Monolayer Honeycomb Borophene: A Promising Anode Material with a Record Capacity for Lithium-Ion and Sodium-Ion Batteries

Two-dimensional (2D) materials are a promising candidate for the anode material of lithium-ion battery (LIB) and sodium-ion battery (NIB) for their unique physical and chemical properties. Recently, a honeycomb borophene (h-borophene) has been fabricated by molecular beam epitaxy (MBE) growth in ultra high vacuum. Here, we adopt the first-principles density functional theory calculations to study the performance of monolayer (ML) h-borophene as an anode material for the LIB and NIB. The binding energies of the ML h-borophene-Li/Na systems are all negative, indicating a steady adsorption process. The diffusion barriers of the Li and Na ions in h-borophene are 0.53 and 0.17 eV, respectively, and the anode overall open-circuit voltages for the LIB and NIB are 0.747 and 0.355 V, respectively. The maximum theoretical storage capacity of h-borophene is 1860 mAh•g-1 for NIB and up to 5268 mAh•g-1 for LIB. The latter is more than 14 times higher than that of commercially used graphite (372 mAh•g-1) and is also the highest theoretical capacity among all the 2D materials for the LIB discovered to date. Our study suggests that h-borophene is a promising anode material for high capacity LIBs and NIBs.

With the increasing demand of the performance for environmentally friendly electric vehicles and improving requirements of the stability for the portable electric device, the rechargeable batteries with high capacity, superior energy density, high power density, and long cycle life are in urgent demand. 1 Lithium-ion battery (LIB) is one of the most widely used rechargeable batteries because of its lightweight, small size and good safety. [2][3][4] Due to the limitation of the reserves of lithium (Li) element on Earth, the abundant reserves of sodium (Na) element also stimulate the research interests of lowcost sodium-ion battery (NIB) of the scientists. [5][6][7] To further satisfy the rapid development of the energy storage market demands, we make an effort to seek the LIBs and NIBs with better performance. Generally, one of the most efficient ways to improve the performance of the LIBs and NIBs is to find new anode materials to take the place of the commercial graphite anode with a relatively low theoretical specific capacity of 372 mAh·g −1 . 4,8,9 2D materials are regarded as promising candidates of anode materials of the LIB and NIB due to several advantages: [10][11][12] (i) a small volume expansion related to their thin atomic thickness resulting in a good cyclability, (ii) a low diffusion barrier associated with a few dangling bonds at the surface leading to a high chargedischarge rate, (iii) a low absolute value of binding energy pertaining to surface weak interaction causing a proper open-circuit voltage of the anode, (iv) a high surface-to-mass ratio leading to abundant adsorption sites corresponding to a high capacity. Many firstprinciples calculations study the properties of 2D materials as anode materials of the LIB or NIB,  and these 2D materials all present higher specific capacities and lower diffusion barriers than conventional graphite, such as graphene and graphdiyne. 4,8,9,13,14,17 Experimentally, the capacities of graphdiyne-based LIB, graphene hybrid-based LIB and SnS/graphene-based NIB are found to be 901, 784 and 940 mAh·g −1 , respectively, [35][36][37] and these experimental results generally coincide well with previous theoretical findings. 13,14,17 Borophene, a new type of III group 2D materials, has been theoretically predicted with 16 different types by the structural searching method, 38 and it has been shown to exist on the Ag (111), Au (111) and Cu (111) surfaces by using first-principles calculations. 39,40 The 2D monolayer (ML) borophene with 2-Pmm symmetry on the Ag (111) substrate has been successfully synthesized in 2015 for the first time. 41 Independently, Feng et al. also used molecular beam epitaxy (MBE) to grow another two boron sheets (named as β 12 and χ 3 ) on the Ag (111) surface. 42 By employing MBE growth, Li et al. successfully fabricated an attractive 2D ML honeycomb borophene (h-borophene) by choosing an Al (111) surface as the substrate in 2018. 43 Very recently, Wu et al. reported the production of large-area borophene up to 100 μm 2 on the Cu (111) surface. 44 Subsequently, Kiraly et al. synthesized the sixth kind of borophene growing on the Au (111) surface. 45 The above six kinds of borophenes are metallic. Due to their good electric conductivity, lightweight and inheritance excellent property from 2D materials, borophene is naturally considered as a suitable alternative electrode material of the energy storage device, especially in the LIB or NIB. A series of density functional theory (DFT) results of borophene adsorption and diffusion properties are calculated and show that borophene is a suitable anode material of the LIB/NIB. [46][47][48][49][50][51] The few-layer borophene-based capacity device exhibits impressive electrochemical performance with a wide potential window of up to 3.0 V, excellent energy density as high as 46.1 Wh kg −1 at a power density of 478.5 W kg −1 and excellent cycling stability with 88.7% retention of the initial specific capacitance after 6000 cycles, indicating good performance of borophene energy storage device. 52 However, the adsorption ability of the Li and Na ions on h-borophene has not been investigated. Among all the existing borophene, h-borophene with non-buckled structure has the least molar mass per unit cell and the highest density of hexagonal hole offering more adsorption sites, suggestive of a higher capacity than any other phases of borophene. Hence, it is very important to understand the Li and Na ions adsorption and diffusion properties of h-borophene as an anode material.
