Li adsorption and diffusion on the surfaces of molybdenum dichalcogenides MoX2 (X = S, Se, Te) monolayers for lithium-ion batteries application: a DFT study

We study some of the most high performance electrode materials for lithium-ion batteries. These comprise molybdenum dichalcogenide MoX2 (molybdenum disulfide MoS2, molybdenum diselenide MoSe2, molybdenum ditelluride MoTe2). The stability is studied by calculating cohesive energy and formation energy. Structural, electronic, and electrical properties are well defined, and these structures show a direct gap. Lithium adsorption at different sites, theoretical storage capacity, and lithium diffusion path are determined. Our study findings suggest that the adsorption of Li on the preferred site on the surface of the MoX2 monolayer maintains its semiconductor behavior. Comparing the activation energy barrier of these structures with other monolayers such as graphene or silicene, we found that MoX2 shows low lithium diffusion energy and good storage capacity, which indicates that the MoX2 is well suited as an anode material for lithium-ion batteries. Our research can offer new ideas for experimental and theoretical design and new anode materials for lithium-ion batteries (LIB). The studies were performed with Quantum ESPRESSO package based on density functional theory (DFT), plane waves, and pseudopotentials (PWSCF) to calculate the physical properties of MoX2 (X = S, Se, Te), lithium adsorption, and diffusion on their surfaces and the storage capacity of these structures. The BoltzTraP code is used to calculate thermoelectric properties.


Introduction
Over the past few years, the increase in human mobility has involved the development of portable and electric systems, which means increasing energy demand.However, the depletion of oil resources, the scarcity of fossil fuels, and the concerning levels of environmental pollution have sounded a clear warning, prompting humanity to shift away from conventional energy acquisition methods.Instead, there is a growing imperative to embrace renewable energy sources such as solar energy, wind energy, geothermal energy, and tidal energy [1].These energies are usually linked to energy storage systems.In principle, producing electric energy involves converting a particular form of energy (photons, chemical reaction, temperature, etc.) into an electric current.Among the various technologies developed to date, there are, for example, fuel cells, batteries or accumulators, photovoltaic cells, or even thermoelectric cells.The battery, notably the lithium-ion (LIB) and sodium-ion battery [2][3][4][5], stands out as the most prevalent energy storage device.This essential electrochemical unit generates electrical energy through the direct conversion of chemical energy.Lithiumion batteries, as a prime example, have found extensive application in powering portable electronic devices.Furthermore, they hold promise for use in electric vehicles 378 Page 2 of 9 (EVs) and intelligent grid systems [1][2][3][4].The particularity of Li-ion batteries lies in the fact that any material capable of reversibly inserting Li + ions is a potential candidate to act as an electrode [6].Over the past century, researchers have made significant efforts to develop and discover suitable new electrode materials that can give sufficient specific capacitance, cyclic lifetime, high-rate capacity, and safety.
Graphite was the initial material employed in the first commercial implementation of Li-ion batteries.However, it has a notably low specific capacity of 372 mAh/g [5].This limitation has driven researchers to explore numerous alternative materials, including metallic oxides, as potential anode materials, boasting higher theoretical capacities.Presently, the research focus has shifted towards materials with a two-dimensional (2D) structure due to their exceptional chemical stability and broad applicability in electrochemical processes, making them highly promising in the realm of energy storage technologies [7].These 2D materials come in diverse structural forms, each showcasing distinct properties related to the adsorption and diffusion of metal ions.Notable examples include graphene and 2D transition metal dichalcogenides, among others, which are being used as anode materials in this context.
Transition metal dichalcogenides (TMDs) have gained significant attention thanks to their unique layered structures and primarily semiconductive electronic properties.Despite weak van der Waals forces between layers, they possess strong intra-layer bonding, making them ideal candidates for exfoliation into two-dimensional (2D) materials [8].This process of dimensional reduction transforms their typically indirect band gaps, as seen in their three-dimensional (3D) forms, into direct band gaps [9], typically falling in the range of 1 to 2 eV [10,11].This alteration in band structure equips TMDs with the capability to switch between metallic and semiconducting states, rendering them versatile for various applications in electronics, optoelectronics, and solar cells [12][13][14][15].Consequently, numerous TMD materials, whether in single-layer, few-layer, or heteroform arrangements, have been proposed and explored as potential anode materials for lithium-ion batteries, in both theoretical and experimental contexts [8].
Recent research has unveiled that monolayer transition metal oxides and dichalcogenides (MoX 2 ) exhibit properties that surpass those of graphene [16] and σ-PXene [17], the two-dimensional counterparts of graphite and silicon.There have been numerous studies exploring the properties of TMDs in various scenarios.To date, only a handful of MoX 2 compounds have been successfully synthesized as single monolayers, and some have been exfoliated into thin sheets.These materials have been created using a range of techniques, including physical vapor deposition, chemical vapor deposition, and liquid-phase exfoliation method [18].The focus of our current study revolves around group VI elements, specifically molybdenum disulfide (MoS 2 ), molybdenum diselenide (MoSe 2 ), and molybdenum telluride (MoTe 2 ).Monolayer MoX 2 (X = S, Se, Te) possesses three distinct crystalline structures: a hexagonal (2H) or honeycomb structure [19,20], an octahedral (1T) structure with a centrally located bee shape, and a deformed octahedral structure (1T′) [21,22].These structures can be envisioned as a two-dimensional hexagonal lattice of positively charged Mo atoms sandwiched between two hexagonal lattices of negatively charged X atoms.The specific arrangements of Mo and X atoms determine these structural variations.
For Li-ion batteries, selecting high-efficiency anode materials is paramount, demanding characteristics such as substantial capacity, robust stability, and enhanced ion mobility.For this purpose, it is necessary to know the different electrochemical properties of the materials, which reside in the microscopic interactions within these materials.To understand the microscopic electronic phenomena at the origin of the production and storage of energy, the methods of quantum chemistry, such as density functional theory (DFT) methods, can provide valuable assistance.These methods make it possible to go back to the crystalline structures to band structures and to determine the electronic density.In this work, we aim to study 2D-MoX 2 in their more energetically stable forms according to theoretical DFT calculations and their interaction with lithium atoms.We also aim to look for the most preferable material for lithium adsorption in order to continue our study in the near future, trying to improve the performance of the chosen material by using it in a different form and situation.A thorough analysis is conducted to examine the structural, electronic properties, as well as the adsorption and diffusion behavior of Li atoms on the surface.

