Origin and Acceleration of Insoluble Li2S2−Li2S Reduction Catalysis in Ferromagnetic Atoms‐based Lithium‐Sulfur Battery Cathodes

Abstract Accelerating insoluble Li2S2−Li2S reduction catalysis to mitigate the shuttle effect has emerged as an innovative paradigm for high‐efficient lithium‐sulfur battery cathodes, such as single‐atom catalysts by offering high‐density active sites to realize in situ reaction with solid Li2S2. However, the profound origin of diverse single‐atom species on solid‐solid sulfur reduction catalysis and modulation principles remains ambiguous. Here we disclose the fundamental origin of Li2S2−Li2S reduction catalysis in ferromagnetic elements‐based single‐atom materials to be from their spin density and magnetic moments. The experimental and theoretical studies disclose that the Fe−N4‐based cathodes exhibit the fastest deposition kinetics of Li2S (226 mAh g−1) and the lowest thermodynamic energy barriers (0.56 eV). We believe that the accelerated Li2S2−Li2S reduction catalysis enabled via spin polarization of ferromagnetic atoms provides practical opportunities towards long‐life batteries.


Introduction
Lithium-sulfur (LiÀ S) batteries have been regarded as the most promising energy storage system due to the high theoretical capacity (1675 mAh g À 1 ) and natural abundance of sulfur element. [1] The high-energy and long-life LiÀ S batteries rely on the cathodes with efficient polysulfide redox capability. In typical polysulfide redox chemistry, the sulfur reduction reaction (SRR) undergoes a complex conversion process from the sulfur molecule (S 8 ) to soluble Li 2 S x (LiPSs, 4 � x � 8), ultimately generating insoluble Li 2 S 2 and Li 2 S. [2] Fundamentally, the inherent sluggish SRR kinetics result in low sulfur utilization and shuttle effect of the soluble polysulfides. [3] This has led to two associated trends in recent cathode design of LiÀ S batteries: catalytic sites with sufficient adsorption/bonding capability to polysulfides and fast catalytic conversion of polysulfide intermediates.
Theoretical calculations suggest that the rate-determining step in most of the SRR processes is the solid-solid conversion from Li 2 S 2 to Li 2 S due to the sluggish solid diffusion and poor interface contact between catalysts and Li 2 S 2 . [4] Therefore, the sluggish electrodeposition of Li 2 S and the associated accumulation of Li 2 S x and dead sulfur have long been considered as the root cause for the rapid capacity fading of cathodes. [5] The key point to overcoming this sluggish process relies on a strategy that weakens the SÀ S bond and promotes the Li 2 S 2 dissociation to accelerate the insoluble Li 2 S 2 À Li 2 S reduction catalysis. [6] However, the influences and roles of diverse polysulfide redox catalysts on Li 2 S 2 dissociation remain unclear, which is of great importance to be discovered for the future design of efficient and long-cycling LiÀ S battery cathodes. [7] Due to the much less molecular movement ability in the solid phase than that in solution, catalytic sites with high activity and density are needed for the polysulfide redox materials to realize an efficient in situ reaction with solid Li 2 S 2 . Therefore, to accelerate the solid-solid conversion kinetics, both geometric and electronic structures of the cathode materials should be considered. Single-atom catalysts (SACs), comprising monodispersed metal active sites offer a theoretical 100 % atom utilization, therefore, will form an atomic-level contact/catalytic interface for promoting solid-state Li 2 S 2 /Li 2 S conversion. [8] Recently, diverse "SACs" cathodes have been reported in enhancing LiÀ S battery performances, for instance, the ferromagnetic elements (Fes = Fe, Co, and Ni)-based cathodes with metal-N 4 structures have been demonstrated to possess enhanced polysulfide catalytic conversion ability. [9] Regrettably, the insoluble Li 2 S 2 À Li 2 S reduction mechanisms via taking the FEs-based SACs is unclear, and the corresponding correlation between the catalytic activities and electronic structures of FEsÀ N 4 remain undiscovered.
