Energy is of increasingly important concern for global sustainable development since non-renewable fossil fuels are being rapidly depleted. Developing clean and renewable energies, such as wind and solar, is essential to reducing greenhouse gas emissions. Intermittence and fluctuation are crucial challenges when converting these energies to electricity. It is a priority to develop advanced energy storage technologies to utilize wind or solar electricity effectively. Rechargeable batteries provide the invaluable advantage of highly flexible energy storage on various levels ^[1][2][1,2]. Various rechargeable batteries have been developed, including lead–acid, nickel–metal hydride, and lithium-ion batteries ^[3][4][5][3,4,5]. However, they are plagued by low energy density, which fails to meet the enormous energy storage demands of various application scenarios, like electric vehicles and grids.

Lithium-sulfur (Li-S) batteries have emerged among various advanced battery systems as one of the most promising candidates ^[6][7][8][6,7,8]. Due to the electrochemical reaction of lithium metal with sulfur by redox processes (2Li + S = Li₂S), Li-S batteries display a considerably huge energy density of 2600 Wh·kg⁻¹, greatly exceeding the current lithium-ion battery systems. Furthermore, they possess the considerable merits of abundant resources, environmental friendliness, and safety. Despite tremendous efforts in exploiting reliable Li-S batteries, their commercialization still has hurdles [9]. The poor conductivity of sulfur cathodes inevitably leads to sluggish electrochemical reaction kinetics with high battery polarization. Moreover, polysulfide intermediates can be dissolved and then diffuse to the electrolyte, resulting in the erosion of lithium anodes. The polysulfide shuttling leads to the heavy failure of electroactive species and poor cycling stability of Li-S batteries. Therefore, it is crucial to synchronously alleviate the polysulfide shuttling and facilitate the electrochemical reaction kinetics, achieving the entire capability of Li-S batteries.

Designing reliable sulfur cathodes is an effective approach to improving the performance of Li-S batteries. Developing advanced sulfur host and separator-modified materials has been demonstrated as a practical approach to promoting cathode conductivity and accelerating sulfur electrochemical kinetics ^[10][11][12][10,11,12]. Carbons, metals, single atoms, and compounds have been employed as sulfur hosts, which significantly increase the capacity and cycling stability of Li-S batteries resulting from the strong anchoring and catalytic effects on sulfur species ^{[13][14][15][16]}[13,14,15,16]. However, it is challenging to discover and screen these host materials by trial and error. Seeking regular theoretical methods for predicting and validating the essential properties of sulfur host materials can facilitate an understanding of electrocatalytic effects during the conversion process in Li-S batteries ^[17][18][17,18]. Theoretical calculations have proven to be a powerful method to examine the electrocatalytic mechanisms in Li-S batteries ^{[19][20][21][22]}[19,20,21,22]. Unlike experimental approaches, theoretical calculations can predict the interaction of host materials with sulfur species on the atomic/molecular scale. This considerably facilitates the exploitation of advanced sulfur cathode materials for practical applications.

Theoretical calculations show tremendous advantages in assisting the design and screening of efficient catalyst materials for Li-S batteries. In particular, density functional theory (DFT) calculations have been extensively employed in Li-S batteries. DFT calculations can predict the physical/chemical properties of materials simply using the intrinsic properties of atoms instead of adding any empirical parameters. Currently, DFT is one of the most powerful techniques to simulate the electronic structures of catalyst materials and investigate the interaction between sulfur species and catalyst materials. Based on the DFT calculations, the behavior of catalyst materials can be well explained at the molecular level. The calculated results can further guide the tailoring and optimization of catalyst materials for Li-S batteries. In addition, the Gibbs free energy of the sulfur reduction reaction can be properly obtained with DFT calculations, which can act as an important indicator to evaluate and compare the activities of different catalyst materials. Moreover, the calculation of lithium-ion diffusion barriers and Li₂S decomposition barriers can provide deep insights into the charge transfer mechanisms in Li-S batteries. All the calculations associated with experimental works accelerate the development of advanced catalyst materials for Li-S batteries.

