Borophene as a 2D anode material for lithium ion batteries:

The rapid development of electronic products has inspired scientists to design and explore novel
electrode materials with an ultrahigh rate of charging/discharging capability, such as two-
dimensional (2-D) nanostructures of graphene and MoS2. In this study, another 2-D nanosheet,
that is a borophene layer, has been predicted to be utilized as a promising anode material for
high-performance Li ion battery based on density functional theory calculations. Our study has
revealed that Li atom can combine strongly with borophene surface strongly and easily, and exist
as a pure Li+ state. A rather small energy barrier (0.007 eV) of Li diffusion leads to an ultrahigh
diffusivity along an uncorrugated direction of borophene, which is estimated to be 104 (105)
times faster than that on MoS2 (graphene) at room temperature. A high Li storage capacity of
1239 mA·h/g can be achieved when Li content reaches 0.5. A low average operating voltage of
0.466 V and metallic properties result in that the borophene can be used as a possible anode
material. Moreover, the properties of Li adsorption and diffusion on the borophene affected by
Ag (111) substrate have been studied. It has been found that the influence of Ag (111) substrate
is very weak. Li atom can still bind on the borophene with a strong binding energy of −2.648 eV.
A small energy barrier of 0.033 eV can be retained for Li diffusion along the uncorrugated
direction, which can give rise to a high Li diffusivity. Besides, the performances of borophene-
based Na ion battery have been explored. Our results suggest that an extremely high rate
capability could be expected in borophene-based Li ion battery. 2nd

Two-dimensional (2D) materials as electrodes” is believed to be the trend for future Li-ion and
Na-ion battery technologies. Here, by using first-principles methods, we predict that the recently
reported borophene (2D boron sheets) can serve as an ideal electrode material with high
electrochemical performance for both Li-ion and Na-ion batteries. The calculations are
performed on two experimentally stable borophene structures, namely β12 and χ3 structures. The
optimized Li and Na adsorption sites are identified, and the host materials are found to maintain
good electric conductivity before and after adsorption. Besides advantages including small
diffusion barriers and low average open-circuit voltages, most remarkably, the storage capacity
can be as high as 1984 mA h g−1 in β12 borophene and 1240 mA h g−1 in χ3 borophene for both Li
and Na, which are several times higher than the commercial graphite electrode and are the
highest among all the 2D materials discovered to date. Our results highly support that
borophenes can be appealing anode materials for both Li-ion and Na-ion batteries with extremely
high power density. 3rd
Allotropes of Borophene:

4th Monolayer Honeycomb Borophene:

H-borophene is a Promising Anode Material with a Record Capacity for Lithium-Ion and
Sodium-Ion Batteries.

Two-dimensional (2D) materials are a suitable agent for the anode material of lithium-ion battery
(LIB) for its unique physical properties and chemical characteristics. Latterly, a honeycomb
borophene (h-borophene) has been assembled by molecular beam epitaxy rise in a large vacuum.
Now, we assume the first-principles DFT calculations to study the behavior of monolayer h-
borophene as an anode material for the LIB. The binding energies of the ML h-borophene-Li/Na
systems are all negative, shows a steady adsorption process. The diffusion barriers of the Li and
Na ions in h-borophene are 0.53 and 0.17 eV, and the anode overall open-circuit voltages for the
LIB and NIB are 0.747 and 0.355 V, respectively. The maximum conceptual storage ability 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 determine on time. Our study
propose that h-borophene is a promising anode material for high capacity LIBs and NIBs.

Computational Methods:

All Calculations were carried out using DFT in connection with the exchange correlation energy
described by the generalized gradient approximation (GGA) in the scheme proposed by Perdew–
Burke–Ernzerhof (PBE) as implemented in the Vienna ab initio simulation package (VASP). The
periodic boundary conditions are applied in three directions (x, y and z directions), 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. Van der Waals interaction is taken into account using the semi-
empirical dispersion correction of DFT-D3 approach. 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. 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. 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.

