Universal‐Descriptors‐Guided Design of Single Atom Catalysts toward Oxidation of Li2S in Lithium–Sulfur Batteries

Abstract

The sulfur redox kinetics critically matters to superior lithium–sulfur (Li–S) batteries, for which single atom catalysts (SACs) take effect on promoting Li₂S redox process and mitigating the shuttle behavior of lithium polysulfide (LiPs). However, conventional trial‐and‐error strategy significantly slows down the development of SACs in Li–S batteries. Here, the Li₂S oxidation processes over MN₄@G catalysts are fully explored and energy barrier of Li₂S decomposition (E_b) is identified to correlate strongly with three parameters of energy difference between initial and final states of Li₂S decomposition, reaction energy of Li₂S oxidation and LiS bond strength. These three parameters can serve as efficient descriptors by which two excellent SACs of MoN₄@G and WN₄@G are screened which give rise to E_b values of 0.58 and 0.55 eV, respectively, outperforming other analogues in adsorbing LiPs and accelerating the redox kinetics of Li₂S. This method can be extended to a wider range of SACs by coupling MN₄ moiety with heterostructures and heteroatoms beyond N where WN₄@G/TiS₂ heterointerface is predicted to exhibit enhanced catalytic performance for Li₂S decomposition with E_b of 0.40 eV. This work will help accelerate the process of designing a wider range of efficient catalysts in Li–S batteries and even beyond, e.g. alkali‐ion‐Chalcogen batteries.

Introduction

Rechargeable lithium–sulfur (Li–S) batteries are regarded as the ideal next generation energy storage devices for their highenergy-density and low cost.^[1,2] The earth-abundant sulfur cathode gives a high theoretical specific capacity of 1675 mAh g⁻¹, which confers a high theoretical energy density of 2600 Wh kg⁻¹ to Li–S batteries.^[3–5] Despite all the mentioned merits, these cells were found to be restricted to a sequence of obstacles that result in poor battery performance during cycling.^[6] Among them, the practical challenge named “shuttle effect” is a primary reason for the recession of Li–S batteries.^[7] During the discharge process, soluble long-chain lithium polysulfide (LiPs), Li₂S_n (n = 4, 6, 8), can diffuse through the separator to the lithium metal anodes and be reduced to the short-chain LiPs, Li₂S_n (n = 1, 2). These reduction products proliferate back to the cathode and are reoxidized to long-chain LiPs, which leads to the irreversible capacity fading as well as low Coulombic efficiency.^[8–10]

To address these issues and, particularly, avoid the deleterious shuttle effect, significant research efforts have been dedicated to searching for anchoring materials which are efficient in the immobilization of soluble intermediates. There are two main methodologies, namely physical confinement and chemical adsorption.^[11,12] Although carbon materials have been integrated into cathode for hosting sulfur or LiPs, it was demonstrated that the nonpolar pristine carbon manifest weak adsorption strength to polar LiPs,^[2] indicating that physical confinement is far from meeting the requirement to suppress the shuttle effect. Therefore, various of materials including metal oxides,^[13,14] sulfides,^[15–17] carbonaceous materials,^[18,19] have been investigated, which exhibit stronger chemical adsorption for LiPs.^[6,20] However, only strengthening the affinity between anchoring materials and LiPs cannot significantly suppress the shuttle effect because of the sluggish kinetics of the conversion of immobilized LiPs and Li₂S, thereby rendering the cathode surface unexpected accumulation of LiPs and increasing the chances of LiPs diffusion toward anode. Moreover, the LiPs accumulation would cause unrestrained deposition of Li₂S which is difficult to be fully oxidized during charge process due to high energy barrier (E_b) for decomposition, which will lead to the decrease of rate capability. Therefore, increasing research attention has recently been paid to the acceleration of conversion kinetics, in which the transformation from insoluble of Li₂S to long-chain LiPs was highlighted.^[21–23]