2. Electronic Structures

The electronic structure of sulfur host materials essentially determines the electrocatalytic activity in Li-S battery conversion reactions. The electronic structure of sulfur host materials can be finetuned with various experimental approaches, such as doping, heterostructures, and defect engineering ^[23][24][25][23,24,25]. Therefore, it is essential to study the electronic structures of sulfur host materials computationally. This can support the planning of experiments and guide the interpretation of experimental results. DFT calculations are the typical method to study the electronic structures of sulfur hosts, including band structure, density of states, and the charge distribution between sulfur species and sulfur host molecules ^[26][27][28][26,27,28].

2.1. Band Structures

Electronic band structures reveal the electronic levels in crystal structures, which can be used to explain the electronic conductivity of crystals ^[29][30][29,30]. Since sulfur cathodes are electronic conductors, high conductivity benefits the electron transport and the conversion of sulfur species. Therefore, band structure calculations can guide the prediction and screening of efficient sulfur cathode materials. In particular, by calculating the band structures of electrode materials, the width of the band gap can be determined, revealing their conductivity. Materials possessing a negligible energy band gap show metallic properties. However, insulators originating from wide band gaps result in their low conductivity. Due to the relatively narrow band gaps of less than 3 eV, semiconductors display moderate conductivity and can further be enhanced by structure modulation. DFT calculations have been used to explain the conductivity increase in catalysts by building heterostructures for Li-S batteries ^{[31][32][33][34][35]}[31,32,33,34,35]. Tang and co-workers constructed Co₃O₄/ZnO heterojunctions embedded in N-doped carbon nanocages as sulfur hosts (CZO/HNC) [31]. DFT calculations confirmed that Co₃O₄/ZnO exhibited an optimized band structure with better conductivity. ZnO and Co₃O₄ possess broad band gaps of 3.39 and 1.56 eV, respectively, implying semiconducting properties. In contrast, the Co₃O₄/ZnO heterojunctions revealed a negligible energy band gap, suggesting high conductivity. This result was validated by four-probe resistivity experiments, in which Co₃O₄/ZnO heterojunctions displayed the highest conductivity of 6.6 × 10⁻³ S m⁻¹. This heterostructure facilitated ion diffusion and promoted the polysulfide conversion with stable Li-S batteries, which was validated by the experimental results. Cyclic voltammetry (CV) of a symmetric cell indicated that CZO/HNC exhibited a stronger current response in contrast to Co₃O₄/HNC and ZnO/HNC. As a result, sulfur cathodes with CZO/HNC presented the optimized rate capability in comparison with the other two counterparts. Recently, another paper on CoSe₂@TiSe₂-C heterostructures has also reported the band structures to predict the conductivity [32]. CoSe₂@TiSe₂-C possessed a minor energy band gap of 0.017 eV, which indicated a metallic nature. Relatively broad band gaps were observed in CoSe₂ (0.589 eV) and TiSe₂-C (0.024 eV). The highly conductive CoSe₂@TiSe₂-C was able to facilitate the conversion kinetics from polysulfides to Li₂S and promote Li₂S dissociation. When acting as the interlayer in Li-S batteries, CoSe₂@TiSe₂-C allowed the sulfur cathode to deliver the highest capacity.

