Abstract
Designing new materials with novel topological properties and reduced dimensionality is always desirable for material innovation. Here we report the design of a twodimensional material, namely Be_{5}C_{2} monolayer on the basis of density functional theory computations. In Be_{5}C_{2} monolayer, each carbon atom binds with five beryllium atoms in almost the same plane, forming a quasiplanar pentacoordinate carbon moiety. Be_{5}C_{2} monolayer appears to have good stability as revealed by its moderate cohesive energy, positive phonon modes and high melting point. It is the lowestenergy structure with the Be_{5}C_{2} stoichiometry in twodimensional space and therefore holds some promise to be realized experimentally. Be_{5}C_{2} monolayer is a gapless semiconductor with a Diraclike point in the band structure and also has an unusual negative Poisson’s ratio. If synthesized, Be_{5}C_{2} monolayer may find applications in electronics and mechanics.
Introduction
Carbon in known molecules and materials typically has tetrahedral tetracoordination (for example, diamond), planar tricoordination (for example, graphite) or linear dicoordination (for example, ethyne) arrangements. Especially, the tetrahedral preference of tetracoordinate carbon compounds, which was deduced by van’t Hoff^{1} and Lebel^{2} more than a century ago, is one of the major foundations of organic chemistry. In 1968, Monkhorst^{3} first discussed an exceptional bonding pattern of carbon, namely planar tetracoordinate carbon (ptC), by proposing a planar methane (D_{4h}), which is actually not a minimum energy structure. Later in 1970, by insightful analysis of ptC bonding in the hypothetical planar methane, Hoffman et al.^{4} suggested that ptCs can be stabilized electronically by replacing H atoms in planar methane by σ donors (to facilitate electron transfer to electrondeficient σ bonds) or π acceptors (to delocalize the unfavourable lone pair of ptC). Along this line, in 1976 Collins et al.^{5} theoretically devised the first ptCcontaining molecule 1, 1dilithiocyclopropane. One year later Cotton and Millar^{6} synthesized the first ptCcontaining molecule, although the unique ptC configuration was not recognized at that time. Ever since, ptC chemistry has been a subject of extensive studies^{7,8,9}. Numerous ptC species have been designed theoretically^{10,11,12,13,14,15} and some global minimum structures, such as CAl_{4}^{+} (ref. 16), CAl_{4}^{2+} (ref. 17) and CAl_{3}Si^{−} (ref. 18) have been observed experimentally. More excitingly, besides ptC, many molecules containing planar pentacoordinate carbon (ppC)^{19,20,21,22} and hexacoordinate carbon (phC)^{23,24,25} have been designed computationally. The rulebreaking chemical bonding in these planar hypercoordinate carbons can lead to completely new molecules and materials, which are of fundamental importance to chemistry and materials science.
The unique topology and dimensionality may lead to exceptional properties of materials. It is not a surprise to witness the growing interest in designing ptCcontaining solids and nanostructures in recent years^{26,27,28,29,30}. Especially, stimulated by the extensive studies of graphene^{31,32} and inorganic layered materials^{33,34}, many twodimensional (2D) materials with rulebreaking chemical bonding have been designed computationally^{35,36,37,38,39,40,41,42}. For example, on the basis of ptC molecule CB_{4} (ref. 43), Wu et al.^{35} designed the first ptCcontaining 2D material, namely B_{2}C graphene, which was later confirmed to be only a local minimum^{44}. Li et al.^{36} and Dai et al.^{37} predicted that Al_{2}C monolayer in its lowestenergy configuration have all C atoms being ideal ptC. More interestingly, Li et al.^{45} demonstrated recently that one C atom can bind to six beryllium (Be) atoms in an almost planar manner, yielding a phCfeaturing 2D material with a Be_{2}C stoichiometry. With intriguing structural and electronic properties, these 2D materials are expected to have important applications in some specific fields.
In contrast to ptC and phC, no attempt exists for extending ppC into solids until now. Motivated by the successful design of ptC and phCcontaining materials, we are quite curious whether it is possible to extend ppC into solids. Addressing this issue would deliver not only unique structures but also some fantastic properties, which is of both theoretical and practical importance.