In this work, we provide a comparative study on the fundamental origin of insoluble Li 2 S 2 À Li 2 S reduction catal-ysis in FEs-based SAC cathodes with different metal-N 4 sites. Through a series of theoretical studies, we disclose that the spin polarization (FeÀ N 4 > CoÀ N 4 > NiÀ N 4 ) can provide spin electrons to reduce antibonding orbitals occupation in Li 2 S 2 À FEsÀ N 4 and enhance the FEsÀ S interaction, thereby weakening the strength of the SÀ S bond in Li 2 S 2 , and eventually accelerating the Li 2 S 2 À Li 2 S reduction catalysis at cathode interface. Meanwhile, we have synthesized a series of FEs-based single-atom sites loaded on hierarchical porous carbon (HP-SAFEs) as cathode materials to verify the proposed mechanism. Thereafter, systematically spectroscopic, structural, and electrochemical studies have demonstrated that the FeÀ N 4 -based cathodes exhibit the fastest Li 2 S 2 À Li 2 S reduction kinetics and the highest capacity retention of 578 mAh g À 1 after 200 cycles under 1 C (1 C = 1675 mA g À 1 ), which is far exceeding those of HP-SACo (512 mAh g À 1 ) and HP-SANi (454 mAh g À 1 ) based batteries. Our findings suggest that the spontaneous spin polarization of ferromagnetic atoms can accelerate insoluble Li 2 S 2 À Li 2 S reduction catalysis, thus offering a new strategy to design high-energy and long-life polysulfide reduction catalysts for practical LiÀ S batteries.

Results and Discussion
To disclose the origin of insoluble Li 2 S 2 À Li 2 S reduction catalysis for the FEs-based SAC cathodes with different metal-N 4 sites, the adsorption and dissociation free energies of Li 2 S 2 are calculated by taking the density function theory (DFT) method. It has been reported that the d orbitals of transition metal centers play a crucial role in the interaction with reaction intermediates. [10] The change of d orbitals can modify the related electronic structures, which in turn affect the reaction energy barrier. For the polysulfide reduction catalysts, the effective electronic states of intermediates (Li 2 S 2 and Li 2 S) are usually dominated by the p orbitals of sulfur. [11] The hybridization between d orbitals of metal centers and p orbitals of sulfur will largely affect the catalytic activities. Therefore, the d-p orbital hybridization between different FEs-based SACs and Li 2 S 2 are explored to predict their reaction free energies. The partial projected density of state (PDOS) of the FEsÀ N 4 ( Figure S1, Supporting Information) shows that the electronic states of d orbitals (FeÀ N 4 ) present an asymmetry that originated from the uneven distribution of electrons in spin up and spin down. In comparison, this asymmetry of d orbitals in CoÀ N 4 is weaker and eventually disappears completely in the NiÀ N 4 center. The asymmetry of d orbitals for FEsÀ N 4 will cause spontaneous spin polarization that can provide spin electrons, which is beneficial for bonding with polysulfide molecules. [9b, 12] In order to quantify the spin polarization of FEs-based SAC, their spin density and magnetic moments are calculated. Figure 1a and Figure S2 (Supporting Information) shows that FeÀ N 4 possessed the largest spin density and magnetic moment of 1.91 μ B , suggesting its superior spin polarization degree compared to the CoÀ N 4 and NiÀ N 4 .