Single atom catalysts (SACs) have been proved efficient for catalyzing various of electrochemical reactions, which accordingly attracted much research attention on their applications in Li–S batteries. Up to now, MN₄@G is the most considered model of SACs with metal coordinated by four N atoms embedded in graphene, which also inspired recent research efforts on their applications as sulfur hosts of Li–S batteries.^[24–26] The employment of SACs as anchoring materials can not only immobilize soluble intermediates but also accelerate redox kinetics of Li₂S deposition.^[27,28] However, the mechanism of Li₂S decomposition catalyzed by SACs is far less understood and thus the key parameters affecting the catalytic performance of SACs remain unclear. Therefore, the design of SACs for Li–S batteries relies solely on the conventional trial-and-error method. Given numerous degrees of freedom for adjusting the local atomic environments, the catalytic properties of SACs can be tuned accordingly in a wide range,^[29,30] which necessitate more advanced and efficient design strategy. High throughput calculations have been widely implemented to search for high efficiency SACs for various electrochemical reactions such as oxygen reduction reaction (ORR), oxygen evolution reaction (OER), hydrogen evolution reaction (HER), and N₂ reduction reaction (NRR).^[31–33] Therefore, this could be an optimal strategy as well to screen SACs as high performance of anchoring materials for Li₂S decomposition in Li–S batteries. To this regard, suitable descriptors are critical for screening high performance SACs for Li₂S decomposition which enables exploring efficiently the configurational phase space of SACs. Although E_b of Li₂S decomposition could be utilized as a descriptor, direct calculation of E_b consumes a large number of computational resources using the climbing-image nudged elastic band (CI-NEB) method,^[34] which hinders significantly the implementation of high throughput calculations. Therefore, to search for simple and easily obtained descriptors correlating well with E_b of Li₂S dissociation is essential but challenging.

Herein, a series of graphene-supported SACs as anchoring materials for Li–S batteries were systematically investigated, using density functional theory (DFT) simulations, to deepen the understanding of the mechanism underlying Li₂S oxidation and accordingly identify the key parameters strongly correlated with the E_b of Li₂S decomposition. The relationship of E_b and nine key parameters were extensively investigated, and we identified three of them possessing the strongest correlation with E_b which can serve as descriptors to screen SACs with excellent catalytic performance for accelerating Li₂S oxidation from 30 systems. This descriptor-based strategy was also extended to other catalysts containing structural features other than MN₄ moiety.

Results

As shown in Figure 1, SACs labeled as MN₄@G were modeled by depositing transition metal (TM) atoms onto the nitrogen doped graphene. The average bond lengths of TMN bonds are listed in Table S1 (Supporting Information). After the geometric optimization, SACs have two type morphologies (shown in Figure 1a,b). Most of the metal atoms (V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Tc, Ru, Rh, Pd, Ag, Os, Ir, Pt, and Au) prefer the in-plane atomic arrangement, while the rest (Sc, Ti, Y, Zr, Nb, Mo, Cd, Lu, Hf, Ta, W, Re, and Hg) are somewhat different, with the TM atom sticking out of the plane.

Figure 1. Structural features of MN4@G. a,b) Top and side views of the two types of relaxed structures of monolayer MN4@G, with the metal atom in the graphene plane or sticking out of the plane. c) Transition metal elements we considered across the periodic table, where 3d, 4d, and 5d represent 3d, 4d, and 5d transition metals, respectively.

Various of initial adsorption configurations of Li₂S on MN₄@G were considered and only the most stable adsorption patterns are shown in Figure 2a, where taking VN₄@G and TaN₄@G as examples for illustrating the Li₂S adsorption the Li atoms are adsorbed at the hollow sites and the S atom tends to be adsorbed near the metal atom. As presented in Figure 2b and Table S2 (Supporting Information), the adsorption energies of Li₂S are lower than −2.0 eV in most of the cases, exhibiting a stronger affinity to Li₂S than that on graphene and consistent with the previous works.^[15,35,36] The strongest binding strength toward Li₂S was found on TaN₄@G, with the E_ads value of −5.15 eV and the weakest interaction took place on AuN₄@G (E_ads = −1.23 eV). Group IIIB, IVB, VB, and VIB elements exhibit ultrastrong adsorption strength to Li₂S (E_ads are all less than −3.0 eV), while VIII and IB elements show poor adsorption properties. The E_ads of Li₂S on VN₄@G, MnN₄@G, FeN₄@G, CoN₄@G, NiN₄@G, and ZnN₄@G are −3.93, −2.61, −2.81, −2.53, −1.47, and −2.53 eV, respectively, which is in good agreement with the previous report.^[36] The substrates of AgN₄@G with Li₂S adsorption and HgN₄@G show significant structural distortions (as shown in Figure S1a,b in the Supporting Information). In this concern those two substrates are not studied further.

