Penta-BxNy sheet: a density functional theory study of two-dimensional material

By using density functional theory with generalized gradient approximation, we have carried out detailed investigations of two-dimensional BxNy nanomaterials in the Cairo pentagonal tiling geometry fully composed of pentagons (penta-BxNy). Only penta-BN and BN2 planar structures are dynamically stable without imaginary modes in their phonon spectra. Their stabilities have been further evaluated by formation energy analysis, first-principles molecular dynamics simulation, and mechanical stability analysis. Penta-BN2 is superior to penta-BN in structural stability. Its stability analysis against oxidization and functional group adsorption as well as its synthesizing reaction path analysis show possibilities in fabricating penta-BN2 on experiment. Furthermore, the penta-BN2 could be transferred from metallic to semiconducting by ionizing or covalently binding an electron per dinitrogen. Also, it has been found to have superior mechanical properties, such as the negative Poisson’s ratio and the comparable stiffness as that of hexagonal h-BN sheet. These studies on the stabilities, electronic properties, and mechanical properties suggest penta-BN2 as an attractive material to call for further studies on both theory and experiment.

Scientific RepoRts | 6:31840 | DOI: 10.1038/srep31840 corresponds to the layer structure of T12-carbon bulk 19 . Inspired by this finding, pentagonal sheet materials of CN 2 20 , hydrogenated silicene 21 , and B 2 C 22 have been recently reported. The pentagonal arrangement of atoms induces high energy density in CN 2 , superior flexibility and bipolar magnetic properties in hydrogenated silicene, and tunable band gap in B 2 C. In comparison with graphene, lots of inorganic nanosheets also have hexagonal lattice characters, such as the h-BN, SiC, MoS 2 etc., while the non-hexagonal cases are to some sense rare. So, the questions could be raised: could the non-hexagonal lattice be stable for most planar or quasi-planar nanostructures; will the non-hexagonal structures bring new electronic properties in view of the structure-property exploration for advanced nanomaterials? As a contribution to these issues, we have carried out a detailed investigation on the pentagonal penta-B x N y nanosheets. Their thermodynamic and kinetic stabilities have been carefully evaluated. Considering the fabrication conditions, we have also examined their stabilities against oxidization, functional group adsorption, and charge state. The electronic and mechanical properties of the stable penta-B x N y nanomaterials have also been discussed.

Results
The Cairo pentagonal tiling is the structural geometry fully composed of pentagons, which is schematically shown in Fig. 1 with the repeated unit highlighted by a × b. Arranging B and N atoms at possible positions in the repeated unit, we have carefully optimized the geometrical structures of penta-B x N y nanosheets and calculated their phonon spectra, respectively. In our studies, the number of B atoms ranges from 0 to 6, which simultaneously requires that of N atoms to reversely change from 6 to 0 to meet the requirement of 6 atoms in the primitive unit cell. Only BN (B:N = 3:3) and BN 2 (B:N = 2:4) sheets are found to be dynamically stable without imaginary modes, which are presented in Fig. 2. Unlike the Cairo pentagonal tiling, the penta-BN and BN 2 sheet structures are found to be slightly buckled to release local steric strain. The penta-BN consists of four atomic layers which are the top layer of dinitrogen, the second layer of boron, the third layer of atomic nitrogen, and the bottom layer of boron again, resulting in four different groups of atoms as marked in Fig. 2a. The atomic arrangement shows CM space symmetry and the thickness between top and bottom layers is measured to be 1.37 Å. As tabulated in Table 1, the charge populations on B 1 , B 2 , dinitrogen, and atomic nitrogen species are 2.2, 1.5, 11.9, and 7.0 electrons calculated by Bader analysis 23,24 , respectively. The lengths are 1.34, 1.60, 1.36, and 1.78 Å for the l 1 , l 2 , l 3 , and l 4 bonds, respectively. However, in the penta-BN 2 sheet, there are only two composition species. The atomic B atoms form one atomic layer being sandwiched between the top and bottom dinitrogen layers, showing P m 42 1 layer group symmetry. The thickness is 1.26 Å. The boron atom and dinitrogen are calculated to have 1.0 and 12.1 electrons. The l 1 and l 2 bonds are 1.34 and 1.55 Å in length. For the penta-BN and BN 2 nanosheets, the in-plane lattice constants are calculated to be 3.75 and 3.63 Å, respectively.