2.2. Densities of States

Densities of states (DOS) are generally the state number at specific energy levels that electrons can occupy, i.e., the electron state number per unit energy per unit volume. The DOS can be an essential indicator to understand the physical properties of materials since they provide a simple approach to characterizing complex electronic structures. DOS calculations can ascertain the overall state distribution as a function of spacing and energy between energy bands in semiconductors. DOS are typically analyzed from two aspects: the local DOS (LDOS) and the partial (or projected) DOS (PDOS). The LDOS signify that specific atoms of the system contribute electronic states to various parts of the energy spectra. The PDOS indicate the projection of atomic orbitals (s, p, or d) on the densities of states, which provides contributions based on the angular momentum. The DOS calculations play a critical role in predicting and analyzing the electrochemistry of Li-S batteries. The DOS analyses can readily identify the width of the band gap of electrode materials, which evaluates the conductivity of electrode materials. For instance, electrode materials with band gaps of more than 3 eV between the top of the valence band and the bottom of the conduction band are considered to have insulating properties. A band gap between 1 and 3 eV calculated from DOS indicates that electrode materials are semiconductors. Electrode materials with metallic conductivity present narrow band gaps of less than 1 eV. Therefore, a smaller band gap means a better conductivity for electrode materials. Since the electrochemical conversion of sulfur cathodes is rather sluggish due to the insulating nature of sulfur, catalyst materials with good conductivity are a prerequisite for rapid charge transfer and catalytic conversion of sulfur cathodes [16]. As a result, the electrochemical conversion of elemental sulfur to the discharging product Li₂S is significantly accelerated owing to the enhanced conductivity of the electrode materials [17]. The detrimental shuttle effect of polysulfides can be further suppressed. Therefore, Li-S batteries are expected to achieve high sulfur utilization and excellent cycling performance. Moreover, as the strong interaction between catalysts and sulfur species can affect the DOS of catalyst molecules, the detailed DOS analyses interpret the orbital overlapping or hybridization between sulfur species and catalyst molecules, implying the catalytic mechanisms of Li-S batteries. In addition, DOS calculations can also determine the d-band center (ε_d) of catalysts in Li-S batteries, which is a critical descriptor to analyze the catalytic activities ^[25][36][25,36]. According to the d-band theory, catalysts with a higher value of ε_d calculated from DOS suggest a stronger catalytic activity, which better promotes the conversion kinetics for Li-S batteries.

2.3. Charge Distribution

Understanding the interaction between molecules is beneficial to obtaining insights into the nature of intermolecular bonding. This understanding effectively guides the design of catalyst materials. Charge distribution calculations are powerful approaches to evaluating intermolecular interactions, which can uncover atoms’ electronic structures and chemical environments. With Bader charge analysis and differences in charge density, the charge transfer and the numerical values for the bond strength of interacting atoms or molecules can be evaluated. In Li-S batteries, the adsorption and catalysis processes of sulfur species on catalysts involve complicated electron transfers, which are challenging to investigate with experimental approaches. By contrast, charge distribution analyses can clearly present the electron transfer and charge density at the interface of catalysts and sulfur species at the molecular level. Therefore, the chemical bonding interaction between catalyst molecules and sulfur species can be identified, contributing to the understanding of catalytic mechanisms in Li-S