DFT Simulation-Based Design of 1T-MoS2 Cathode Hosts for Li-S Batteries and Experimental Evaluation

The main challenge in lithium sulphur (Li-S) batteries is the shuttling of lithium polysulphides (LiPSs) caused by the rapid LiPSs migration to the anode and the slow reaction kinetics in the chain of LiPSs conversion. In this study, we explore 1T-MoS2 as a cathode host for Li-S batteries by examining the affinity of 1T-MoS2 substrates (pristine 1T-MoS2, defected 1T-MoS2 with one and two S vacancies) toward LiPSs and their electrocatalytic effects. Density functional theory (DFT) simulations are used to determine the adsorption energy of LiPSs to these substrates, the Gibbs free energy profiles for the reaction chain, and the preferred pathways and activation energies for the slow reaction stage from Li2S4 to Li2S. The obtained information highlights the potential benefit of a combination of 1T-MoS2 regions, without or with one and two sulphur vacancies, for an improved Li-S battery performance. The recommendation is implemented in a Li-S battery with areas of pristine 1T-MoS2 and some proportion of one and two S vacancies, exhibiting a capacity of 1190 mAh/g at 0.1C, with 97% capacity retention after 60 cycles in a schedule of different C-rates from 0.1C to 2C and back to 0.1C.


Introduction
The rechargeable lithium-sulphur (Li-S) batteries feature the advantages of high theoretical energy density, low toxicity, and low cost, making them promising candidates as the next-generation energy storage technology. Despite extensive development in materials for the cathode, separator, and electrolyte [1], the migration of lithium polysulphides (LiPSs) to the anode and the slow reaction kinetics are still the key challenges that hinder their commercial applications. The impact of the LiPSs migration and shuttling effect is active material loss, rapid capacity fading, poor cycling stability, and severe anode corrosion [2]. Although a solid electrolyte would not allow any shuttling of LiPSs [3], it would also substantially reduce the diffusion rate of the Li + ions [3][4][5], compared to that of cations in liquid electrolytes [5,6]. Efforts to eliminate the problem of LiPSs migration while using a liquid electrolyte have focussed on trapping the soluble LiPSs in the cathode via physical confinement or attraction to functional groups in the cathode host. Nanostructured cathode hosts of hollow carbon particles [7] and micro/mesoporous carbon [8,9] offer physical confinement, despite their limited sulphur loading and inability of cyclic S 8 to fill ultra-micropores [10,11], where the redox reactions and Li + ion diffusion are expected to take place on the solid surface [12]. Added functional groups such as -OH, -COOH, and -NH 2 or N-and O-doped carbon have also shown an increased adsorption energy for the carbonaceous hosts in relation to LiPSs, with the adsorption energy predicted to be in the range of 0.5 to 2 eV via density functional theory (DFT) simulations [13][14][15]. Cathode hosts that both trap LiPSs and also act as electrocatalysts are of the greatest interest for the Li-S batteries: trapping LiPSs slows down their migration, while a fast redox reaction to the next stage in the reaction chain ensures a longer discharge curve to higher capacity. Single atom catalysts (SACs) of TM-N 4 -C (TM = Co, Fe, V, and W) are of this type, showing promise of good electrocatalysts with the DFT-predicted adsorption energies of soluble LiPSs in the range of 1.3 to 4.3 eV [16][17][18][19]. However, a low concentration (1-2 at.%) of these single atoms can be achieved in practice in real materials without particle segregation, which makes it challenging if high loading of single atoms for high overall performance is aimed [20]. Polar hosts, such as transition-metal carbides [21,22], oxides/hydroxides [23,24], sulphides [25,26], selenides [27], nitrides, phosphides [28], and their composites [29,30] instead prove to be more promising to enhance the anchoring capability towards polysulphides intermediates and the kinetics of the LiPSs redox reactions, as they act across the full material surface. Among the polar materials, however, only metal sulphides exhibit enhanced electronic conductivity and catalytic properties at a very high kinetic rate of sulphur electrochemistry during cell operation [31][32][33].
The literature provides a number of DFT simulations on different MoS 2 -based hosts to boost the anchoring effect of the pristine 2H-MoS 2 toward LiPSs and therefore reduce its dissolution in the chosen electrolyte [26,47,[49][50][51]. The DFT predicted adsorption energies of LiPSs by a pristine 1T-MoS 2 monolayer were also reported in the range of 0.64 to 2.9 eV, compared with 0.1 to 0.8 eV by a pristine 2H-MoS 2 monolayer [26]. In a separate study, the calculated adsorption energies of LiPSs adsorbed on a pristine 1T-MoS 2 monolayer were reported in the range of 1.1 to 1.4 eV, which were significantly higher than those of graphene supported 1T-MoS 2 and free-standing graphene [47]. Despite different reported values of adsorption energies for pristine 1T-MoS 2 , research is still ongoing for an ideal anchoring material with enhanced electrocatalytic effects, good electrical and ionic conductivity, improving the electrochemical performance of Li-S batteries. To our knowledge, the binding effects of the defected 1T-MoS 2 structures towards LiPSs have not yet been explored. Additionally, the catalytic activity for the LiPSs conversion reactions on the sulphur-deficient 1T-MoS 2 structures is not known, although the conversion reaction of LiPSs on 2H-MoS 2 and 2H-MoS 2 -2S during the discharge process [51], has been studied using the Gibbs free energy profiles.
