Surface‐Dependent Electrocatalytic Activity of CoSe2 for Lithium Sulfur Battery

Electrocatalysts play key roles in improving the performance of lithium sulfur (Li‐S) batteries. Here, the electrocatalytic activity of different CoSe2 surfaces for the polysulfide redox reactions in Li‐S batteries, by means of first‐principle calculations is considered. The authors demonstrate that there are obvious differences in surface energy (0.7–2.34 J m−2), adsorption energy for lithium polysulfides (LiPSs) (1.2–3.5 eV), Gibbs free energy of sulfur reduction reaction (SRR) (0.37–1.16 eV), and Li2S decomposition barrier (0.15–0.94 eV) among different CoSe2 surfaces, and thus lead to the different electrocatalytic activity for different CoSe2 surface. The stoichiometric CoSe2 surface with high surface energy, such as the (001) surface, tends to have stronger adsorption energy and larger SRR Gibbs free energy for LiPSs. The surface electron states are mainly dominated by p–d hybridization orbitals and the p‐band center is vital for the surface electrocatalytic properties. Such surface‐dependent mechanism may shed light on the design of sulfur host materials for high‐performance Li‐S batteries.


Introduction
Li-S battery is regarded as one of the most promising next-generation energystorage solutions due to the high theoretical capacity (≈1675 mAh.g −1 ) and energy density (≈2600 Wh.kg −1 ). However, the chemistry is plagued by sluggish sulfur reduction kinetics and the polysulfides (PS) shuttling effect. These effects limit rate capability and cycle life. [1,2] To solve the above problems, noble cathode host materials with good conductivity and suitable adsorption energy for LiPSs are incorporated into Li-S batteries. [3] Recent studies have found that high electrocatalytic activity of the host materials can not only accelerate the rate of sulfur redox reaction and improve the efficiency of charge and discharge process for lithium sulfur (Li-S) batteries but also reduce the accumulation of LiPSs to prevent shuttling effect, thereby reducing the loss of capacity and improving cycle performance. [4] Recently, the bulk transition-metal chalcogenides metal materials have been demonstrated experimentally to be excellent lithium-sulfur cathode material owning to their metallic conductivity and well-electrocatalytic performance. [5][6][7][8][9][10][11][12][13] In particular, the conductive orthorhombic marcasite-type CoSe 2 (space group Pnnm) [14] exhibits a high specific capacity of 1264 mAh.g −1 with a low capacity decay and improving electrochemical performance. [7] Considering different surfaces of CoSe 2 , such as (100), (010), (001) surfaces are experimentally accessible, [15] understanding the roles of these surfaces in these processes is urgently needed. Remarkably, the recent experimental work demonstrated that the exposure ratio of (001) surface in the facet CoSe 2 (001) nanosheets is controllable by thermodynamics methods. [16] This offers a promising approach for controlling the surface structure of CoSe 2 and thereby the electrocatalytic activity. Besides, compared with the intensive theoretical works on the two-dimensional (2D) host materials, [17][18][19][20][21] heterojunctions, [22][23][24][25][26] single-atom catalytic effects, [27,28] surface modification, [20,29] and heteroatoms doping [30] for Li-S batteries, theoretical studies on the surface-dependent redox electrochemical performance for bulk materials for Li-S batteries are scarce.
In this contribution, we performed first-principle calculations to study the intrinsic mechanism of electrocatalytic activity for different CoSe 2 surfaces. Unlike other theoretical Electrocatalysts play key roles in improving the performance of lithium sulfur (Li-S) batteries. Here, the electrocatalytic activity of different CoSe 2 surfaces for the polysulfide redox reactions in Li-S batteries, by means of first-principle calculations is considered. The authors demonstrate that there are obvious differences in surface energy (0.7-2.34 J m −2 ), adsorption energy for lithium polysulfides (LiPSs) (1.2-3.5 eV), Gibbs free energy of sulfur reduction reaction (SRR) (0.37-1.16 eV), and Li 2 S decomposition barrier (0.15-0.94 eV) among different CoSe 2 surfaces, and thus lead to the different electrocatalytic activity for different CoSe 2 surface. The stoichiometric CoSe 2 surface with high surface energy, such as the (001) surface, tends to have stronger adsorption energy and larger SRR Gibbs free energy for LiPSs. The surface electron states are mainly dominated by p-d hybridization orbitals and the p-band center is vital for the surface electrocatalytic properties. Such surfacedependent mechanism may shed light on the design of sulfur host materials for high-performance Li-S batteries.
calculations of lithium-sulfur batteries, we discussed the possible relationship between the surface energy and the electrocatalytic performance of Li-S batteries for the first time. Our simulations show that different surfaces of the same material could even have a great influence on SRR, the p-orbitals are very important for catalytic activity, and special surface channels are conducive to the charging process. Our work provides new ideas for both experimental design and theoretical simulation of Li-S batteries.
We started from the surface energies (γ s ) of the above CoSe 2 surfaces. Surface energy is expected to governs a wide range of surface-driven processes, such as the rate of sintering, the stress needed for crack growth, wettability and adhesion, dissolution, adsorption, nucleation, phase transformations and chemical reactions, the shape and growth of particles, and heterogeneous catalysis. [31,32] For example, there is a quantitative correlation between surface energy and adsorption energy of CO molecular. [33] The nanoparticle-based catalysts could be designed theoretically on the basis of surface energy calculations. [34] The surface energy γ s was calculated by the following expression: [35,36] Here, A is the surface area of the slab. E slab is the total energy of the fresh surface without structure relaxation. CoSe bulk 2 µ and Co slab µ are the chemical potentials of bulk CoSe 2 unit and Co atom in slab, respectively. For the stoichiometric surfaces with (1/2n Se -n Co ) = 0, we would find that Therefore, one can obtain the exact numerical values of surface energy for the stoichiometric surfaces. However, for nonstoichiometric surface, we need to introduce an auxiliary parameter represent the surfaces are in the Co-rich and Co-poor environment, respectively.
The calculated surface energies of (010), (001), (101), Coterminated (100), and Se-terminated (100) of CoSe 2 surfaces with different thicknesses are presented in Figure S1 (Supporting Information). The surface energies are well converged when the surface thickness is more than four layers. The converged surface energies of those surfaces are plotted in respectively. The surface energy of (101) surface is comparable with that of Mg (001) surface (0.86 J m −2 ). [32] For the Se-terminated (100) surface, the surface energy ranges from 0.7 to 1.12 J m −2 , and is much lower than that of the Co-terminated (100) surface, which is in the range of 1.92-2.34 J m −2 . The large surface energy of the Co-terminated (100) surface can be attributed to the existence of abundant uncoordinated cobalt metal bonds. Se-terminated (100) surface have the smallest (largest) surface energy in Se-rich (Co-rich) environment, whereas the Co-terminated (100) surface shows opposite trend. The above results indicate that the Co-terminated (100) surface is energetically most unfavorable. The higher surface energy makes the Co-terminated (100) surface less thermodynamically stable, and probably stronger absorption ability to molecules.
Surface reconstruction is evitable in these surfaces once they are formed. The relaxed surface structures of (101), (010), (001), Se-terminated (100), and Co-terminated (100) surfaces of CoSe 2 are shown in Figure 2. The original structures of these surfaces are well-preserved except for the Se-terminated (100) surface. Grooves are formed on the (010) surface, as shown by the black arrow in Figure 2b. The Se-terminated (100) surface is obviously reconstructed as presented in Figure 2d, which indicates lower structural stability for surface Se atom. A more detailed atomic structural information of Se-terminated (100) surface is shown in Figure S2 (Supporting Information).

