A Novel Two-Dimensional TiClO as a High-Performance Anode Material for Mg-Ion Batteries: A First-Principles Study

Searching for efficient electrode materials with excellent electrochemical performance is of great significance to the development of magnesium-ion batteries (MIBs). Two-dimensional Ti-based materials are appealing for use in MIBs due to their high cycling capability. On the basis of density functional theory (DFT) calculations, we comprehensively investigate a novel two-dimensional Ti-based material, namely, TiClO monolayer, as a promising anode for MIBs. Monolayer TiClO can be exfoliated from its experimentally known bulk crystal with a moderate cleavage energy of 1.13 J/m2. It exhibits intrinsically metallic properties with good energetical, dynamical, mechanical, and thermal stabilities. Remarkably, TiClO monolayer possesses an ultra-high storage capacity (1079 mA h g−1), a low energy barrier (0.41–0.68 eV), and a suitable average open-circuit voltage (0.96 V). The lattice expansion for the TiClO monolayer is slight (<4.3%) during the Mg-ion intercalation. Moreover, bilayer and trilayer TiClO can considerably enhance the Mg binding strength and maintain the quasi-one-dimensional diffusion feature compared with monolayer TiClO. All these properties indicate that TiClO monolayers can be utilized as high-performance anodes for MIBs.


Introduction
Lithium-ion batteries (LIBs) have dominated the portable device industry and the electric vehicle market in the last 30 years due to their high energy density and repeated cycling stability [1,2]. However, the shortage and uneven geographical distribution of lithium resources significantly affect the large-scale application of LIBs [3][4][5]. Rechargeable MIBs have been regarded as a potential alternative to LIBs because of their abundant resources, intrinsic nontoxicity, and high theoretical capacity [6][7][8][9]. However, the research on MIBs is still in its infancy, and several serious problems need to be resolved. One of the most critical challenges is the irreversible formation of a passivation layer on the surface of the Mg anode in most electrolyte species, resulting in sluggish diffusion of Mg ions [10]. Therefore, identifying novel anode materials as alternatives to Mg metal would be an effective method to overcome this obstacle.
Since the synthesis of graphene by Geim et al. [11,12] in 2004, two-dimensional (2D) materials have captured a great deal of research interest in the field of electrochemistry [13]. As compared to bulk materials, 2D materials possess huge surface areas and dense ion insertion positions, which make them one of the most optimal choices for electrode materials. However, only a few synthesized 2D materials can be utilized as anodes for high-performance MIBs. For instance, WS 2 monolayer, as one of the transition metal disulfides, has been extensively explored as an electrode material for ion battery applications. It exhibits a high storage capacity (361 mA h g −1 ) when used as an anode material for MIBs [14]. However, the inferior conductivity of pristine WS 2 seriously restricts its rate and cycling capability. Phosphorene, which is exfoliated from layered black phosphorus, shows a high Mg capacity (865 mA h g −1 ) and a rather low Mg diffusion barrier (0.09 eV) along the All spin-polarized density functional theory (DFT) calculations are carried out using the Cambridge sequential total energy package (CASTEP) [25]. The norm-conserving pseudopotentials are carried out to describe the electron-ion interaction [26]. The plane-wave cut-off energy is set to 1100 eV for all the calculations. A vacuum space of 20 Å is constructed to minimize the virtual interlayer interactions under the periodic boundary condition. The generalized gradient approximation (GGA) of the Perdew-Burke-Ernzerhof (PBE) functional is used as the exchange-correlation functional [27]. The long-range van der Waals (vdW) forces are considered via the DFT-D3 method with Grimme correction [28]. The hybrid Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional is adopted to obtain an accurate band structure [29]. The Brillouin zone (BZ) is sampled with a 30 × 26 × 1 Monkhorst-Pack k-grid [30]. The two-point steepest descent (TPSD) [31] is implemented in the geometry optimizations, in which the convergence threshold is set as 5 × 10 −7 eV/atom in energy and 10 −3 eV/Å in force. The phonon band dispersions are calculated with the finite displacement method [32]. The thermal stability is assessed by carrying out ab initio molecular dynamics (AIMD) simulations [33] in the NVT ensemble in a supercell of 4 × 4 × 1 at 600 K. The total simulation lasts 10 ps, with a time step of 1 fs. The climbed image nudged elastic band (CI-NEB) method is employed to investigate the diffusion energy barrier for the migration of Mg atoms on TiClO [34].