In this work, by means of density functional theory (DFT) computations, we first confirm that the ppC molecule Be_{9}C_{2}^{4−} is a local minimum on the potential energy surface. Based on the structural characters of Be_{9}C_{2}^{4−}, we design a ppCcontaining 2D material, namely Be_{5}C_{2} monolayer, in which each C atom binds to five Be atoms to form a quasiplanar pentacoordinate moiety. Our Be_{5}C_{2} monolayer has rather good thermal and kinetic stabilities and is energetically the most favourable isomer in 2D space. Dramatically, the electronic band structure of Be_{5}C_{2} monolayer has a Diraclike point at the Fermi level, endowing an intriguing semimetallic feature. More interestingly, Be_{5}C_{2} monolayer possesses a negative Poisson’s ratio, which is rather rare in nanostructures. These fascinating properties make Be_{5}C_{2} monolayer a promising candidate for future applications in electronics and mechanics.
Results
Be_{9}C_{2}^{4−} as the inspiring ppC species for 2D monolayer
Our design of periodic 2D Be_{5}C_{2} monolayer is initially inspired by our finding of the ppC molecule, namely Be_{9}C_{2}^{4−}, which has singlet ground state and D_{2h} symmetry (Fig. 1a). Computed at B3LYP level of theory with 6–311+G*(d, p) basis set, Be_{9}C_{2}^{4−} is a local minimum with the lowest vibrational frequency of 158.5 cm^{−1}. In this molecule, each C atom binds to five Be atoms to form a ppC moiety of Be_{5}C, which has been shown to be a local minima^{20}. Structurally, Be_{9}C_{2}^{4−} can be viewed as two Be_{5}C moieties fused by sharing one Be atom. The C–Be bond lengths are in the range of 1.70–1.76 Å, whereas the Be–Be bond lengths are in the range of 2.02–2.39 Å.
According to the natural population analysis, each ppC of Be_{9}C_{2}^{4−} possesses a 2.18 e negative charge (−0.40 e according to the Hirshfeld charge population analysis) and the natural electron configuration is 2s^{1.42}2p_{x}^{1.47}2p_{y}^{1.66}2p_{z}^{1.60}, indicating that ppCs in Be_{9}C_{2}^{4−} are essentially stabilized through Be σdonation and delocalization of carbon 2p_{z} electrons. The computed Wiberg bond index for C–Be bonds are 0.52 and 0.61, respectively, resulting in a total Wiberg bond index of 2.81 for each ppC. Moreover, we also scrutinized the molecular orbitals of Be_{9}C_{2}^{4−} to get more information on its stabilization mechanism. As shown in Fig. 1b, the highly delocalized π (for example, HOMO7 and HOMO8) and σ (for example, HOMO3, HOMO4 and HOMO5) orbitals can help maintain the planar configuration.
Geometric properties of Be_{5}C_{2} monolayer
The fusing of two Be_{5}C moieties to Be_{9}C_{2}^{4−} reminds us of the roadmap of fusing benzene rings to polycyclic aromatic hydrocarbons (for example, naphthalene and anthracene) and then to 2D infinite graphene. Inspired by the ppCcontaining Be_{9}C_{2}^{4−}, we designed a new 2D inorganic material, namely Be_{5}C_{2} monolayer by generalizing the structural characters of Be_{9}C_{2}^{4−}. As shown in Fig. 2a, 1 unit cell of Be_{5}C_{2} monolayer consists of 8 C atoms and 20 Be atoms with the optimized lattice parameters being a=8.92 Å and b=9.21 Å, respectively. Similar to Be_{9}C_{2}^{4−}, in Be_{5}C_{2} monolayer each C atom binds to five Be atoms to form a ppC moiety of Be_{5}C and two neighbouring Be_{5}C moieties share one Be atom (Be_{1}) to form a Be_{9}C_{2} moiety in the a (Be_{9}C_{2}I) or b (Be_{9}C_{2}II) direction. Especially, one Be_{9}C_{2}I moiety is fused with four neighbouring Be_{9}C_{2}II moieties by sharing the peripheral Be atoms (Be_{2}) and vice versa, leading to the formation of a 2D network with four Be_{9}C_{2} moieties in one unit cell. The optimized coordinates of Be_{5}C_{2} monolayer are presented in Supplementary Table 1. It is noteworthy that the Be_{5}C_{2} monolayer is remarkably buckled rather than an exactly planar structure (Fig. 2b). The buckling, measured by the vertical distance between the bottommost Be atoms and the uppermost Be atom, is as high as 2.14 Å. Even so, the ppCs in Be_{5}C_{2} monolayer still have a good planarity (Supplementary Fig. 1). According to our computations, the total degrees of five Be–C–Be angles for ppCs in Be_{9}C_{2}I and Be_{9}C_{2}II moieties are 371.44° and 364.84°, respectively, which are a little higher than the ideal 360°. Interestingly, when Be_{9}C_{2}^{4−} is neutralized by four protons (H^{+}), the obtained Be_{9}C_{2}H_{4} molecule is also severely buckled (Supplementary Fig. 2). In Be_{5}C_{2} monolayer, the length of C–Be_{1} bonds (1.66 Å, 1.68 Å) is much shorter than that of C–Be_{2} bonds (1.73 Å, 1.74 Å). Moreover, our computations revealed that Be_{5}C_{2} monolayer has a nonmagnetic ground state, indicating that there are no unpaired electrons in Be_{5}C_{2} monolayer.