Figure 2. Adsorption and decomposition of Li2S on MN4@G. a) The adsorption patterns of Li2S on two typical SACs of VN4@G and TaN4@G, respectively. b) The adsorption energy of Li2S on MN4@G. c) The energy profiles of Li2S decomposition process on selected substrates. For a clear display, the element symbols represent the corresponding SACs hereafter. d) Energetically preferable Li2S decomposition pathways.

The reaction kinetics during charging process is dominated by the Li₂S decomposition.^[8] We therefore investigated the catalytic performance of fourteen randomly selected SACs in Li₂S oxidation by calculating the decomposition barriers using CI-NEB method. The energy profiles are shown in Figure 2c and the energetically optimal reaction pathways for Li₂S decomposition are shown in Figure 2d, where three kinds of paths are identified based on their lengths. The decomposition of Li₂S on VN₄@G follows the manner of path II, on NbN₄@G and TaN₄@G path III, and on the other substrates path I. The adsorption state Li₂S undergoes LiS bond breaking process to form LiS cluster and a single Li ion. It can be clearly seen that VN₄@G, TaN₄@G and NbN₄@G shows the best catalytic properties with the E_b values of 0.70, 0.80, and 0.82 eV, respectively, and in comparison, the greatest E_b value that reaches to 1.99 eV was found on PdN₄@G. It should be noted that Li₂S on VN₄@G undergoes an energetically more favorable decomposition process compared to that reported in the literature,^[35] which is attributed to its shorter decomposition pathway. Li₂S decomposition barriers on various SACs including CrN₄@G, MnN₄@G, FeN₄@G, CoN₄@G, NiN₄@G, ZnN₄@G, RuN₄@G, RhN₄@G, PtN₄@G, and AuN₄@G are 1.48, 1.44, 1.66, 1.66, 1.85, 1.64, 1.70, 1.58, 1.84, and 1.90 eV in the given order. These results are consistent with the previous studies.^[35]

To dig more deeply into the mechanism of Li₂S decomposition, it is straightforward to examine the intensity of Li–S interaction after the Li₂S adsorption as illustrated in Figure 3a. Hence, Crystal Orbital Hamilton Population (COHP) analysis was introduced to evaluate the interaction of Li and S atoms as Li₂S was trapped by the SACs^[37,38] and the “bond energies” can be characterized by the interatomic COHP values.^[39] Therefore, the integrated values of COHP (ICOHP), calculated by the corresponding energy integral below Fermi level (E_f) (Figure 3a), were used to quantitatively explore the bonding strength of Li–S bond. The smaller value of ICOHP represents a stronger interatomic interaction and vice versa. As can be seen in Figure 3b, the desirable linear correlation between these two variables is evidenced, which is proven by the good coefficient of determination value (R²) of 0.91. The ICOHP values of Li–S interaction on VN₄@G, NbN₄@G, and TaN₄@G surfaces are −3.71, −3.30, and −3.36, which are larger than those for their analogues demonstrating weaker chemical bonds of Li–S and lower E_b values in the former three SACs. Note that, the data point for VN₄@G is a statistical outlier because it possesses lower ICOHP than that for NbN₄@G and TaN₄@G but gives rise to smaller E_b. This discrepancy could be attributed to the additional substrate affinity to Li atoms (see Figure S2, Supporting Information). As listed in Table S3 (Supporting Information), in VN₄@G the lowest average values of ICOHP of Li–N and Li–C are around −1.11 and −0.71, lower than those for TaN₄@G and NbN₄@G, which means a stronger binding strength between Li and VN₄@G facilitating the decomposition of Li₂S.^[40] The structure of Li₂S adsorbed on NiN₄@G and AuN₄@G are the least to be decomposed, reflected by the most negative ICOHP values of −4.12 and −4.19 up to E_f severally. The quantitative bond strength for other cases can be found in Figure S3 (Supporting Information). These results indicate that the ease of Li₂S decomposition is dominated by the LiS bond strength in the absorbed phase of Li₂S.