Adsorption and Electronic Properties
We further studied the polysulfide redox reaction occurred on the above-relaxed CoSe 2 surfaces. Before the Li-S battery is assembled, the cathode material CoSe 2 needs to be mixed with sulfur. Thus, one must analyze the interaction between the surface and sulfur. We optimized the structures of the CoSe 2 surfaces with adsorption of S 8 molecular. The energetically most favorable adsorption sites and the atomic configurations are shown in Figure S3 (Supporting Information). From this figure, we can find that S 8 molecules prefer to align parallel to the CoSe 2 surfaces. It is noteworthy that, during the structure optimization, the energy decreased drastically as shown by red arrow in Figure 3a, which indicates irreversible structure modification, and the S 8 molecules were destroyed by the Co-terminated (100) surface as shown in Figure 3b, similar to the case of a previous work. [37] The high affinity and strong adsorption of the Co-terminated (100) surface to sulfur molecules is attributed to the high surface energy as calculated above. Therefore, we no longer consider the clean Co-terminated CoSe 2 (100) surface as the cathode material for Li-S batteries. It should at least be functioned with sulfur or selenium, which is beyond the scope of this article.
For the discharging process of the Li-S battery, Li atoms in anode arrive at the cathode, and the S 8 molecules in cathode are first reduced to soluble long-chain LiPSs (Li 2 S 8 , Li 2 S 6 , and Li 2 S 4 ), and finally reduced to solid Li 2 S 2 and Li 2 S. At the solid-liquid interface between cathode and electrolyte, the soluble long-chain LiPSs may shuttle across the separator to react with and deposit on the lithium anode, resulting in rapid capacity fading. Thus, a large binding energy between cathode material and soluble Li 2 S 8 , Li 2 S 6 , and Li 2 S 4 is expected to avoid the dissolution of long-chain LiPSs and prevent the shuttling effect. The binding energy E b of the LiPSs and S 8 molecular with the CoSe 2 surfaces were computed using the following expression: b p s s ub ps sub where E ps is the energy for isolated LiPSs/S 8 . E ps+sub and E sub are the energies of substrate with and without LiPSs/S 8 , respectively. The binding energies of LiPSs/S 8 on these CoSe 2 surfaces are plotted in Figure 4. The corresponding adsorption atomic configurations are presented in Figures S3-S7 (Supporting Information). For comparison, the binding energies of longchain soluble LiPSs species Li 2 Sx (x = 4, 6, 8) with typical electrolyte solvents, namely 1,3-dioxolane (DOL) and 1,2-dimethoxyethane (DME) are also presented in Figure 4. [38] The binding energies between the Li 2 Sx (x = 4, 6, 8) and electrolyte solvents ranges from 0.79 to 0.98 eV, which are close to the values reported in previous works. [39,40] The adsorption energy of S 8 on the (101), (010), (001), and Se-terminated (100) surfaces are 0.96, 1.07, 1.21, and 0.8 eV, respectively. The low binding energy indicates that the interaction between substrate and S 8 is dominated by weak vdW interactions. There are obvious