For the kinetically stable penta-BN and BN 2 sheets, we have also evaluated the melting temperatures to estimate their heat stabilities by using the first-principles molecular dynamics (MD) simulations. In order to minimize the special constraints due to the periodic conditions, the method of supercell has been adopted in our MD simulations to explore the possibilities in structure reconstruction or melting. The energy barrier protecting the geometrical structure to stay at the local minima on potential surface could be estimated by checking whether the structure reconstruction would happen during the MD simulations. The MD simulations have been performed by heating structures to the temperature of 300 K, with an increase of 50 K for the successive simulations. For each study, the simulation lasts for 6 ps with time step of 1 fs. At the end of each simulation, the final structure has been carefully examined. As shown in Fig. 3, the penta-BN could withstand the temperature as high as 450 K, while the melting of penta-BN 2 would not occur below the temperature of 1000 K. In Fig. 4, the mechanical effects on the stabilities of penta-BN and BN 2 nanostructures have been estimated. Beside the primitive unit cell, the 4 × 4 supercell has been adopted to release the special constraints due to the periodic conditions. Our calculations clearly show that both of them could withstand biaxial strain up to 12% before the structures start to collapse, suggesting nice static stabilities. However, before mechanical failure, phonon instability known as Kohn anomaly might occur 25 . After applying tensile strain, we have also calculated phonon spectra correspondingly. As shown in Fig. 5, one of the acoustical phonon branches start to have imaginary modes for penta-BN under 6.2% strain and penta-BN 2 under 7.8% strain, whose deformation energies are calculated to be 0.58 eV and 1.06 eV, respectively. These suggest penta-BN 2 to be stiffer than penta-BN, agreeing with the conclusions obtained in our MD simulations. The melting temperature for penta-BN is quite lower as compared with that of penta-BN 2 . Also, by applying the finite distortion method 19 , we have calculated the linear elastic constants. Following the standard Voigt notation 26 , the elastic strain energy per unit area can be written as where ε xx and ε yy are the uniaxial strains respectively applied along x and y directions, and ε xy is the equi-biaxial strain. C 11 , C 22 , C 12 , and C 66 are the components of elastic modulus tensor, which could be obtained by calculating the second partial derivative of strain energy with respect to strain. According to Born-Huang criteria 27 , the . The blue and brown balls are for N and B atoms. In (a), B 1 and B 2 stand for the boron atoms at three-and four-coordinate sites, respectively. N and N di are for the atomic nitrogen atom and dinitrogen. The l 1 , l 2 , l 3 , and l 4 are used to stand for the non equivalent bonds, respectively. In (b), B 1 and N di stand for the atomic boron atom and dinitrogen composition species of penta-BN 2 , respectively. Accordingly, the l 1 and l 2 account for the non equivalent bonds.

Structure Lattice
Bond Length Charge     , we have also estimated the in-plane Young's moduli in Table 2. The penta-BN 2 has a value of 224 N/m being close to the 271 N/m of h-BN monolayer, which is stiffer than the penta-BN, being in the line of the above studies 28 . Interesting, the Poisson's ratio C 12 /C 11 = −0.03 of penta-BN 2 is negative to render it attractive in view of both scientific and technological investigations 29 .

Discussion
The penta-BN consists of the fragments of 3-coordinate B atom, 4-coordinate B atom, dinitrogen N di , and atomic N, which have 6.85, 4.60, − 0.70, and 7.86 eV formation energies as calculated by below formula.
where E p-B x N y , E frag , and E □ are the total energies calculated for the penta-B x N y nanostructure, the composition fragment, and the vacancy defected penta-B x N y structure optimized after removing the fragment. In the calculation, a supercell of 5 × 5 has been adopted to minimize the structural deformation effects from the neighboring images of vacancy defect. Though the reactions of the atomic B and N atoms are exothermic, the reaction of dinitrogen is endothermic as referred to N 2 molecule. As to its electronic properties, our bandstructure calculations show penta-BN to be indirect band gap semiconductor (see Fig. 6a). Its conduction band minimum and valence band maximum are located at Γ and M points, respectively. Here, we must point out that the composition fragments include both dinitrogen and atomic nitrogen, which in combination with the above studied stabilities may challenge its fabrication on experiment.