Figure 3. Potential descriptors for Li2S decomposition. a) Schematic diagram for the mechanism of Li2S decomposition and COHP for VN4@G. Scatters of Eb versus ICOHP of Li–S interaction b), ΔE c), ΔE(*LiS) d), Eads (LiS) e), and φ f), respectively. The red lines in b–f) represent the corresponding linear relationships. The correlation functions and R2 values are also given.

We next investigated several simple parameters and explored their correlations with E_b. We considered the energy difference of initial and final states of Li₂S decomposition (ΔE) essential for calculating E_b based on CI-NEB method, which can be defined as: ΔE = E(*Li+*LiS) − E(*Li₂S), where E(*Li+*LiS) and E(*Li₂S) represent the energies of final and initial states as illustrated in Figure 2d. The adsorbates with an asterisk “*” on the upper left refers to the adsorption state. As shown in Figure 3c, the fitted equation can be described as: E_b = 1.07 × ΔE + 0.16 (ΔE > 0 eV), with the remarkable R² of 0.98, signaling that there is an extremely strong positive correlation between ΔE and E_b. To this end, ΔE could be used as an effective adsorption descriptor, with which we can precisely estimate the E_b values for evaluating the catalytic performance of SACs toward Li₂S oxidation.

To a significant degree the catalytic performance of a metal is determined by the affinity strength of the reaction intermediates of Li₂S decomposition on the surface of the catalyst.^[41] As the first step of charging process in Li–S batteries, decomposition of Li₂S could also be described by *Li₂S → *LiS + Li⁺ + e⁻ where Li⁺ is isolated in vacuum instead of being adsorbed on SACs, which is different from the process aforementioned for calculating E_b based on CI-NEB method. To calculate reaction energy is a prevailing method to evaluate the performance of catalysts for electrochemical reactions. Thereby we here introduced reaction energy ΔE(*LiS) = E(*LiS) + E(Li)_bcc − E(*Li₂S) as a possible adsorption descriptor for Li₂S oxidation, where E(*LiS), E(Li)_bcc, E(*Li₂S) refer to the total energy of adsorbed LiS cluster, energy of single Li atom in bcc bulk phase and total energy of adsorbed Li₂S, respectively. Using the scaling relationships, E_b as a function of ΔE(*LiS) was plotted in Figure 3d which could be described by the equation of E_b = 0.87 × ΔE(*LiS) + 0.38 with R² = 0.92.

Inspired by the previous works of water splitting^[42] and CO₂ reduction,^[43] we explored the possibility of adsorption energy of LiS (E_ads (LiS)) serving as an additional descriptor for Li₂S oxidation. Using the scaling relations, E_b as a function of E_ads (LiS) was investigated (R² = 0.84, illustrated in Figure 3e). Although there is a relatively large standard deviation appears for the data of E_ads (LiS), it still resonates roughly with the results from ICOHP, ΔE, and E(*LiS) (Figure 3b–d) in particular for those VN₄@G, TaN₄@G, and NbN₄@G.

Recently, a descriptor φ having all parameters related to intrinsic properties of catalytic center,^[31] which can be expressed as φ = θ × (χ_M + αn_Nχ_N)/χ_S, containing the information of valence electrons in the occupied d orbit of TM atom (θ) and the electronegativity of its ligand atoms (χ) has been proposed to design electrocatalysts toward ORR, OER, and HER.^[32,44] We set up φ in the same way, where a is set to 1, and n_N, χ_N, and χ_S are the number of nearest-neighbor nitrogen atoms, electronegativity of nitrogen and sulfur, respectively. Its correlation with E_b was explored. As can be seen from Figure 3f that the linear relationship between φ and E_b is not so remarkable as represented by a low R² value of 0.78. This might be caused by the fact that φ does not precisely describe the intrinsic properties of SACs. As we found that φ is greatly determined by the periodic law, reflected by θ and χ_M, and the electronegativity of N has a very limited modification to the goodness of fit of φ-E_b relationship (see Figure S4, Supporting Information).