In this study, we use DFT simulations to design 1T-MoS 2 hosts for Li-S batteries by assessing a pristine 1T-MoS 2 substrate, an 1T-MoS 2 -1S (with one sulphur vacancy) and an 1T-MoS 2 -2S (with two sulphur vacancies) in terms of their binding energy with LiPSs, the Gibbs free energy profiles for the full polysulphide reaction chain from S 8 to Li 2 S to identify the rate-limiting step in the conversion reactions, and the reaction pathway from Li 2 S 4 to Li 2 S, as this section of the pathway is considered the flattest part of the profile with ratelimiting sections [17]. The TSS (transition state search) task of DFT is employed to predict the activation energy barriers to chemical reactions to determine reaction pathways for the typically slow reaction chain of Li 2 S 4 to Li 2 S 2 and then to Li 2 S for the different 1T-MoS 2 substrates. Furthermore, a Li-S battery is evaluated experimentally with a 1T-MoS 2 cathode host combining the structures investigated in DFT, then its performance is compared to a typical sulphur cathode with a carbonaceous host.

DFT Simulations
The optimised 1T-MoS 2 and its defected (MoS 2 -1S and MoS 2 -2S) structures, as well as the optimised configurations of Li 2 S n (n = 1, 2, 4, 6, and 8), are shown in Figure 1. All structures and the average bond lengths are in a good agreement with high-accuracy first-principles calculations reported so far [17,52].
on the sulphur-deficient 1T-MoS2 structures is not known, although the conversion reaction of LiPSs on 2H-MoS2 and 2H-MoS2-2S during the discharge process [51], has been studied using the Gibbs free energy profiles.
In this study, we use DFT simulations to design 1T-MoS2 hosts for Li-S batteries by assessing a pristine 1T-MoS2 substrate, an 1T-MoS2-1S (with one sulphur vacancy) and an 1T-MoS2-2S (with two sulphur vacancies) in terms of their binding energy with LiPSs, the Gibbs free energy profiles for the full polysulphide reaction chain from S8 to Li2S to identify the rate-limiting step in the conversion reactions, and the reaction pathway from Li2S4 to Li2S, as this section of the pathway is considered the flattest part of the profile with ratelimiting sections [17]. The TSS (transition state search) task of DFT is employed to predict the activation energy barriers to chemical reactions to determine reaction pathways for the typically slow reaction chain of Li2S4 to Li2S2 and then to Li2S for the different 1T-MoS2 substrates. Furthermore, a Li-S battery is evaluated experimentally with a 1T-MoS2 cathode host combining the structures investigated in DFT, then its performance is compared to a typical sulphur cathode with a carbonaceous host.

DFT Simulations
The optimised 1T-MoS2 and its defected (MoS2-1S and MoS2-2S) structures, as well as the optimised configurations of Li2Sn (n = 1, 2, 4, 6, and 8), are shown in Figure 1. All structures and the average bond lengths are in a good agreement with high-accuracy firstprinciples calculations reported so far [17,52]. For the adsorption of Li2Sn (n = 1, 2, 4, 6, and 8) on pristine 1T-MoS2 and the defected structures, the vertical distances between two Li atoms to the surfaces were set initially according to the reported data [51] and then further adjusted by the DFT simulations of energy minimisation, see Figure 2. For the investigation of Li2S8 adsorption, the Li-Li bond was considered perpendicular to the 1T-MoS2 (001) structures, such that the Li2S8 molecule lied flat above the surface, consistent with the reported optimisation results [25,51]. For the adsorption of Li 2 S n (n = 1, 2, 4, 6, and 8) on pristine 1T-MoS 2 and the defected structures, the vertical distances between two Li atoms to the surfaces were set initially according to the reported data [51] and then further adjusted by the DFT simulations of energy minimisation, see Figure 2. For the investigation of Li 2 S 8 adsorption, the Li-Li bond was considered perpendicular to the 1T-MoS 2 (001) structures, such that the Li 2 S 8 molecule lied flat above the surface, consistent with the reported optimisation results [25,51]. and are the adsorption energy of the system and the minimum Li-substrate distance, respectively. Figure 3 presents the adsorption energies of the LiPSs intermediates (Li2Sn, n = 1, 2, 4, 6, and 8) on the 1T-MoS2 substrates in comparison with SACs TM-N4-C (TM = Co, Fe, V, and W) and graphene. For Li2S, Li2S2 and, especially, Li2S4, whose migration to the anode is critical in suppressing the subsequent cascade reactions, the strength of binding energy follows the order of graphene < Co-N4-C < Fe-N4-C < 1T-MoS2 pristine < 1T-MoS2-1S < V-N4-C < W-N4-C < 1T-MoS2-2S. The strongest binding affinity amongst all substrates is observed for 1T-MoS2-2S, with the binding energies of 5.38, 5.14, and 4.04 eV for Li2S, Li2S2, and Li2S4, respectively. For Li2S6 and Li2S8, although the 1T-MoS2 substrates with sulphur vacancies perform better than Co-N4-C and Fe-N4-C, they do exhibit weaker affinity than V-N4-C and W-N4-C. The observed stronger adsorption energies of the MoS2 substrates with the shorter lithium polysulphide chains indicates gradually reinforced chemical interaction from the lithium ions. This is in contrast with the weakest binding strength of the single atom catalysts with Li2S4, especially for V-N4-C and W-N4-C, indicating the chance of Li2S4 migration to the anode before it has the chance to transform to the precipitating solid Li2S2 and Li2S. Our results on the binding energies for the pristine 1T-MoS2 showed an energy range of 0.7-3.3 eV which is in a good agreement with those of Dong et al. [26], but not completely in line with those of He et al. [47]. To the best of our knowledge, we are the first to report the binding energies of LiPSs with the defected 1T-MoS2, with one and two sulphur vacancies.  