Computational details
The physical properties of materials can be obtained by the laws of quantum mechanics based on different approximations adopted in the ab initio approach to solving the Schrödinger famous equation.In this regard, our calculations are carried out using first principles of the plane wave method within density functional theory (DFT) [23] using pseudo-potentials.The exchange-correlation (XC) function is approximated with generalized gradient approximation (GGA) using the Perdew-Burke-Ernzerhof (PBE) function [24].All numerical calculations are carried out by using Quantum ESPRESSO software [25].In self-consistent field (SCF) calculations, the Brillouin zone (BZ) is sampled using a special 4 × 4 × 1 k-point mesh Monkhorst-Pack for (2 × 2 × 1) monolayer MoX 2 (X = S, Se, Te) cell.To achieve optimization, the BFGS method is employed, involving the adjustment of all atomic positions and lattice constants.This Page 3 of 9 378 optimization process minimizes both the total energy and atomic forces.The convergence for the cutoff energy E cut was chosen to be h . The BoltzTraP code [26], based on the semi-classical BoltzTrap equation combined with the results obtained from the electronic structure, is used to calculate electric and thermic properties.To identify the minimum energy path and saddle points between predefined initial and final positions, we employ the nudged elastic band (NEB) method [27], which is implemented within the quantum espresso code.