Structure and Cleavage Energy of Bulk TiClO
The bulk TiClO crystallizes in a layered structure of the FeOCl type, where buckled bilayers of Ti-O are separated by Cl ions, as shown in Figure 1a [35]. The unit cell is orthorhombic, with space group Pmmn (No. 59). The optimized lattice constants are a = 3.255 Å, b = 3.977 Å, and c = 7.716 Å, which are in good accordance with the experimental data (a = 3.365 Å, b = 3.789 Å, and c = 8.060 Å) [36]. In addition, bulk TiClO is metallic, with energy levels crossing the Fermi level ( Figure 1b). (a = 3.365 Å, b = 3.789 Å, and c = 8.060 Å) [36]. In addition, bulk TiClO is metallic, with energy levels crossing the Fermi level ( Figure 1b). In general, liquid-phase exfoliation and mechanical cleavage are two main techniques for obtaining monolayer structures from their bulk counterparts. To assess the viability of exfoliating the TiClO monolayer from its layered bulk crystal, we calculate the cleavage energy (Ecl) of the TiClO monolayer. To simulate the actual exfoliation process, we construct a five-layer slab model of TiClO in which only the top layer is removable. As shown in Figure 1c, the value of Ecl increases with the increase of the separation distance (d) and gradually converges to a constant number of ~1.13 J/m 2 at about 10 Å. This value is comparable to those of some layered materials, such as Ca2N (1.09 J/m 2 ) [37], GeP3 (1.14 J/m 2 ) [38], and CaP3 (1.30 J/m 2 ) [39], indicating the high feasibility of exfoliating the TiClO monolayer from its bulk crystal.

Structure and Stability of Monolayer TiClO
The fully optimized geometrical structure of an exfoliated TiClO monolayer is presented in Figure 2a  In general, liquid-phase exfoliation and mechanical cleavage are two main techniques for obtaining monolayer structures from their bulk counterparts. To assess the viability of exfoliating the TiClO monolayer from its layered bulk crystal, we calculate the cleavage energy (E cl ) of the TiClO monolayer. To simulate the actual exfoliation process, we construct a five-layer slab model of TiClO in which only the top layer is removable. As shown in Figure 1c, the value of E cl increases with the increase of the separation distance (d) and gradually converges to a constant number of~1.13 J/m 2 at about 10 Å. This value is comparable to those of some layered materials, such as Ca 2 N (1.09 J/m 2 ) [37], GeP 3 (1.14 J/m 2 ) [38], and CaP 3 (1.30 J/m 2 ) [39], indicating the high feasibility of exfoliating the TiClO monolayer from its bulk crystal.