In this article, we study the adsorption and diffusion processes of the Li and Na ions on the surface of ML h-borophene through the first-principles DFT calculations and obtain three important parameters (the diffusion barrier height, the average OCV and the maximum theoretical storage capacity) to evaluate the performance of the LIB and NIB. We find that the Li and Na atoms prefer to stay in the hollow site (H site) on ML h-borophene. The maximum theoretical storage capacity for the ML h-borophene based LIB is 5268 mAh·g −1 , which is more than 14 times larger than that of the commercially used graphite-based LIB (372 mAh·g −1 ). 4,53 The theoretical specific capacity of the ML h-borophene based NIB (1860 mAh·g −1 ) is 53 times as high as that of graphite-based NIB (35 mAh·g −1 ). 54 The estimated average OCVs of the ML hborophene based LIB and NIB are 0.747 and 0.355 V, respectively. At the end of the discussion part, we compare the theoretical performance parameters of ML h-borophene as an anode material for the LIB/NIB with those of other ML 2D materials. [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34] Computational Methods All Calculations were carried out using DFT in connection with the exchange correlation energy described by the generalized gradient approximation (GGA) [55][56][57] in the scheme proposed by Perdew-Burke-Ernzerhof (PBE) 58 as implemented in the Vienna ab initio simulation package (VASP). [59][60][61] The periodic boundary conditions are applied in three directions (x, y and z directions), 62 and a vacuum space of at least 20 Å in the z direction is used to simulate ML h-borophene to avoid image-image interactions. The projector-augmented wave (PAW) method with a cutoff energy of 400 eV is employed in our study. 63 Van der Waals interaction is taken into account using the semi-empirical dispersion correction of DFT-D3 approach. 64 The Methfessel-Paxton smearing with order N = 1 method was employed for ions relaxation of Li/Na atom-ML hborophene system with a recommendation width of 0.2 eV. For this step, a k-mesh density of 0.02 Å −1 under the Monkhorst-Pack method is sampled in the Brillouin zone with convergence threshold 10 −5 eV for energy and 0.01 eV Å −1 for force. 65 The tetrahedron smearing method with a width of 0.01 eV was employed for a single point calculation to obtain the PDOS and very accurate total energy values. The climbing image nudged elastic band (CI-NEB) method implemented in VASP transition state tools is used to determine the metal cationic minimum energy diffusion pathways and the corresponding energy barriers. 66 In this step, the algorithm to relax the ions into their energy minimization transition state is required in agreement with the previous calculation of initial and final state. We adopt completely same k-mesh density and convergence accuracy as ion relaxation both in the single point calculations and transition state calculations. The first-principles molecular dynamics (FPMD) simulations are performed using Nosé-Hoover thermostat employed in the canonical-ensemble at the finite temperatures with a time step of 1 fs and a 3 × 3 × 1 k-point meshes. 67,68

Results and Discussion
Crystal structures and adsorption ability of an isolated Li/Na atom on ML h-borophene.-The pristine lattice parameter of ML hborophene is a = 3.0 Å with two borium (B) atom sites (as shown in Fig. 1a), which is in good agreement with the previous experimental report. 43 Before we studied the adsorption ability of the Li/Na atom adsorbed system, the stability of the isolated ML h-borophene should be confirmed first. We evaluate the stability of ML hborophene by calculating the average formation energy (E form ) defined as E form = E B -E tot , where E B is the energy of an isolated B atom, and E tot is the total energy per atom of ML borophene. The average formation energy of ML h-borophene is the lowest one (5.29 eV atom −1 ) among all the studied ML borophenes including ML 2-Pmm (6.11 eV atom −1 ), β 12 (6.15 eV atom −1 ), X 3 (6.16 eV atom −1 ) and β 1S (6.08 eV atom −1 ) borophene, but the positive average formation energy value of ML h-borophene still shows a certain degree of stability. The structural parameters and the average formation energy are listed in Table SI (available online at stacks. iop.org/JES/167/090527/mmedia) of supplementary materials. To further demonstrate the stability of the isolated ML h-borophene, we perform the FPMD simulation of ML h-borophene, and the isolated ML h-borophene is with small deformation at 500 K for 5 ps (as shown in Fig. 6a). The structural snapshot reveals that the isolated ML h-borophene has a good thermodynamic stability.
