New crystal structure prediction of fully hydrogenated borophene by first principles calculations

New crystal structures of fully hydrogenated borophene (borophane) have been predicted by first principles calculation. Comparing with the chair-like borophane (C-boropane) that has been reported in literature, we obtained four new borophane conformers with much lower total-energy. The most stable one, washboard-like borophane (W-borophane), has energy about 113.41 meV/atom lower than C-borophane. In order to explain the relative stability of different borophane conformers, the atom configuration, density of states, charge transfer, charge density distribution and defect formation energy of B-H dimer have been calculated. The results show that the charge transfer from B atoms to H atoms is crucial for the stability of borophane. In different borophane conformers, the bonding characteristics between B and H atoms are similar, but the B-B bonds in W-borophane are much stronger than that in C-borophane or other structures. In addition, we examined the dynamical stability of borophane conformers by phonon dispersions and found that the four new conformers are all dynamically stable. Finally the mechanical properties of borophane conformers along an arbitrary direction have been discussed. W-borophane possesses unique electronic structure (Dirac cone), good stability and superior mechanical properties. W-borophane has broad perspective for nano electronic device.

In this work, the structural stability, band structures, charge density distribution and mechanical properties of borophanes with different configurations have been studied by first principles calculations. We obtained four new conformers with much lower total-energy than that of C-borophane. Furthermore, we established the relative stability of different borophane conformers. By analyzing the atom configurations and the total-energies of borophane conformers, we found the configuration in which B atoms are staggered by zigzag mode along the a direction, and staggered by up and down wrinkle mode along the b direction is the most stable one. Furthermore, we explain the stability of borophane conformers by analyzing density of states, charge transfer, charge density distribution and defect formation energy of B-H dimer. The results show that the charge transfer from B atoms to H atoms is crucial for the stability of borophane. The charge density distribution and defect formation energy of B-H dimer show that the B-B bonds in W-borophane are stronger than that in C-borophane. Moreover, we examined the dynamical stability of borophane conformers by calculating the phonon dispersions. Finally the electronic structures and the mechanical properties of the C-borophane and the four new conformers have been discussed.

Computational details
All calculations are performed using the Quantum-Espresso package 39 . Ultrasoft pseudopotentials 40 are used for all atoms and the exchange-correlation approximation is evaluated through the Perdew-Burke-Ernzerh (PBE) 41 functional. The kinetic-energy cutoff of plane-waves is set to be 50 Ry. The atomic positions and lattice constants are fully relaxed, until the forces on all atoms are less than 0.01 eV/Å. A large vacuum region (20 Å) is included along z direction to eliminate the interlayer interactions.
The four nonzero elastic constants of a 2D material are c 11 , c 22 , c 12 and c 66 . The Young's modulus along the a and b directions can be written as 42

Results and Discussion
Crystal structures and stability. In order to study the influence of H adsorption on the atomic and electronic structure of borophene, we calculated the borophene with a single H atom adsorption in the 6 × 2 × 1 supercell. Four different adsorption sites have been taken into consideration. Our results show that the most stable adsorption site is the top site of B atom. Significant shifts of B atoms have been observed when the H atom is adsorbed on the top site. The local atomic structure schematic of borophene with one, two and three H atoms adsorption have been shown in Fig. 1. The shifts of B atoms and the average adsorption energy of H atoms are listed in Table 1. As shown in Fig. 1(a), in the single H atom adsorption, the shift of the B atom (B3) bonded with the H atom is about 0.32 Å along Z direction. For the two first neighbor B atoms (B2 and B4) of the B atom bonded with the H atom, the shifts along the negative Z direction are both about 0.3 Å. However, for the second and third neighbor B atoms of B3, the shifts along z direction are only 0.04 and 0.03 Å, indicating that H atom induced atomic distortion is mainly imposed to the first neighbor B atom of the B atom bonded with H atom. For two H atoms adsorbed borophene, two configurations have been shown. As shown in Fig. 1(b), two H atoms adsorbed on two neighbor B atoms. Adsorption of H atom on B2 atom will lead the shift of B3 atom along negative Z direction. However, adsorption of H atom on B3 atom will make B3 atom move along positive Z direction. For B3 atom, the atomic shifts induced by the two adsorbed H atoms are not along the same direction. However, in H2-B ( Fig. 1(c), for B3 atom, the atomic distortion induced by the two adsorbed H atoms are consistently, leading to that the average adsorption energy of H atom in H2-B configuration is 0.38 eV/H higher than that in H2-A. For three H atoms adsorption, in H3-A, three H atoms are adsorbed on the three neighbor B atoms, while, in H3-B, three H atoms are adsorbed on the three next neighbor B atoms. Similarly, the configuration H3-B is much more stable than H3-A. More specifically, the average adsorption energy of H atoms in H3-B configuration is 0.65 eV/H higher than that in H3-A. In addition, by analyzing the partial density of states of H and B atoms in H3-A and H3-B (as shown in Fig. 2), we found that the orbital hybridization between H (s) and B (p z ) in H3-B is much stronger than that in H3-A.