Structure and Stability of Monolayer TiClO
The fully optimized geometrical structure of an exfoliated TiClO monolayer is presented in Figure 2a are close to those of the bulk phase. As shown in Figure 2b, each TiClO monolayer is composed of six close-packed atomic layers sequenced Cl-Ti-O-O-Ti-Cl. Each Cl atom bonds with two Ti atoms, and each Ti atom bonds with two Cl atoms and four O atoms. The bond lengths of Ti-O and Ti-Cl are 2.058 and 2.476 Å, respectively. The materials used as anodes for MIBs should have good energy, dynamical, mechanical, and thermal stability. Firstly, we calculate the cohesive energy ( ) to examine the energy stability of TiClO monolayer, which can be described as: where , , and refer to the total energies of a single Ti, Cl, and O atom, respectively. The denotes the total energy of monolayer TiClO. , and are the number of Ti, Cl, and O atoms in the TiClO monolayer, respectively. The positive cohesive energy represents a structure that is stable. The of TiClO monolayer (7.42 eV/atom) is higher than that of 2D Ti2BN (4.90 eV/atom) [40] and comparable to that of 2D Ti2C (7.49 eV/atom) [41] calculated at the same theoretical level, denoting that the TiClO monolayer is energetically stable. We further evaluate the thermodynamic stability of TiClO monolayers by computing the formation energy ( ) from the following equation: = ( + + − )/3. , and are the total energies of Ti, Cl, and O atoms in bulk titanium, chlorine molecules, and oxygen molecules, respectively.
is the total energy of the TiClO monolayer. The calculated formation energy of the TiClO monolayer is 0.34 eV, confirming that the TiClO monolayer is thermodynamically stable. The materials used as anodes for MIBs should have good energy, dynamical, mechanical, and thermal stability. Firstly, we calculate the cohesive energy (E b ) to examine the energy stability of TiClO monolayer, which can be described as: where E Ti , E Cl , and E O refer to the total energies of a single Ti, Cl, and O atom, respectively. The E TiClO denotes the total energy of monolayer TiClO. x, y and z are the number of Ti, Cl, and O atoms in the TiClO monolayer, respectively. The positive cohesive energy represents a structure that is stable. The E b of TiClO monolayer (7.42 eV/atom) is higher than that of 2D Ti 2 BN (4.90 eV/atom) [40] and comparable to that of 2D Ti 2 C (7.49 eV/atom) [41] calculated at the same theoretical level, denoting that the TiClO monolayer is energetically stable. We further evaluate the thermodynamic stability of TiClO monolayers by computing the formation energy (E f ) from the following Equation: E Cl and E O are the total energies of Ti, Cl, and O atoms in bulk titanium, chlorine molecules, and oxygen molecules, respectively. E TiClO is the total energy of the TiClO monolayer. The calculated formation energy of the TiClO monolayer is 0.34 eV, confirming that the TiClO monolayer is thermodynamically stable. Then, we compute the phonon spectra to investigate the dynamical stability. As shown in Figure 2c, no imaginary phonon modes are observed in the whole Brillouin zone, indicating the dynamic stability of TiClO. We further determine the mechanical stability by examining the elastic constants. The obtained elastic constants are C 11 [42], suggesting TiClO monolayer is mechanically stable. Moreover, we confirm the thermal stability of monolayer TiClO by performing AIMD simulations at a temperature of 600 K for the 4 × 4 × 1 supercell. As illustrated in Figure 2d, the TiClO monolayer maintains its structure without relevant distortions after heating for 10 ps, indicating that it is thermally stable.

Electronic Property of Monolayer TiClO
To better understand the electronic properties of TiClO monolayers, we calculate their band structure and orbital-projected density of states (DOS). As illustrated in Figure 3a, the TiClO monolayer possesses metallic characteristics as several energy levels cross the Fermi level with both PBE and HSE06 functionals, ensuring good electronic conductivity. The partial DOS suggests that the metallic states in the vicinity of Fermi level are predominantly contributed by Ti-d orbitals, while the O-p, Cl-p, and Cl-d orbitals only make a small contribution (Figure 3b). To further explore the mechanism of chemical bonding, we also compute the electron localization function (ELF) of the TiClO monolayer. As presented in Figure  Then, we compute the phonon spectra to investigate the dynamical stability. As shown in Figure 2c, no imaginary phonon modes are observed in the whole Brillouin zone, indicating the dynamic stability of TiClO. We further determine the mechanical stability by examining the elastic constants. The obtained elastic constants are C 11 = 106.93 N/m, C 12 = 21.20 N/m, C 22 = 108.47 N/m, and C 66 = 39.44 N/m, which satisfy the Born-Huang criteria (C 11 C 22 − C 12 2 > 0, C 66 > 0) [42], suggesting TiClO monolayer is mechanically stable. Moreover, we confirm the thermal stability of monolayer TiClO by performing AIMD simulations at a temperature of 600 K for the 4 × 4 × 1 supercell. As illustrated in Figure  2d, the TiClO monolayer maintains its structure without relevant distortions after heating for 10 ps, indicating that it is thermally stable.