Then it is important to know exactly the favorable adsorption sites to evaluate the adsorption ability of an isolated Li/Na atom on the ML h-borophene surface. We use a 2 × 2 ML h-borophene supercell with one Li/Na atom located on to investigate the adsorption properties, and such a supercell is large enough to avoid the interaction between the Li/Na atoms in the adjacent periodic structure. Three types of high symmetry adsorption sites are considered (as shown in Fig. 1a): the hollow site above the center of the hexagon (H site), the bridge site on the bond of B-B (B site) and the atom point site on the top of a B atom (T site). After geometric optimization, all the studied Li/Na atoms remain in their initial place except for the Li at an initial bridge site. The adsorbed Li at the bridge site would automatically shift to the hollow site. The total energy of a Li/Na atom adsorbed on the H site of 2 × 2 ML hborophene is the lowest one among that of a Li/Na atom adsorbed on the H, B and T sites, and the exact total energy of each corresponding structure is summarized in Table I.
To evaluate the adsorption ability of the Li and Na atoms on ML h-borophene, the binding energy (E b ) can be defined as where E MxB8 , E B8 and E M are the total energy of the 2 × 2 ML hborophene adsorbed by the metal atoms, pristine 2 × 2 ML hborophene and per metal atom (M = Li or Na) in bulk of metal, respectively, and n is the number of metal atoms adsorbed on 2 × 2 ML h-borophene. According to Eq. 1, the lower binding energy of the Li/Na atom adsorbed on ML h-borophene is, the more favorable exothermic and spontaneous reaction between the Li/Na atom and ML h-borophene is.  Diffusion of Li and Na ions on the ML h-borophene surface.-One of the most important parameters to evaluate the performance of the LIB/NIB is the charge-discharge rate, namely the Li/Na ions mobility on the host material. The high charge-discharge rate reflects a good rate capability of the LIB/NIB. Usually, we obtain the charge-discharge rate by estimating the molecular diffusion constant (D) of the metal ions. D is temperature-dependent and positively related to the ion mobility μ. As described by the Arrhenius equation, 18,27,70 where d, ʋ, E a and k B are the diffusion distance of the Li/Na ion, the frequency of the hoping process, the diffusion barrier height (the activation energy) and Boltzmann's constant, respectively, and T is the environmental temperature. A high charge-discharge rate is related to a large ion mobility, corresponding to a low diffusion barrier height. To study the diffusion barrier of the Li/Na ion on ML h-borophene, we examine the optimal diffusion path along the zigzag and armchair directions of ML h-borophene. The expecting pathways along both the zigzag (H → B → H) (as shown in Fig. 2a) and the armchair directions (H → T → B → T → H) (as shown in Fig. 2b) between two nearest neighboring H sites (the most favorite binding sites) are explored by considering the high structural symmetry of ML h-borophene. The diffusion energy profiles along the zigzag and armchair directions are illustrated in Figs. 2c and 2d, respectively. The diffusion barrier height along the zigzag direction is 0.53 and 0.17 eV for the Li and Na ions, respectively, and the corresponding pathway lengths are both about 3.69 Å (Fig. 2c). Along the zigzag direction, the B site is the maximum state as shown in the energy profile ( Fig. 2c) and is energetically higher than the H site by about 0.53 and 0.17 eV for the Li and Na ions, respectively. The diffusion barrier height along the armchair direction is 0.54 and 