Results and discussions
Structure and stability of MoX 2 (X = S, Se, Te) The molybdenum dichalcogenides MoS 2 , MoSe 2 , and MoTe 2 crystallize in a structure that consists of alternating infinite triatomic layers arranged in a hexagonal manner X-Mo-X (trigonal-prismatic 2H-MoS 2 [28]).In molybdenum dichalcogenide monolayers, the distance between the atomic planes is sufficiently large and separated by a void region, preventing unwanted interactions between successive layers.In the present work, the lattice parameters after optimization agree with those found previously by other authors [29].
We consider the unit cell to make the optimization calculation of the structural parameters, and we perform a complete relaxation of the primitive cell of the system.The structural parameters of the unit cells were calculated for each material.The lattice parameter a, interatomic distances between the metal and the nearest chalcogen d Mo-X , the distance between the nearest chalcogen atoms d X-X , and the angles θ X-Mo-X between the studied chalcogen S, Se, and Te with the closest transition metal Mo are calculated using the PBE functional and presented in Table 1.The results obtained are consistent with previous work, with deviations not exceeding 0.0141 Å.
We notice a difference between the lattices parameters calculated for each element; the variation of the atomic radius can explain these differences through these atoms.
The stability of structures is an essential step before any use of a material which is evaluated by the cohesive energy.Cohesive energy values in the positive range indicate that the bound structure is energetically favorable compared to the free atoms of its constituent elements.
The cohesive force between the atoms is determined using the cohesive energy calculations [30]: where E x and E Mo are the total energies of the free atoms X and M; N is the number of atoms per unit cell, E MoX2 is the total energy of the MoX 2 structure.The adsorption energy of the system is defined as follows [8,17]: (1)   Where E MX 2 , E Li et E MoX 2 +Li areed bare monolayer, Li and the optimized MX 2 + Li system, respectively.Table 2 shows the cohesive energies obtained by our calculations and those found previously.The calculated cohesive energies with respect to the constituent free atoms are positive and between 12 and 15 eV, indicating the energetic stability of the structures and strong bonding.The highest cohesion energy is obtained for MoS 2 with an energy of 14.22 eV.
By combining the cohesive energies with the parameters obtained by optimization previously, the difference in chalcogen affects not only the lattice parameters but also the cohesive energies.In our calculations, it can be seen that E coh (MoS 2 )>E coh (MoTe 2 ).Using Bader analysis [31], more charge is transferred from the transition metal to the more electronegative chalcogen atoms.Since the Mo atoms transfer fewer electrons to the chalcogen atoms, the corresponding sheets will have lower cohesive energies than other MoX 2 systems studied by other works such as WX 2 (X = S, Se, Te) [29].

Electronic and thermoelectric properties of MoX 2 monolayer
The performance of a battery is based on the electronic structure of an electrode.Density functional theory (DFT) calculations, which rely on electron density, enable us to investigate the electronic structure of the electrode comprehensively.This approach provides insights into various aspects, including molecular orbitals, density of states, band structure, and charge distribution.These properties are invaluable for analyzing and assessing the performance of battery materials.
The electronic band structure is crucial in the solidstate physics due to the insights that offers into the spectrum of energy levels available for electrons within a solid material.The band gap, a critical concept, is intricately linked to the material's electronic conductivity.An important property that gives more information about the behavior and electronic character of a material is the density of state, which essentially provides information about how electronic energy levels are occupied by electrons in a given material.The DOS complements the electronic band structure since it allows us to understand the latter.Based on the knowledge of the density of states, most of the transport properties are determined and the nature of the chemical bonds between the atoms of a crystal or molecule.From the partial density of state (PDOS) curves, we can evaluate the principal character of each region.
Figure 2 shows the electronic band structure and the calculated total and partial electronic density of states of MoX 2 sheets (X = S, Se, Te), using the PBE functional to describe the exchange and correlation energy part.We can see that the MoS 2 , MoSe 2 , and MoTe 2 monolayers are a direct gap semiconductors with band gap values of 1.702 eV, 1.36 eV, and 1.066 eV, respectively, which is in agreement with theoretical [28][29][30] works.At the same time, the density of state curves can be divided into two sets of states, separated by a gap.In the valence band between −7 and −0.5 eV, the bands are mainly composed of the S-3p, Se-4p, and Te-5p orbitals, and the 4d orbital of Mo largely contributes and shows a strong hybridization.Above the Fermi energy, the main contribution is due to the 4d orbital of Mo.
Table 3 shows these materials have semiconducting properties; therefore, they can be used in optoelectronic applications, and as solar energy, luminescence materials, etc.As a result, we can predict a difference in conductivity of these three materials and that MoS 2 will have a low electrical conductivity compared to the other study materials, MoSe 2 and MoTe 2 .
In many industrial applications, converting heat into electrical energy and storage is one of the most critical challenges.In the case of our materials, we have studied the electrical conductivity as a function of chemical potential at a temperature of 300K.MoS 2 , MoSe 2 , and MoTe 2 show similar electrical behavior with some differences.It can be seen that MoTe 2 has a higher electrical conductivity than the other compounds.In addition, MoSe 2 has a higher electrical conductivity than MoS 2 .The results obtained for this simulation are presented in Fig. 3, as well as the thermal conductivity as a function of chemical potential at a temperature of 300K.The thermal conductivity of the three materials is null in the range of chemical potential from −0.1 to −0.05 Ry, while at a chemical potential lower than −0.1 Ry, the thermal conductivity of the three structures increases rapidly and simultaneously, and MoS 2 presents in this range the best thermal conductivity.In the third zone of chemical potential, higher than −0.05 Ry, the thermal conductivity of the MoTe 2 structure starts to increase and reaches its maximum of 9.03 × 10 [14] W.m −1 .K −1 at 0.04 Ry while that of the two other structures remains null until −0.01 and 0 Ry.We also notice that MoTe 2 presents a higher thermal conductivity than the two different structures.

