Optimized crystal structure and metallic characteristics of pristine β12-borophene

The crystal structure of β12-borophene was created based on the Pmm2 space group and an orthorhombic crystal system (Marder 2010). The optimized structure revealed a rectangular primitive unit cell containing 5 boron atoms with a single vacancy, and it had lattice parameters of a = 2.925 Å and b = 5.093 Å. The borophene structure comprises a chain of hollow hexagons and a chain of hexagonal boron atoms, and it appears flat without any corrugations (Fig. 1). These lattice parameters are very close to what was obtained in previous first-principles studies (Zhang et al. 2016; Grixti et al. 2018; Karimzadeh et al. 2023; He et al. 2020), with very minimal discrepancies due to different conditions set for the simulations.

Fig. 1

Top and side views of the crystal structure: A primitive unit cell enclosed in a blue rectangle consisting of 5 boron atoms and a single vacancy. All boron atoms are represented by the color green. Additionally, a and b are the lattice parameters

Furthermore, the dynamical and thermodynamical stabilities of the β12-borophene crystal were assessed before it could be used for further electronic properties predictions: For thermodynamical stability, the cohesive energy (Ecoh) (Sun et al. 2017) was calculated using the equation:

$$}_}}} = }_}}} - } * }_}}}$$

(5)

where Ebulk represents the total energy for the primitive unit cell, n denotes the total number of atoms in a unit cell, and Eiso indicates the total energy for an isolated boron atom. The calculated cohesive energy for β12-borophene was 5.64 eV/atom. Notably, this value aligns with previous reports where cohesive energies of 6.147 eV (Peng et al. 2017) and 5.71 eV (Sun et al. 2017) were observed. The cohesive value obtained shows that β12-borophene is stable thermodynamically. The effects of dynamics and temperature on the structure’s stability have been explored elsewhere, where the phonon dispersion spectrum was calculated, and the analysis revealed no negative frequencies. Moreover, for thermal stability, ab initio molecular dynamics (AIMD) was utilized to analyze structural distortion at extreme temperatures, indicating that β12-borophene is dynamically and thermodynamically stable (Peng et al. 2017; Mortazavi et al. 2017).

After evaluating the stability of β12-borophene, its electronic properties in its pure form were investigated by calculating the total density of states (TDOS), the projected density of states (PDOS), and bands structure (Fig. 2). The findings revealed that it exhibits metallic properties, as evidenced by overlapping conduction and valence bands, indicating a zero band gap along the Fermi level. The primary orbitals along the Fermi level were identified as the boron atom 2p-orbitals, with minimal contributions from s-orbitals. These outcomes are in line with previously reported studies (Luo et al. 2017; Feng et al. 2016b; Li et al. 2020a; Grixti et al. 2018) where it was observed that the valency and conduction bands overlap with a high concentration of electronic states along the Fermi level. This indicates the excellent metallic characteristics of the β12-borophene and lays the groundwork for further exploration of its electronic properties following the adsorption of other species.

Fig. 2

Density of states (DOS) and bands structure of pristine β12-borophene: a Total density of states (TDOS) and projected density of states (PDOS), b bands structure of β12-borophene. The dashed red line denotes the Fermi level

Species configurations on β12-borophene

During the discharging process, lithium atoms are oxidized and diffuse to the cathode electrode via the electrolyte. Upon reaching the surface of the cathode electrode, they combine with O2 from the ambient environment to form LiO2 in the presence of electrons, a reaction mechanism known as the oxygen reaction reduction (ORR) (Bruce et al. 2012; Aurbach et al. 2016). As part of this mechanism, the formed LiO2 is adsorbed at the surface of the cathode electrode, giving rise to numerous possible configurations and orientations. Bearing this in mind, different potential adsorption sites were identified and labeled as sites A to H within the supercell (Fig. 3).