In comparison, the penta-BN 2 nanostructure is composed of only atomic boron and dinitrogen fragments, which is in form similar to the experimentally fabricated Ti 8 C 12 metallo-carbohedrene composed of only Ti atoms and C 2 dimers 30 . Similarly, our previous studies of calcium metal cabides also support the C 2 dimers as preferable composition fragments 31,32 . The composition of dinitrogen could also be seen in the recently reported carbon nitride materials 33,34 . These studies shed light on the possibilities in synthesizing the dinitrogen composed penta-BN 2 nanostructure. The formation energies of B atom and dinitrogen compositions of penta-BN 2 are calculated to be 10.77 and 0.04 eV, respectively, showing exothermic reaction properties. Besides, we have vertically displaced a single B atom or dinitrogen from the planar structure step by step. At each step, by freezing the vertical distance between the displaced fragment and the nanosheet, the total energy has been calculated after structural optimization. The energy barriers are found to be 4.40 and 2.04 eV to remove a single B atom and dinitrogen, respectively, supporting the structural stability of penta-BN 2 . Also, we have estimated the possibility in synthesizing it by the reaction channel through introducing atomic boron species into the source of nitrogen molecules such as the liquid nitrogen. Actually, a similar fabrication method was previously applied to successfully synthesize transition metal nitrides by compressing metal and N 2 molecules at high pressure 35,36 . A boron atom could bind three N 2 molecules in maximum through exothermic reaction to form B(N 2 ) 3 complex, which could then meet each other by overcoming 0.68 eV energy barrier to produce the pentagonal building block of penta-BN 2 nanostructure, indicating the possibility for its experimental fabrication.
The bandstructure of penta-BN 2 presented in Fig. 6b shows conducting properties. Its work function is calculated to be 3.3 eV being comparable to those of simple metals such as the 3.68 eV of Mg and the 4.28 eV of Al. When supporting on substrate, the penta-BN 2 might donate electrons, which would in turn affect its electronic properties. After ionizing one electron per dinitrogen, we have again calculated the electronic properties, which suggest the semiconducting properties as shown in Fig. 6c. Due to the fact that the dinitrogens are located on the outer sides to be naked in the quasi-planar nanostructure, they may be capped by functional groups in fabrication, which may affect the structural stability. In our studies, the hydroxyl group is adopted to check the adsorption effects, which may gain presence in experimental studies 37,38 . By adsorbing hydroxyl groups on the penta-BN 2 nanostructure, we have carried full optimization of geometrical structure. Then, the optimized structure has been forwarded to carry out MD simulations which suggest the thermal stability up to 1400 K (> 1000 K of the melting temperature of free-standing penta-BN 2 ), hinting enhanced stability. Also, for the optimized structure fully covered by hydroxyl groups, we have calculated its bandstructure and shown in Fig. 6d. For the adsorption configuration, the Bader charge analysis does not show obvious charge donation from dinitrogen to hydroxyl group. The interatomic distance is 1.45 Å between the O and its nearest N, which is only 6% longer than the sum of atomic radii of O and N atoms. In our charge density study, the charge accumulation could be clearly seen between hydroxyl radical and dinitrogen. Furthermore, we have estimated the localization of electrons of the hydroxyl group adsorbed penta-BN 2 by using the electron localization function (ELF) analysis [39][40][41] , which was introduced in quantum chemistry to measure the parallel spin correlation by defining conditional probability of finding an electron in the neighborhood of another electron with the same spin. ELF is defined as where φ i is the Kohn-Sham orbital, and ρ is the local density. The ELF data of 0.7 between the dinitrogen and the adsorbed hydroxyl radical supports weak localization of electrons along H-O bond. Therefore, the bonding between dinitrogen and hydroxyl radical should be covalent-like. One of the electrons of the highest occupied molecular orbital of the dinitrogen would be bound in the covalent bond, making the conducting property transition from conducting to semiconducting as shown in Fig. 6. Besides the effects of charge states and functional group adsorption, the oxidization of penta-BN 2 nanostructure also needs to be discussed considering the fabrication and application in the presence of oxygen. A supercell of 5 × 5 has been employed for studying the adsorption and dissociation of a single O 2 molecule. The adsorption configurations as shown in Fig. 7 are fully relaxed. The oxygen molecule could parallel cap upon N-N dinitrogen. The O-O bond length would be slightly elongated by 0.5% and the length of the underlying N-N bond would be reduced by 0.7%. The charge gain of O 2 is 0.1 electrons and the charge depletion of the underlying dinitrogen is also 0.1 electrons. Actually, in our studies, we have also calculated the adsorption of H 2 , N 2 , F 2 , NO, and CO gas molecues. The slight charge transfer only happens in the O 2 adsorption. This may be attributed to the fact that only O 2 molecule has the lowest unoccupied molecular orbital to be slightly lower in binding energy than the valence band maximum of penta-BN 2 . In the process of band alignment, nearly neglected charge is transferred from dinitrogen to O 2 molecule. However, the interatomic distance between O and its nearest N is 2.22 Å being of 63% larger than their atomic radius sum 42 , excluding the possibility of obvious orbital overlap between them. Besides the weak overlap indicated by the weak charge transfer, the calculated binding energy of ~0.2 eV for O 2 adsorption may also include the Coulomb energy of the charged dioxygen felt in the local electric field surrounding dinitrogen. The charge accumulation on dinitrogen as presented in Table 1 would induce a local electric field to affect the adsorption of charged or polarized molecules, being like the case of H 2 adsorption on C 60 (OM) 12 (M = Li and Na) clusters 38 . We have used the climbing image nudged elastic band method to study O 2 dissociation [43][44][45][46] , whose activation energy is calculated to be > 2.6 eV to hinder the oxidization of penta-BN 2 . In our studies, we have also investigated the structural stability in the conditions of oxygen molecules. After putting one O 2 molecule upon each dinitrogen, the first-principles molecular dynamics simulation has been carried out at 300 K by using the 4 × 4 supercell. The O 2 would however start to leave the penta-BN 2 at ~1 ps in our MD simulation. Based on these studies, we would like to conclude that the oxidization of penta-BN 2 sheet structure is not easy.