To confirm that the ability of chemisorbing polysulfides is related to the spin polarization degree, we further analyze the molecular orbitals of Li 2 S 2 , FEsÀ N 4 , and Li 2 S 2 À FEsÀ N 4 ( Figure S3, S4, Supporting Information). Results show that among FEsÀ N 4 , the FeÀ N 4 possessing most spin electrons, thus leading to less antibonding orbitals occupation in Li 2 S 2 À FeÀ N 4 and resulting in robust FeÀ S interaction. Furthermore, the optimized adsorption configuration of Li 2 S x (1 � x � 8) on FEsÀ N 4 is considered ( Figure S5, S6, Supporting Information). In the case of FeÀ N 4 and CoÀ N 4 , Li bond with the N/C atom and S bond with Fe or Co atom, respectively. While for the NiÀ N 4 , there is no apparent interaction between S and Ni atoms. Different from Nibased compounds, it is the LiÀ N instead of SÀ Ni interaction promoting NiÀ N 4 absorbing Li 2 S x . The binding strength of Li 2 S x with FEsÀ N 4 sites ( Figure 1b) shows that the FeÀ N 4 has the highest binding energies with S 8 , Li 2 S 6 , and Li 2 S 2 of À 0.96, À 1.28, and À 1.81 eV, respectively, in agreement with the results of the magnetic moment and spin polarization degree.
Considering that the conversion from Li 2 S 2 to Li 2 S involves the dissociation of the SÀ S bond in Li 2 S 2 , the PDOS of Li 2 S 2 À FEsÀ N 4 has been analyzed to reveal the relationship between the adsorption/reduction of Li 2 S 2 on FEsÀ N 4 surface and the electronic structure of the SACs. When the electronic states of FEs interact with the S atom, the hybridized energy levels will split into the anti-bonding states (normally go across the Fermi level (E f )) and the bonding states (below the E f ) ( Figure S7, Supporting Information). The strength of the FEsÀ S interaction depends on the position of the antibonding state, and the higher the position of the anti-bonding state, the stronger the interaction. As shown in Figure 1c, the d-band centers (ɛ d ) of FEsÀ N 4 exhibit ɛ d(Fe) (À 0.79 eV) > ɛ d(Co) (À 1.74 eV) > ɛ d(Ni) (À 2.32 eV), meaning the ɛ d(Fe) in Li 2 S 2 À FeÀ N 4 is closer to the Fermi level. This leads to a stronger interaction between Li 2 S 2 and FeÀ N 4 than the Li 2 S 2 À CoÀ N 4 and Li 2 S 2 À NiÀ N 4 , which corresponds to the order of adsorption energy, thus consequently weakening the SÀ S bonds in Li 2 S 2 . [13] Meantime, the Li 2 S 2 À FeÀ N 4 shows more electron occupation on its d orbitals near the Fermi level makes it more prone to accept or lose electrons, which suggests an excellent electron transfer ability of Fe sites and offers benefit to the following Li 2 S 2 reduction reaction. [14] Furthermore, an obvious charge redistribution between the Li 2 S 2 and FEsÀ N 4 can be observed in the diagrams of charge density differences. The number of charge transfers between the FEs and S bond has been calculated by Bader charge analysis (Figure 1d-f); there are 0.20, 0.18, and 0 j e j charges that transfer from S atom to FEs atoms, respectively, suggesting the strongest electron exchange between S and Fe atoms. To further learn the actual states of SÀ S interaction, the PDOS of S in Li 2 S 2 À FEsÀ N 4 is analyzed. As shown in Figure 1g, the (s p) orbitals of S2 (the S that directly connects to Fe) match well with S1 in Li 2 S 2 À NiÀ N 4 , indicating a strong SÀ S bond. This degree of matching is weakened in Li 2 S 2 À CoÀ N 4 and Li 2 S 2 À FeÀ N 4 , where the latter is particularly pronounced, implying a weakened SÀ S bond due to the transfer of internal charge from the S2 to Fe site.
We then calculate the bond lengths of SÀ S and FEsÀ S in Li 2 S 2 À FEsÀ N 4 to reveal their internal interactions (Fig-ure 1h). Notably, the SÀ S bond lengths show a trend of FeÀ N 4 (2.120 Å) > CoÀ N 4 (2.103 Å) > NiÀ N 4 (2.101 Å), while the FEsÀ S bond lengths present an order of d FeÀ S (2.24 Å) < d CoÀ S (2.31 Å) < d NiÀ S (3.29 Å), thus indicating a strong interaction and electron transfer within FeÀ S, therefore effectively weakening the SÀ S bond in Li 2 S 2 . The free energy diagrams for the Li 2 S 2 À Li 2 S reduction catalysis in FEs-based SAC show that the FeÀ N 4 site (0.56 eV) displays the lowest thermodynamic energy barrier compared to the CoÀ N 4 (0.60 eV) and NiÀ N 4 (0.88 eV), respectively ( Figure 1i). All the calculation results reveal that the FeÀ N 4 catalyst presents the easiest Li 2 S 2 À Li 2 S reduction conversion activity, indicating that the spin polarization is responsible for its enhanced FEsÀ S interaction and accelerated solid-solid catalytic conversion, which will also be further confirmed by our following experimental results.