Then we studied the atomic, electronic structures and stability of fully hydrogenated borophene. The crystal structures of seven borophane conformers are displayed in Fig. 3. For convenience of description, we named the seven conformers as Plane-Square-type borophane (PS-borophane), Plane-Triangle-type borophane (PT-borophane), Chair-like borophane, Boat-like borophane (B-borophane), Twist-Chair-Boat-type borophane (TCB-borophane), Triangle-type borophane (T-borophane) and Washboard-like borophane, respectively. The unit cells are marked by the black dashed rectangles. The optimized lattice constants, B-H bond lengths, buckling heights and the total-energy difference relative to C-borophane are listed in Table 2. In the seven borophane conformers, each B atom is hydrogenated with an H atom, namely, the ratio of B:H is 1:1. The C-borophane configuration has been reported, previously 20, 27, 43 . As shown in Fig. 3(e) and (f), C-Borophane has a buckled configuration and the buckling height is 0.80 Å, which is smaller than that of borophene (0.91 Å) 8 . In C-borophane, Scientific RepoRts | 7: 609 | DOI:10.1038/s41598-017-00667-x Hydrogen atoms alternate on both sides of the borophene sheet. B atoms are aligned along the a direction and staggered by up and down wrinkle mode along the b direction. For comparison, two planner conformers (PSand PT-borophane) that all hydrogen atoms bond with B atoms at the same side have been taken into consideration. In PS-borophane, each B atom bonds with four neighboring B atoms. In other six conformers, each B atom bonds with six neighboring B atoms. In PS-borophane, all B atoms are aligned along the a and b direction. In PT-borophane, B atoms are aligned along the a direction, however, staggered by zigzag mode along the b direction. The total-energy difference relative to that of C-borophane and the schematic drawings of different conformers are shown in Fig. 4. PS-and PT-borophane have total-energy difference 685.93 and 425.67 meV/atom higher than C-borophane, respectively, indicating that the buckled configuration is more stable than the planner configurations.
C-, B-, TCB-, T-and W-borophane are all buckled configurations. In B-borophane, for convenience of description, we regard the four neighboring B atoms that constitute a parallelogram and the four H atoms that bond with the four B atoms at the same side as a small unit, as shown in Fig. 4(e). The small units are aligned  along the a direction, however, staggered by up and down wrinkle mode along the b direction. B-borophane has energy 7.94 meV/atom lower than C-borophane. In TCB-borophane, pairs of hydrogen atoms alternate on both sides along the a and b direction. Similarly, we regard the two neighboring B atoms that bond with two H atoms at the same side and the two H atoms as a small unit, as shown in Fig. 4(f). The small units are staggered by zigzag mode along the a direction, and staggered by up and down wrinkle mode along the b direction. TCB-borophane has energy 73.85 meV/atom lower than C-borophane. In T-borophane, ternate hydrogen atoms alternate on both sides along the a and b direction. We regard the three neighboring B atoms that constitute a triangle and the three H atoms that bond with the three B atoms at the same side as a small unit, as shown in Fig. 4(g). The small units are staggered by up and down wrinkle mode along the a and b direction. T-borophane has energy 110.66 meV/atom lower than C-borophane. In W-borophane, B atoms are staggered by zigzag mode along the a direction, and staggered by up and down wrinkle mode along the b direction. W-borophane has energy difference about 113.41 meV/atom lower than C-borophane. Compared with C-borophane (wrinkle along b direction), W-borophane has buckled configuration along both a and b direction, leading to superior mechanical properties along a direction. Specifically, the ultimate tensile strain along a direction of W-borophane is 0.17, which is larger than that of C-borophane (0.12). In order to further affirm the relative stability of different borophane conformers, different exchange-correlation functionals with local density approximation (LDA) and general gradient approximation (GGA, such as typical PBE, and PW91) have been used to check the trend of the total-energy differences. PBE and PW91 are both belong to GGA exchange-correlation functional, therefore, the energy difference (ΔE) obtained by PBE and PW91 are highly consistent. The overestimation of the cohesive energy at the LDA level has been reported 44 , resulting in the distinct difference of ΔE at the LDA and GGA level. On the whole, the trends of energy differences obtained by the three exchange-correlation functionals are consistent. This further indicates that the stability of the new borophene conformers is independent or less dependent on the form of exchange-correlation functionals. It is interesting that the energy difference between T-and W-borophane is only 2.75 meV/atom under the stress-free states. Under ≥0.05 biaxial tensile stains, the total-energy of T-borophane change to be lower than that of W-borophane, indicating that there exists a structural phase transition between T-and W-borophane under increasing biaxial tensile strains.