Fig. 3

Possible identified adsorption sites within the unit cell: A, B, C, D, E, F, G, and H sites

Lithium-ion (Li) on β12-borophene

As previously mentioned, the formation of LiO2 involves the combination of Li and O2. Consequently, configurations of all the species of interest were introduced on the surface of the crystal structure. Initially, the focus was on Li by positioning it at different sites (Fig. 3). Eight adsorption sites were considered and labeled as follows: (a) SITE A: at the top of the bridge between hollow hexagons, (b) SITE B: top of the center of the hollow hexagon, (c) SITE C: top of the boron atom and center of the hexagon, (d) SITE D: top of the triangle of boron atoms, (e) SITE E: top of the boron atom bonded to four borons, (f) SITE F: top of the boron atom part of the bridge between hollow hexagons, (g) SITE G: top of the triangle of boron atoms, and (h) SITE H: top of the boron atom bonded to five borons. As shown in Fig. 4, the configurations in their initial (left) and final (right) stages of relaxation were examined. Following a full system relaxation, it was observed that the positions for configurations at SITE A, SITE B, SITE C, SITE G, and SITE H remained unchanged, while SITE D and SITE F migrated towards SITE A and SITE H. This shifting of configurations suggests that the previous sites were not energetically favorable and moved towards the most stable sites.

Fig. 4

Initial (left) and final (right) configurations of Li on β12-borophene: a side and plan views of SITE A, b side and top views of SITE B, c side and top views of SITE C, d side and top views of SITE D, e side and top views of SITE E, f side and top views of SITE F, g side and top views of SITE G, and h side and top views of SITE H. The lithium and boron atoms are represented by the colors grey and green, respectively

To have a deeper insight into the adsorption of Li, the adsorption energies were calculated, resulting in values ranging from − 2.24 to − 1.27 eV as detailed in Table 1. Notably, the configuration at SITE B exhibited the highest negative value (− 2.24 eV), suggesting to be the most strongly adsorbed and stable. Furthermore, the calculated binding distances ranged from 2.00 to 2.59 Å (Table 1), with the configuration at SITE B displaying the shortest binding distance (2.00 Å) as depicted in Fig. 4b. This outcome points to a strong interaction with the substrate, aligning with the finding that Li is strongly adsorbed on top of the center of the hollow hexagon of β12-borophene. These results correlate with previously reported DFT work (Karimzadeh et al. 2023; Zhang et al. 2016), where it was found that the Li atom adsorbed on top of the hollow site has the highest adsorption energy. Hence, it is the most stable configuration as compared to others.

Table 1 The calculated properties of optimized configurations of Li at different sites of β12-borophene: Adsorption sites, adsorption energies and binding distancesOxygen molecule (O2) on β12-borophene

As a next step, various configurations for O2 were explored at different sites and orientations, as illustrated in Fig. 5: (a) SITE 1A: top of the bridge with O2 axis parallel and its atoms facing boron atoms, (b) SITE 1B: top of the hollow hexagon with O2 axis facing the boron atoms, (c) SITE 1C: top of the bridge and the molecule axis facing the adjacent hollow hexagons, (d) SITE 1D: top of the hollow hexagon with O2 axis facing the bridges of a chain of hollow hexagons, (e) SITE 1E: top of the hexagon of boron atoms with molecule axis perpendicular to the chain of hexagons, (f) SITE 1F: top of the hexagon of boron atoms with O2 axis parallel to the chain of hexagons of boron atoms, (g) SITE 1G: O2 on top of the bond of boron atoms in the hexagon, and (h) SITE 1H: O2 axis facing the hollow hexagon and hexagon of boron atoms.