To verify the above-proposed mechanism, we have synthesized a series of HP-SAFEs (Figure 2a) as Li 2 S 2 À Li 2 S reduction catalysts to assemble LiÀ S batteries by utilizing silica embedded nanocubic metal-organic precursor with in situ FEs doping ( Figure S8, Supporting Information). First, the precursors are pyrolyzed at 900°C in the Ar atmosphere; after removing silica, secondary thermal treatment is conducted to obtain the HP-SAFEs. All the synthesized HP-SAFEs exhibit cubic morphologies with rough surfaces ( Figure S9, Supporting Information); meantime, obvious mesoporous are found under scanning electron microscopy (SEM). The control sample of hierarchical porous N-doped carbon without metal atoms doping (HP-NC) is also prepared. The similar specific surface areas and pore structures of the HP-SAFe (1079 m 2 g À 1 ), HP-SACo (1002 m 2 g À 1 ), HP-SANi (1056 m 2 g À 1 ), and HP-NC (1130 m 2 g À 1 ) are validated by the N 2 adsorption/desorption analysis (Figure 2b and c, Figure S10, Supporting Information).
To further explore the electronic structure and coordination environment of HP-SAFEs, we first analyze the highresolution X-ray photoelectron spectroscopy (XPS) of N 1s spectra. The result shows that pyridinic N in HP-NC has a binding energy of 398.35 eV, while it shifts to 398.55 eV for HP-SAFEs ( Figure S11, Supporting Information), which suggests that the metal ions are bonded with pyridinic N to form the atomic metal-N x sites. [15] Table S2, Supporting Information). The Fe region scan shows two main peaks in the Fe 2p 3/2 at the binding energy of 709.20 and 711.70 eV, which correspond to the Fe 2 + and Fe 3 + oxidation states, respectively. Ni 2p and Co 2p spectra also present a similar oxidation state of Co 2 + /Co 3 + (780.13 and 781.60 eV) and Ni 2 + (854.66 and 855.67 eV). [16] No zero-valent metal peaks can be found for all the XPS spectra of HP-SAFEs, thus indicating no metallic particles or clusters in these HP-SAFEs.
The atomic-scale structure of the representative HP-SAFe is future observed under a spherical aberrationcorrected scanning transmission electron microscope (AC-STEM). Figure 2g-i and Figure S14 (Supporting Information) show abundant bright dots, indicating the atomic distribution of Fe atoms in the porous carbon substrate; no Fe clusters or particles can be observed. The X-ray absorption near-edge structure (XANES) and extended Xray absorption fine structure (EXAFS) spectroscopy are performed to further reveal the coordination environment and valence state of Fe atoms. The XANES curves at the Fe K-edge show that the position of HP-SAFe is located between those of Fe 3 O 4 and Fe 2 O 3 , corroborating the valence state is between Fe 2 + and Fe 3 + , meantime HP-SACo corroborates the valence state between Co 2 + and Co 3 + , and HP-SANi between Ni 0 and Ni 2 + (Figure 3a-c). Fourier-transforms (FTs) and wavelet-transforms (WTs) images from the EXAFS spectra of HP-SAFEs depict that the FEs is found to be bonded as FEsÀ N/C/O. [17] No obvious metal peak in the FTs spectrum of HP-SAFEs is observed, revealing their atomic dispersion (Figure 3d-l). The least-squares EXAFS fitting parameters at the Fe K-edge of HP-SAFe show the FeÀ N bond length of 1.99 Å and coordination number of 4.1, which are very similar to that determined for FePc (2.01 Å, n = 4.0) (Figure 3g, Figure S15 and Table S3, Supporting Information). Meanwhile, HP-SACo and HP-SANi show the CoÀ N and NiÀ N bond length of 1.75 Å and 1.71 Å with coordination number of 4.0 and 4.1, respectively (Figure 3h and i). Based on the above analysis, we suggest that the isolated FEs atoms in HP-SAFEs are tetra-coordination by N atoms and form a typical FEsÀ N 4 structure in the HP-NC matrix.