Electronic Property of Monolayer TiClO
To better understand the electronic properties of TiClO monolayers, we calculate their band structure and orbital-projected density of states (DOS). As illustrated in Figure  3a, the TiClO monolayer possesses metallic characteristics as several energy levels cross the Fermi level with both PBE and HSE06 functionals, ensuring good electronic conductivity. The partial DOS suggests that the metallic states in the vicinity of Fermi level are predominantly contributed by Ti-d orbitals, while the O-p, Cl-p, and Cl-d orbitals only make a small contribution (Figure 3b). To further explore the mechanism of chemical bonding, we also compute the electron localization function (ELF) of the TiClO monolayer. As presented in Figure 3c

Mg Adsorption on Monolayer TiClO
In order to explore the feasibility of a TiClO monolayer as an anode material for MIBs, we studied the adsorption of an isolated Mg atom on TiClO by constructing a 3 × 3 × 1 supercell. As shown in Figure 4a, five possible adsorption sites with high structural symmetry are chosen, denoted as T1, H1, H2, T2, and T3. During the structural relaxation, the adsorbed Mg atom at site H2 would move to the near site T3, and the Mg atom on site T2 would finally shift to the neighboring site T1. However, the Mg on site H1 stays still. The adsorption energy ( ) of a Mg atom on a TiClO monolayer is defined as:

Mg Adsorption on Monolayer TiClO
In order to explore the feasibility of a TiClO monolayer as an anode material for MIBs, we studied the adsorption of an isolated Mg atom on TiClO by constructing a 3 × 3 × 1 supercell. As shown in Figure 4a, five possible adsorption sites with high structural symmetry are chosen, denoted as T 1 , H 1 , H 2 , T 2 , and T 3 . During the structural relaxation, the adsorbed Mg atom at site H 2 would move to the near site T 3 , and the Mg atom on site T 2 would finally shift to the neighboring site T 1 . However, the Mg on site H 1 stays still. The adsorption energy (E ads ) of a Mg atom on a TiClO monolayer is defined as: T3 possesses a higher of 1.47 eV, indicating that the adsorption process between Mg atom and TiClO monolayer is an exothermic and spontaneous process. In order to examine the electronic property of Mg-adsorbed TiClO, we calculate the PDOS of the TiClO monolayer for Mg adsorbed at the most favorable site, as depicted in Figure 4b. The PDOS structure shows that the metallic states of the TiClO monolayer are mainly contributed by Mg-s and Ti-d orbitals. Therefore, TiClO can maintain its metallic character after the adsorption of Mg, providing good electrical conduction during the charge/discharge process. Furthermore, we calculate the electron density difference to gain insight into the adsorption mechanism of the Mg atom on the surface of the TiClO monolayer. As shown in Figure 4b  In order to examine the electronic property of Mg-adsorbed TiClO, we calculate the PDOS of the TiClO monolayer for Mg adsorbed at the most favorable site, as depicted in Figure 4b. The PDOS structure shows that the metallic states of the TiClO monolayer are mainly contributed by Mg-s and Ti-d orbitals. Therefore, TiClO can maintain its metallic character after the adsorption of Mg, providing good electrical conduction during the charge/discharge process. Furthermore, we calculate the electron density difference to gain insight into the adsorption mechanism of the Mg atom on the surface of the TiClO monolayer. As shown in Figure 4b

Mg Diffusion on Monolayer TiClO
For an efficient anode of MIBs, the high mobility of the Mg ion is a key requirement that directly affects the rate performance. Therefore, we calculate the energy barriers of one Mg atom on the TiClO monolayer. Site T 3 is the energetically most stable adsorption site, and site H 1 is the second stable adsorption site. We investigate two typical diffusion pathways (path I and path II) between the nearest energetically favorable adsorption sites (Figure 5a), namely, T 3 → T 3 and T 3 → H 1 → T 3 . When the Mg atom diffuses along path I, there is only one peak point (TS1). While there are two peak points (TS2) when the Mg atom diffuses along path II, the TS positions are above of Ti atoms (Figure 5b). The Mg diffusion barriers along the path I (II) are about 0.41 (0.68) eV, which are higher than those of some typical 2D materials such as MnSb 2 S 4 (0.32 eV) and TiS 3 (0.29 eV) [43,44]. However, these results are much lower than those of BSi (0.86 eV) [45] and MoS 2 (1.12 eV) [46], suggesting that Mg has tremendous diffusion capability along the armchair direction on the TiClO monolayer. The temperature-dependent diffusion constant (D) can be estimated by the Arrhenius equation [47]: where E a and k B represent the energy barrier and Boltzmann constant, respectively. T is the environmental temperature. The Mg mobility along path I is about 10 4 times faster than that along path II, showing the quasi-one-dimensional diffusion feature of TiClO.