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Co-S bonds for CoSe 2 (001) surface adsorbed with S 8 molecular and thus results in larger binding energy. The binding energies of these CoSe 2 surfaces to Li 2 S 2 and Li 2 S are larger than 2.18 eV, suggesting the strong chemical interaction between them. The soluble Li 2 S 4 , Li 2 S 6 , and Li 2 S 8 species exhibit moderate binding energy ranging from 1.20 to 2.90 eV. These large adsorption energies of cathode material can well prevent the shuttle effect for Li-S batteries. It can be further found that (101) and (010) surfaces have similar adsorption energy, while the (001) surface has the largest adsorption energy. The surface with larger surface energy tends to have a stronger adsorption capacity, which indicates that there may be a relationship between adsorption energy and surface energy. Generally, the calculation of adsorption energy requires larger resources; however, the calculation of surface energy is more economic. It helps us to evaluate the adsorption properties of cathode materials more conveniently.
We further discussed the electronic properties for different surfaces and bulk CoSe 2 . The partial electron density of state (PDOS) projected onto the s, p, and d orbitals of outermostlayer atoms of relaxed (101), (001), (010), and Se-terminated (100) surfaces of CoSe 2 , and all atoms of bulk CoSe 2 are shown in Figure 4b. The work function for (101), (001), (010), and Se-terminated (100) surfaces of CoSe 2 are 4.75, 4.90, 4.97, and 5.02 eV, respectively. The states are mainly contributed by p and d orbitals for both these surfaces and bulk. p-and d-band center are often used as descriptor for catalysis. [41,42] The p-band centers of the CoSe 2 surfaces (101), (001), (010), and Se-terminated (100) are located at -7.69, -7.35, -7.57, and -7.66 eV, respectively. The d-band centers of the above surfaces are located at -6.28, -6.36, -6.43, and -6.74 eV, respectively. The locations of the p(d)-band centers are indicated by the red(orange) dotted line in Figure 4b. Due to the difficulty of determining the electrostatic potential in vacuum for bulk CoSe 2 , we roughly align the electron energy range of bulk CoSe 2 with that of the Se-terminated CoSe 2 (100) surface. Although the absolute energy for the electron state of the bulk CoSe 2 is not available here, the energy difference is accessible. Compared with bulk CoSe 2 , the energy differences between the p-band center and d-band center of studied CoSe 2 surfaces as indicated by the black arrows in Figure 4b decrease, while the widths of the d-band peak increase. It is obvious that the (001) CoSe 2 surface has the highest p-band center and the largest width of the d-band among the studied surfaces. Analyzing the data, a higher p-band center would lead to a higher surface energy and stronger adsorption. However, the lift of the p-band center is the result of p-d hybridization. Generally, high surface energy implies too large instability of a surface, which tends to decrease its surface tension and increase its stability, and vice versa. One way to reduce its surface tension is by adsorbing molecules. However, the quantitative relationship between surface energy and adsorption strength as well as the underlying physical picture is still under debate. For CoSe 2 surfaces, it is probably due to hybridization of the p--d states and gives rise to a higher p-band, thus leading to higher surface energy and stronger adsorption.