Crystal structures and adsorption ability of an isolated Li/Na atom on ML h-borophene

The pristine lattice parameter of ML h-borophene is a = 3.0 Å with two borium (B) atom sites
which is in good agreement with the previous experimental report. 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 h-borophene by calculating
the average formation energy (Eform) defined as Eform = EB – Etot, where EB is the energy of an
isolated B atom, and Etot 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), β12 (6.15 eV atom−1), X3 (6.16 eV atom−1)
and β1S (6.08 eV atom−1) borophene, but the positive average formation energy value of ML h-
borophene still shows a certain degree of stability.
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. The structural snapshot reveals that the isolated ML h-borophene has a good
thermodynamic stability.

Figure 1 (a) Side and (b) top view of the freestanding ML h-borophene. The yellow dots indicate
three high symmetry adsorption sites (B, T, H sites). The rhombus indicates the outline of the
pristine unit cell of ML h-borophene. dz is the distance between the adsorption atom to the ML h-
borophene surface.
Absorption:

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 h-borophene is the lowest
one among that of a Li/Na atom adsorbed on the H, B and T sites.

Table I. Summary of the adsorption ability of an isolated Li/Na atom on ML h-borophene. da is

the minimum Li/Na-B atom-to-atom distance projected in the z direction. Et is the total energy of
the ML h-borophene-Li/Na adsorption system. Eb 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 h-borophene.
Li atom Na atom

Adsorption Hollo
site w Bridge Top Hollow Bridge Top

Adsorpting
distance da (Å) 1.41 — 2.11 1.99 2.30 2.41

Total
energy Et (eV) −46.89 — −46.33 −45.90 −45.72 −45.70

Binding
energy Eb (eV
atom−1) −1.06 — −0.50 −0.68 −0.50 −0.48

Charge
transfer (e−) 0.84 — 0.88 0.76 0.79 0.79

To evaluate the adsorption ability of the Li and Na atoms on ML h-borophene, the binding
energy (Eb) can be defined as
where EMxB8, EB8 and EM are the total energy of the 2 × 2 ML h-borophene adsorbed by the metal
atoms, pristine 2 × 2 ML h-borophene 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. Eb's of the Li and Na ions adsorbed on the H site are −1.06 and −0.68 eV atom−1, respectively.
Those on the T site are −0.50 and −0.48 eV atom−1, respectively. Eb of the Na ion adsorbed on
the B site is −0.50 eV atom−1. The values of Eb of different adsorption sites are collected in
Table I. The absolute values of Eb on the H site are all larger than those of the B and T sites,
indicating both the Li and Na ions preferring to stay on the H site. Thus, the following studies
concentrate on the H site configurations. The distances from the Li/Na atoms at the H site to the
ML h-borophene layer (dZ) (Fig. 1b) are 1.41 (Li) and 1.99 (Na) Å. The Na atom has the larger
distance to the surface of ML h-borophene and also the smaller binding energy with ML h-
borophene. The absolute values of the Eb for Li (−1.10 eV atom−1) and Na (−0.46 eV atom−1)
atom adsorbed on graphene are comparable to those on ML h-borophene, indicating the stability
of the Li/Na atoms-ML h-borophene systems. The binding energy is not corrected with zero-
point energy and entropy contributions. Such kind of corrections could change the relative
stability of the configurations with close total energy, but we do not expect the relative energy
relation between the H and T (B) sites will be affected because of the large energy difference
between the H and T (B) sites.

Diffusion
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,

where d, ʋ, Ea and kB 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) and the armchair directions (H →
T → B → T → H) 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 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 Along the zigzag direction, the B
site is the maximum state as shown in the energy profile 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. 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 β12 (0.66 eV) and χ3 (0.60 eV)
borophene and comparable to some well-known anode materials including TiO2-based
polymorphs (∼0.5 eV) and silicon (0.57 eV). 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 MoS2 (0.68 eV), MoN2 (0.56 eV), χ3 borophene (0.34 eV), β12 borophene (0.33
eV), NiC3 (0.23 eV) and TiC3 (0.18 eV), 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. 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
1013 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 cm2 s−1, respectively. The diffusion constant of the Li ion on
ML h-borophene is one order of magnitude larger than that of c-Si (3.60 × 10−12 cm2 s−1).