and, especially, Li 2 S 4 , whose migration to the anode is critical in suppressing the subsequent cascade reactions, the strength of binding energy follows the order of graphene < Co-N 4 -C < Fe-N 4 -C < 1T-MoS 2 pristine < 1T-MoS 2 -1S < V-N 4 -C < W-N 4 -C < 1T-MoS 2 -2S. The strongest binding affinity amongst all substrates is observed for 1T-MoS 2 -2S, with the binding energies of 5.38, 5.14, and 4.04 eV for Li 2 S, Li 2 S 2 , and Li 2 S 4 , respectively. For Li 2 S 6 and Li 2 S 8 , although the 1T-MoS 2 substrates with sulphur vacancies perform better than Co-N 4 -C and Fe-N 4 -C, they do exhibit weaker affinity than V-N 4 -C and W-N 4 -C. The observed stronger adsorption energies of the MoS 2 substrates with the shorter lithium polysulphide chains indicates gradually reinforced chemical interaction from the lithium ions. This is in contrast with the weakest binding strength of the single atom catalysts with Li 2 S 4 , especially for V-N 4 -C and W-N 4 -C, indicating the chance of Li 2 S 4 migration to the anode before it has the chance to transform to the precipitating solid Li 2 S 2 and Li 2 S. Our results on the binding energies for the pristine 1T-MoS 2 showed an energy range of 0.7-3.3 eV which is in a good agreement with those of Dong et al. [26], but not completely in line with those of He et al. [47]. To the best of our knowledge, we are the first to report the binding energies of LiPSs with the defected 1T-MoS 2 , with one and two sulphur vacancies. The higher adsorption energy for 1T-MoS2 with sulphur vacancies toward LiPSs intermediates, especially the lower order sulphides Li2S, Li2S2, and Li2S4, compared with 1T-MoS2 pristine can be explained based on the charge density. Research showed that the sulphur deficiency in the MoS2 structure resulted in larger charge densities of surrounding S atoms and therefore a tighter bond with Li atoms [51]. This would enhance the interaction with the LiPSs intermediates, providing more thermodynamics and kinetic driving force for binding and finally causing an increased stabilisation effect. Overall, Figure 3 illustrates that 1T-MoS2-2S (two sulphur vacancies) has better capability in trapping all sulphides than 1T-MoS2 and 1T-MoS2-1S.
To evaluate the catalytic effect of 1T-MoS2 substrates, different disproportionation reaction pathways for the slow conversion of Li2S4 to Li2S were investigated: (i) a two-step process: Li2S4 → Li2S2 + S2 followed by Li2S2 → Li2S + S; (ii) a one-step process: Li2S4 → Li2S + S3. Figure 4 depicts the optimised geometry of the adsorbed Li2S2 ( Figure 4A-C) and its dissociated products ( Figure 4D-F) on the surface of 1T-MoS2 substrates for the last reaction: Li2S2 → Li2S + S of pathway (i) above, as obtained by the DFT simulations. Figures S1 and S2 also show the optimised geometry of the adsorbed Li2S4 and its dissociated products on the surface of 1T-MoS2 substrates for the first reaction: Li2S4 → Li2S2 + S2 of pathway (i) and the reaction: Li2S4 → Li2S + S3 of pathway (ii), respectively. In the different structures in Figures 4, S1, and S2, the separated S atom, S2 or S3 molecules on 1T-MoS2 substrates is either on the top of the MoS2 structure (1T-MoS2 pristine) or embedded in the MoS2 structure (1T-MoS2 -1S) or in the void space created by the vacancies (1T-MoS2 -2S). Figure 5 shows the dissociation, , and activation, , energies and atomic structures of reactants and products for the disproportionation reactions of (A) Li2S4 → Li2S2 + S2, (B) Li2S4 → Li2S + S3, and (C) Li2S2 → Li2S + S on pristine 1T-MoS2, 1T-MoS2-1S, and 1T-MoS2-2S. The reaction coordinate and energy change of the transition state (TS) (as found from the transition-state search method (TSS)) and product, with respect to the reactant are further presented, with the calculated and values. Considering the two pathways (i) and (ii), starting from Li2S4 to ultimately reaching Li2S, Figure 5 illustrates that reaction pathway (ii), Li2S4 → Li2S + S3, is the preferred pathway for 1T-MoS2 pristine and 1T-MoS2-1S cathode hosts, as the activation and dissociation energies of this reaction (which are 1.73 and 0.32 eV, respectively) are lower than those of the reactions of pathway (i) (which are 2.30 and 0.68 eV, respectively). Hence, for these two molybdenum disulphide substrates the preferred pathway could be through direct conversion of Li2S4 to Li2S, The higher adsorption energy for 1T-MoS 2 with sulphur vacancies toward LiPSs intermediates, especially the lower order sulphides Li 2 S, Li 2 S 2 , and Li 2 S 4 , compared with 1T-MoS 2 pristine can be explained based on the charge density. Research showed that the sulphur deficiency in the MoS 2 structure resulted in larger charge densities of surrounding S atoms and therefore a tighter bond with Li atoms [51]. This would enhance the interaction with the LiPSs intermediates, providing more thermodynamics and kinetic driving force for binding and finally causing an increased stabilisation effect. Overall, Figure 3 illustrates that 1T-MoS 2 -2S (two sulphur vacancies) has better capability in trapping all sulphides than 1T-MoS 2 and 1T-MoS 2 -1S.