0.19 eV for the Li and Na ions, respectively, and the corresponding pathway lengths are both about 5.90 Å (Fig. 2d). Along the armchair direction, the B site is the intermediate state as shown in the energy profile and is also energetically higher than the H site by about 0.53 and 0.17 eV for the Li and Na ions, respectively. The T site is the transition state, as shown in the energy profile and is energetically higher than the H site by about 0.54 and 0.19 eV for Li and Na ions, respectively. Although the diffusion barrier height of the Li/Na ion is not very apparent dependent on the diffusion path, the corresponding diffusion pathway length of the Li/Na ion along the zigzag is shorter than that along the armchair direction. Besides, the density of the diffusion barrier (determined by ratio of the number of the diffusion barrier height with a height of over 0.5 (for Li)/0.15(for Na) eV to the corresponding pathway length) along the zigzag direction is also less than that along the armchair direction. Obviously, the Li and Na ions prefer to migrate along the zigzag direction than the armchair direction on ML h-borophene because of the lower diffusion barrier height, the shorter pathway length and the lower density of the high diffusion barrier.
The Li ion has a higher diffusion barrier height than that of the Na ion and thus migrates harder on the ML h-borophene surface. But the diffusion barrier height of the Li ion on ML h-borophene (0.53 eV) is still smaller than those on ML β 12 (0.66 eV) and χ 3 (0.60 eV) borophene 46 and comparable to some well-known anode materials including TiO 2 -based polymorphs (∼0.5 eV) 71 and silicon (0.57 eV). 72 The diffusion barrier of the Na ion on ML h-borophene with a height of 0.17 eV is smaller than those on many other 2D materials, such as ML MoS 2 (0.68 eV), 25 MoN 2 (0.56 eV), 31 χ 3 borophene (0.34 eV), 46 β 12 borophene (0.33 eV), 46 NiC 3 (0.23 eV) 22 and TiC 3 (0.18 eV), 73 suggesting a high charge-discharge rate of the ML h-borophene based NIB. We can conclude that the diffusion barrier height of the Na ion is 0.36 eV lower than that of the Li ion, and both the Li and Na ions on ML h-borophene have high ion mobilities and good rate capabilities of the LIB and NIB because of the relatively low diffusion barriers. Based on the discussion above, we make an effort to obtain the diffusion constant of the Li/Na ion on ML h-borophene by using Eq. 2. Here, we use the diffusion distance along the zigzag direction with the value of 3.69 Å as d, and the hoping frequency ʋ is taken from a typical value of 10 13 s −1 . At the 300 K, the diffusion constant D values of the Li and Na ions on ML h-borophene are 1.72 × 10 −11 and 1.90 × 10 −5 cm 2 s −1 , respectively. The diffusion constant of the Li ion on ML hborophene is one order of magnitude larger than that of c-Si (3.60 × 10 −12 cm 2 s −1 ). 74 Li/Na storage capacities of ML h-borophene and average opencircuit voltages.-The maximum theoretical storage capacity is a highly important indicator to evaluate the performance of the LIB/ NIB. To estimate the maximum capacity as reasonable as we can, the anode material should satisfy several requirements: i) It should adsorb the Li/Na ions as much as possible until its highest concentration; ii) Before reaching the maximum concentration of the Li/Na ions, the binding energy (calculated by the Eq. 1) of each concentration is negative; iii) The structure of the anode materials do not have irreversible deformation; iv) There is no Li/Na ion pushed out of the anode material surface. 15,50 Here, we employ the 2 × 2 supercells of ML h-borophene with an increasing Li/Na ion on both sides of the host material. We only increase one metal atom each Table I. Summary of the adsorption ability of an isolated Li/Na atom on ML h-borophene. d a is the minimum Li/Na-B atom-to-atom distance projected in the z direction. E t is the total energy of the ML h-borophene-Li/Na adsorption system. E b is the average energy (per Li/Na atom) required to remove the Li/Na atoms from ML h-borophene. Charge transfer is the number of electrons losing from the Li/Na atom to ML hborophene.