Mg Diffusion on Monolayer TiClO
For an efficient anode of MIBs, the high mobility of the Mg ion is a key requirement that directly affects the rate performance. Therefore, we calculate the energy barriers of one Mg atom on the TiClO monolayer. Site T3 is the energetically most stable adsorption site, and site H1 is the second stable adsorption site. We investigate two typical diffusion pathways (path I and path II) between the nearest energetically favorable adsorption sites (Figure 5a), namely, T3 → T3 and T3 → H1 → T3. When the Mg atom diffuses along path I, there is only one peak point (TS1). While there are two peak points (TS2) when the Mg atom diffuses along path II, the TS positions are above of Ti atoms (Figure 5b). The Mg diffusion barriers along the path I (II) are about 0.41 (0.68) eV, which are higher than those of some typical 2D materials such as MnSb2S4 (0.32 eV) and TiS3 (0.29 eV) [43,44]. However, these results are much lower than those of BSi (0.86 eV) [45] and MoS2 (1.12 eV) [46], suggesting that Mg has tremendous diffusion capability along the armchair direction on the TiClO monolayer. The temperature-dependent diffusion constant ( ) can be estimated by the Arrhenius equation [47]: where and represent the energy barrier and Boltzmann constant, respectively. is the environmental temperature. The Mg mobility along path I is about 10 4 times faster than that along path II, showing the quasi-one-dimensional diffusion feature of TiClO.

Theoretical Specific Capacity and Open Circuit Voltage
The specific capacity is also a critical parameter for the practical application of ion batteries. We further investigate Mg atoms adsorbed on both sides of the TiClO monolayer and evaluate the theoretical maximum specific capacity with a 3 × 3 × 1 supercell

Theoretical Specific Capacity and Open Circuit Voltage
The specific capacity is also a critical parameter for the practical application of ion batteries. We further investigate Mg atoms adsorbed on both sides of the TiClO monolayer and evaluate the theoretical maximum specific capacity with a 3 × 3 × 1 supercell (Ti 18 where E Mg x TiClO and E TiClO are the total energies of the Mg x -TiClO system and the pristine TiClO monolayer, respectively. The x is the concentration of Mg atoms adsorbed in the TiClO monolayer. The E Mg indicates the total energy of an isolated Mg atom of bulk Mg metal. As illustrated in Figure 6a, four considered Mg adsorption conformers (Mg x TiClO, x = 0.5, 1, 1.5, and 2) lie on the solid line of the convex hull, suggesting that these structures are thermodynamically stable.