To evaluate the catalytic effect of 1T-MoS 2 substrates, different disproportionation reaction pathways for the slow conversion of Li 2 S 4 to Li 2 S were investigated: (i) a two-step process: Li 2 S 4 → Li 2 S 2 + S 2 followed by Li 2 S 2 → Li 2 S + S; (ii) a one-step process: Li 2 S 4 → Li 2 S + S 3 . Figure 4 depicts the optimised geometry of the adsorbed Li 2 S 2 ( Figure 4A-C) and its dissociated products ( Figure 4D-F) on the surface of 1T-MoS 2 substrates for the last reaction: Li 2 S 2 → Li 2 S + S of pathway (i) above, as obtained by the DFT simulations. Figures S1 and S2 also show the optimised geometry of the adsorbed Li 2 S 4 and its dissociated products on the surface of 1T-MoS 2 substrates for the first reaction: Li 2 S 4 → Li 2 S 2 + S 2 of pathway (i) and the reaction: Li 2 S 4 → Li 2 S + S 3 of pathway (ii), respectively. In the different structures in Figure 4, Figures S1 and S2, the separated S atom, S 2 or S 3 molecules on 1T-MoS 2 substrates is either on the top of the MoS 2 structure (1T-MoS 2 pristine) or embedded in the MoS 2 structure (1T-MoS 2 -1S) or in the void space created by the vacancies (1T-MoS 2 -2S). Figure 5 shows the dissociation, E d , and activation, E a , energies and atomic structures of reactants and products for the disproportionation reactions of (A) Li 2 S 4 → Li 2 S 2 + S 2 , (B) Li 2 S 4 → Li 2 S + S 3 , and (C) Li 2 S 2 → Li 2 S + S on pristine 1T-MoS 2 , 1T-MoS 2 -1S, and 1T-MoS 2 -2S. The reaction coordinate and energy change of the transition state (TS) (as found from the transition-state search method (TSS)) and product, with respect to the reactant are further presented, with the calculated E a and E d values. Considering the two pathways (i) and (ii), starting from Li 2 S 4 to ultimately reaching Li 2 S, Figure 5 illustrates that reaction pathway (ii), Li 2 S 4 → Li 2 S + S 3 , is the preferred pathway for 1T-MoS 2 pristine and 1T-MoS 2 -1S cathode hosts, as the activation and dissociation energies of this reaction (which are 1.73 and 0.32 eV, respectively) are lower than those of the reactions of pathway (i) (which are 2.30 and 0.68 eV, respectively). Hence, for these two molybdenum disulphide substrates the preferred pathway could be through direct conversion of Li 2 S 4 to Li 2 S, by-passing the Li 2 S 2 formation step. However, for 1T-MoS 2 -2S, reaction pathway (i) is preferred, consisting of a first step of Li 2 S 4 → Li 2 S 2 + S 2 followed by the second step of Li 2 S 2 → Li 2 S + S, as determined from their lower relative energy change, the activation barrier and dissociation energy values which compared well with those of Li 2 S 4 → Li 2 S + S 3 . These results mean that the minimum amount of energy that must be provided to the reactant components (Li 2 S 4 ) to lead to a chemical reaction for the Li 2 S 4 → Li 2 S + S 3 pathway is only met on 1T-MoS 2 pristine and 1T-MoS 2 -1S cathodes and for Li 2 S 4 → Li 2 S 2 + S 2 pathway is only met on 1T-MoS 2 -2S. Figure 5 further indicates a considerable activation energy difference between 1T-MoS 2 -1S and 1T-MoS 2 -2S throughout all reaction pathways. This can be explained based on the relationship between activation energy of a chemical reaction and its rate. In fact, molecules can only complete the reaction once they have reached the top of the activation energy barrier. Therefore, for the higher barriers, fewer molecules will have enough energy to make it over the barrier at any given moment, leading to a lower reaction rate, and for the lower barriers, more molecules will have enough energy to make it through, resulting in an increased reaction rate. Thereby, in Figure 5, very fast reaction rate for the reaction of Li 2 S 4 → Li 2 S + S 3 on 1T-MoS 2 pristine and 1T-MoS 2 -1S cathodes is predicted but for the reaction of Li 2 S 4 → Li 2 S 2 + S 2 , followed by Li 2 S 2 → Li 2 S + S, on 1T-MoS 2 -2S, a reduced reaction rate is expected. by-passing the Li2S2 formation step. However, for 1T-MoS2-2S, reaction pathway (i) is preferred, consisting of a first step of Li2S4 → Li2S2 + S2 followed by the second step of Li2S2 → Li2S + S, as determined from their lower relative energy change, the activation barrier and dissociation energy values which compared well with those of Li2S4 → Li2S + S3. These results mean that the minimum amount of energy that must be provided to the reactant components (Li2S4) to lead to a chemical reaction for the Li2S4 → Li2S + S3 pathway is only met on 1T-MoS2 pristine and 1T-MoS2-1S cathodes and for Li2S4 → Li2S2 + S2 pathway is only met on 1T-MoS2-2S. Figure 5 further indicates a considerable activation energy difference between 1T-MoS2-1S and 1T-MoS2-2S throughout all reaction pathways. This can be explained based on the relationship between activation energy of a chemical reaction and its rate. In fact, molecules can only complete the reaction once they have reached the top of the activation energy barrier. Therefore, for the higher barriers, fewer molecules will have enough energy to make it over the barrier at any given moment, leading to a lower reaction rate, and for the lower barriers, more molecules will have enough energy to make it through, resulting in an increased reaction rate. Thereby, in Figure 5, very fast reaction rate for the reaction of Li2S4 → Li2S + S3 on 1T-MoS2 pristine and 1T-MoS2-1S cathodes is predicted but for the reaction of Li2S4 → Li2S2 + S2, followed by Li2S2 → Li2S + S, on 1T-MoS2-2S, a reduced reaction rate is expected.  The main observation from all the results of Figure 5 is the lowest activation and dissociation energies for 1T-MoS2-1S compared to other molybdenum disulphide substrates throughout all reactions. This highlights the high catalytic activity of 1T-MoS2-1S The main observation from all the results of Figure 5 is the lowest activation and dissociation energies for 1T-MoS 2 -1S compared to other molybdenum disulphide substrates throughout all reactions. This highlights the high catalytic activity of 1T-MoS 2 -1S which results in spontaneous conversion reactions on the surface, with minimum energy requirement to proceed along the discharge of a Li-S battery.