Li atom
Na atom time to obtain the next step concentration to obtain the sensitive average adsorption energy during the whole processing with the concentration smaller than 1. The charge/discharge processing can be described by the following half-cell reaction:   using Eq. 1. After the top two steps, we found that with the concentration x of the Li ions increasing from 0.125 to 2.125, the binding energy E b (as shown in Fig. 3a) increases from −1.07 to −0.03 eV atom −1 , indicating the instability of the high concentration system. The most stable configurations of the adsorbed Li ions on the 2 × 2 ML h-borophene surface at the concentrations from 0.125 to 1 and 1.25 to 2.125 are listed in Figs. 4a-4h and 5a-5d, respectively, and no obvious deformation happens to ML hborophene in these Li ion adsorption systems. Combining the binding energy E b and the degree of deformation of ML hborophene, we can conclude that the maximum concentration (x max ) of the lithiation process is at the value of 2.125.
Due to the structure of the Li 2.125 B owning a strategic concentration in our cases, it is necessary to give some detailed description of its structure. Figure 5d is the structure of the concentration of the Li 2.125 B. We adopt the 2 × 2 ML h-borophene supercells, and the system actually contains eight B atoms and 17 li atoms. The initial structure of the Li 2.125 B has nine Li atoms above the ML hborophene layer and eight Li atoms below the ML h-borophene layer, so the chemical environment on two sides of ML h-borophene is not the same. The different chemical environment of both sides of ML h-borophene results in the different adsorption behaviors of the Li ions. The distance between the lowest Li ion of the second Li layer and the first Li layer is 1.87 Å, and this distance can be regarded as the minimum distance between the two Li layers. However, the distance between the squeezed out Li ion and the second Li layer is 1.64 Å, and it is smaller than the minimum distance of two Li layers (1.87 Å). Therefore, the uppermost Li ion belongs to the second Li layer after carefully check its interlayer distance.
For the NIB, the x values of the Na 1 B 8 , Na 2 B 8 , Na 3 B 8 , Na 4 B 8 , Na 5 B 8 and Na 6 B 8 are 0.125, 0.250, 0.375, 0.500, 0.625 and 0.750, respectively. The matching binding energy E b is shown in Fig. 3b, and the Na 7 B 8 with a positive E b determines that the maximum concentration (x max ) of the Na ion adsorbed on the 2 × 2 ML hborophene surface is at the value of 0.750. The most stable configurations of the Na 0.125 B, Na 0.25 B, Na 0.375 B, Na 0.5 B, Na 0.625 B and Na 0.75 B are shown in Figs. S1a-S1f. From the optimized structure illustrated by Figs. 4-5 and S1a-S1f, ML hborophene does not suffer from an apparent structural change, indicating a good rechargeable recycle property of the LIB/NIB.