In order to examining the dynamical stability of borophane conformers, we calculated the phonon dispersions. Phonon dispersion is an important parameter to estimate the dynamical stability of crystal structure. Imaginary frequencies along any high-symmetry direction of the Brillouin zone are indications of dynamic instability of the crystal structure. The calculated phonon dispersions of B-, TCB-, T-and W-borophane are shown in Fig. 5. For the four new borophane conformers, no imaginary frequencies were found along the high-symmetry directions of the Brillouin zone, indicating that the four new borophane conformers are all dynamically stable.
Electronic structures. In order to further explain the excellent stabilities of W-borophane, we analyzed the electronic structures of different borophane conformers to obtain a deep insight of the bonding characteristics and stabilization mechanism. A simple and clear picture of electronic bonding in boron sheet has been reported 45 . A structure that optimally fills in-plane bonding states (s, p x and p y ) should be most preferable 45 . In borophene, in-plane sp 2 antibonding states are partly occupied. Hence, borophene is unstable and prone to donate electrons 46 . In hydrogenated borophene, there exist a charge transfer from B atoms to H atoms, leading to that the in-plane bonding states are completely filled and the antibonding states are empty; moreover, the out-of-plane bonding states are also fully filled. Finally, the Fermi level is exactly located at the valley bottom of the total density of states. Consequently, full hydrogenated borophene is stable. The band structures and density of states of B-, TCB-, Tand W-borophane are displayed in Fig. 6. The four new borophane conformers all possess a Dirac cone. The band structure of C-borophane shows clearly a Dirac cone along the Γ-X direction 27,43 . Similarly, the band structure of B-borophane shows a Dirac cone along the Γ-X direction. However, for TCB-, T-and W-borophane, the Dirac cones are along the Γ-Y direction. Furthermore, in order to analyze the electronic bonding of W-borophane, we  Fig. 7. By analyzing the energy rang and peak position, we found that there exists a strong orbital hybridization between s orbit of H atoms and p z orbit of B atoms. Furthermore, from the partial density of states near the Fermi level, we can found that the Dirac electron is mainly contributed by the p x and p y electron of B atoms for W-borophane. A similar phenomenon has been observed in C-borophane 27 .
In order to confirm the aforementioned charge transfer, we calculated the deformation charge density of C-, B-, TCB-, T-and W-borophane. The deformation charge density is defined as the difference between the total charge density (ρ  r ( )) in the solid and the superposition of independent atomic charge densities ( ρ placed at the atomic sites of the same solid, the equation can be written as The yellow areas represent electron accumulation ( ρ ∆ >  r ( ) 0), and the blue areas represent electron depletion ( ρ ∆ <  r ( ) 0). As shown in Fig. 8, a charge transfer from B atoms to H atoms is clearly shown. By comparing the electronegativity of boron and hydrogen, we can find that the electronegativity of hydrogen (2.2) is larger than that of boron (2.04). Therefore, the charge transfer from B atoms to H atoms is reasonable. Similarly, a charge transfer from silicon (1.9) to hydrogen (2.2) atom has been found in hydrogenated silicene 47 . However, the electronegativity of carbon (2.55) is larger than that of hydrogen (2.2), on the contrary, a charge transfer from H atoms to C atoms has been observed in graphane 32 .