After validation that the HP-SAFEs display similar morphologies, surface areas, pore structures, and metal contents, it is reliable to use these synthesized HP-SAFEs to explore and compare the Li 2 S 2 À Li 2 S reduction activities of SAFEs experimentally. After heating the mixture of HP-SAFEs and sulfur at 155°C, the resulted S@HP-SAFEs containing 80 wt % sulfur ( Figure S16, Supporting Information) are used as cathodes in LiÀ S batteries. The cubic morphology of S@HP-SAFEs can be well-maintained after sulfur is immitted ( Figure S17, S18, Supporting Informa- tion). The electrocatalysis of polysulfides and conversion of insoluble Li 2 S 2 to Li 2 S is explored by cyclic voltammetry (CV); all the curves of S@HP-SAFe, S@HP-SACo, and S@HP-SANi show clearly two reduction peaks (I C1 and I C2 ) that are ascribed to the reduction of S 8 (I C1 ) and whereupon conversion to Li 2 S (I C2 ), respectively (Figure 4a). The peak current densities of I C2 follow the order of S@HP-SAFe (À 1.91 mA mg À 1 ) > S@HP-SACo (À 1.37 mA mg À 1 ) > S@HP-SANi (À 1.10 mA mg À 1 ), which suggests that the S@HP-SAFe cathode can effectively facilitate the Li 2 S deposition. [18] The determination of Tafel slopes offer the kinetic parameters to illustrate the catalytic activities of the polysulfide electrocatalyst at different voltage intervals. Figure 4b and Figure S20 (Supporting Information) show that the S@HP-SAFe delivers the smallest Tafel slopes (55.68 and 36.20 mV dec À 1 ) at both two reduction stages, indicating its faster reaction kinetics than S@HP-SACo and S@HP-SANi. More importantly, the reduction kinetics of the liquidsolid reaction from polysulfides to Li 2 S are investigated to reveal the nucleation behaviors of solid-state Li 2 S on the electrode surface, which is proceeded with a potentiostatic method at 2.05 V after the first galvanostatic discharging process at a current of 0.112 mA. The integral areas of the current peaks that corresponds to the nucleation of Li 2 S are calculated based on Faraday's law. [19] The value for the HP-SAFe is 226 mAh g À 1 , which is much higher than that for HP-SACo (208 mAh g À 1 ) and HP-SANi (177 mAh g À 1 ), thus suggesting that HP-SAFe has the fastest catalytic deposition ability of Li 2 S as depicted by our theoretical calculation (Figure 4c and d, Figure S21, Supporting Information). The electrodeposition morphology of the Li 2 S on cathodes is investigated by SEM and energy-dispersive spectroscopy (EDS) mapping analysis. It is found that Li 2 S is uniformly deposited on the surface of HP-SAFe with approximately 100 % coverage, which is attributed to the low energy barriers of Li 2 S nucleation and growth on HP-SAFe (Figure 4e, Figure S22, Supporting Information). While the HP-SANi exhibits an insufficient coverage on the cathode surface with isolated Li 2 S deposition (Figure 4f, Figure S22, Supporting Information).