As we mentioned before, the maximum theoretical storage capacity (C) is an important parameter to evaluate the performance of the LIB/NIB and is highly focused on its improvement. It depends on the concentration (x) of the Li/Na ions adsorbed on the 2 × 2 hborophene surface and can be calculated by: Where x max is the maximum concentration of M x B (M = Li or Na), and F is the Faraday constant with a value of 26801.48 mAh mol −1 , and M B is the Molar Mass of one B atom (10.811 g mol −1 ). Generally speaking, F and M B could be regarded as constant in a certain system, and thus the maximum theoretical storage capacity C is totally determined by the maximum concentration. The binding energy will be weaker with the increasing of the Li/Na ion concentration. The judgment of the maximum concentration is that the binding energy of the system is near zero. The higher the concentration of Li/Na ions is, the higher the capacity will be. In our studied systems, the calculated maximum theoretical storage capacity C is extremely high with a value of 5268 mAh·g −1 for the LIB and 1860 mAh·g −1 for the NIB. It is noteworthy that the maximum theoretical storage capacity C of the LIB for ML h-borophene as an electrode is the highest capacity among all reported 2D materials, and the comparison with other 2D anode materials will be discussed at the end of this part. We also defined the volumetric capacity C v (mAh·cm −3 ) as the product of the gravimetric capacity C g (mAh·g −1 ) and the effective density of our sample ρ (g·cm −3 ). 75 The above maximum theoretical storage capacity C is equivalent to the gravimetric capacity C g . To estimate the C v , we should know the effective density ρ first. Here, we adopt the distance between the first  17 With the increasing concentration of the Li/Na ions adsorbed on ML h-borophene, the binding energy grows up, indicating a possible poor thermodynamic stability of the high concentration systems. Therefore, it is necessary to check the stability of the high adsorption concentration system, such as Li 2.125 B and Na 0.750 B. After the FPMD simulations, there is no apparent structural deformation in the Li 2.125 B system at 300 K for 5 ps, as illustrated in Fig. 6b, showing a good thermodynamic stability of the Li adsorbed system. The Na 0.75 B system at 300 K for 5 ps reveals that a high adsorption concentration of the Na ions induces the deformation of ML hborophene. A puckering of the ML h-borophene substrate in the z direction with a value of 0.28 Å (as shown in Fig. 6c) reveals that the Na 0.75 B system is not as stable as the Li 2.125 B system, but such a small deformation of the ML h-borophene substrate in the Na 0.75 B system should not make a big influence to its systemic stability. So our result of the Na 0.750 B remains reliable.
Furthermore, we also estimate another important indicator average OCV to reflect the energy density of the LIB/NIB, which is defined as 76 where y is the electronic charge of the M (M = Li or Na) ions (here y =1). From this equation, the OCV is related to the binding energy E b and required to be a positive result. A low OCV of the anode materials would be equivalent to a high energy density, while an ultralow OCV for the anode materials would result in the metal plating and the dendrite formation of the adsorbed metal. 48 76 Therefore, ML h-borophene should be a suitable anode material for both the LIBs and NIBs.
Electronic properties of the Li/Na ions adsorbed on ML hborophene.-Additionally, the good electronic conductivity of the anode materials plays a crucial role in the performance of the LIB and NIB, particularly in the rate capability. Unlike many other 2D materials owning the semiconducting/semi-metallic electronic properties, ML h-borophene is naturally metallic, and its PDOS is illustrated in Fig. 7a. There is a Dirac state at the energy of 3.33 eV, but the Dirac state is far away from the Fermi level of ML h-borophene, and such an electronic state makes no influence on the metallic property of ML h-borophene and is in good agreement with the previous experiment. 43 Hence, it is expected that the pristine ML h-borophene has enough electronic states to transfer the electrons as an anode material. The PDOS of the most stable Li/ Na ion adsorption configurations of 2 × 2 ML h-borophene at every concentration are also calculated because the insertion of the Li/Na ions into the anode materials could influence the electronic property of the pristine ML h-borophene substrate. To further illustrate the electronic conductivity of ML h-borophene with the adsorbed metal ions, the PDOS of the Li ions adsorption configurations of ML hborophene are shown in Figs. 7b-7i and Figs. 8a-8d, and the PDOS of the Na ions adsorption configurations of ML h-borophene are shown in Figs. S2a-S2f. As we can see, the electronic structure of the ML h-borophene undergoes some changes upon the Li/Na ion adsorption as a consequence of electron transfer from the Li/Na atoms to ML h-borophene. However, we find that the PDOS profiles near the Fermi level are all non-zero, and intrinsically metallic property of ML h-borophene remains unchanged during the whole process, and an excellent electronic conductivity of ML h-borophene is maintained. It suggests that ML h-borophene keep its good electrical conductivity characteristics after the adsorption process of the Li/Na ions, which paves the way for its application as the anode materials for the LIB/NIB.