A comparison of the activation energies for the typical last reaction Li 2 S 2 → Li 2 S + S on 1T-MoS 2 substrates against our previously published results on the single atom catalysts and graphene [17]   which results in spontaneous conversion reactions on the surface, with minimum energy requirement to proceed along the discharge of a Li-S battery. A comparison of the activation energies for the typical last reaction Li2S2 → Li2S + S on 1T-MoS2 substrates against our previously published results on the single atom catalysts and graphene [17] again confirms the superior catalytic activity of 1T-MoS2-1S against all studied catalysts with the lowest value ( follows the order of graphene (2.73 eV) > Fe-N4-C (1.71 eV) > Co-N4-C (1.66 eV) > W-N4-C (1.10 eV) > V-N4-C (1.01 eV) > 1T-MoS2-1S (0.27 eV). Therefore, it is expected that 1T-MoS2-1S could promote a fast LiPSs reaction and conversion to the final product. Figure 6 displays the relative Gibbs free energy profiles for the LiPSs disproportionation reactions on 1T-MoS2 substrates against graphene and TM-N4-C (TM = Co, Fe, V, and W) SAC materials, where an initial spontaneous exothermic reaction from S8 to Li2S8 is followed by a flatter profile with thermoneutral, or a small degree of exothermic or endothermic trends depending on substrate. It can be observed that the first step of Li2S8 production from S8 reactant is the most spontaneous according to the order: 1T-MoS2-2S > 1T-MoS2-1S > 1T-MoS2 > SACs. This means that the fastest reaction kinetics occurred on the 1T-MoS2-2S surface with Gibbs free energy value of -10.14 eV for the first conversion step.  Figure 3 which demonstrates the adsorption energies of the different 1T-MoS2 substrates towards Li2S8 are reducing, we could speculate that the amount of Li2S8 quantity produced on 1T-MoS2-2S would be prevented from migrating to the anode during discharge and be ready for the next reaction step at the surface of the cathode host.  Figure 3 which demonstrates the adsorption energies of the different 1T-MoS 2 substrates towards Li 2 S 8 are reducing, we could speculate that the amount of Li 2 S 8 quantity produced on 1T-MoS 2 -2S would be prevented from migrating to the anode during discharge and be ready for the next reaction step at the surface of the cathode host. The subsequent steps to Li 2 S 6 and Li 2 S 4 are almost thermoneutral for the 1T-MoS 2 substrates, indicating slower reactions than the first step. Thereafter, the preferred direct pathway is a little endothermic for 1T-MoS 2 and a little exothermic for 1T-MoS 2 -1S, but the energy required for 1T-MoS 2 is still less than the energy required for graphene [17], demonstrating the effectiveness of 1T-MoS 2 and 1T-MoS 2 -1S to reach good conversion to the final product Li 2 S. The 1T-MoS 2 -2S substrate guides the reaction mechanism along a two-step pathway, an almost thermoneutral step of Li 2 S 4 to Li 2 S 2 and a last endothermic step to Li 2 S of 1.52 eV, the same as for graphene substrate [17]. The very slow reaction conversion of Li 2 S 2 to Li 2 S plays a major limiting role in the utilisation of sulphur in Li-S batteries and has been identified as the rate-limiting step for the conversion of LiPSs species. Amongst all three of the investigated 1T-MoS 2 cathode hosts, 1T MoS 2 -1S offers the best substrate for the Li 2 S 4 to Li 2 S conversion, while 1T-MoS 2 without defects offers the best substrate for the Li 2 S 4 production and 1T-MoS 2 -2S offers the best substrate for the spontaneous Li 2 S 8 production and adsorption at the surface of cathode host. Taking also into account that 1T-MoS 2 -2S and then 1T-MoS 2 -1S have the highest adsorption energy towards LiPSs (Figure 3), it is clear that a balance of pristine 1T-MoS 2 and defected with 1S and 2S vacancies would be best to combine the strengths of each 1T-MoS 2 material and counteract any disadvantages. Figure 7 displays the atom-projected PDOS plots for 1T-MoS 2 , 1T-MoS 2 -1S, and 1T-MoS 2 -2S structures, for the adsorbed Li 2 S 4 and the products of the disproportionation reactions throughout the preferred reaction pathways for each substrate in the conversion of Li 2 S 4 to Li 2 S. The up and down spins states of electrons in the PDOS data before Li 2 S 4 adsorption and throughout the conversion reactions were symmetrically distributed which reflects the non-magnetic properties of the based molecules even after the conversion reactions. It must be mentioned that here for the sake of simplicity and clarity in the graphs only the up spin states of electrons are presented in Figure 7. For the 1T-MoS 2 , 1T-MoS 2 -1S, and 1T-MoS 2 -2S structures before adsorption of Li 2 S 4 , the hybridized DOS intensities for Mo and S atoms below the Fermi level, where there is a high probability of the electrons occupied-states, confirm the inherent covalent binding between the nearest neighbour atoms, in line with previous observations in the literature [53]. The DOS intensities for Mo above the Fermi level demonstrate its partly metallic character as a transition metal. This can be explained based on the availability of electrons unoccupied-states of Mo for the binding. After adsorption of Li 2 S 4 on the 1T-MoS 2 substrates, the DOS intensities near-Fermi level exhibit a sudden increase for both Mo and S atoms, indicating occupation of the available states by the Li 2 S 4 electrons. Figure 8 further depicts the orbital projected PDOS plots of d, p, and s orbitals of Mo, S, and Li atoms, respectively, after adsorption of Li 2 S 4 and for the dissociation reactions for all substrates. The plots reveal that the d states have coupled with the p states and have crossed the Fermi level, demonstrating a strong hybridisation between Mo d and S p orbitals throughout the disproportionation reactions. The electron doping effect of Li can also cause the chemical potentials to be shifted towards the unoccupied d bands, and therefore the composite systems to remain metallic. This confirms that the loss of energy with lithiation is plausible, as was already observed in our binding energy results (see Figure 3).