batteries. Modulating the electronic state of metal phosphides, Zhou et al. incorporated N- and P-doped porous carbons into Ni and Co phosphides nanoparticles (NiCoP-NPPC) as catalysts for Li-S batteries ^[37][53]. The tailoring improved the reaction kinetics of sulfur cathodes and achieved a dendrite-free lithium anode. The authors analyzed the interaction between sulfur and transition metals using charge density difference analyses. In contrast to NPPC and CoP-NPPC, NiCoP-NPPC exhibited a higher electron density. Meanwhile, the accumulated and depleted charge might accelerate the charge transport from NPPC to NiCoP. The calculation results indicated a distinct interfacial charge interaction, improving the anchoring and considerably facilitating the electrochemical kinetics of sulfur cathodes. Consequently, sulfur cathodes with CoP-NPPC obtained a high initial capacity of 1184 mAh g⁻¹ at 0.5 C. By calculating the interfacial charge distribution, Lu et al. confirmed the presence of the built-in electric field (BIEF) in the NbB₂-MXene heterostructure ^[38][54]. The redistributed charge and the defective boundaries in the heterostructure resulted in more exposed active sites, thus enlarging the anchoring sites and catalytic active sites. These structural advantages enhanced the electrochemical kinetics of the polysulfide conversion. When being used as the sulfur host, NbB₂-MXene allowed sulfur cathodes to present a boosted rate performance, with a capacity of 679 mAh g⁻¹ even at 2 C. Moreover, the composite cathodes maintained a high capacity of 866 mAh g⁻¹ at 0.2 C after 100 cycles. The charge density difference analyses can further support the DOS results of the bonding states. Yi et al.’s DOS calculation proved the Fe-S bonding of the adsorbed ^∗LiS and ^∗Li₃S₂ on the Fe single atoms (* is the active site of catalysts) ^[39][49]. The authors observed the clear accumulated charge between Fe and S atoms from the charge density difference. By inducing strain relaxation, Sun et al. tuned the structures of bimetallic MoNi₄ nanoalloys ^[40][55]. The strained MoNi₄ (s-MoNi₄) balanced the anchoring and catalytic effects on Li-S batteries. The introduction of the lattice strain altered the bond length of Ni-Mo, broadening the d band and downshifting the d-band center toward the Fermi level. Using the Bader charges, the authors studied the charge transfer interaction of Li₂S with s-MoNi₄ and pure MoNi₄. After adsorbing Li₂S, s-MoNi₄ accepted the charge of 0.8227 e, whereas MoNi₄ accepted 0.9127 e. This result indicated that a slight charge transfer occurred between s-MoNi₄ and Li₂S, meaning a weaker charge interaction and thus facilitating the desorption of polysulfides. Wan et al. analyzed the electronic distribution of the ultra-thin NiSe₂-CoSe₂ heterostructured nanosheets using charge density difference calculations ^[41][38]. In contrast to NiSe₂ and CoSe₂, NiSe₂-CoSe₂ displayed a localized enhancement of the positive/negative electron clouds. It can be concluded that more electron transfers occurred between the interfacial domains of NiSe₂-CoSe₂ heterostructures, which significantly anchored and catalyzed sulfur species. With simulated deformation charge density calculations, Dong et al. validated that the dual Fe-Co single-atom pairs exhibited stronger adsorption towards Li₂S₆ than Fe or Co single atoms ^[42][56]. The dual Fe-Co sites with combined effects induced the charge redistribution of atom pairs, promoting polysulfide reduction and Li₂S decomposition. Wang et al. indicated an enhanced interaction between polysulfides and Ni₃B nanoparticles on B-doped graphene (Ni₃B/BG) ^[43][57]. The Bader charge calculations revealed more charge transfer from Li₂S₄ and Li₂S to Ni₃B/BG (0.813 and 0.592 e) than that to BG (0.592 and 0.092 e), which effectively accelerated their conversion kinetics. Furthermore, highly accumulated charge density was detected at the interface of Ni₃B and BG. The charge redistribution allowed a smooth charge transport channel, boosting sulfur species’ redox kinetics.