Crystal structures and adsorption ability of a Li/Na atom on multiple layer h-borophene.-To advance our study, we model the bilayer (BL), trilayer (TL) and four-layer (FL) h-borophene adsorption system as the representative of the multiple layer system. To confirm the stability of the multiple layer borophene system, we defined average formation energy (E form ) as E form = E B − E tot , where E B is the energy of an isolated B atom, and E tot is the total energy per atom of multiple layer borophene. We optimized the geometry structures of the two h-borophene layers stacked together in either AA or AB arrangement and obtain the average formation energy of the AA (5.76 eV atom −1 ) and AB (5.94 eV atom −1 ) stacking system. The higher energy structure corresponding to the AB stacking is with a lattice constant of 3.0 Å, a puckering (Δ) of 0.16 Å within each layer and an interlayer distance of 1.46 Å as shown in Fig. S3a. Similarly, we check the stability of the AA and AB arrangement of the TL and FL h-borophene system. The average formation energies of the TL AA and AB stacking systems are 5.85 and 6.09 eV atom −1 , respectively. The more stable TL AB stacking h-borophene has a lattice constant of 3.0 Å and an interlayer distance of 1.60 Å as given in Fig. S3b. For the FL, the average formation energies of the AA and AB stacking systems are 5.84 and 6.19 eV atom −1 , respectively. The FL AB stacking h-borophene owns a lattice constant of 3.0 Å, a puckering (Δ) of 0.13 Å within the first/ fourth layer, a puckering of 0.25 Å within the second/third layer, a distance between the first (third) to the second (fourth) layer of 1.56 Å and a distance between the second to the third layer of 1.72 Å as shown in Fig. S3c. In all the AB staking systems, the even layer of multiple layer h-borophene is shifted 0.89 Å along the long diagonal axis relative to the odd layer of multiple layer h-borophene. Comparing the average formation energy of ML (5.29 eV atom −1 ), BL (5.94 eV atom −1 ), TL (6.09 eV atom −1 ) and FL (6.19 eV atom −1 ) h-borophene, the related h-borophene system become more and more stable with the increasing of the number of hborophene layers. We use these AB configurations to study the adsorption interaction of the Li/Na atoms with multiple layer hborophene.
Before studying the Li/Na atom adsorption ability of multiple layer h-borophene, we should know the most stable adsorption sites to evaluate the adsorption ability of an isolated Li/Na atom on the multiple layer h-borophene surface. In order to make our adsorption ability results of ML h-borophene comparable to that of multiple layer h-borophene, we still use a 2 × 2 h-borophene supercell with one Li/Na atom adsorbed on to investigate the adsorption properties. Considering the symmetry of the multiple layer h-borophene lattice, there are seven typical types of possibly the most stable adsorption sites. We mark these typical adsorption sites from 1 to 7 in Figs. S3a-S3c, and the adsorption sites 1 to 6 are the sites located on the surface of the multiple layer h-borophene system, while the site 7 is the interlayer adsorption site. After geometric optimization, all the Li/Na atoms adsorbed on the interlayer site 7 automatically shift to the surface of the multiple layer h-borophene system, indicating a Li/ Na atom surface adsorption characteristic of the h-borophene system.