In summary, the new two-dimensional nanostructures of B x N y with Cairo pentagonal tiling geometry have been carefully investigated. Only penta-BN and BN 2 are found to be kinetically stable which do not have imaginary modes in the calculated phonon spectra. Besides, we have also discussed their stabilities from the sides of: (1) the formation energies of structural composition fragments; (2) the thermal stabilities indicated by the melting temperatures found in our molecular dynamics simulations; and (3) the mechanical stabilities to sustain mechanical strain. The penta-BN 2 composed of only atomic boron and dinitrogen species has superior stability than penta-BN, which may be synthesized by introducing atomic boron atoms into the source of nitrogen molecules such as the liquid nitrogen. Also, our studies on the oxygen molecule adsorption and its dissociation suggest the stability of penta-BN 2 sheet against oxidization. Its stability has also been evaluated against hydroxyl group adsorption. The bandstructure study of penta-BN 2 sheet shows conducting properties. Due to the charge accumulation, the dinitrogen may tend to donate electrons when the sheet structure of penta-BN 2 is supported on substrate. By ionizing one electron per dinitrogen, the charged penta-BN 2 would be changed to be semiconducting. For the hydroxyl group adsorbed penta-BN 2 , each hydroxyl group could bind one electron of each dinitrogen in the covalent-like bond, which could also make the metal-semiconductor transition. Here, we would like also to mention Yagmurcukardes et al.'s studies of pentagonal B 2 N 4 and B 4 N 2 on the bandstructures and mechanical properties (for example, the stiffness) 47 . In comparison, we have investigated all the possible pentagonal monolayer structure candidates by changing composition species in the primitive unit cell. Only penta-BN and BN 2 are found to be dynamically stable. As for the penta-BN 2 which was also previously investigated by Yagmurcukardes and coworkers 47 , more detailed studies on its structural stability have been performed, for example, the thermal stability estimated by first-principles molecular dynamics simulations, the thermodynamic stability evaluated by formation energy analysis. Besides, considering the potential usages, we have also carefully studied its stability against oxidization and functional group adsorption. The effects of substrate and functional group adsorption on its transport properties are also discussed in our studies. Furthermore, in order to facilitate experimental fabrication, we have also carried out synthesizing reaction path analysis. So, we would like to conclude that our studies contribute to give more comprehensive theoretical results on the possible pentagonal boron nitride monolayer materials, including detailed stability analyses, effects of oxidization and functional group adsorption, transport property modifications, and potential synthesizing reaction path investigations.

Methods
Our first-principles calculations were performed within the framework of density functional theory with a plane wave basis set as implemented in the Vienna ab initio simulation package (VASP) 48,49 . The cutoff energy for plane-wave basis set was chosen to be 400 eV. The projector augmented-wave (PAW) method was used 49 . The exchange and correlation energy was described by the generalized gradient approximation with Perdew, Burke, and Ernzerhof (PBE) parameterization 50 . The nanostructure of penta-B x N y was placed in xy plane of the supercell with a 15 Å vacuum in z direction, which is large enough to ignore the effects from its neighboring images. The Monkhorst-Pack k-mesh of 15 × 15 × 1 was applied to sample k points in the first Brillouin zone for integrating electronic properties 51 . All the atoms were fully relaxed with force converge up to 0.02 eV/Å. The calculated total energy was converged to 10 −5 eV. The first-principles molecular dynamics (MD) simulations lasted for 6 ps with time step of 1 fs. The MD simulations were preformed starting from the temperature of 300 K. Due to the intensive computing loading of MD simulations, the melting temperature was only estimated with the precision of 50 K. Our Bader charge analysis was carried out by using the code developed by Henkelman et al. 24,52,53 . Phonon properties were calculated with the finite displacement method as implemented in Phonopy 54 . In calculating the phonon spectra, the energy convergence criteria were set to 10 −8 eV for total energy and 0.1 meV/Å for Hellmann-Feynman force.