Experimental Evaluation
Based on the recommendations of the DFT simulations in Section 2.1, the 1T-MoS2 material used as cathode host combines 1T-MoS2, 1T-MoS2-1S, and 1T-MoS2-2S regions, amounting to a vacancy concentration of 6 × 10 13 cm −2 of which 87% is 1S vacancies and 13% is 2S vacancies according to the data from material characterisation via high angle annular dark-field (HAADF) scanning transmission electron microscope (STEM) imaging from a previous study by our group for hydrogen evolution reaction [54]. Figure 10 presents the experimental data from the electrochemical testing. Figure 10A depicts a maximum specific capacity of 1190 mAh gS −1 and 655 mAh gS −1 upon discharge at 0.1C and 1C, respectively, which is superior than Li-S cells in the literature with carbon cathode hosts and the same separator and electrolyte tested in galvanostatic charge-discharge (GCD): for example, a Li-S cell with carbon nanofibre host exhibited 930 mAh gS −1 and 556 mAh gS −1 upon discharge at 0.1C and 1C, respectively [55]. The reaction plateau at 2.1V is corresponding to the conversion of Li2S4 into Li2S, described as the following equation (considering S8 as the starting reactant in discharge): 2Li2S4 + 12Li + + 12e -↔ 8Li2S, consistent with the DFT simulations that predict this to be the preferred pathway for cathode host pristine 1T-MoS2 and 1T-MoS2-1S.
CV at different rates in Figure 10B displays a distinct peak upon charge and two distinct peaks upon discharge at the typical voltage positions as expected in Li-S cells [55,56]. The CV rate dependence of the overpotential and intensity of CV peaks is as expected in battery cells [57]. The polarisation at 0.2 mV s −1 is lower than expected, compared to the CV curve at 0.1 mV s −1 , because the faster scan rate of 0.2 mV s −1 leaves shorter time for reaction and thus the reaction is less sufficient or it might result to a large amount of sulphide production over the solution saturation point that leads to early precipitation that might block good electron transport for further reaction. The cell demonstrates good cyclability in Figure 10A,C (97% capacity retention after 50 cycles in the schedule of Figure  10C) and almost 100% coulombic efficiency in Figure 10D, all attributed to the elimination of the shuttling of polysulphides given the high adsorption energy and good electrocatalytic properties for the related cathode host material as predicted by the DFT simulations. The fall of capacity of the cell cycled at 1C in Figure 10D, from 625 to 460 mAh gS −1 after 200 cycles, is attributed to issues of solid precipitation (sulphur precipitation in charge or Li2S precipitation in discharge) at the moderately high C-rate, rather than any shuttling effects, given that the capacity is stabilised at 460 mAh gS −1 after 200 cycles till a total 500 cycles tested so far.

Experimental Evaluation
Based on the recommendations of the DFT simulations in Section 2.1, the 1T-MoS 2 material used as cathode host combines 1T-MoS 2 , 1T-MoS 2 -1S, and 1T-MoS 2 -2S regions, amounting to a vacancy concentration of 6 × 10 13 cm −2 of which 87% is 1S vacancies and 13% is 2S vacancies according to the data from material characterisation via high angle annular dark-field (HAADF) scanning transmission electron microscope (STEM) imaging from a previous study by our group for hydrogen evolution reaction [54]. Figure 10 presents the experimental data from the electrochemical testing. Figure 10A depicts a maximum specific capacity of 1190 mAh g S −1 and 655 mAh g S −1 upon discharge at 0.1C and 1C, respectively, which is superior than Li-S cells in the literature with carbon cathode hosts and the same separator and electrolyte tested in galvanostatic charge-discharge (GCD): for example, a Li-S cell with carbon nanofibre host exhibited 930 mAh g S −1 and 556 mAh g S −1 upon discharge at 0.1C and 1C, respectively [55]. The reaction plateau at 2.1 V is corresponding to the conversion of Li 2 S 4 into Li 2 S, described as the following equation (considering S 8 as the starting reactant in discharge): 2Li 2 S 4 + 12Li + + 12e − ↔ 8Li 2 S, consistent with the DFT simulations that predict this to be the preferred pathway for cathode host pristine 1T-MoS 2 and 1T-MoS 2 -1S.
CV at different rates in Figure 10B displays a distinct peak upon charge and two distinct peaks upon discharge at the typical voltage positions as expected in Li-S cells [55,56]. The CV rate dependence of the overpotential and intensity of CV peaks is as expected in battery cells [57]. The polarisation at 0.2 mV s −1 is lower than expected, compared to the CV curve at 0.1 mV s −1 , because the faster scan rate of 0.2 mV s −1 leaves shorter time for reaction and thus the reaction is less sufficient or it might result to a large amount of sulphide production over the solution saturation point that leads to early precipitation that might block good electron transport for further reaction. The cell demonstrates good cyclability in Figure 10A,C (97% capacity retention after 50 cycles in the schedule of Figure 10C) and almost 100% coulombic efficiency in Figure 10D, all attributed to the elimination of the shuttling of polysulphides given the high adsorption energy and good electrocatalytic properties for the related cathode host material as predicted by the DFT simulations. The fall of capacity of the cell cycled at 1C in Figure 10D, from 625 to 460 mAh g S −1 after 200 cycles, is attributed to issues of solid precipitation (sulphur precipitation in charge or Li 2 S precipitation in discharge) at the moderately high C-rate, rather than any shuttling effects, given that the capacity is stabilised at 460 mAh g S −1 after 200 cycles till a total 500 cycles tested so far. The 1T-MoS2 cathode host material of this study, combined with 1 and 2 sulphur vacancies, is a significant advance compared with relevant sulphide-based cathode hosts in the literature. For example, N-doped MoS2 based on 1T/2H mixed phase MoS2 [58] exhibited similarly good cyclability as displayed in Figure 10C in this study but lower discharge capacity (1030 mAh gS −1 ) at 0.1 C than our results in Figure 10A. A mesoporous carbon/ZnS/CuS nanocomposite cathode [59] reached a high specific capacity of 1457 mAh gS −1 at first discharge at 0.1 C but not so good cyclability after a schedule of 50 cycles at different C-rates (1000 mAh gS −1 at 0.1 C in cycle 45) compared to our results in Figure 10C.

