-MT cathode materials were prepared by a sol-gel method. The sodium carbonate (Na₂CO₃, A.R., 99%, Tianjin Guangfu Chemical Reagent), dihydroxybis (ammonium lactato) titanium solution [C₆H₁₈N₂O₈Ti, A.R., 50 weight % (wt %) in water, Aladdin], manganese acetate tetrahydrate [Mn(CH₃COO)₂·4H₂O, A.R., 99%, Macklin], ammonium dihydrogen phosphate (NH₄H₂PO₄, A.R., 99%, Macklin), citric acid monohydrate (C₆H₈O₇·H₂O, A.R., 99%, Aladdin), iron nitrate [Fe(NO₃)₃, A.R., 99%, Macklin], and vanadyl sulfate (VOSO₄, A.R., 99%, Macklin) were used as raw materials. First, Mn(CH₃COO)₂·4H₂O, Fe(NO₃)₃, and vanadyl sulfate VOSO₄ were dispersed in 15 ml of deionized water (A solution). After it completes dissolution, the stoichiometric amount of C₆H₁₈N₂O₈Ti solution was added into A solution while stirring at 80°C. Then, the saturated citric acid solution prepared by C₆H₈O₇·H₂O was added into the above solution drop by drop to ensure full chelation with metal ions and the formation of gels (B solution). The molar ratio of V:Fe:Ti:Mn was 0.35:0.15:0.5:1. Citric acid served as both the chelating agent and carbon source. After stirring 10 min, the 15-ml solution of dissolved NH₄H₂PO₄ and Na₂CO₃ was added into the B solution. When deionized water was evaporated at 80°C, sol was converted into gel. The wet gel was dried at 120°C for 12 hours in a vacuum oven to form dry gel. Last, the final compound Na_3.5MnTi_0.5V_0.35Fe_0.15(PO₄)₃ (EDM-MT) was obtained by annealing for 12 hours at 600°C under argon atmosphere. The Na₃MnTi(PO₄)₃(P-MT) sample was prepared via the same progress without the Fe(NO₃)₃ and VOSO₄. For comparison, Na_3.5MnTi_0.5Fe_0.5(PO₄)₃ and Na_3.5MnTi_0.5V_0.5(PO₄)₃ control samples were synthesized using the same procedure by replacing the Fe/V precursor combination with stoichiometric amounts of Fe(NO₃)₃ or VOSO₄, respectively.

Material characterization

X-ray diffraction (XRD) patterns were collected using a Bruker D8 Advance diffractometer with Cu Kα radiation (λ = 0.15418 nm) over a 2θ range of 10° to 80°. Morphology, elemental distribution, and particle size were characterized by scanning electron microscopy (SEM, Hitachi SU8000) and HRTEM (JEOL-2100F, 200 kV) equipped with energy-dispersive x-ray spectroscopy. Valence states of the prepared EDM-MT and P-MT material were determined through XPS analysis conducted on an ESCALab 220i-XL electron spectrometer from VG Scientific using Al Kα radiation at 300-W power level. The XPS spectra were calibrated using the C–C component of the C 1s spectrum at 284.8 eV. The Shirley background subtraction method was applied for all spectra. The same peak assignment and fitting strategy were applied to all spectra collected at different etching depths. During fitting, the peak positions and FWHM were constrained within reasonable ranges based on the corresponding chemical states. Charge correction was performed before analysis, and identical Ar⁺ sputtering conditions were applied for all depth profiles. EPR (Bruker A300-10/12, Germany) was used to detect the type and intensity of defects in the sample. XAFS spectroscopy measurements were performed in transmission mode on a RapidXAFS 2 M instrument (Anhui Absorption Spectroscopy Analysis Instrument Co. Ltd.) operating at 20 kV and 20 mA using a Si (531) spherically bent crystal analyzer with a 500-mm radius of curvature. Mn L-edge XAS measurements were carried out in the total electron yield mode at the BL20U2 beamline of the Shanghai Synchrotron Radiation Facility. The spectra were calibrated using the standard beamline energy calibration procedure. Magnetic properties were measured with a SQUID-VSM magnetometer (MPMS-3 system, Quantum Design, USA). The carbon contents of the as-synthesized P-MT and EDM-MT powders were quantified by CHN and sulfur (CHNS) elemental analysis using an EA3000 elemental analyzer (EuroVector, Italy).