Sulfur Reduction Reaction Process
We then turn to the discharging progress of sulfur reduction reaction (SRR), which contains complex multistep involving 16 electrons. [43,44] The overall chemical equation is www.advmatinterfaces.de S 8 + 16Li + + 16e − → 8Li 2 S. The elementary steps for generating a Li 2 S molecule are described as follows: [43,45]  where * indicates reaction site. The reaction Gibbs free energy of each step is given by ΔG = ΔE+ ΔE ZPE -TΔS. The ΔE, ΔE ZPE , and ΔS are the differences of DFT-calculated energy, zero-point energy, and entropy between products and reactants, respectively. T is the temperature. To calculate the entropy contribution of the changes in Gibbs free energy between the products and the reactants, we used finite differences to determine the Hessian matrix and the vibrational frequencies of a system. Two displacements (±0.02 Å) were applied for each direction and ion. To save resource, we fixed the host materials, and only adsorbed molecules were allowed to vibrate. Only zone-centered (Γ-point) frequencies were calculated and considered. The data were analyzed by using the VASPKIT code. [46] The overall reaction Gibbs free energy ΔG is determined by the maximum reaction Gibbs free energy among all steps. The computed zero-point energy (E ZPE ) and entropy (TS) at 300 K for S 8 and LiPSs species anchored on different CoSe 2 surfaces are listed in Table S1 (Supporting Information). The data indicate that S 8 molecular and LiPSs on different surfaces have similar E ZPE and TS. The difference of E ZPE and TS for certain LiPSs on these CoSe 2 surfaces are less than 0.05 and 0.1 eV, respectively, for S 8 molecules and LiPSs. Thus, one can evaluate the SRR reaction Gibbs free energy by using the same E ZPE and TS values with an accuracy of about ±0.1 eV. The calculated reactions Gibbs free energy of these surfaces for each step are plotted in Figure 5. The conversion from S 8 to Li 2 S 8 is a spontaneous exothermic process. The thermodynamically sluggish step that has maximum Gibbs free energy barrier for the (101) surface is from Li 2 S 6 to Li 2 S 4 with ΔG = 0.37 eV. For the (010), (001), and Se-terminated (100) surfaces, the thermodynamically sluggish steps are from Li 2 S 4 to Li 2 S 2 with ΔG = 0.42 eV, ΔG = 1.16 eV, and ΔG = 0.59 eV, respectively. For comparison, the theoretical value of overall reaction Gibbs free energies ΔG for different surfaces of CoSe 2 and other materials are list in Table 1. The Gibbs free energy of SRR occurred on the (101), (010), and Seterminated (100) surfaces of CoSe 2 are much lower than that in vacuum (0.91 eV), [43] on V 2 CO 2 (1.08 eV) [47] and the N-doped graphene surface (1.21 eV), [45] and comparable with that on Co 3 O 4 (0.54 eV) [48] and Fe 3 GeX 2 (X = Te, Se, S) monolayer (0.35-0.41 eV), [43] confirming that these CoSe 2 surfaces largely reduce the Gibbs free energy barrier of SRR in the discharge process and thus improve the electrochemical performance of Li-S batteries. However, the large SRR Gibbs free energy for the CoSe 2 (001) surface would lead to low conversion kinetics and continued accumulation of LiPSs in the electrolyte that exacerbate the shuttling effect. Notably, the order of the overall SRR Gibbs free energy ΔG for the stochiometric CoSe 2 surfaces is (101) < (010) < (001), which is consistent with the order of surface energies.