Furthermore, we investigated the bonding characteristics in C-and W-borophane by analyzing the charge density distributions and defect formation energy of a B-H dimer. The in-plane bonds (B-B bonds) are stronger that out-of-plane π-bonds (B-H bonds). In PT-, C-, B-, TCB-, T-and W-borophane, the B-H bond lengths are almost the same, indicating that the bonding characteristics between B and H atoms are uniform. Similar phenomenon has been reported in different conformers of hydrogenated silicene 47 . Hence, it is imperative to analyze the bonding characteristics between B and B atoms in borophane conformers. The 2D charge density contours of C-and W-borophane are shown in Fig. 9. We have selected two typical planes in C-and W-borophane. Plane1 is perpendicular to z coordinate axis and contains a B-B bond. Three nearest neighboring B atoms that constitute a    triangle determine plane2. Comparing the charge density distribution of C-with W-borophane, we can find that more electrons gathered along the B-B bond direction in W-borophane than that in C-borophane, indicating that the B-B bonds in W-borophane are stronger than that in C-borophane. In order to quantitative describe the bonding strength of B-B bonds, we calculated the defect formation energy of a B-H dimer in C-and W-borophane. The defect formation energy E form can be expressed as where E def /E per is the total energy of the supercell with/without the B-H dimer defect, and N def /N per denote the atom numbers of the supercell with/without the B-H dimer defect. As shown in Fig. 10, when the defect concentration η = 1/24, the defect formation energy of a B-H dimer is only 0.40 eV for C-borophane, however, that value change to 0.95 eV for W-borophane. The defect formation energy of B-H dimer in W-borophane is much higher than that in C-borophane, indicating that the B-B bonds in W-borophane are much stronger than that in C-borophane. It is agree well with the results of charge density distributions.
Mechanical properties. In addition, we calculated the elastic constants, Young's modulus, shear modulus, and Poisson's ratios of B-, TCB-, T-and W-borophane. As listed in Table 3, the Young's modulus of C-borophane along the a and b direction are 172. 24 and 110.59 N/m 43 . For C-and B-borophane, the Young's modulus along the a direction is much larger than that along the b direction. By analyzing the atomic structure of C-and B-borophane, we found that B atoms are aligned along the a direction, however, staggered by up and down wrinkle mode along the b direction. Under uniaxial tensile stains along the a direction, the B-B bonds along the a direction were elongated, significantly. However, the uniaxial tensile strains along the b direction can be released  due to the buckled configuration. For C-and B-borophane, the ratio (Y a /Y b ) of Young's modulus along the a and b direction are 1.56 and 2.37, respectively. However, the ratio is reduced to 1.13 for W-borophane. Similarly, we found that all B atoms in W-borophane are staggered along the a and b direction, therefore, the uniaxial strains along the a and b direction can be released. In addition, we also calculated the mechanical properties of B-, TCB-, T-and W-borophane along an arbitrary direction. The results are shown in Fig. 11. For isotropic materials, the Young's modulus and shear modulus are independent of the direction. The polar diagrams of Young's modulus and shear modulus are perfect circles. The larger degree of deviation from a perfect circle, the stronger anisotropy the materials possess. The Young's modulus and shear modulus of C-borophane are strongly dependent on the direction 43 . However, for W-borophane, the Young's modulus and shear modulus tend to more isotropic.    . 2D charge density contour of two typical planes in C-and W-borophane. Plane1 is perpendicular to z coordinate axis and contains a B-B bond. Three nearest neighboring B atoms that constitute a triangle determine plane2. The red area represents the electron is dense in the area, however, the blue area represents the electron is sparse in the area.

Conclusions
In summary, with first principles calculations we have studied the structure stability, electronic structures and mechanical properties of borophane with different configurations. Comparing with C-boropane, we obtained four new conformers with much lower total-energy. By analyzing the atomic arrangements and the total energies in different conformers, we found that the configuration that B atoms are staggered by zigzag mode along the a direction and staggered by up and down wrinkle mode along the b direction is the most stale one. The most stable one, W-borophane, has energy difference about 113.41 meV/atom lower than C-borophane. The charge transfer from B atoms to H atoms is crucial for the stability of borophane. Furthermore, the results of charge density distribution show that more electrons gathered along the B-B bond direction in W-borophane than that in C-borophane, moreover, the defect formation energy of B-H dimer in W-borophane is much higher than that in C-borophane, both indicating that the B-B bonds in W-borophane are stronger than that in C-borophane. By calculating the phonon dispersions of the four new borophane conformers, we found no imaginary frequencies along the high-symmetry directions of the Brillouin zone, indicating that the four new conformers are all dynamically stable. The band structures of the four new conformers all show a Dirac cone along Γ-Y or Γ-X direction. Furthermore, from the partial density of states near the Fermi level, we can found that the Dirac electron is mainly contributed by the p x and p y electron of B atoms. The unique electronic structure results in high carrier mobility, making borophane a promising material for nano electronic device. Finally the mechanical properties of borophane conformers along an arbitrary direction have been discussed. The results show that the Young's modulus and shear modulus of C-borophane are highly anisotropic. However, for W-borophane, the Young's modulus and shear modulus tend to more isotropic.  Table 3. Elastic constants c ij , shear modulus G, Young's modulus Y in N/m, and Poisson's ratio ν of C-, B-, TCB-, T-and W-borophane. The angle is measured relative to the a direction. Isotropic (anisotropic) behavior is associated to a circular (noncircular) shape.