Mg Adsorption Property on Bilayer TiClO
Up until now, we have only explored the feasibility of Mg adsorption and diffusion on monolayer TiClO. Nevertheless, it is difficult to obtain a satisfactory electrode using the monolayer material in practical applications. Hence, we further evaluate whether the Mg atom could be adsorbed on bilayer TiClO. Two typical adsorption situations are considered: (1) Mg adsorption on the outer surface of bilayer TiClO; and (2) Mg insertion into the interlayer of bilayer TiClO. We perform the geometry optimization for the Mg-substrate systems by considering several possible adsorption sites (Figure 7a).
When the adsorption of Mg atoms happens on the surface of bilayer TiClO, sites T3 and H1 are the two most stable adsorption positions among all the considered sites, with the of 1.76 and 1.62 eV, respectively. Clearly, the existence of a second TiClO layer enhances the interaction between Mg and substrate during the adsorption process. As for the Mg insertion into the interlayer of bilayer TiClO, the Mg atom prefers staying at site V with of 1.45 eV. Clearly, the Mg atom is prone to adsorb on the outside surface rather than embed in the interlayer. Therefore, we can conclude that site T3 is the most favorable position for Mg on the bilayer TiClO as well as the TiClO monolayer.
In order to shed more light on the interaction between Mg and the outside surface of bilayer TiClO, we investigate the PDOS structure and Hirshfeld charge analysis. As illustrated in Figure 7b, the calculated PDOS clearly shows the metallic character of the Mgbilayer TiClO system, which ensures excellent electronic conduction in the practical application of the electrode. According to PDOS analysis, the bands near the Fermi level are mainly originated from Ti-d and Mg-p orbitals, whereas the contribution from Cl-d and Mg-s states is limited. Moreover, the Hirshfeld charge analysis suggests charge transfer of ~0.55 electrons from Mg to bilayer TiClO at site T3, which is higher than that of TiClO The maximum theoretical capacity of the TiClO monolayer can be obtained from the equation: where z is the valance electron number (z equals 2 for Mg), x max represents the highest concentration of Mg ions, F is the Faraday constant (26801 mA h mol −1 ), and M TiClO denotes the molar mass of the TiClO monolayer. The computed theoretical specific capacity of TiClO monolayer reaches up to 1079 mA h g −1 , which is superior to those of some reported 2D materials, such as C 2 N (588 mA h g −1 ) [48], Ti 2 C (687 mA h g −1 ) [49], VO 2 (815 mA h g −1 ) [50], phosphorene (865 mA h g −1 ) [16], and TiS 2 (957 mA h g −1 ) [51]. In addition, the lattice expansions of a and b for a fully magnesiated TiClO monolayer are 4.3% and 3.7%, respectively, suggesting its excellent cycling stability. The open circuit voltage (OCV) is a determinative factor for high-performance MIBs. The OCV of Mg x TiClO is defined as follows: where E Mg x 1 − substrate and E Mg x 2 − substrate represent the total energies of Mg x 1 TiClO and Mg x 2 TiClO, respectively. E Mg denotes the total energy of a Mg atom in the bulk metal. As depicted in Figure 6b, the calculated OCVs for Mg x TiClO are in the range of 0.62-1.33 V, with a numerical average OCV of 0.96 V, which are in the range of those of typical anode materials, such as graphite (~0.20 V) [52] and TiO 2 (1.50 V) [22]. Both high specific capacities and suitable OCVs suggest that the TiClO monolayer has great potential for application in MIBs.

Mg Adsorption Property on Bilayer TiClO
Up until now, we have only explored the feasibility of Mg adsorption and diffusion on monolayer TiClO. Nevertheless, it is difficult to obtain a satisfactory electrode using the monolayer material in practical applications. Hence, we further evaluate whether the Mg atom could be adsorbed on bilayer TiClO. Two typical adsorption situations are considered: (1) Mg adsorption on the outer surface of bilayer TiClO; and (2) Mg insertion into the interlayer of bilayer TiClO. We perform the geometry optimization for the Mg-substrate systems by considering several possible adsorption sites (Figure 7a). Then, we calculate the diffusion barriers on the outer surface of bilayer TiClO. Two different diffusion pathways are investigated, namely, path A (T3 → T3) and path B (T3 → H1 → T3), which are the same as those of the monolayer (Figure 7b). In the case of path A, the Mg atom moves directly between two neighboring sites T3 with a diffusion barrier of 0.53 eV. Nevertheless, the energy barrier along path B is 0.71 eV. The Mg mobility along path A is approximately 10 3 times faster than that of path B, demonstrating the quasi-onedimensional diffusion behavior of bilayer TiClO. In a word, the TiClO bilayer can When the adsorption of Mg atoms happens on the surface of bilayer TiClO, sites T 3 and H 1 are the two most stable adsorption positions among all the considered sites, with the E ads of 1.76 and 1.62 eV, respectively. Clearly, the existence of a second TiClO layer enhances the interaction between Mg and substrate during the adsorption process. As for the Mg insertion into the interlayer of bilayer TiClO, the Mg atom prefers staying at site V with E ads of 1.45 eV. Clearly, the Mg atom is prone to adsorb on the outside surface rather than embed in the interlayer. Therefore, we can conclude that site T 3 is the most favorable position for Mg on the bilayer TiClO as well as the TiClO monolayer.
In order to shed more light on the interaction between Mg and the outside surface of bilayer TiClO, we investigate the PDOS structure and Hirshfeld charge analysis. As illustrated in Figure 7b, the calculated PDOS clearly shows the metallic character of the Mg-bilayer TiClO system, which ensures excellent electronic conduction in the practical application of the electrode. According to PDOS analysis, the bands near the Fermi level are mainly originated from Ti-d and Mg-p orbitals, whereas the contribution from Cl-d and Mg-s states is limited. Moreover, the Hirshfeld charge analysis suggests charge transfer of~0.55 electrons from Mg to bilayer TiClO at site T 3 , which is higher than that of TiClO monolayer and further demonstrates the enhancement of Mg binding strength in bilayer TiClO.
Then, we calculate the diffusion barriers on the outer surface of bilayer TiClO. Two different diffusion pathways are investigated, namely, path A (T 3 → T 3 ) and path B (T 3 → H 1 → T 3 ), which are the same as those of the monolayer (Figure 7b). In the case of path A, the Mg atom moves directly between two neighboring sites T 3 with a diffusion barrier of 0.53 eV. Nevertheless, the energy barrier along path B is 0.71 eV. The Mg mobility along path A is approximately 10 3 times faster than that of path B, demonstrating the quasi-one-dimensional diffusion behavior of bilayer TiClO. In a word, the TiClO bilayer can remarkably enhance the Mg adsorption energy and maintain the quasi-one-dimensional diffusion feature.