Li 2 S Decomposition Process
For the recharging process of the Li-S battery, the S 2− ion of Li 2 S is oxidized to sulfur accompanied by the decomposition of Li 2 S. A low Li 2 S decomposition energy barrier will increase the utilization of active materials and reduce the formation of dead Li 2 S, which are quite crucial for high-performance Li-S   [48] SAV@NG 0.84 [49] CoSe 2 (101) 0.37 this work Co-Co 3 O 4 0.46 [48] TM-BHT 0.8-0.91 [50] CoSe 2 (100) 0.59 this work Co 3 O 4 0.54 [48] V 2 CO 2 1.08 [47] CoSe 2 (010) 0.42 this work graphene 1.07 [49] VO 2 -V 2 CO 2 0.69 [47] Vacuum 0.91 [43] NG 0.88 [49] N/G 1.21 [45] Fe 3 GeX 2 (X = Te, Se, S) monolayer 0.35-0.41 [43] SACo@NG 0.72 [49] Co-N/G 0.71 [45] www.advmatinterfaces.de batteries. [43] Here, we consider the Li 2 S decomposition process from an intact Li 2 S molecule into a LiS cluster and a single Li ion (Li 2 S → LiS + Li + + e − ). The energy profile and its' corresponding detailed decomposition paths are shown in Figure 6. Ni (1.23 eV) on N-doped graphene. [27,45,51] Unlike the one-step decomposition mechanism of other surfaces, the Li 2 S decomposition process along the channel of (010) surface as donated by the black arrow in Figure 2b is a two-step jumping mechanism. The Li atom first hops onto the bridge site A of the two-faced Se atoms on both sides of the surface channel from its initial site O and then jumps into the hollow site B, which is near the top center of the four adjacent surface Se atoms. The initial site O, bridge sites A and hollow site B are present in Figure S8 (Supporting Information). The diffusion activation barriers are 0.15 and 0.12 eV for the Li atom jump of OA and AB steps, respectively. Thus, the rate-limited step is from the initial site O to the bridge site A. The diffusion of Li along the vertical direction of the above channel is also discussed, where the activation barrier is 0.37 eV. The decomposed path and the corresponding energy profile are presented in Figure S9 (Supporting Information). The ultralow decomposition barrier on the (010) surface benefits from its suitable surface channel.

Conclusions
In summary, based on first-principle calculations, we demonstrate that there exist obvious surface-dependent electrocatalytic properties for different CoSe 2 surfaces. Co-terminated CoSe 2 (100) surface with high surface energy is not stable for Li-S batteries. The results shows that all studied CoSe 2 surfaces have moderate adsorption energy for LiPSs, which is large than 1.21 eV and can effectively prevent the shuttle effect. The CoSe 2 (101) and (010) surfaces, and Se-terminated CoSe 2 (100) surface significantly reduce the SRR reaction Gibbs free energy to 0.37, 0.42, and 0.59 eV, respectively, and essentially enhance the electrocatalytic performance of the Li-S battery. However, the CoSe 2 (001) surface will prevent the SRR process. Due to the assist of the suitable surface channel, the CoSe 2 (010) surface has ultralow Li 2 S decomposition barrier (0.15 eV) that is much lower than other CoSe 2 surfaces. The higher p-band center, the higher surface energy and stronger adsorption energy and larger SRR Gibbs free energy for LiPSs. In practical use, it should expose CoSe 2 (010) surface as much as possible to improve electrocatalytic performance. Such surface-dependent mechanism may shed light on the design of sulfur host materials for high-performance Li-S batteries. In addition, the process of SRR in Li-S batteries is very complicated, and involves multiple factors, such as the manufacture of the cathode electrode, electrolyte component, and types of additives. Although the adsorption energy for lithium polysulfides, the Gibbs free energy of the SRR, and the Li 2 S decomposition barrier in this paper is not exactly the same as in the actual situation, we can still provide a relatively qualitative catalytic performance and explore the effect of the cathode host material, which has been confirmed in many works of Li-S research. The multifactor (especially the effect of electrolyte) for SRR need to be further studied in future research.

Experimental Section
The first-principle calculations were performed by using the VASP code [52][53][54] within density functional theory (DFT). Plane waves with the energy less than 450 eV were used as the basis to expand the Kohn-Sham electron wavefunctions. The pseudopotential for electronic-ion interaction was treated by the projector-augmented wave method (PAW). [55,56] The generalized gradient approximation (GGA) in the expression proposed by Perdew, Burke, and Ernzerhof (PBE) [57] was adopted for the exchange-correlation functional. The atomic structures were optimized by using the conjugate gradient (CG) algorithm with the energy precision and force convergence criteria were set as 10 −5 eV and 0.01 eV Å −1 , respectively. A vacuum of about 12 Å was adopted to eliminate the interaction between two adjacent slabs. The Brillouin zone (BZ) integration was sampled using the 3×3×1 k-mesh according to the Monkhorst-Pack method [58] for the 5×5 supercell. The van der Waals interaction was included by the DFT-D3 method of Grimme. [59] The spin polarization is not considered because the CoSe 2 is paramagnetic. [60] The energy barriers for decomposition of Li 2 S to LiS molecule and diffusion of a lithium ion were determined by using the Climbing-Image-Nudged-Elastic-Band (CI-NEB) method. [61] The force convergence criteria of CI-NEB were set to 0.03 eV Å −1 .

Supporting Information
Supporting Information is available from the Wiley Online Library or from the author.