Adsorption and diffusion of Li on the surfaces of MoX 2 monolayer
It is well-known that positive adsorption energy values imply repulsion between Li and MoX 2 , and therefore, Li cannot be adsorbed on the compound.Consequently, this compound is not an ideal anode for Li batteries.For negative values of the adsorption energy, there is an attraction between Li and the compound.Therefore, Li adsorption means that the compound is an excellent candidate for anode material.
In our investigation of lithium adsorption on optimized monolayer TMD systems, we begin by constructing a supercell with dimensions of 2 × 2 × 1.Following the insertion of a lithium atom, we proceed to optimize the supercell.There are four potential adsorption sites for a single Li atom that we consider [19], as illustrated in Fig. 4.These sites are as follows: the upper site of the transition metal atom (T Mo ); the upper site of the chalcogen atom (Tx); the hollow site (H), located at the center of the hexagon, and the bridge site, positioned in the middle of the bond between the nearest Mo and X atoms (T′).To assess the energetic stability of Li atoms at these possible adsorption sites, we initially position the Li atom 2Å above the atoms in the z-direction at the respective sites.Throughout the optimization process, we identify the configurations with the highest adsorption  1.066 1.07 [29] 378 Page 6 of 9 energies.The corresponding adsorption energies of the most favorable energetically site for Li adsorption are given in Table 3, as well as the electronegativity of the chalcogen atoms.The upper site of the transition metal atom T Mo is the most favorable energetically for the adsorption of Li on MoS 2 , MoSe 2 , and MoTe 2 with energies of −0.995 eV, −0.851 eV, and −0.931 eV respectively.The second favorable site for Li in MoS 2 , MoSe 2 , and MoTe 2 systems is the hollow (H) site-the center of the hexagon-with adsorption energies of −0.678 eV, −0.783 eV, and −0.741 eV, respectively.It is clear that the upper site of the chalcogen atom (Tx) is not favorable for binding an Li atom since the energies obtained are positive, which implies that there is a repulsion between the monolayer and the Li atom; in other words, that the repulsive potential energy increases, except for the MoSe 2 system.The adsorption energy of a single lithium atom on the TMDs we studied shows a direct correlation with the rising electronegativity of chalcogen atoms.
This indicates that the attractive potential energy increases in MoX 2 TMDs (where X = S, Se, Te) as the electronegativity of the chalcogen atom increases.Table 4 For all studied MoX 2 -Li systems, Li is located above the Mo metal atom.The electronic band structure of Liadsorbed systems with the most stable configurations is given in Fig. 5.
We notice that all the gap energies obtained after the insertion of a single lithium atom are sufficiently small compared to those obtained before the adsorption.
Moreover, by comparing the results of Table 3 with those of Table 5, the adsorption of a single lithium atom allows modifying the semiconducting properties of the MoX 2 compounds in their monolayer form which is in good agreement with other theoretical works where the MoX 2 (M = Mo, W; X = O, S, Se, Te) turn into metal upon Li adsorption [8].The system MoS 2 keeps its semiconductor character during lithium adsorption with a decrease in the gap energy value (from 1.71 to 1.64 eV).The two other compounds, MoSe 2 and MoTe 2 , start to lose their semiconductor character by the adsorption of a single Li atom.We also notice that the gap energy for MoSe 2 and MoTe 2 is vastly lower than that of the MoS 2 compound, which shows that MoSe 2 and MoTe 2 possess a higher electrical conductivity than MoS 2 .
The charging and discharging process in Li-ion batteries, which heavily relies on the mobility of Li-ions, plays a pivotal role in determining the suitability of MoX 2 monolayers as anode materials for these batteries.To determine the energy barriers on the surfaces during diffusion and the diffusion path, we use the NEB (nudged elastic band) method to understand the migration properties of Li-ions on the MoX 2 surface.For a single Li diffusion, we consider the T Mo -H-T Mo path linking the two nearest stable (Mo) sites.The Li atom is localized and its position optimized above the two separately related Mo metal sites.
In Fig. 6, the graphs are in the positive energy range.The activation energy barrier values for Li diffusion are  Storage capacity is a crucial performance parameter for evaluating battery anode materials.In our study, the charging and discharging of the MoX 2 anode may be described by the following chemical equation: where n is the number of adsorbed lithium ions, and MoX 2 Li n represents the product after charging.We have considered the monolayer 2 × 2 × 1 of MoX 2 as substrate, so it might be possible to reduce the charging process to the  adsorption of Li + on both sides of MoX 2 until it reaches its full capacity (Fig. 7).Once the Li atoms are added, the adsorption energy is calculated as well.Then we calculated the specific capacities for MoX 2 using the following equation [32]: where n represents the number of adsorbed ion Li, e is the elementary charge, N A the Avogadro constant, and M MoX2 is the molar mass of MoX 2 .The theoretical capacity rises linearly with the addition of atoms, according to Eq. ( 4).These results (Table 6) are significantly higher than the theoretical electrode capacities of traditional electrodes.For instance, the theoretical electrode capacities of VS 2 and Mo 2 N monolayers are 466 and 432 mAh/g, respectively [5,33].Our calculations have shown that unit-cell MoS 2 monolayer has a remarkable larger theoretical capacity when compared to MoSe 2 and MoTe 2 on the one hand, and to other 2D structures like 2D phosphorene (434) [34] and 2D Ti 3 C 2 (447.8mAh/g) [35] on the other hand.As a result of our findings, we can say that the molybdenum dichalcogenides monolayer MoX 2 , and notably the MoS 2 , could be a promising material for anodes in Li-ion batteries.