Fig. 5

Initial (left) and final (right) configurations of O2 on β12-borophene: a side and top views of SITE 1A, b side and top views of SITE 1B, c side and top views of SITE 1C, d side and top views of SITE 1D, e side and top views of SITE 1E, f side and top views of SITE 1F, g side and top views of SITE 1G, and h side and top views of SITE 1H. The oxygen and boron atoms are represented by colors red and green, respectively

After relaxing the systems, it was observed that most of the configurations changed their positions and orientations (Fig. 5). For example, the configuration at SITE 1B (Fig. 5b) diffused towards the edge of a hollow hexagon, with the molecule slanting, indicating instability. Similarly, the configuration at SITE 1D (Fig. 5d) diffused towards the hexagon with boron atoms and also slanted. In contrast, the configuration at SITE 1H (Fig. 5h) migrated towards the hexagon of boron atoms and oriented parallel to the substrate. Except for the configuration at SITE 1A, which maintained its position and orientation, all the other configurations diffused towards SITE 1A. Notably, all the configurations that diffused formed covalent bonds with boron atoms. This formation of covalent bonds between the O2 and β12-borophene is consistent with previously predicted first-principles results (Luo et al. 2017; Mortazavi et al. 2017). Moreover, the formation of the covalent bonds shows the stability of the systems.

To have further insights into the mechanisms of the configurations, the adsorption energies, bond lengths, and binding distances of O2 were calculated as detailed in Table 2. The adsorption energies ranged from − 5.15 to − 1.8 eV, with the configuration at SITE 1A exhibiting the most negative adsorption energy (− 5.15 eV), indicative of strong adsorption. Spontaneous adsorption towards oxygen is particularly significant as it allows the material to prevent it from dissociating into the electrolyte and migrating toward the negative electrode (anode), thereby preventing corrosion and potential battery failure. Next, the O2 bond lengths were calculated and ranged from 1.29 to 1.46 Å. These values were compared to the O2 in a vacuum (1.20 Å) and the variations indicate the effect of O2-substrate interactions. Furthermore, the O2 binding distances were calculated and ranged from 1.69 to 2.75 Å (Table 2), with the configuration at SITE 1A having the shortest distance (1.69 Å). Given its high adsorption energy and the shortest binding distance, the configuration at SITE 1A was considered the most energetically stable configuration compared to the others.

Table 2 The calculated properties of optimized O2 configurations at different sites of β12-borophene; adsorption energies, binding distances and O2 bond lengthsLithium superoxide (LiO2) on β12-borophene

For the LiO2 on β12-borophene system, identifying potential adsorption sites around the vacancy (Fig. 6) were strategically generated. This decision was based on the understanding that the vacancy is the region where the most stable sites for the configurations of LiO2 (Fig. 4a) and O2 (Fig. 5d) are located. The identified sites include: (a) Li facing the bridge with O2 on top of the hollow hexagon with its axis facing boron atoms (SITE 2A), (b) Li positioned on top of the boron atom and O2 on top of the hollow hexagon (SITE 2B), (c) Li located above O2, with the O2 axis facing the bridge (SITE 2C), (d) O2 positioned on top of the boron atoms at the bridge and Li on top of the hollow hexagon (SITE 2D), (e) Li facing the hollow hexagon with O2 on top and its axis perpendicular to the bridges of the chain of hollow hexagons (SITE 2E), (f) Li facing the hollow hexagon with the O2 axis oriented facing the boron atoms (SITE 2F), (g) O2 on top of the bridge with its axis parallel to boron atoms, with Li atom on top (SITE 2G), and (h) Li facing the bridge with O2 on top and its axis parallel to the bridge (SITE 2H).

Fig. 6

Initial (left) and final (right) configurations of LiO2 on β12-borophene: a side and top views for SITE 2A, b side and top views of SITE 2B, c side and top views of SITE 2C, d side and top views of SITE 2D, e side and top views of SITE 2E, f side and top views of SITE 2F, g side and top views of SITE 2G, and h side and top views of SITE 2H; the lithium, oxygen and boron atoms are represented by color grey, red and green, respectively

After relaxing the systems, the configurations maintained their positions and orientations. However, the binding distances for the configurations varied (Table 3). The binding distances were calculated by considering the distances between Li-substrate and O2-substrate. The Li-substrate binding distances ranged from 1.55 to 5.21 Å, while the O2-substrate distances ranged from 1.54 to 3.48 Å. Furthermore, the adsorption energies were calculated and ranged from − 3.70 to − 0.88 eV (Table 4). Among the configurations tested, the one at SITE 2D exhibited had shortest binding distance and the most negative adsorption energy, this is due to the covalent bonds formed between O2 and boron (Fig. 6d). These results suggest that it is the most energetically stable configuration.