3. Binding Energy between Sulfur Species and Catalysts

Since the adsorption of polysulfides is critical to suppressing the polysulfide shuttling, the investigation of the interactions of catalysts with sulfur species is beneficial to unraveling the adsorption mechanisms. Therefore, the binding energy can be a good indicator. Since different crystal surfaces of catalysts may possess different binding energies, the selection of representative surfaces for binding energy calculations is critical. X-ray diffraction characterization can provide reasonable surfaces of catalysts for calculations. In addition, choosing surfaces with different atom ratios is another approach because it can fairly evaluate the contribution of different surface atoms to anchoring sulfur species ^[44][58]. Binding energy calculations are now a typical approach to predicting or validating the adsorption ability of catalysts towards sulfur species ^[45][59]. The binding energy (E_b) between sulfur species and catalysts is defined as follows: where E_t, E_s, and E_c represent the energies of sulfur species adsorbed on catalysts, sulfur species, and catalysts, respectively. A smaller negative E_b value means a stronger binding ability. In some reports, −E_b is defined to indicate the binding energy, i.e., a higher positive E_b value means a stronger binding ability. Due to the intrinsic property of catalyst materials, their binding energies towards sulfur species vary. Generally, carbon-based catalysts show a relatively weak binding energy, while metal compounds and single atoms possess stronger adsorption towards sulfur species. For instance, Pu et al. compared the binding energies of Fe₃P and pure carbon towards various sulfur species ^[46][60]. Fe₃P displayed relatively high binding energies in a range of 0.55 to 2.95 eV towards sulfur species, which were stronger than those of pure carbon (0.43–0.65 eV). Due to the electronegativity difference, the sulfur from polysulfides readily interacted with the iron from Fe₃P. The proper anchoring was beneficial to anchoring sulfur species and accelerating their catalytic conversion. Wang et al. calculated the binding energies of CoP towards sulfur species ^[47][61]. The results show that CoP (211) had an excellent adsorption capacity of 2–8 eV towards sulfur species. The similar binding energy of CoP towards sulfur species was also confirmed by Zhang et al. ^[48][62]. Structure regulation, like doping, can improve the binding energy of carbon-based catalyst materials ^[49][50][63,64]. Yang et al. validated that introducing pyridinic-N to porous carbon fibers resulted in a strong adsorption energy of −2.20 eV towards Li₂S₄ ^[51][65]. Metal sulfide catalysts display favorable adsorption and catalytic activities towards sulfur species ^[52][53][66,67]. Liu et al. revealed that the cation doping of MoS₂ significantly promoted the anchoring and the catalytic effects on polysulfides compared to the inactive MoS₂ ^[54][41]. V-doped MoS₂ possessed stronger adsorption of polysulfides and allowed sulfur cathodes to have a high initial capacity of 1607 mAh g⁻¹ at 0.2 C. Dai et al. validated that the Co-doped NiS₂ (Co-NiS₂) nanoparticles showed a stronger adsorption towards sulfur species than NiS₂ ^[55][39]. A single component generally exhibits relatively weak adsorption towards sulfur species. Combining two or more components to construct heterostructures can overcome this shortage ^[52][56][57][66,68,69]. For example, Zeng et al. designed the ternary heterostructure Na_0.67Ni_0.25Mn_0.75O₂ (NNMO)-MnS₂-Ni₃S₄ with three active centers to obtain cascade catalysis for polysulfides ^[58][70]. Based on the binding energy calculations, NNMO delivered higher binding energies for all sulfur species than MnS₂ and Ni₃S₄. The binding energies of long-chain polysulfides on MnS₂ were stronger than those on Ni₃S₄, while short-chain polysulfides were favorably anchored on Ni₃S₄ compared to MnS₂. Finally, sulfur cathodes with the ternary heterostructure exhibited excellent rate performance. Wang et al. calculated the binding energy of Co₃O₄/ZnO heterostructures towards sulfur species [31]. The results suggested that Co₃O₄/ZnO displayed the strongest adsorption compared to the individual Co₃O₄ or ZnO. A similar conclusion has also been made by Wan et al., who confirmed that the NiSe₂-CoSe₂ heterostructure displayed enhanced adsorption of sulfur species compared to NiSe₂ and CoSe₂ ^[41][38]. Other metal compounds, like oxides and nitrides ^[59][60][61][71,72,73], have also shown strong adsorption towards sulfur species, which can effectively mitigate the shuttle effects. For example, Wang et al. designed a core-shelled heterostructure containing Ni₃B nanoparticles dispersed on B-doped graphene (Ni₃B/BG) to boost the reaction kinetics of Li-S batteries ^[43][57]. DFT calculations have determined the adsorption properties of polysulfides.