Computational Method
The simulation framework which takes into account the atomic and electronic properties of 1T-MoS2 (including pristine, defected with sulphur vacancies of 1T-MoS2-1S and 1T-MoS2-2S) was first implemented in VESTA software. The lattice parameters were optimised by allowing the supercell lattice vectors and ionic positions to change in a simulation box with the vacuum space of 35 Å in the Z-direction. A (4 × 4) supercell of MoS2 monolayer consisting of 48 atoms, which contains 16 Mo and 32 S, was made up of the primitive cell of MoS2. The supercell size was selected so that the 1S or 2S vacancy concentration in 1T-MoS2-1S and 1T-MoS2-2S, respectively, matched the total vacancy concentration of the material used in the experimental section of this study, reported as 6 × 10 13 cm −2 in Section 2.2. CASTEP was then employed to perform all spin-polarised DFT simulations for the interaction between the lithium sulphide species and each MoS2 substrate [60]. A spin polarisation of 2 was used. The exchange and correlation potential was The 1T-MoS 2 cathode host material of this study, combined with 1 and 2 sulphur vacancies, is a significant advance compared with relevant sulphide-based cathode hosts in the literature. For example, N-doped MoS 2 based on 1T/2H mixed phase MoS 2 [58] exhibited similarly good cyclability as displayed in Figure 10C in this study but lower discharge capacity (1030 mAh g S −1 ) at 0.1 C than our results in Figure 10A. A mesoporous carbon/ZnS/CuS nanocomposite cathode [59] reached a high specific capacity of 1457 mAh g S −1 at first discharge at 0.1 C but not so good cyclability after a schedule of 50 cycles at different C-rates (1000 mAh g S −1 at 0.1 C in cycle 45) compared to our results in Figure 10C.

Computational Method
The simulation framework which takes into account the atomic and electronic properties of 1T-MoS 2 (including pristine, defected with sulphur vacancies of 1T-MoS 2 -1S and 1T-MoS 2 -2S) was first implemented in VESTA software. The lattice parameters were optimised by allowing the supercell lattice vectors and ionic positions to change in a simulation box with the vacuum space of 35 Å in the Z-direction. A (4 × 4) supercell of MoS 2 monolayer consisting of 48 atoms, which contains 16 Mo and 32 S, was made up of the primitive cell of MoS 2 . The supercell size was selected so that the 1S or 2S vacancy concentration in 1T-MoS 2 -1S and 1T-MoS 2 -2S, respectively, matched the total vacancy concentration of the material used in the experimental section of this study, reported as 6 × 10 13 cm −2 in Section 2.2. CASTEP was then employed to perform all spin-polarised DFT simulations for the interaction between the lithium sulphide species and each MoS 2 substrate [60]. A spin polarisation of 2 was used. The exchange and correlation potential was calculated using the generalised gradient approximation (GGA) exchange correlation function as described by Perdew−Burke− Ernzerhof (PBE) [61], and the Brillouin zone was sampled with the Monkhorst-Pack grid using a 2 × 2 × 1 K-point mesh. The valence electrons identified on a plane-wave basis were used with a cut-off energy of 500 eV to ensure the precision of calculations and the tight convergence criteria (energy and force tolerance of 10 −5 eV and 10 −4 eV/A • , respectively). The van der Waals (vdW) dispersion correction as described by Grimme's empirical method was further considered for all the simulations [62].

Computational Models
The studied 1T-MoS 2 consisted of one molybdenum sheet sandwiched by two sulphur sheets, forming an S-Mo-S structure, where the weakly interacting layers were held together by van der Waals interactions. The (001) facet as the largest exposed surface [51], was selected for simulation of the catalysts. The adsorption sites were chosen at hexagonal close packed (HCP) and face centred cubic (FCC) positions on all catalysts, as recommended [51]. For the defected 1T-MoS 2 (001) surface, the model was constructed by deleting one or two Top site S atoms at the centre position (S-deficiency), and therefore, the additional S-deficiency position was further investigated as the adsorption site. The atoms of the catalysts were also relaxed during the optimisation process. The polysulphides modelled were: Li 2 S x , x = 1, 2, 4, 6, and 8, which are the typical polysulphides produced in Li-S batteries with electrolyte 1M LiTFSI in DOL/DME solvent mixture 1:1 v/v [63,64].