Table 3 Relaxed LiO2 configurations at different sites of β12-borophene: Adsorption sites, adsorption energies and binding distances between Li and O2 with the surfaceTable 4 Calculated adsorption energy, binding distances, and quantified charge densityTopological and quantitative analysis of charge density difference distributions

Following the calculation of adsorption energies and identification of the most energetic configurations, a detailed understanding of the electronic interactions between the adsorbates and the substrate was gained by calculating the charge density difference distributions. This was followed by a comprehensive topological analysis of the charge iso-surfaces (Fig. 7). Furthermore, using the Bader analysis scheme (Tang et al. 2009; Henkelman et al. 2006), the charge was quantified and later compared to the adsorption energies. The results revealed that; for Li on β12-borophene there was an accumulation of charge (yellow) towards the substrate from the lithium-ion (Fig. 7a). This demonstrates the low electronegativity of lithium-ion and its tendency to donate about 0.88 |e| to the substrate. The transferred electric charge confirms ionic bonding in the Li-substrate system. Then for O2 on β12-borophene (Fig. 7b), it was found that despite the formation of covalent bonds, charge depleted (blue) from the β12-borophene and accumulated (yellow) towards O2. This indicates the high electronegativity of oxygen, and because of the covalent bonds formed, a charge of 1.98 |e| was shared between the O2 and the substrate. This significant quantified charge shared explains why O2 has a big negative adsorption energy value. Finally, for LiO2 on β12-borophene (Fig. 7c), the charge distribution mechanism is complex. Initially, the charge is accumulated (yellow) by the substrate and depleted (blue) from the lithium atom, transferring a quantified charge of about 0.89 |e|. Then the charge is accumulated (yellow) towards O2 and depleted (blue) from the β12-borophene, sharing about 1.76 |e| due to covalent bond formation. Therefore, the total electronic charge transferred between lithium superoxide and the substrate is determined to be 0.86 |e|. When analyzing the adsorption energies of Li, O2, and LiO2 with their corresponding quantified charge densities (Table 4), it becomes evident why the adsorption energy values for Li (− 2.24 eV) and LiO2 (− 3.70 eV) are smaller than for O2 (− 5.15 eV).

Fig. 7

Charge density difference distribution of adsorbed species on β12-borophene: a Li on β12-borophene, b O2 on β12-borophene, and c LiO2 on β12-borophene. The charge depletion and accumulation are represented by blue and yellow colors, respectively

Ultimately, from the analysis above it is very evident that the values of the adsorption energies correspond to the quantified charge densities transferred, showing that the larger the quantity of charge being transferred the more the adsorbate is being anchored onto the substrate. After comparing the binding distances and the quantified charges, it was found that for Li (2.00 Å) and LiO2 (1.79 Å), the binding distances are longer than for O2 (1.69 Å). Showing that the shorter the binding distance, the larger the quantity of charge being transferred. The values obtained suggest a strong electronic interaction between O2 and the substrate.