Li/Na storage capacities of ML h-borophene and average open-circuit 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 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.

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 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:

Where M = (Li, Na), and n is the number of adsorbed metal ions. The average adsorption energy
of each concentration can be described by Eq. 1. A negative value of the average adsorption
energy indicates that the Li/Na ions in the LIBs/NIBs prefer to get adsorbed on the h-borophene
surface, whereas a positive value of the adsorption energy means that the Li/Na ions are hard to
get adsorbed on the h-borophene surface during the charging process.
To obtain the maximum adsorption concentration of the Li/Na ions adsorbed on the 2 × 2 ML h-
borophene surface, we gradually increase the number of the Li/Na ions on the h-borophene
surface. The concentration of the Li/Na ions adsorbed on the h-borophene surface is represented
by the LixB/NaxB. The x values of the LixB are 0.125, 0.25, 0.375, 0.5, 0.625, 0.75, 0.875,
1.000, 1.250, 1.750, 2.000 and 2.125 corresponding to the Li1B8, Li2B8, Li3B8, Li4B8, Li5B8, Li6B8,
Li7B8, Li8B8, Li10B8, Li14B8, Li16B8 and Li17B8, respectively. According to the previous calculation
of the most stable adsorption site of the Li/Na ions on the ML h-borophene surface, we only
consider the Li/Na ions adsorbed on the H sites of both sides of the 2 × 2 ML h-borophene
surface. After the H sites fully adsorbed, we put the Li ions on the T sites to continually
increasing the concentration x from 1 to 2.125. Firstly, we calculate the different adsorption
structures of the Li ions with the same concentration x and get the structure with the lowest total
energy among all configurations at this concentration. Secondly, we calculate the binding energy
of the lowest total energy configuration to check the stability of the systems after adsorbed the
metal atoms using Eq. above. 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 Eb (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 h-borophene in these Li ion adsorption
systems. Combining the binding energy Eb and the degree of deformation of ML h-borophene,
we can conclude that the maximum concentration (xmax) of the lithiation process is at the value of
2.125.
8-Pmmn

The orthorhombic 8-Pmmn borophene is an energetically and structurally stable structure. It

possesses tilted anisotropic DCs, and its ground state energy is lower than that of the α -sheet
structures and any other analogs.

First-principles calculations on monolayer 8-Pmmn borophene are reported to reveal

unprecedented electronic properties in a two-dimensional material. Based on a Born effective
charge analysis, 8-Pmmn borophene is the first single-element-based monolayered material
exhibiting two sublattices with substantial ionic features. The observed Dirac cones are actually
formed by the pz orbitals of one of the inequivalent sublattices composed of uniquely four atoms,
yielding an underlying hexagonal network topologically equivalent to distorted graphene. A
significant physical outcome of this effect includes the possibility of converting metallic 8-
Pmmn borophene into an indirect band gap semiconductor by means of external shear stress. The
stability of the strained structures is supported by a phonon frequency analysis. The Dirac cones
are sensitive to the formation of vacancies only in the inequivalent sublattice electronically
active at the Fermi level.

Using first-principles many-body perturbation theory, we investigate the optical properties of 8-

Pmmn borophene at two levels of approximations; the GW method considering only the
electron–electron interaction and the GW in combination with the Bethe–Salpeter equation
including electron–hole coupling. The band structure exhibits anisotropic Dirac cones with
semimetallic character. The optical absorption spectra are obtained for different light
polarizations and we predict strong optical absorbance anisotropy. The absorption peaks undergo
a global redshift when the electron–hole interaction is taken into account due to the formation of
bound excitons which have an anisotropic excitonic wave function. 1st

Structure:
5th