We then computed the deformation electronic density of Be_{5}C_{2} monolayer to elucidate its bonding nature. The deformation electronic density is defined as the total electronic density excluding those of isolated atoms. As clearly shown in Fig. 2c, some electrons are extracted from the 2s orbitals of Be atoms and well delocalized over C–Be bonds, indicating that C atoms form multicentre covalent bonds with neighbouring Be atoms, which is crucial for stabilizing the ppC moieties. The similar stabilizing mechanism has been found in ptC and phCcontaining 2D materials^{35,36,37,38,39,40,45}. According to the Hirshfeld charge popular analysis, C, Be_{1} and Be_{2} atoms in Be_{5}C_{2} monolayer possess a −0.32, +0.16 and +0.12 e charge, respectively. The buckling of Be_{5}C_{2} monolayer stretches the Be–Be distances and probably helps reduce the otherwise even stronger repulsive interactions between Be atoms.
We also used the recently developed Solid State Adaptive Natural Density Partitioning (SSAdNDP) method^{46} to better understand the unique chemical bonding of Be_{5}C_{2} monolayer. According to our results (Supplementary Fig. 3), there is no classical twocentre–twoelectron (2c–2e) C–Be bond in Be_{5}C_{2} monolayer. For one unit cell of Be_{5}C_{2} monolayer, the SSAdNDP search revealed twentyfour 3c–2e Be–C–Be σbonds (responsible for the bonding within the Be_{5}C units), four 4c–2e σbonds on four Be squares and eight 6c–2e πbonds over eight Be_{5}C units, accounting for 72 electrons per unit cell. This bonding pattern is consistent with the symmetry of Be_{5}C_{2} monolayer. Especially, the existence of delocalized σ and πbonds could essentially stabilize the ppCs in Be_{5}C_{2} monolayer.
Stability of Be_{5}C_{2} monolayer
Although Be_{5}C_{2} monolayer has rather intriguing structural properties, we are unclear whether it is a stable structure. To assess the stability, we first computed the cohesive energy of Be_{5}C_{2} monolayer, which is defined as: E_{coh}=(nE_{C}+mE_{Be}−E)/(n+m), in which E_{C}, E_{Be} and E are the total energies of a single C atom, a single Be atom and Be_{2}C monolayer, respectively; n and m are the number of C and Be atoms in the supercell, respectively. According to our computations, Be_{5}C_{2} monolayer has a cohesive energy of 4.58 eV per atom. As a reference, the cohesive energies of the experimentally realized 2D silicene^{47,48} and phosphorene^{49,50} are 3.71 and 3.61 eV per atom, respectively. As silicene and phosphorene are composed of covalent bonds, the even higher cohesive energy can ensure that Be_{5}C_{2} monolayer is a strongly connected network.