We also explored the correlation of E_b and intrinsic properties of adsorbed phase of Li₂S, e.g., the changes of bond length, bond angle, charge of Li₂S, and charge of Li atom. Upon the deposition of Li₂S, the larger the variations in bond length and bond angle of Li₂S are, the weaker of the bonding strength of LiS bond is.^[45] The variation behaviors of bond length and bond angle with respect to elements coincide roughly with that for E_b, with correlation coefficients of 0.83 and 0.43, respectively. It can be seen from Figure S5a,b (Supporting Information) that the largest elongation of bond length is observed on VN₄@G, TaN₄@G, and NbN₄@G, reaching 0.29, 0.37, and 0.36 Å apiece, and the greatest variation in bond angle also occurred on TaN₄@G and NbN₄@G substrates, reaching absolute values of 21.35° and 25.37°, which are much larger than that on VN₄@G (16.18°). These results generally indicate that VN₄@G, TaN₄@G, and NbN₄@G substrates could weaken the bonding of Li and S atoms, which is known as adsorption activation.^[21] In contrast, Li₂S adhere to NiN₄@G, PdN₄@G, PtN₄@G, and AuN₄@G can maintain the structure similar to the pristine one indicating their worse catalytic performance than TaN₄@G and NbN₄@G for the Li₂S decomposition. More details of bond length and bond angles of adsorbed Li₂S are shown in Table S4 (Supporting Information). Moreover, Bader charge analysis^[46] was performed to investigate the adsorption induced charge variations of Li₂S (Figure S5c, R² = 0.12, Supporting Information) and Li atom (Figure S5d, R² = 0.76, Supporting Information), respectively. In particular, the adsorption induced charge difference of Li in Li₂S varies roughly linearly with respect to E_b, indicating that the activation of Li atom is more beneficial to the decomposition of Li₂S.

Overall, based on the 14 randomly selected systems of SACs we gained in-depth understanding the mechanism of Li₂S decomposition and extracted the relationships of E_b and nine parameters (Figure 3; and Figure S5, Supporting Information). Among them, ΔE, ΔE(*LiS), and ICOHP can better correlate with E_b than E_ads (LiS), φ, and other parameters evidencing by their better goodness of fit, which could serve as descriptors for fast screening.

We focus mainly on three descriptors of ΔE, ΔE(*LiS), and ICOHP to explore their predictive capability for estimating E_b and further to screen high performance SACs for Li₂S decomposition. Before that we first validated the prediction capability of ΔE using the available data from the literature about the decomposition barriers of Li₂S over other SACs anchored on N doped graphene and pristine C₂N.^[35,47,48] As shown in Figure 4a, the data points all fall near the predicted line, indicating the robustness of ΔE−E_b linear relationship. This gives us confidence that this descriptor of ΔE can provide efficient theoretical guidance for fast screening active SACs for Li–S batteries. Thus, the descriptor of ΔE was utilized to evaluate the catalytic performance of all SACs systems by calculating E_b values based on the equation of E_b = 1.07 × ΔE + 0.16 (ΔE > 0) as shown in Figure 4a.

Figure 4. Prediction and screening of efficient catalysts among MN4@G. Prediction and screening for active SACs based on ΔE a), ΔE(*LiS) b), and ICOHP c), where the gray symbols represent the predicted results and colorful symbols in a) represent the CI-NEB results reported in this work or previous works. The black lines are the correlation functions obtained in previous discussion.

As can be seen from Figure 4a, those SACs with significantly low decomposition barriers (E_b < 0.85 eV) are found to be WN₄@G, MoN₄@G, NbN₄@G, TaN₄@G, VN₄@G, and ReN₄@G which comprise middle transition metal atoms having both partially occupied d orbitals and enough d electrons. In particular, SACs of Mo and W on N₄@G are predicted to be the potential catalysts with the highest catalytic activity, which even have lower E_b than VN₄@G benchmark.^[35] This means that among 30 SACs MoN₄@G and WN₄@G could catalyze Li₂S oxidation with the fastest kinetics. Their low E_b values could also be reflected by the variation in bond length and the Bader charge of Li atom upon adsorption where the most significant change occurs for Li₂S on WN₄@G and MoN₄@G, as shown in Figure S6 (Supporting Information). Again, the prediction power of these three descriptors was validated by the E_b for WN₄@G, MoN₄@G directly calculated using CI-NEB method (Figure 4; and Figure S7, Supporting Information). Amazingly, the CI-NEB method obtained E_b values of 0.55 and 0.58 eV are nicely consistent with the results of 0.61 and 0.61 eV given by ΔE-E_b relationship. Note that the final state of Li₂S disassociation on CuN₄@G suffers from lattice deformation (Figure S1c, Supporting Information), and hence CuN₄@G was not furtherly studied.