4. Gibbs Free Energy

Gibbs free energy, denoted as G, is defined as follows: G = H − TS,   (2) where H, T, and S are the enthalpy, temperature, and entropy, respectively. The change in Gibbs free energy (ΔG) can indicate the chemical reaction direction under constant pressure and temperature. For example, when ΔG shows a positive value, the reaction cannot be spontaneous. Negative values correspond to spontaneous reactions. Since a catalytic reaction involves the adsorption and desorption of reactants on the catalyst’s surface, the ΔG calculations can evaluate the activities of catalysts and the rate-determining step. By calculating the correlation between overpotential and ΔG in the oxygen reduction reaction, Nørskov et al. successfully explained the activities of metal catalysts ^[62][74]. ΔG can be an effective descriptor for seeking idealized catalyst materials ^[50][64]. Similarly, the ΔG calculations have been applied to investigate the electrochemistry of Li-S batteries. For example, ΔG can reveal which reaction step is spontaneous and which reaction step is rate-determining in Li-S batteries ^[63][75]. Ji and co-workers initially employed the ΔG calculation to explain the catalytic activities of single-atom Co for sulfur cathodes ^[64][76]. Typically, the electrocatalytic sulfur reduction reaction from S₈ to Li₂S during discharging can be considered as follows: where * is the active site of catalysts. The calculated ΔG for the corresponding reaction process can be written as follows: In Equations (3)–(7), G(Li⁺) + G(e⁻) are written in the form of G(Li), which is considered in the computational hydrogen electrode approach ^[62][74]. Therefore, during the sulfur reduction reaction (SRR) process, the rate-determining step can be determined by the calculated ΔG. Du et al. calculated the ΔG for two SRR catalysts: N-doped graphene (N/G) and single-atom Co in N-doped graphene (Co-N/G). They validated that the S₈ reduction to Li₂S₈ was an exothermic spontaneous reaction in which ΔG < 0. The following reduction processes to discharge products are endothermic or almost thermoneutral. The rate-determining step was the conversion from Li₂S₂ to Li₂S, which presented the highest ΔG. Co-N/G indicated a lower ΔG than N/G for the Li₂S₂ reduction, implying a more favorable reaction pathway. Based on the ΔG calculations, various catalyst materials have been predicted, such as single atoms ^[65][77], metal oxides ^[66][67][68][78,79,80], sulfides ^[69][81], nitrides ^[70][71][82,83], and heterostructures ^[72][73][84,85], which present accelerated conversion kinetics for Li-S batteries. Because of the maximized atomic utilization and excellent catalytic activities, single atoms present accelerated conversion kinetics for sulfur cathodes. Single atoms with Fe ^[74][48], Co ^[75][86], Ni ^[76][87], Cu ^[77][88], and W ^[78][44] as active sites have been confirmed to be promising electrocatalysts, which considerably restrain the polysulfide shuttling. The coordination environment of single atoms plays a key role in catalytic activities. Zhang et al. noticed the catalytic activities of edge-distributed single-atom sites. To achieve edge-distributed single-atom Fe, they incorporated Fe single atoms in N-doped porous carbon (Fe-NPC) into CNTs ^[79][89]. This composition promoted polysulfide anchoring and conversion. The ΔG calculations supported the favorable catalytic activities resulting from the Fe-N₄ moieties with edge distribution. In the rate-determining step, Fe-N₄ with edge distribution decreased the Li₂S deposition barrier (0.72 eV) compared to the in-plane Fe-N₄ (0.87 eV), revealing faster redox kinetics. Meanwhile, the energy barrier of the Li₂S₄ reduction on Fe-N₄ with edge distribution also decreased to 0.53 eV in contrast to that on the in-plane Fe-N₄ surface (0.60 eV), implying promoted polysulfide conversion and hence a mitigated shuttle effect. Recently, Ren et al. designed a single-atom Fe catalyst containing an S-doped periphery (Fe-NSC), which presented enhanced polysulfide adsorption and facilitated sulfur conversion [16]. Compared with the pristine Fe-N₄ moieties, the Fe-NSC configuration had more accumulated charge density. The calculations indicated that the Fe-NSC-based catalysts decreased the ΔG of the Li₂S deposition. This result showed a more favorable pathway for sulfur reduction at the Fe-NSC sites, thus achieving excellent cycling life of sulfur cathodes. By regulating the coordination numbers of active sites, the intrinsic catalytic activities of single atoms can be significantly enhanced. Xiao et al. prepared novel single-atom catalysts composed of Fe-N₅ moieties embedded in the N-doped carbon matrix (Fe-N₅/NC) ^[80][90]. The resultant Fe-N₅/NC exhibited strong adsorption to polysulfides and considerable catalytic effects on the redox conversion of Li-S batteries. Sulfur cathodes with the Fe-N₅/NC catalysts displayed a high initial capacity at 0.1 C (1519 mAh g⁻¹). The ΔG calculations implied that the biggest barrier was the Li₂S₂ reduction. Co single atoms have been determined to catalyze the redox conversion of sulfur cathodes ^[81][82][91,92]. Wang et al. engineered planar Co-N₄ in N-doped graphene mesh. The fabricated single-atom catalysts (SA-Co/NGM) obtained high atom utilization when catalyzing the polysulfide conversion ^[83][93]. The authors calculated the ΔG of S₈ to Li₂S on N-doped carbon (NC) and CoN₄ to reveal the improved conversion kinetics. Heterostructures integrate the advantages of the individual component to achieve increased catalytic effects on sulfur cathodes. For instance, Meng and co-workers developed a CoS₂/ZnS heterostructure that can bidirectionally catalyze sulfur cathodes [33]. Zhu et al. synthesized heterogeneous MnO-Mo₂C nanoparticles on porous carbon (MnO-Mo₂C/C) to host sulfur ^[84][94]. MnO-Mo₂C decreased the energy barrier of Li₂S deposition to 3.38 eV compared to the single MnO (4.63 eV). Similar conclusions were made by Huang et al., who fabricated La₂O₃-MXene heterostructures to promote the conversion kinetics of sulfur cathodes ^[85][95].