Gibbs free energies and potential of the adsorbed LiO2 during ORRs mechanism

As earlier mentioned, in the Li − O2 battery the mechanisms rely on the oxygen reduction reactions (ORRs). The proposed mechanism to form the LiO2 as the intermediate discharge product at the surface of the cathode is as follows (Yang et al. 2018; Ji et al. 2017):

$$}^ (}) + }^ + }_} (}) + \beta_}} \left( } \right) \to }_}^ \left( } \right)$$

(6)

Here, LiO∗ represents the complex system (LiO2 adsorbed on the β12-borophene). Therefore, to obtain the free energies, the following equation was used (Xu et al. 2018; Yang et al. 2018):

$$\Delta }(}_}^ ) = \Delta }(}^ + }^ + }_} + \beta_}} \to }_}^ ) = }_}^ }} - }_}}} - }_}_ }} - }_}}$$

(7)

By employing the calculated values of the chemical potentials (Table 5) and Eq. 7, we derived the Gibbs free energies (Fig. 8b). Subsequently, using Eq. 4, the potentials were calculated and determined the overpotential (− 1.87 V) the complete reactions. The moderate value of overpotential obtained indicates that the formation of LiO2 at the surface of the β12-borophene is spontaneous.

Table 5 The calculated chemical potentials (CPs) for all the species involved in the ORR mechanism; Li, O2, and pristine β12-borophene and adsorbed LiO2Fig. 8

a Increased concentration of the LiO2 on β12-borophene, and b Gibbs free energies in the ORR process

Metallic characteristics for systems of species on β12-borophene

After calculating the Gibbs free energy changes, the electronic transport characteristics were investigated for all the species involved in the reactions. This was achieved by calculating the density of states for the following systems: (i) Li on β12-borophene, (ii) O2 on β12-borophene, and (iii) LiO2 on β12-borophene. These results were then compared with the electronic structures of pristine β12-borophene (Fig. 2).

For Li on β12-borophene (Fig. 9a, b), the Fermi level shifted upwards, and the bands moved downwards. This shift was attributed to the high tendency of lithium ions to donate electrons. Furthermore, the orbital levels along the Fermi level increased (Fig. 9a), suggesting easier drifting of the electrons between the valency and conduction bands. In terms of the projected density of states at the vicinity of the Fermi level, the 2p-orbitals of the boron atoms dominated, with minimal contribution from the 2 s-orbitals of the lithium atom. Despite the minimal orbital state contribution from the lithium atom, there was an electronic structural transformation (Fig. 9a). Next, for O2 on β12-borophene (Fig. 9c, d), a noticeable downward shift of the Fermi level towards the valence bands was observed, while the bands themselves moved upwards. This shift was attributed to the propensity of O2 to accept electrons, resulting in unoccupied electronic states in the valence bands. The orbital levels along the Fermi level decreased significantly (Fig. 9d). The primary contributors to the local orbitals along the Fermi level were the boron atom’s 2p-orbitals, with minimal contribution from the oxygen atom’s 2p-orbitals. The hybridization of oxygen and boron atoms’ orbitals (up and down) caused a significant transformation of electronic states along the Fermi level (Fig. 9c). Despite the drastic change in the electronic structure, the overlap of the valence and conduction bands indicated the preservation of metallic characteristics. Finally, for LiO2 on β12-borophene (Fig. 9e, f), an upward shift of the Fermi level was noted and a corresponding downward movement of the bands compared to O2 on β12-borophene (Fig. 9a, b). There was a significant increase in the electronic states along the Fermi level, leading to a change in the electronic structure of the system. The projected density of states along the Fermi level was predominantly influenced by the boron atom’s 2p-orbitals, with minimal contributions from oxygen 2p-orbitals (Fig. 9e). It is noted that the increase in orbital levels along the Fermi level signifies enhanced conductivity, demonstrating that despite adsorbing the insulating LiO2, the material maintained its metallic characteristics.

Fig. 9

Spin-orbitals density of states and bands structures: a–b Li on β12-borophene, c–d O2 on β12-borophene, (e–f) LiO2 on β12-borophene. The Fermi level is set at zero mark and denoted by a dashed red line

Diffusion energy barrier

The diffusion energy barrier of an electrode is a significant electronic property in determining the rate at which species (ions) diffuse between the electrodes during the charging and discharging processes. To evaluate this property, the nudged elastic band (NEB) scheme was used (Jónsson et al. 1998; Henkelman and Jónsson 2000).