Conclusion
The structural, electronic, and thermoelectric properties of MoX 2 (X = S, Se, Te) monolayers were investigated using DFT simulations.The indirect gap for 3D MoX 2 (X = S, Se, Te) becomes a direct gap passing to the 2D material, which can be used in several applications.We investigated lithium atoms adsorption and diffusion behavior on different adsorption sites for each MoX 2 system.We found that the lithium atom is adsorbed on MoS 2 relatively stronger than other considered MoX 2 materials.The upper site of the transition metal atom T Mo is the most favorable energetically for the adsorption of Li.It can be concluded from  calculations that the adsorption of a single Li atom affects the gap energy by decreasing and subsequently affecting the semiconducting character by raising the number of adsorbed Li atoms.The diffusion barriers obtained using the nudged elastic band NEB method are between 0.22 and 0.28 eV.By calculating the storage capacity, the 2D materials studied have an enormous lithium storage capacity superior to that of usual 2D structures, in particular that of MoS 2 .Results were in good agreement with other theoretical studies using different functional and methods.Therefore, all these results indicate that these materials can perform well in LIB with high electronic properties.
The optimization was performed by minimizing the total energy and atomic forces by varying the unit cell parameters in the lattice and constant atomic positions.The crystal structure of MoS 2 , MoSe 2 , and MoTe 2 sheets are shown in Fig. 1.The Mo atoms occupy a sublattice of a hexagonal sheet sandwiched between two layers of X (S, Se, Te) atoms.

Fig. 1
Fig. 1 Top and side views of the MoS 2 structures

Fig. 2
Fig. 2 Energy band structure and electronic density of states of (a) MoS 2 , (b) MoSe 2 , and (c) MoTe 2 .The Fermi level is set at zero

Fig. 3 4
Fig. 3 Electric and thermal conductivities as a function of chemical potential at a temperature of 300K

( 3 )Fig. 5
Fig. 5 Energy band structure and electronic density of states of (a) MoS 2 + Li, (b) MoSe 2 + Li, and (c) MoTe 2 + Li.The Fermi level is set at zero

Fig. 6 2 Fig. 7
Fig.6 Corresponding energy values of a single Li adsorbed on MoX 2 monolayers along the diffusion path between the two nearest Mo atoms

Table 1
Structural parameters of the optimized systems MoX 2 compared to experimental and theoretical works MoX 2

Table 3
Band gap energy of MoX 2 monolayers

Table 4
Adsorption energy of a single lithium of the most favorable energetically site for Li adsorption and electronegativity of the chalcogen atoms

Table 5
Band gap energy of MoX 2 + Li systems

Table 6
Specific capacities for MoX 2