The stability of Be_{5}C_{2} monolayer can be further confirmed by its phonon dispersion curves. As shown in Fig. 3a, no appreciable imaginary phonon mode is present, suggesting the good kinetic stability of Be_{5}C_{2} monolayer. Remarkably, the highest frequency of Be_{5}C_{2} monolayer reaches up to 1,120 cm^{−1}, which is higher than those of MoS_{2} monolayer (473 cm^{−1})^{51}, silicene (580 cm^{−1})^{52} and our recently designed phCcontaining Be_{2}C monolayer (1,020 cm^{−1})^{45}, indicating robust C–Be bonds in Be_{5}C_{2} monolayer. The analysis of partial phonon density of states (DOS; Fig. 3b) revealed that the highest frequency of Be_{5}C_{2} monolayer is mainly contributed by C–Be_{1} bonds.
Moreover, to examine the thermal stability of Be_{5}C_{2} monolayer, we performed firstprinciples molecular dynamic (FPMD) simulations using a 2 × 2 supercell. Our three simulations at temperature of 1,000, 1,500 and 2,000 K show that Be_{5}C_{2} monolayer can maintain its structural integrity throughout a 10ps FPMD simulation up to 1,500 K, but is seriously disrupted at 2,000 K, suggesting that Be_{5}C_{2} monolayer has a melting point between 1,500 and 2,000 K (Supplementary Fig. 4). We also performed optimizations for the distorted structures from MD simulations. After full atomic relaxation, those structures from MD simulations at 1,000 and 1,500 K can recover the initial configuration of Be_{5}C_{2} monolayer. The above results demonstrate that Be_{5}C_{2} monolayer has a remarkable thermal stability.
The moderate cohesive energy, all positive phonon modes and good thermal stability can ensure that Be_{5}C_{2} monolayer is at least a local minimum structure on the potential energy surface. However, is the ppCcontaining Be_{5}C_{2} monolayer a global minimum? It is noteworthy that the global minimum structure is more likely to be achieved than the local minimum structures experimentally. For example, many isomers of graphene, such as Haeckelite graphene^{53}, Tgraphene^{54} and pentagraphene^{55} have been designed computationally, but none of them has been realized experimentally. Therefore, we performed a global search for the lowestenergy structure of Be_{5}C_{2} monolayer in the 2D space using firstprinciplesbased particleswarm optimization (PSO) method as implemented in CALYPSO code. After a comprehensive search, we obtained three stable isomers of 2D Be_{5}C_{2}, which are labelled as Be_{2}C_{5}I, Be_{2}C_{5}II and Be_{2}C_{5}III, respectively. As shown in Fig. 4a, Be_{2}C_{5}I is actually the above discussed ppCfeaturing Be_{5}C_{2} monolayer. Interestingly, in Be_{2}C_{5}II (Fig. 4b) and Be_{2}C_{5}III (Fig. 4c), each C atom binds to five Be atoms to form a ppC moiety of Be_{5}C and the Be_{9}C_{2} moieties also can be found in these two isomers. Be_{2}C_{5}I is 50 and 101 meV per atom lower in energy than Be_{2}C_{5}II and Be_{2}C_{5}III, respectively, indicating that Be_{2}C_{5}I is the global minimum structure in the 2D space. Therefore, the ppCfeaturing Be_{5}C_{2} monolayer holds great potential to be realized experimentally.
Electronic properties of Be_{5}C_{2} monolayer
With such interesting structural characteristics, does Be_{5}C_{2} monolayer also have intriguing properties? To address this issue, we computed the band structure of the lowestenergy Be_{5}C_{2} monolayer. As shown in Fig. 5a, Be_{5}C_{2} monolayer is gapless or semimetallic with the conduction band minimum (CBM) and valence band maximum (VBM) meeting at the Fermi level, which is quite similar to that of graphene. However, the meeting point of Be_{5}C_{2} monolayer is located on the path from G (0, 0, 0) point to Y (0, 0.5, 0) point rather than on a highsymmetry point as for graphene. Especially, the conduction and valence bands around the Fermi level exhibit a linear dispersion relation, suggesting that the meeting point of Be_{5}C_{2} monolayer is also Diraclike. Considering that the PBE functional tend to underestimate the band gap, we recomputed the band structure of Be_{5}C_{2} monolayer using the hybrid HSE06 functional^{56} and found that the dispersion of the valence and conduction bands at the Fermi level is similar to that predicted by PBE and no appreciable band gap can be identified (Supplementary Fig. 5). Thus, the gapless property of Be_{5}C_{2} monolayer is solid.