The boosted catalytic deposition of Li 2 S on HP-SAFe is directly monitored by the in situ X-ray diffraction (XRD) technique, which provides clear insights into the deposition activity of Li 2 S. The cell is first discharged at a rate of 0.1 C, during which a series of XRD spectra are recorded at different voltages. The contour pattern of the S@HP-SAFe cathode shows an obvious transition signal of crystalline α-S 8 to Li 2 S during the discharge process (Figure 4g). While the S@HP-SANi cathode displays a much weaker Li 2 S signal at the end of the discharge process (Figure 4h), suggesting a poor polysulfides conversion property. After disclosing the order of Li 2 S 2 À Li 2 S reduction ability for S@HP-SAFEs, we also perform the long-term cycling experiments at a high rate of 1 C to compare the cathode performances (Figure 4i and j). The S@HP-SAFe exhibits the best cycling stability with 97.6 % Coulombic efficiency and reversible specific capacities of 578 mAh g À 1 after 200 cycles (0.11 % decay per cycle), which is higher than those of the S@HP-SACo (512 mAh g À 1 , 0.15 % decay per cycle) and S@HP-SANi (454 mAh g À 1 , 0.16 % decay per cycle).
Since the HP-SAFe has displayed the best performances on the Li 2 S 2 À Li 2 S reduction catalysis by both theoretical and experimental analysis. To explain the importance and kinetics of atomic Fe sites in LiÀ S batteries, we then take a further analysis on the catalytic role and mechanisms of HP-SAFe by using the HP-NC as the control sample. The kinetics of polysulfide reductions in the liquid phase is conducted by CV of symmetric cells with identical working and counter electrodes in 0.5 M Li 2 S 6 electrolyte (Figure 5a). The CV of HP-SAFe exhibits four pronounced reduction/ oxidation peaks located at À 0.44 V (peak A), 0.05 V (peak B), 0.45 V (peak C), and À 0.05 V (peak D). These peaks can be assigned to the electrochemical reactions of Li 2 S 6 on the electrodes, including the reduction of Li 2 S 6 to Li 2 S (peak A), the reconstitution of Li 2 S 6 by the oxidation of Li 2 S (peak B), the oxidation of Li 2 S 6 to generate S 8 (peak C), and the reduction of S 8 to Li 2 S 6 (peak D). [20] The CV of HP-NC, HP-SACo, and HP-SANi also show four reduction/oxidation peaks, but their peak currents are significantly lower than the HP-SAFe. Thus, the CV results clearly indicate that the HP-SAFe electrode provides the best electrochemical kinetics for polysulfide conversion. [21] In order to investigate the lithium diffusion properties, the CV curves of S@HP-SAFe and S@HP-NC cathodes containing similar amounts of sulfur under different scanning rates are investigated (Figure 5b). All reduction and oxidation peak currents are linear with the square root of scanning rates ( Figure S24, Supporting Information), from which the lithium diffusivity could be estimated according to the classical Randles Sevcik equation. [20,22] As shown in Figure 5c, the slopes of the S@HP-SAFe electrode are higher than that of the S@HP-NC electrode in all sulfur conversion steps, implying the faster lithium diffusivity and better polysulfide reaction kinetics. [19b, 23] To confirm the application potential of the S@HP-SAFe cathode, we then conduct the long-term cycling experiments at the charge/discharge rate of 0.5 C ( Figure S26, Supporting Information) and 2 C. At 0.5 C, apparently, the S@HP-SAFe exhibits a much higher initial capacity of 882.4 mAh g À 1 and per cycle capacity decay of 0.18 % (150 cycles) than those of S@HP-NC (774.1 mAh g À 1 and 0.25 %, respectively). Moreover, when subjected to a highrate cycling evaluation at 2 C, the S@HP-SAFe shows an initial capacity of about 700 mAh g À 1 and a small capacity decay of 0.087 % per cycle over 400 cycles (Figure 5d), which is comparable with the state-of-the-art polysulfide catalysts (Figure 5e, and Table S4, Supporting Information). As shown in Figure S27, S28 (Supporting Information), the S@HP-SAFe exhibits a series of advantageous discharge capacities of 1542, 899, 761, 689, and 639 mAh g À 1 when cycled at 0.1, 0.2, 0.5, 1.0, and 2.0 C, respectively. When the specific current is switched back to 0.1 C, a high discharge capacity of 794 mAh g À 1 can be maintained. To further demonstrate the excellent potential of the as-designed S@HP-SAFe cathode for constructing practically viable LiÀ S batteries, we prepare two composite cathodes with very high sulfur loading of 3.25 and 4.13 mg cm À 2 . Notably, the corresponding S@HP-SAFe cathodes exhibit high reversible average areal capacity of 2.42 and 2.80 mAh cm À 2 under steady cycling for 80 cycles at 0.1 C, thus achieving a stable polysulfide reduction electrochemistry (Figure 5f).