Regarding the investigations of the reaction pathway and catalytic effects, a model of LiPS disproportionation reactions was considered for the formation of Li 2 S from Li bulk and S 8, as described by Equations (1)-(5): The adsorption, E ads , and dissociation, E diss , energies were calculated for the fully relaxed structures as: where E (MoS 2 sub +LiPs) is the total energy of the adsorbed polysulfide on 1T-MoS 2 substrate, E MoS 2 sub is the individual energy of 1T-MoS 2 substrate, E LiPs is the energy of an isolated LiPs molecules in a cubic lattice with a cell length of 30 Å, and E (MoS 2 sub+dissosiated LiPs) is the total energy of the dissociated polysulfide on 1T-MoS 2 substrate. The dissociation energy, E diss , is the required energy to break a bond and form separate molecular fragments. The relative Gibbs free energies were calculated from the total energies of the examined configurations, based on the disproportionation reactions on the cathode host, as described by the general equation as below: The activation energy was additionally calculated from the results of the transition state search (TSS) task of DFT simulation based on the transition states between the Li 2 S n (i.e., reactant) and decomposed Li 2 S n (i.e., product). The complete linear synchronous transit and quadratic synchronous transit (LST/QST) methods were used for the TSS task, where the root mean square forces per atom convergence criterion was set to be 10 −3 eV/Å. The LST method performed a single interpolation to a maximum energy and the QST method alternated searches for an energy maximum with constrained minimisations in order to refine the transition state to a high degree, where their combination interpolated a reaction pathway to find a transition state.

Materials and Experimental Methods
Chemically exfoliated 1T-MoS 2 as described in [65] was used as a cathode host in Li-S battery cells that were assembled in an argon-filled glove box. Specifically, the cathode of 1T MoS 2 -sulphur composite (60 wt% sulphur) was prepared by vacuum filtrating the dispersion of 20 mg 1T-MoS 2 and 30 mg sulphur powders in carbon disulphide solution (5.0 M in THF) over an anodic aluminium oxide membrane (0.02 µm pore size), followed by drying at room temperature. The areal sulphur loading was 2 mg cm −2 . The prepared 1T MoS 2 -sullfur composite (60 wt% sulphur) cathode, carbon-coated aluminium foil current collector, Li foil anode, and Celgard 2400 separator were assembled into CR2032 coin cells. The electrolyte was composed of 1.0 M LiTFSI with 0.2 M LiNO 3 dissolved in DOL/DME (v/v = 1:1) solvents. The electrolyte/sulphur (E/S) ratio was controlled as 15 µL/mg S. The assembled Li-S coin cells were galvanostatically cycled within the potential window of 1.7-2.8 V on Land battery cycler at various C rates (1C = 1672 mAh/mgS). CV testing was also performed within the potential window of 1.5-3.0 V on biologic VSP-300 potentiostat.

Conclusions
In this study, first principle DFT simulations were carried out to design 1T-MoS 2 cathode hosts for Li-S batteries, where the effect of S vacancies was evaluated by investigating pristine 1T-MoS 2 , 1T-MoS 2 -1S, and 1T-MoS 2 -2S. The investigations focussed on the adsorption properties of the 1T-MoS 2 host materials with respect to the polysulphides Li 2 S x ; x = 1, 2, 4, 6, and 8; the change of the Gibbs free energy along the reaction steps in the reaction chain to convert S 8 to Li 2 S, and the electrocatalytic properties of the MoS 2 host materials and identification of the preferred pathway for the second reaction stage to convert Li 2 S 4 to Li 2 S that is typically slow in Li-S batteries. The results were also compared to SACs TM-N 4 -C (TM = Co, Fe, V, and W) and graphene cathode hosts [17]. It was observed that the binding affinities of 1T-MoS 2 substrates toward polysulphides with the shorter lithium polysulphide chains experienced a gradual strength, where 1T-MoS 2 -2S exhibited significant adsorption ability for all LiPSs intermediates among the examined cathode hosts.
The Gibbs free energy profiles indicated that all 1T-MoS 2 substrates yielded more spontaneous production of Li 2 S 8 than the SACs and graphene, with 1T-MoS 2 -2S and 1T-MoS 2 -1S exhibiting twice and four times, respectively, lower energy than that of SACs. Given the relatively high adsorption energy of S-vacancy containing 1T-MoS 2 materials (3.7 and 2 eV, respectively), we believe these hosts will be able to retain the Li 2 S 8 molecules in the cathode to proceed with the next reaction steps. The Gibbs energy profiles for the next two reaction steps to Li 2 S 6 and Li 2 S 4 showed almost thermoneutral processes for the 1T-MoS 2 substrates with vacancies and a little exothermic reaction for the pristine 1T-MoS 2 , facilitating conversion to Li 2 S 4 which is well adsorbed by all substrates. Thereafter, direct conversion from Li 2 S 4 to Li 2 S (solid precipitate) is the preferred pathway for 1T-MoS 2 and 1T-MoS 2 -1S, with the reaction being a little exothermic on 1T-MoS 2 -1S, and low activation energies of 0.47 eV and 0.32 eV on 1T-MoS 2 and 1T-MoS 2 -1S, respectively. The preferred conversion pathway on 1T-MoS 2 -2S includes two steps: a thermoneutral reaction from Li 2 S 4 to Li 2 S 2 with an activation energy of 3.89 eV and an endothermic reaction from Li 2 S 2 to Li 2 S (solid precipitate) with an activation energy of 2.41 eV. The intermediate product Li 2 S 2 is highly retained on 1T-MoS 2 -2S with an adsorption energy of 5.1 eV. The conclusion was that a combination of 1S and 2S vacancies and pristine 1T-MoS 2 would best benefit from the specific strengths of each type of 1T-MoS 2 . The following experimental evaluation of a Li-S battery cell with the 1T-MoS 2 cathode through electrochemical testing depicted very good discharge specific capacity of 1190 mAh g S −1 at 0.1 C-rate, 100% coulombic efficiency, and 97% capacity retention after 60 cycles in a schedule of different C-rates from 0.1 C to 2 C and back to 0.1 C. This successfully confirmed the results and design of the DFT investigation in proving that migration of the soluble polysulphides to the anode and the "shuttling" effect have been eliminated.