A first principles investigation on the structural, mechanical, electronic, and catalytic properties of biphenylene

Recently, a new two-dimensional allotrope of carbon (biphenylene) was experimentally synthesized. Using first-principles calculations, we systematically investigated the structural, mechanical, electronic, and HER properties of biphenylene. A large cohesive energy, absence of imaginary phonon frequencies, and an ultrahigh melting point up to 4500 K demonstrate its high stability. Biphenylene exhibits a maximum Young’s modulus of 259.7 N/m, manifesting its robust mechanical performance. Furthermore, biphenylene was found to be metallic with a n-type Dirac cone, and it exhibited improved HER performance over that of graphene. Our findings suggest that biphenylene is a promising material with potential applications in many important fields, such as chemical catalysis.


Method
First-principles calculations were implemented in the Vienna ab initio simulation package 18 , using the Perdew-Burke-Ernzerhof exchange-correlation functional within the projector-augmented wave method (cut-off energy 800 eV) 19,20 . A Γ-centred 8 × 8 × 1 k-mesh was used to sample the first Brillouin zone. To eliminate the interactions between adjacent layers, a 25 Å thick vacuum space was added perpendicular to the biphenylene network. The energy and ionic force convergence were set to 10 -8 eV and 10 -4 eV/Å, respectively. The phonon dispersion calculations were performed using density functional perturbation theory in the Phonopy code 21 . Ab initio molecular dynamics (AIMD) simulations were performed using the canonical ensemble with the temperature regulated by the Nosé−Hoover thermostat 22 . The LOBSTER code is employed to calculate the crystal orbital Hamilton population 23,24 .

Results and discussion
Structure and stability. To establish a reference benchmark, we systematically investigated the structural properties and stabilities of monolayer biphenylene. Figure 1a shows the atomic structure of biphenylene. The unit cell has a rectangular geometry (space group Pmmm; group no. 47) with six carbon atoms. The lattice constants of monolayer biphenylene are a = 3.76 Å and b = 4.52 Å. The b/a ratio of 1.20 and the presence of different atomic arrangements along the x and y directions suggest an anisotropic structure. As a non-benzenoid carbon allotrope, biphenylene is constructed from octagonal, tetragonal, and hexagonal rings, which causes slight variations in the carbon-carbon bond lengths. As shown in Fig. 1a, the carbon − carbon bond lengths l 1 , l 2 , and l 3 are 1.45, 1.46, and 1.41 Å, respectively, which are similar to those of graphene (1.42 Å), indicating the robust structure of biphenylene. The electron localisation function (ELF) from the aspect of the (0 0 1) plane is shown in Fig. 1a to illustrate the bonding behaviour. A value of 1 for the ELF, denoted by red colour, corresponds to perfect localization. We find the highest ELF value in the middle of the carbon−carbon bond is 0.93, indicating that strong covalent bonds exist between the carbon atoms. Noteworthily, the values of integrated crystal orbital Hamilton population at the Fermi level are − 9.35, − 9.03, − 10.07 for the l 1 , l 2 , l 3 , respectively, the smallest value of − 10.07 implies the l 3 bonding is the strongest one.
We demonstrate the stability of biphenylene by means of cohesive energy, phonon spectrum, and AIMD simulations. The cohesive energy E C is calculated as (6E carbon − E total )/6, where E carbon and E total represent the total energies of a carbon atom and a unit cell, respectively. The E C value obtained for biphenylene is 7.40 eV/ atom, which is higher than that of MoS 2 (5.02 eV/atom) and boron nitride (7.07 eV/atom) and close to that of graphene (7.85 eV/atom). The phonon dispersion and phonon density of states are shown in Fig. 1b. There are 18 branches (3 acoustic and 15 optical) in the phonon dispersion of biphenylene, and no imaginary frequencies are observed. The maximum frequency is as high as 1657 cm −1 , indicating good dynamic stability. The phonon states contributed by the C 1 and C 2 carbon atoms are coupled in the entire range. The results of AIMD simulations at various temperature are shown in Fig. 1c. No structural distortion, bond breaking, or phase transition is observed at 300 K. Even heat up to 4500 K, the structure is still intact, and finally melt at 4600 K, demonstrating the excellent thermal stability of biphenylene. Overall, our simulation results confirm the excellent stabilities of biphenylene, that is why the biphenylene monolayer can be successfully fabricated experimentally 17 .
Mechanical properties. The elastic constants were calculated to be C 11 = 294 N/m, C 22 = 240 N/m, C 12 = C 21 = 91 N/m, and C 66 = 83 N/m. These values satisfy Born-Huang stability criteria 25 , C 11 C 22 -C 12 2 > 0 and C 66 > 0, suggesting that the biphenylene structure is mechanically stable. We further evaluated the Young's modulus and Poisson's ratio of biphenylene. The orientation-dependent Young's modulus E(θ) and Poisson's ratio ν(θ) were determined using the following equations: www.nature.com/scientificreports/ To elucidate the anisotropic mechanical properties of biphenylene, the polar 2D Young's moduli and Poisson's ratio diagrams were calculated. As shown in Fig. 2a,b, the mechanical properties of biphenylene are anisotropic in the plane. For both E(θ) and ν(θ), the largest value is along the x direction, and the smallest value is along the y direction. The Young's moduli of biphenylene along the x (E x ) and y directions (E y ) are 259.7 and 212.4 N/m (corresponds to 764 and 625 GPa), respectively. The Poisson's ratio is 0.38 along the x direction and 0.31 along the y direction. The Young's modulus of biphenylene is much higher than that of black phosphorene (83 N/m) 26 and MoS 2 (123 N/m) 27 , close to that of BN (E x = E y = 275 N/m) 28 , and slightly smaller than that of graphene (E x = E y = 340 N/m) 29 . These results indicate the robust mechanical properties of biphenylene.
The strain−stress curves under uniaxial (tensile strain from 0 to 30%) and biaxial strains (tensile strain from 0 to 20%) are displayed in Fig. 2c,d, respectively. Figure 2c shows that the fracture strain (strength) is 22% (28.81 N/m) along the x direction and 16% (23.13 N/m) along the y direction. The phonon dispersions were also employed to confirm the determined fracture strains, and the results are shown in Fig. S1. There are no imaginary frequencies in the phonon spectra until the fracture strains are reduced to 21% along the x direction and 14% along the y direction under uniaxial strain. Hence, we corrected the fracture strain (strength) to 21% (28.69 N/m) along the x direction and 14% (22.34 N/m) along the y direction. The fracture strain for biaxial strain (strength) was reduced to 16% (23.50 N/m). After the correction using the phonon spectra (Fig. S1), it was further reduced to 11% (21.07 N/m). Notably, the predicted fracture strengths of biphenylene are larger than those of black phosphorene, which has a fracture strength limit of 10 N/m along the x direction and 4 N/m along the y direction 30 . Thus, biphenylene exhibits robust mechanical properties. Fig. 3 shows several bands across the Fermi level, indicating that biphenylene is metallic; this agrees well with the experimental dI/dV spectra reported previously 17 . The total density of states shown in Fig. 3 indicates several peaks across the Fermi level, for example, at 0.22 and 0.58 eV. We further analysed the projected density of states and found that the states near the Fermi level are mainly contributed by the p z orbitals of the carbon atoms. As the sp 2 -hybridized allotrope of carbon, the formed n-type Dirac cone approaches (0.64 eV above) the Fermi energy level along the Y − Γ line. Such tilted Dirac cones have been reported in other 2D materials such as Be 5 C 2 31 , Pmmn boron 32 , and FeB 3 33 . The origin of the Dirac cone can be attributed to the out-of-plane p z orbitals, as shown in Fig. 3b.