To understand the reason for the improved reduction reaction kinetics of the HP-SAFe toward the catalytic conversion of polysulfide intermediates, we have conducted a comprehensive first-principles calculation. As shown in Figure 6a, the Fe center presents a Bader charge of À 1.09 j e j , which changes the originally electroneutral Fe into positively charged. Meanwhile, the charge density differences show that there is charge transfer from Fe to N atoms, thus presenting a state of charge depletion on top of the metal center, which may offer favorable interaction to the polysulfide intermediates. To further understand the electronic structures, the PDOS of HP-SAFe has been calculated and shown in Figure 6b. The d z 2 orbital perpendicular to the basal plane remains unoccupied near the Fermi level. [24] Meantime, the HP-SAFe demonstrates a nearly negligible band gap between the conduction band and the valence band; thus, it may boost the electron transfer during reduction catalysis. [14] Then, the PDOS of Li 2 S 2 on HP-SAFe has also been investigated; the p z and p x /p y orbitals of sulfur can hybridize with the d z 2 and d xz /d yz orbitals of iron, respectively (Figure 6c, Figure S29, Supporting Information). This suggests the strong d-p coupling and electronic interaction in the FeÀ S pair. The optimized adsorption structures of Li 2 S 2 on HP-NC and HP-SAFe are then shown in Figure 6d, where the SÀ S bond lengths in Li 2 S 2 are 1.98 Å and 2.12 Å, respectively, suggesting the SÀ S bond in HP-SAFe is easier to break. Subsequently, the relative free energy landscape for the discharging process from S 8 to Li 2 S on the HP-NC and HP-SAFe surface have clearly revealed that the Li 2 S 2 À Li 2 S reduction catalysis exhibits a larger thermodynamic energy barrier compared to the other steps on both substrates, suggesting that the Li 2 S deposition process was the rate-determine step during discharging (Figure 6e). [25] The HP-SAFe surface shows an energy barrier of 0.56 eV in the Li 2 S 2 À Li 2 S reduction process, which is significantly lowered than the HP-NC (1.23 eV). With these results, we can conclude that the Li 2 S 2 reduction and Li 2 S deposition process is thermodynamically favorable on the HP-SAFe surface, thus resulting in a much higher cathode performance than the others. [7]

Conclusion
We have demonstrated for the first time that the fundamental origin of insoluble Li 2 S 2 À Li 2 S reduction catalysis in FEsbased single-atom materials (Fe, Co, Ni) should be related to their spontaneous spin polarization (FeÀ N 4 > CoÀ N 4 > NiÀ N 4 ). Among FEsÀ N 4 , the FeÀ N 4 possessing most spin electrons undoubtedly result in robust FeÀ S interaction in Li 2 S 2 À FeÀ N 4 , and then weaken the SÀ S bond, accelerating insoluble Li 2 S 2 À Li 2 S reduction catalysis. As a result, cathode with HP-SAFe exhibits the fastest deposition kinetics of Li 2 S (226 mAh g À 1 ) and the lowest thermodynamic energy barriers (0.56 eV). Remarkably, the corresponding S@HP-SAFe cathodes exhibit high reversible average areal capacity of 2.8 mAh cm À 2 at sulfur loading of 4.1 mg cm À 2 for 80 cycles, suggesting its practical opportunities towards highenergy and long-life LiÀ S batteries.