Then, we will focus on the stability of the surface adsorption site 1 to 6 to find the most stable position of a Li/Na atom adsorbed on the BL, TL and FL h-borophene. Calculating the adsorption energy is a good way to reflect the stability and study the adsorption ability of the multiple layer h-borophene system. In order to calculate the adsorption energy in the BL system, we use Eq. 1 and replace E MxB8 and E B8 with the total energy of the 2 × 2 BL/TL/FL h-borophene adsorbed by the metal atoms and pristine 2 × 2 BL/TL/FL hborophene, respectively. The "binding" and "adsorption" are used interchangeably in our cases. After the optimization of BL hborophene with a Li atom adsorbed on the site 1, 2, 3 and 4, the isolated Li atom of the four systems will stay on or shift to the site 1 with the adsorption energy of −2.11 eV atom −1 . For the BL hborophene with a Li atom adsorbed on the site 5 and 6, the isolated Li atom of the two systems will move to the middle of the site 1 and 6 with the adsorption energy of −2.68 eV atom −1 , and this position is the most stable adsorption site of the Li atom-BL h-borophene system as illustrated in Fig. S4a. Optimized the BL h-borophene with a Na atom adsorbed on the site 1 and 6 systems, the isolated Na atom of the two systems will stay on or shift to the site 1 with the adsorption energy of −0.74 eV atom −1 . The Na atom adsorbed on the site 4 of the BL h-borophene surface stay on its initial position, and the adsorption energy is −1.20 eV atom −1 . The BL h-borophene with a Na atom adsorbed on the site 2, 3 and 5, the isolated Na atom of the three systems will move to the position shown in Fig. S4d, and the adsorption energy of this system is −1.25 eV atom −1 .
In the TL system, the isolated Li or Na adsorbed on the site 1, 2, 3, 4, 5 and 6 will stay on or move to the site 1, and the structure of the most stable a Li atom-TL h-borophene and a Na atom-TL hborophene are illustrated in Figs. S4b and S4e, respective, and the adsorption energy is −1.68 eV atom −1 for the Li atom adsorption system and −1.06 eV atom −1 for the Na atom adsorption system. The adsorption situation in the FL system is quite similar to that in the TL system. The isolated Li adsorbed on the site 1, 2, 3, 4, 5 and 6 of the FL h-borophene system will stay on or shift to the site 1 (as shown in Fig. S4c) with the adsorption energy of −1.36 eV atom −1 . The isolated Na adsorbed on the site 3 of the FL h-borophene system will stay on its initial position with the adsorption energy of −0.24 eV atom −1 , and the Na atom adsorbed on the other sites will stay on or move to the site 1 (as illustrated in Fig. S4f) with the adsorption energy of −0.75 eV atom −1 . Finally, we summarize the structural parameters and the adsorption energy of a Li/Na adsorbed on ML/BL/TL/FL h-borophene in Table SII. By comparing the adsorption energy of the Li/Na atom-ML/BL/TL/FL h-borophene system, we find that the adsorption energy increases with the number of the h-borophene layers, and when the number of layers is increased to enough number, the adsorption energy of the multiple layer h-borophene system will be very close to that of ML system due to the surface adsorption characteristic of the Li/Na atom adsorption system.

Conclusions
We investigate the LIB and NIB performance of 2 × 2 ML hborophene as the anode electrodes by studying the adsorption ability, transition states, geometry and electronic structures using firstprinciples DFT calculations. ML h-borophene as the anode materials of the LIB and NIB has good electrical conductivity before and after the adsorption process, proper average OCVs of 0.747 V for the LIB and 0.355 V for the NIB, and small structural distortions. In addition, Na ion has a low diffusion barrier with a height of 0.17 eV on the ML h-borophene surface, and the maximum concentration Na 0.75 B corresponds to a high capacity of 1860 mAh·g −1 . Although the diffusion barrier of the Li ion (0.53 eV) is not as low as that of the Na ion, it is still comparable to those of some well-known anode materials, such as TiO 2 -based polymorphs (∼0.5 eV). As a highly attractive finding, ML h-borophene is predicted to yield ultra-high storage capacities of 5268 mAh·g −1 for the Li ions. Comparing the DFT results pertaining to the LIB performance of more than thirty reported ML 2D anode materials with that of ML h-borophene, we conclude that the theoretical maximum storage capacity of ML hborophene is the highest one among all the studied ML 2D materials. Our study highly supports that ML h-borophene is a promising anode material for both the LIBs and NIBs with good conductivity, high energy density, good recharge rate capacity and high storage capacity, especially an extremely high storage capacity for the LIB. NIB. The ML 2D materials covered with the purple shadows have lower diffusion barriers and smaller maximum storage capacity than ML h-borophene. Some data are taken from the literatures. 78,[81][82][83][84][85]88,89,[90][91][92][93]