ΔE(*LiS) and ICOHP could reproduce the trend of E_b, as shown in Figure 4b,c, generated by ΔE indicating they are also good descriptors for screening SACs although the E_b values predicted by ICOHP and ΔE(*LiS) have bigger discrepancies than by ΔE with respect to those given by CI-NEB method as listed in Table S5 (Supporting Information). The only exception happens to VN₄@G predicted by ICOHP, which has been aforementioned that this big discrepancy is assigned to the relatively strong interaction between Li atoms and substrate. Otherwise, the predictive results of E_ads(LiS), φ and other parameters related to adsorbed Li₂S are significantly different from those predicted by ΔE, ΔE(*LiS), and ICOHP as illustrated in Figure S8, Tables S5, and S6 (Supporting Information), which demonstrate their worse predictive capability due to their weaker correlation with E_b.

Based on the equations of E_b = 1.07 × ΔE + 0.16 (ΔE > 0), E_b = 0.87 × ΔE(*LiS) + 0.38, and E_b = −1.30 × ICOHP −3.49, one can expect SACs with MN₄ moiety possessing better catalytic performance than WN₄@G and MoN₄@G for catalyzing Li₂S oxidation should have ΔE < 0.36 eV, ΔE(*LiS) < 2.22 eV, or ICOHP > −3.11. This needs further investigations.

Before further investigating the performances of MoN₄@G and WN₄@G as anchoring materials in Li–S batteries, we then explored their stability to clarify the experimental feasibility of synthesis. We found that these three SACs are more energetically stable embedded in the center of N₄@G moiety than anchored on the nearby graphene sites, which is shown in Figure S9 (Supporting Information), indicating the feasibility for experimental synthesis. Moreover, the density of states (DOS) of MoN₄@G, WN₄@G, and VN₄@G were investigated in Figure 5a, which reveals that these substrates are electrical conductors without bandgap. Note that VN₄@G was set as a benchmark in this study, which was treated as the optimum catalyst in previous work.^[35]

Figure 5. Electrochemical, adsorption, and reduction performances of the screened SACs. a) The DOS of MoN4@G, WN4@G, and VN4@G, where the Fermi level (the vertical dashed line) was set to zero. b) The adsorption energies of different lithiation states on MoN4@G, WN4@G, and VN4@G. The corresponding Eads values were labeled on the bars. c) Energy profiles for the reduction of sulfur on MoN4@G, WN4@G, and VN4@G. The atomic structures are typical adsorption conformations of S8 and LiPs species on the screened SACs and the benchmark.

DFT calculations were then performed to examine the adsorption performance of those catalysts for all of the reaction intermediates during the redox of sulfur. As demonstrated in Figure 5b, the E_ads of LiPs on MoN₄@G, WN₄@G, and VN₄@G are almost less than −3.0 eV, showing strong adsorption strength. Taking the adsorption of Li₂S₆ as an example, the E_ads are −3.14, −4.29, and −2.96 eV on MoN₄@G, WN₄@G, and VN₄@G, respectively. Previous work demonstrates that strong affinity strength to LiPs can effectively mitigate the shuttle effect.^[15] It can be seen that the E_ads of all intermediates on MoN₄@G and WN₄@G are lower than that on VN₄@G benchmark, exhibiting a stronger adsorption strength, which suggests MoN₄@G and WN₄@G are potential optimum anchoring materials for entrapping LiPs.