Electronic properties. The band structure in
C 11 sin 4 θ + C 11 C 22 − C 2 12 /C 66 − 2C 12 sin 2 θ cos 2 θ + C 22 cos 4 θ (2) ν(θ) = C 12 sin 4 θ − C 11 +C 22 − C 11 C 22 − C 2 12 /C 66 sin 2 θ cos 2 θ + C 12 cos 4 θ C 11 sin 4 θ + C 11 C 22 − C 2 12 /C 66 − 2C 12 sin 2 θ cos 2 θ + C 22 cos 4 θ where ΔE is the adsorption energy of H * species, ΔE zpe is the change in the zero-point energies, T is 298.15 K, ΔS is the difference in the entropy before and after adsorption, and * is the active site. We considered all possible adsorption sites for a single H atom on a 3 × 3 biphenylene supercell. Figure 4a shows the most stable adsorption configuration. According to Fig. 4b, the Gibbs free energy for HER is 0.29 eV at U = 0 eV, which is much smaller than that of 2H-MoS 2 (2 eV) 34 , better than that of g-C 3 N 4 (0.54 eV) 35 and WSSe (0.58 eV) 36 , and comparable to that of recently reported Pd 4 S 3 Te 3 (0.18 eV) 37 . The Gibbs free energy change of pristine graphene for HER is also shown in Fig. 4b. Notably, biphenylene exhibits a significantly higher catalytic activity than pristine graphene (ΔG H = 1.41 eV). To further reveal the improved catalytic performance of biphenylene, we introduced the σ centre theory ( ε s = ∞ −∞ n s (ε)εdε ∞ −∞ n s (ε)dε ). According to the results shown in Fig. 4c, biphenylene has a higher σ centre position (− 7.49 eV) than graphene (− 8.09 eV), which indicates stronger hydrogen bonding ability (a strong correlation between σ centre and ΔG H values is shown in Fig. S2). These results indicate that biphenylene has significant potential for catalysing HER.

Conclusion
Based on first-principles calculations, we systematically explored the structural, mechanical, electronic, and HER properties of biphenylene. Our results show that monolayer biphenylene is stable with a large cohesive energy (7.40 eV/atom) and is characterised by a phonon spectrum with no imaginary frequencies and an ultrahigh melting point up to 4500 K. In addition, a maximum Young's modulus of 259.7 N/m reveals its robust mechanical properties. The determined fracture strains (strengths) are 21% (28.   www.nature.com/scientificreports/ and y directions under uniaxial strain, respectively. Under biaxial strain, the fracture strain (strength) is reduced to 11% (21.07 N/m). The metallic nature with a n-type Dirac cone of biphenylene along with its outstanding performance in HER (ΔG H = 0.29 eV) demonstrate the potential of biphenylene as a catalyst.