Mg Adsorption Property on Trilayer TiClO
In order to further explore the effect of a higher layer structure on Mg adsorption properties, we investigate the adsorption of Mg atoms on trilayer TiClO. Considering the symmetry of the three-layer structure, there are two types of regions for Mg adsorption. One region is on the outside surface of trilayer TiClO, and another region is in the interlayer of two neighboring layers of trilayer TiClO. Several possible adsorption sites are considered, as depicted in Figure 8a,b. After fully optimizing the geometry of Mg-TiClO systems, there are only two sites (site T 3 and site H 1 ) where the Mg atoms can be adsorbed. This phenomenon indicates that Mg atoms can only be adsorbed on the outside surface of trilayer TiClO. The computed adsorption energies of both sites are positive (1.59 eV for site T 3 , 1.36 eV for site H 1 ), indicating the adsorption process between Mg and trilayer TiClO is spontaneous.
The energy barriers on the outside surface of trilayer TiClO are further calculated to evaluate the diffusion capacity of Mg atoms. Two diffusion pathways are considered according to symmetry of structure, as shown in Figure 8c. Path 1: T 3 → T 3 ; path 2: T 3 → H 1 → T 3 . The corresponding energy barriers are 0.45 (path 1) and 0.66 (path 2), which are close to the results of the TiClO monolayer. According to the Arrhenius equation, the mobility of Mg along path 1 is approximately 10 4 times faster than that of path 2 at room temperature, indicating the quasi-one-dimensional diffusion character of trilayer TiClO. To conclude, the Mg adsorption properties of monolayer, bilayer, and trilayer TiClO, adsorption site, adsorption energy, diffusion energy barrier, number of electrons transferred, and electronic properties after adsorption are summarized and listed in Table 1.
close to the results of the TiClO monolayer. According to the Arrhenius equation, the mobility of Mg along path 1 is approximately 10 4 times faster than that of path 2 at room temperature, indicating the quasi-one-dimensional diffusion character of trilayer TiClO. To conclude, the Mg adsorption properties of monolayer, bilayer, and trilayer TiClO, adsorption site, adsorption energy, diffusion energy barrier, number of electrons transferred, and electronic properties after adsorption are summarized and listed in Table 1.

Conclusions
By using first-principles calculations, we theoretically explore the potential feasibility of TiClO monolayer as an anode material for MIBs. Monolayer TiClO could be exfoliated from its bulk crystal with a moderate cleavage energy (1.13 J/m 2 ). It possesses intrinsically metallic properties with excellent energetical, dynamical, mechanical, and thermal stabilities. From an electrochemical storage point of view, TiClO monolayer exhibits low diffusion barriers (0.41−0.68 eV), a suitable average electrode potential (0.96 V), and a high specific capacity (1079 mA h g −1 ). Importantly, the lattice expansion obtained for the fully magnesiated TiClO monolayer is small (<4.3%), demonstrating excellent cycling stability. Compared with pristine TiClO monolayers, bilayer and trilayer TiClO significantly enhance the Mg binding strength and maintain the quasi-one-dimensional diffusion feature. With the successful synthesis of some 2D Ti-based materials (e.g., TiOF, TiCl 2 ) in recent years, our results could provide a reference for the reasonable design of promising anodes based on 2D Ti-based materials.