To gain further insights into the kinetics of lithiation process, the Gibbs free energy profiles for discharge reactions from S₈ to Li₂S were calculated and exhibited in Figure 5c. The entire reversible reaction is complex and the reaction from Li₂S₈ to Li₂S is accompanied by the production of isolated state Li₂S₂ (Equation (3)–(8) in the Supporting Information).^[49] The overall free energy changes are −0.41, −0.33, and −0.82 eV for MoN₄@G, WN₄@G, and VN₄@G, respectively, suggesting that the overall reaction on those substrates are exothermic. Whereas, for individual lithiation step, the conversion from S₈ to Li₂S₄ are exothermic and the subsequent two steps are endothermic. Obviously, the reduction from Li₂S₂ to Li₂S possess the largest positive change of Gibbs free energy, indicating that the conversion from Li₂S₂ to Li₂S is the rate-determining step (RDS) in the entire lithiation process. The reduction kinetics can be characterized by the change of Gibbs free energy of RDS (ΔG_RDS). As can be seen from Figure 5c, the lithiation process of sulfur on MoN₄@G (ΔG_RDS = 4.25 eV) and WN₄@G (ΔG_RDS = 4.36 eV) exhibiting similar efficiency as that on VN₄@G benchmark (ΔG_RDS = 4.24 eV). Given the excellent catalytic performance for Li₂S oxidation, WN₄@G and MoN₄@G exhibit remarkable performance of adsorbing LiPs, accelerating reduction kinetics of Li₂S, which will significantly suppress the shuttle effect and improve the rate performance of Li–S batteries and in particular will be expected to perform better than ever reported VN₄@G. This deserves further experimental investigations.

Conversion of LiPs and Li₂S is critical for suppressing shuttle effect and thus a superior catalyst should keep balance between both oxidation and reduction processes. To confirm the overall catalytic performances of those screened VN₄@G, MoN₄@G, and WN₄@G, we further explored the redox processes of other MN₄@G (M = Ti, Zr, Nb, Tc, Hf, Ta, and Re) which possess ΔE < 1.0 eV. As shown in Figures S10 and S11 (Supporting Information), the free energy diagrams for reduction process over those SACs demonstrate that the RDS is the Li₂S₂ → Li₂S, consistent with previous work.^[24,49,50] When ΔE < 1.0 eV, we now have 10 SACs whose performances are compared based on the values of ΔG_RDS and E_b summarized in Table S7 (Supporting Information). Generally, E_b undergoes significant change by 108% from WN₄@G (E_b = 0.55 eV) to TcN₄@G (E_b = 1.15 eV) indicating a pronounced diversity of catalytic performances of those SACs, while ΔG_RDS varies from ZrN₄@G (ΔG_RDS = 3.83 eV) to TaN₄@G (ΔG_RDS = 5.36 eV) by 40% maximum. Except for Ta, other SACs exhibit comparable capability for reduction process due to similar values of ΔG_RDS. We found SACs (Mo/W/Re/NbN₄@G) are as active as VN₄@G^[35] for both reduction and oxidation of Li₂S. Among them, MoN₄@G and WN₄@G with superior activity for Li₂S oxidization deserve further investigation in experiment.

We revealed that ΔE, ΔE(*LiS), and ICOHP can serve as distinguished descriptors for rationally designing potential catalysts of MN₄@G catalyzing Li₂S decomposition and next we extended this strategy to predict the catalytic performance of various types of 2D materials with dispersed atomic metals for Li₂S decomposition. Recently, various strategies have been proposed to enhance the catalytic performances of SACs toward electrochemical reactions, which involve heterostructures^[51–53] and heteroatoms dopants other than N to tailor the local atomic environments.^[54] Therefore, we used ΔE, ΔE(*LiS), and ICOHP to search for enhanced catalytic performance compared to WN₄@G and MoN₄@G by introducing interface effect and S dopant to modulate electronic properties of active metal center.^[55,56] We constructed three typical models as representatives shown in Figure 6a including two heterostructures (WN₄@G/TiS₂ and WN₄@G/G) and one MN₄@G with tailored local environment (MoN₄S₂@G). WN₄@G/TiS₂ and WN₄@G/G are built by introducing monolayer of TiS₂ and graphene, respectively, while MoN₄S₂@G is realized by doping two sulfur atoms into the second coordination sphere of TM atom. Based on the fitted equation of E_b = 1.07 × ΔE + 0.16, the estimated E_b values of Li₂S for WN₄@G/TiS₂, WN₄@G/G, and MoN₄S₂@G are 0.43, 0.72, and 0.90 eV, respectively. Amazingly, additional CI-NEB calculations give rise to E_b of 0.40, 0.83, and 0.91 eV in the given order, confirming the prediction of descriptor ΔE, as shown in Figure 6b. Whereas the ICOHP of Li–S interaction reproduced the trend but relatively large E_b values (Table 1). On the contrary, based on ΔE(*LiS) one can obtain the largest deviation with those from CI-NEB method in particular for the case of WN₄@G/TiS₂. Moreover, the trend of E_b given by CI-NEB method could not be reproduced by ΔE(*LiS). Therefore, ΔE(*LiS)-E_b relationship needs to be modified for specific ligand environment which needs further investigation.

