Universal-Descriptors-Guided Design of Single Atom Catalysts toward Oxidation of Li2 S in Lithium-Sulfur Batteries.

The sulfur redox kinetics critically matters to superior lithium-sulfur (Li-S) batteries, for which single atom catalysts (SACs) take effect on promoting Li2 S 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 Li2 S oxidation processes over MN4 @G catalysts are fully explored and energy barrier of Li2 S decomposition (Eb ) is identified to correlate strongly with three parameters of energy difference between initial and final states of Li2 S decomposition, reaction energy of Li2 S 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 Eb values of 0.58 and 0.55 eV, respectively, outperforming other analogues in adsorbing LiPs and accelerating the redox kinetics of Li2 S. 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 Li2 S decomposition with Eb 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.[ , ] 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.[ , , ] 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.[ ] Among them, the practical challenge named “shuttle effect” is a primary reason for the recession of Li–S batteries.[ ] During the discharge process, soluble long‐chain lithium polysulfide (LiPs), Li2S (n = 4, 6, 8), can diffuse through the separator to the lithium metal anodes and be reduced to the short‐chain LiPs, Li2S (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.[ , , ]

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.[ , ] 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,[ ] indicating that physical confinement is far from meeting the requirement to suppress the shuttle effect. Therefore, various of materials including metal oxides,[ , ] sulfides,[ , , ] carbonaceous materials,[ , ] have been investigated, which exhibit stronger chemical adsorption for LiPs.[ , ] 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.[ , , ]

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.[ , , ] The employment of SACs as anchoring materials can not only immobilize soluble intermediates but also accelerate redox kinetics of Li2S deposition.[ , ] 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,[ , ] 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).[ , , ] 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,[ ] 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  , 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  , 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.[ , , ] 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.[ ] 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.[ ] 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,[ ] 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.[ ]

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  . 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[ , ] and the “bond energies” can be characterized by the interatomic COHP values.[ ] 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 (R 2) 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.[ ] 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 E b versus ICOHP of Li–S interaction b), ΔE c), ΔE(*LiS) d), E ads (LiS) e), and φ f), respectively. The red lines in b–f) represent the corresponding linear relationships. The correlation functions and R 2 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 R 2 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.[ ] 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 R 2 = 0.92.

Inspired by the previous works of water splitting[ ] and CO2 reduction,[ ] 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 (R 2 = 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,[ ] which can be expressed as φ = θ × (χ M + αn N χ )/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.[ , ] We set up φ in the same way, where a is set to 1, and n N 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 R 2 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.[ ] 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.[ ] 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[ ] was performed to investigate the adsorption induced charge variations of Li2S (Figure S5c, R 2 = 0.12, Supporting Information) and Li atom (Figure S5d, R 2 = 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.[ , , ] As shown in Figure  , 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.[ ] 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  , 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.[ ]

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 E ads 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.[ ] 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).[ ] 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.[ , , ] 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[ ] 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[ , , ] and heteroatoms dopants other than N to tailor the local atomic environments.[ ] 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.[ , ] We constructed three typical models as representatives shown in Figure  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  ). 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 E b given by CI‐NEB method and E b‐ΔE linear relationship for the three substrates, respectively, where CI‐NEB obtained E b 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	E b [ΔE]	E b [ICOHP]	E b [*LiS]	E b [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 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.[ , ]

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.

Conflict of Interest

The authors declare no conflict of interest.

Supporting information

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