5. Lithium-Ion Diffusion Energy Barriers

Lithium-ion diffusion can be used to evaluate the activities of catalysts for Li-S batteries. CV measurements are typically used to determine the lithium-ion diffusion coefficient ^[86][96]. In addition, the diffusion energy barriers of lithium ions on the surfaces of catalysts are good indicators to predict the electrochemical kinetics of Li-S batteries. Cui and co-workers investigated the lithium-ion diffusion on graphene and various sulfides using the climbing-image nudged elastic band method ^[87][97]. The calculation showed that the diffusion barriers of sulfides were smaller than those of graphene, which was in accordance with the experimental analyses. A smaller barrier increases the diffusion rate, which benefits the reaction kinetics between lithium and sulfur. Lithium-ion diffusion can be significantly enhanced by controlling the electronic structures of catalysts. For example, Zhang and co-workers calculated the diffusion barriers of lithium ions on MoS₂, Mn-doped MoS₂, and V-doped MoS₂ ^[54][41]. Compared with MoS₂, the doped MoS₂ showed smaller diffusion barriers (MoS₂, Mn-doped MoS₂, and V-doped MoS₂ were 0.08, 0.05, and 0.05 eV), suggesting accelerated lithium-ion migration after the introduction of doped elements. This was advantageous to promoting the rate performance of sulfur cathodes. Sun et al. fabricated P-vacancy CoP (CoP-Vp) to promote the polysulfide conversion ^[88][98]. Sun et al. confirmed that incorporating high oxygen contents into the CoP surface accelerated the electrochemical kinetics of polysulfides ^[89][99]. The authors calculated the diffusion of lithium ions on CoP with low and high oxygen contents. Lithium ions diffused on CoP with a high oxygen content underwent a decreased barrier of 0.47 eV, meaning a rapid lithium-ion diffusion and accelerated electrochemical conversion of polysulfides. A strain relaxation method has also been reported to tailor the anchoring and catalysis of MoNi₄ nanoalloys for Li-S batteries ^[40][55]. The calculation results implied that the MoNi₄ nanoalloys with superficial 1.59% strain had lower lithium-ion diffusion barriers (2.878 eV) in contrast to MoNi₄ (3.143 eV), accelerating the catalytic conversion of sulfur species. Lithium-ion diffusion barriers can also be used to evaluate the Li deposition/stripping kinetics in Li-S batteries. Lee and co-workers reported that In₂Se₃ can effectively catalyze Li-S batteries and improve the reversibility of lithium deposition ^[90][100]. Acting as a dual-functional additive, In₂Se₃ was found to simultaneously boost the performance of cathodes and anodes for Li-S batteries. The dissolved In³⁺ and Se²⁺ reacted with polysulfides to form LiInS₂ and LiInSe₂, which were incorporated into the SEI and improved the plating and stripping of lithium. This can be concluded by the lithium-ion diffusion calculations. The previous report showed that the optimum pathway of lithium-ion diffusion on Li₂S was along the (100) direction with a low barrier of 0.348 eV. In contrast, the lithium-ion diffusion barriers of LiInS₂ and LiInSe₂ considerably decreased to 0.286 and 0.269 eV, respectively. The smaller lithium-ion diffusion barriers confirmed more uniform lithium-ion migration through the SEI and rapid kinetics for lithium deposition.