Figure 6. Extension of ΔE to SACs beyond MN4. a) The optimized atomic configurations of WN4@G/TiS2(top), WN4@G/G (middle), and MoN4S2@G(bottom). b) Comparison of Eb given by CI-NEB method and Eb-ΔE linear relationship for the three substrates, respectively, where CI-NEB obtained Eb values for WN4@G/TiS2, WN4@G/G, and MoN4S2@G are represented by orange, green and blue dots, respectively. The insert graph is the energy profiles for Li2S decomposition process.

Table 1 Predictive capability of descriptors for SACs beyond MN₄. The E_b values of Li₂S decomposition for the extension systems given by ΔE, ICOHP, ΔE(*LiS), and CI-NEB method. All data are in units of eV

SACs	Eb [ΔE]	Eb [ICOHP]	Eb [*LiS]	Eb [CI-NEB]
WN4@G/TiS2	0.43	0.55	0.92	0.40
WN4@G/G	0.72	0.96	0.79	0.83
MoN4S2@G	0.90	1.02	1.15	0.91

Heterostructure of WN₄@G/TiS₂ possesses the merits of its individual components which will behave better than TiS₂ or WN₄@G in suppressing shuttle effect since WN₄@G/TiS₂ shows superior catalytic performance outperforming WN₄@G monolayer. All these results not only evidence that the incorporation of monolayer TiS₂ could further reduce the energy barrier of Li₂S decomposition over WN₄@G but also confirm the rationality that ΔE and ICOHP can be extended to wider range of catalysts for Li₂S oxidization. Generally, these two parameters could guide further investigations for rationally designing SACs with heterostructures and/or tailored MN_x moiety. Any other catalysts having configurations like MN₄@G/TiS₂ and MN₄S₂@G are expected to have better catalytic performance for Li₂S decomposition when their ΔE < 0.36 eV or ICOHP > −3.11. In addition, we believe this screening strategy could also be extended to screen catalyst in alkali-ion-Chalcogen batteries.^[57,58]

Conclusion

In summary, we systematically investigated the mechanism of Li₂S oxidation catalyzed by graphene supported SACs and identified three out of nine parameters correlating strongly with the energy barrier (E_b) of Li₂S dissociation, which are bond strength (evaluated by ICOHP), energy difference of initial and final states of Li₂S decomposition (ΔE) and reaction energy of Li₂S decomposition (E(*LiS)). The equations describing the relationships of E_b, ΔE, and ICOHP are E_b = 1.07 × ΔE + 0.16 (ΔE > 0), E_b = 0.87 × ΔE(*LiS) + 0.38, and E_b = −1.30 × ICOHP −3.49, respectively. Under the guidance of descriptors ΔE, ΔE(*LiS), and ICOHP, MoN₄@G, and WN₄@G were screened out as optimal catalysts for catalyzing Li₂S oxidation with the E_b values of 0.58 and 0.55 eV, as well as competitive trapping capability and reduction activity, indicating they can serve as superior performance anchoring materials in Li–S batteries. More importantly, the efficient descriptors ΔE and ICOHP could be extended to predict the decomposition barrier of Li₂S on various types of catalysts containing dispersed TM atom centers, such as heterointerface and SACs of MN₄@G with more complex local environment. Heterointerface of WN₄@G/TiS₂ exhibit promising catalytic performance for Li₂S decomposition outperforming WN₄@G by giving rise to E_b of 0.40 eV. We believe that these efficient descriptors of ΔE, E(*LiS), and ICOHP could help in fast screening and designing wider range of electrochemical catalysts in Li–S batteries and even other alkali-ion-Chalcogen batteries.

Acknowledgements

This work was financially supported by National Natural Science Foundation of China (Grants Nos. U1801255 and 51972350), Natural Science Foundation of Guangdong Province (No. 2018A030313881). The calculations were carried out using supercomputers “Tianhe-2” at NSCC Guangzhou.

Conflict of Interest

The authors declare no conflict of interest.

Data Availability Statement

Research data are not shared.