Electrochemical performance tests

The working electrodes were prepared by mixing 70 wt % active material (EDM-MT or P-MT), 20 wt % Ketjen black (KB), and 10 wt % sodium alginate (SA) in deionized water to form a homogeneous slurry, which was coated onto carbon-coated aluminum foil and dried in a vacuum oven at 60°C overnight. The average mass loading of the active material was ∼1.3 mg cm⁻². CR2032-type coin cells were assembled in an argon-filled glove box using sodium metal as the counter and reference electrode and a glass fiber membrane as the separator. The electrolyte consisted of NaClO₄ (1 mol liter⁻¹) dissolved in propylene carbonate (PC) with 5 vol % fluoroethylene carbonate, and 150 μl of electrolyte was added to each cell. All electrochemical measurements were conducted at 25° ± 1°C. Galvanostatic charge-discharge tests were performed within a voltage window of 1.5 to 4.3 V (versus Na⁺/Na) using a Neware battery testing system. CV measurements were carried out on a CHI 750 electrochemical workstation, and the GITT tests were performed using an Arbin BT-2000 system. For full-cell measurements, HC was used as the anode. The electrode loadings were adjusted to achieve a negative-to-positive capacity ratio (N/P ratio) of ∼1.5 based on the reversible capacities of both electrodes. The full cells were tested within a voltage range of 1.45 to 4.3 V.

Calculation method

Theoretical calculation

All first-principles calculations were performed using the Vienna Ab initio Simulation Package (VASP) with the projector augmented-wave (PAW) method (44–46). The exchange-correlation interactions were described using the Perdew-Burke-Ernzerhof (PBE) functional within the generalized gradient approximation (GGA). A conventional hexagonal NASICON cell without further supercell expansion was used. The P-MT model contains 120 atoms with a composition of Na₁₈Mn₆Ti₆P₁₈O₇₂, corresponding to Na₃MnTi(PO₄)₃, whereas the EDM-MT model contains 123 atoms with a composition of Na₂₁Mn₆Ti₃V₂FeP₁₈O₇₂, corresponding to Na_3.5MnTi_0.5V_0.333Fe_0.167(PO₄)₃. Fe and V were randomly distributed over the transition-metal sublattice. The desodiated models were generated by randomly removing six Na atoms from the corresponding cells, equivalent to the extraction of one Na per formula unit, yielding Na₂MnTi(PO₄)₃ (D-MT) and Na_2.5MnTi_0.5V_0.333Fe_0.167(PO₄)₃ (D-EDM-MT). Representative random Fe/V and Na vacancy configurations were used rather than exhaustive configurational enumeration. Spin-polarized calculations were performed with ISPIN = 2. The local magnetic moments and corresponding electronic states obtained from the self-consistent calculations were used to analyze the Mn oxidation-state evolution in the desodiated structures. The plane wave cutoff energy was set to 520 eV, and a 3 × 3 × 1 Monkhorst-Pack k-point mesh was used for Brillouin zone sampling. All structures were fully relaxed until the residual forces were below 0.02 eV Å⁻¹, and the total energy change was below 10⁻⁵ eV. To account for the strong correlation of transition metal 3d electrons, DFT + U calculations were performed using U values of 4.0 eV for Mn, 3.5 eV for Ti, 3.5 eV for Fe, and 4.0 eV for V based on previously reported values. The same U parameters were consistently applied to all corresponding models. The orbital-resolved density of states was obtained from VASP/PAW projections and extracted using VASPKIT. No local coordinate rotation or Wannier function reconstruction was performed; therefore, the t_2g/e_g assignments were used to compare relative orbital contributions and their evolution rather than as rigorous local-orbital occupation numbers. Bader charge analysis was further performed for P-MT and EDM-MT to quantitatively evaluate electron redistribution, with Δe defined as the Bader electron population minus the corresponding ZVAL. In addition, the LOBSTER software was used to perform crystal orbital Hamilton population (COHP) analysis of the materials (47).

Supplementary Materials

This PDF file includes:

Figs. S1 to S42

Tables S1 to S15