6. Li₂S Decomposition Energy Barriers

Because of the insulating nature of Li₂S, its dissociation process during charging should overcome huge energy barriers ^[91][101]. Therefore, accelerating the catalytic Li₂S oxidation benefits sulfur cathodes’ stable capacity and long cycle life. In this case, Zhou et al. proposed the decomposition process of Li₂S ^[87][97]. An intact Li₂S molecule can be decomposed into an individual lithium ion and a LiS cluster as follows: The decomposition process involves the dissociation of Li from the Li₂S molecule, associated with the Li-S bond cleavage. The calculated decomposition barrier of Li₂S can be used to evaluate the activities of catalysts towards Li₂S oxidation. By analyzing the decomposition energy profiles of Li₂S on various sulfides, the authors indicated that decomposition energy barriers were essentially dependent on the binding ability of the isolated lithium ions with the sulfur of sulfides. Due to the strong binding ability, sulfides caused smaller decomposition barriers than carbon since the binding of lithium ions with carbon was much weaker. This conclusion can explain why sulfides can be good catalysts for Li-S batteries. Oxides have been investigated to catalyze the electrochemical conversion of Li-S batteries ^[68][80]. TiO₂ has been confirmed to have favorable chemical adsorption for anchoring polysulfides. However, it is plagued by intrinsically low conductivity, impeding the conversion kinetics of sulfur cathodes. Wei and co-workers developed a high-performance TiO₂ catalyst composed of a rich O-vacancy TiO₂ anatase/rutile homojunction on carbon nanosheets (A/R-TiO₂) ^[92][45]. The heterointerface of A/R-TiO₂ provided effective anchoring and smooth conversion of polysulfides. It also significantly reduced the Li₂S decomposition energy barrier. Yang et al. designed dual Ni-N₄ and Fe-N₄ sites co-anchored on carbon nanocages to catalyze sulfur cathodes ^[74][48]. The high ε_d of the Fe-N₄ sites demonstrated an accelerated sulfur reduction reaction. Meanwhile, Li₂S on the Ni-N₄ sites revealed a metallic nature, leading to strong S 2p DOS near the Femi level and thus allowing small Li₂S dissociation barriers. The calculation confirmed that the decomposition energy barrier of Li₂S on Ni-N₄ centers (1.20 eV) was smaller in contrast to that on Fe-N₄ (1.35 eV). This behavior originated from the moderate anchoring ability of Li₂S on Ni-N₄ (−1.63 eV) compared with that on Fe-N₄ (−2.65 eV). The moderate adsorption of Li₂S typically resulted in favorable decomposition. Song et al. developed dual Zn-Co metal–N/O sites with combined effects on rapid catalytic kinetics for sulfur cathodes ^[93][104]. DFT calculations suggested that the Li₂S decomposition barriers of this dual-core single-atom catalyst were lower than those of the single-core counterpart. Other types of catalysts, such as nitrides ^[94][105], MXene ^[95][106], and heterostructures ^[96][107], have been reported to regulate Li₂S decomposition. Ma et al. constructed a multibranched vanadium nitride (MB-VN) catalyst towards Li-S batteries with high-/low-temperature tolerance ^[71][83]. MB-VN exhibited a small Li₂S decomposition barrier of 0.67 eV, implying a rapid Li₂S dissociation on MB-VN. Zhang et al. reported hierarchically N-doped porous carbon incorporated F-free Ti₃C₂T_x for Li-S batteries ^[95][106]. Ti coordinated with N presented combined effects on decreasing the Li₂S decomposition barriers, hence accelerating the redox kinetics of sulfur cathodes. Tang and co-workers prepared Co-doped P-vacancy FeP catalysts on MXene, which considerably improved the bidirectional Li₂S reaction processes ^[63][75]. The decomposition energy barriers of Li₂S (0.69 eV) on the catalyst were considerably smaller in contrast to those on FeP (1.86 eV). Another MXene-based catalyst designed by Nguyen et al. has also revealed a mitigated energy barrier for Li₂S decomposition ^[56][68].