Before calculating the diffusion energy barriers, potential diffusion paths based on unique symmetries and adjacent stable sites (Fig. 10) were identified in all the systems: Path-1 involves diffusion along the chain of hollow hexagons, Path-2 involves diagonal diffusion towards the adjacent chain of hollow hexagons, and Path-3 involves diffusing perpendicularly between chains of hollow hexagons. After the calculations, the results revealed that: for Li on β12-borophene (Fig. 10a), the energy barriers for paths 1, 2, and 3 were 0.47, 0.69, and 0.67 eV, respectively (Table 6). Path-1 demonstrated the lowest value (0.47 eV), indicating low resistance in that direction. Hence, lithium ions are more likely to diffuse along the chains of hollow hexagons (Liu et al. 2018). For Path-2 and Path-3 energy barrier values were all higher than for Path-1, indicating higher resistance towards these diffusion paths. These values have been consistently reported in most of the previous research works (Liu et al. 2018; Zhang et al. 2016; Mortazavi et al. 2017), with values ranging between 0.4 and 0.7 eV. The minimal variations in the previously reported values and with our work are attributed to different calculation conditions. Thereafter for O2 on β12-borophene (Fig. 10b); paths 1, 2, and 3, energy barrier values were found to be 0.91 eV, 1.55 eV, and 1.42 eV, respectively (Table 6). The lowest energy barrier was along path-1, indicating a preference for O2 to diffuse along the chains of hollow hexagons. In contrast, paths 2 and 3 exhibited higher diffusion energy barriers, suggesting more resistance to diffusion in those directions.

Fig. 10

Top views of possible diffusion paths and energy profiles: a Li on β12-borophene system and energy profile b O2 on β12-borophene system and energy profile, and c LiO2 on β12-borophene system and energy profile. The path-1, path-2, and path-3 on the diffusion energy profiles are represented by lines with black, red, and blue colors, respectively. All the adjacent stable sites on the crystal structure are denoted by A in a blue circle (around the hollow hexagons). The lithium, oxygen, and boron atoms are represented by the colors grey, red, and green, respectively

Table 6 Calculated diffusion energy barriers in different paths

The reported high energy barriers against the O2 are strongly correlated with the material’s strong anchoring (-5.15 eV), indicating significant challenges for O2 diffusion on the β12-borophene. This suggests that the material could prevent O2 from desorbing into the electrolyte and migrating to the negative electrode (anode) during the discharging process. Finally for LiO2 on β12-borophene (Fig. 10c),; energy barrier values for paths 1, 2, and 3 were found to be 1.08, 1.25, and 1.16 eV, respectively (Table 6). Notably, Path-1 had the lowest, followed by Path-3 then Path-2. The lowest energy barrier along Path-1 indicates low resistance, suggesting a preference for diffusion along the chain of hollow hexagons. Therefore, we generalized the diffusion energy barrier for LiO2 on β12-borophene to be 1.08 eV. The results obtained are almost the same as the previously reported on lithium polysulfide diffusing on β12-borophene surface, with the energy barrier values ranging between 1.13 to1.18 eV (Grixti et al. 2018). The minimal difference could be due to the nature of the adsorbate anchored, but ultimately the energy barriers are moderate. Showing the ability of the β12-borophene to allow adsorbates to diffuse effortlessly (Fig. 10).

Most interestingly, all the species were observed to diffuse preferentially along a chain of hollow hexagons (path-1), primarily due to the relatively low diffusion energy barrier in that path. The diffusion energy barrier was found to exhibit anisotropic, due to different values in different directions. The moderate diffusion energy barriers indicate the potential which β12-borophene has to enhance the kinetics of LiO2 on the surface of the cathode electrode, thereby improving the rate of discharging and charging processes.