To obtain deeper insight into the electronic properties of Be_{5}C_{2} monolayer, we analysed its DOS. As shown in Fig. 5b, the DOS is zero at the Fermi level, which further supports the presence of the Dirac cone. The partial DOS analysis shows that the VBM and CBM are contributed by both Be2p and C2p states, and the contribution from Be2p states is much more than that from C2p states. Moreover, we plotted the partial charge densities of the VBM and CBM. As shown in Fig. 5c,d, both VBM and CBM are mainly originated from the delocalized orbitals of Be atoms and partially from the multicentre bonding between C and Be atoms.
Mechanical properties of Be_{5}C_{2} monolayer
Besides the electronic properties, we also investigated the mechanical properties of Be_{5}C_{2} monolayer by examining its elastic constants. As a validation, the computed elastic constants of graphene are C_{11}=C_{22}=342.93 GPa and C_{12}=C_{21}=62.23 GPa respectively, which achieve good agreements with experimental measurements^{57} and previous computations^{58}. For Be_{5}C_{2} monolayer, its elastic constants were computed to be C_{11}=32.90 GPa, C_{22}=130.89 GPa, C_{12}=C_{21}=−5.32 GPa and C_{66}=48.32 GPa, which are in agreement with the mechanical stability criteria for a tetragonal 2D sheet (C_{11}C_{22}−C_{12}^{2}>0, C_{66}>0)^{55}. The inplane Young’s modules along a (Y_{a}) and b (Y_{b}) directions, which can be deduced from the elastic constants by Y_{a}=(C_{11}C_{22}−C_{12}C_{21})/C_{22} and Y_{b}=(C_{11}C_{22}−C_{12}C_{21})/C_{11}, were computed to be 32.68 and 130.03 N m^{−1}, respectively. As Y_{a} is not equal to Y_{b}, Be_{5}C_{2} monolayer is mechanically anisotropic. Moreover, computed at the same level of theory, the inplane Young’s modules of Be_{5}C_{2} monolayer are less than those of graphene (Y_{a}=Y_{b}=331.63 N m^{−1}) but higher than those of phosphorene (Y_{a}=25.50 N m^{−1} and Y_{b}=91.61 N m^{−1}), suggesting that Be_{5}C_{2} monolayer has good mechanical properties.
Remarkably, we noted that Be_{5}C_{2} monolayer has a negative C_{12}, which results in negative Poisson’s ratios of −0.041 (C_{12}/C_{22}) and −0.16 (C_{12}/C_{11}) for a and b directions, respectively. It is noteworthy that the Poisson’s ratio is defined as the negative ratio of transverse to axial strain. The negative Poisson’s ratio indicates that Be_{5}C_{2} monolayer can be compressed or stretched in both two directions at the same time. For a validation, we applied a uniaxial strain of 5% in a and b directions of Be_{5}C_{2} monolayer, respectively. Just as expected, the equilibrium lattice parameters of b and a directions are elongated by ∼0.2 and ∼0.8%, respectively, confirming that Be_{5}C_{2} monolayer indeed has negative Poisson’s ratios.
Discussion
The unusual negative Poisson’s ratio may endow Be_{5}C_{2} monolayer with enhanced toughness and shear resistance, as well as enhanced sound and vibration adsorption. Correspondingly, Be_{5}C_{2} monolayer could find some important applications in the fields of mechanics, tissue engineering and national security. It is worth noting that the negative Poisson’s ratio is rather peculiar, as in nature nearly all materials have a positive Poisson’s ratio, except some socalled auxetic materials^{59}. Recently, Jiang et al.^{60} demonstrated theoretically that singlelayer black phosphorus has a negative Poisson’s ratio due to the unique puckered configuration. However, the negative Poisson’s ratio of phosphorene was observed in the outofplane direction, which is different from that of Be_{5}C_{2} monolayer. Remarkably, the Poisson’s ratio of Be_{5}C_{2} monolayer in the b direction (−0.16) is much higher than that of phosphorene (−0.027)^{60}, rendering Be_{5}C_{2} monolayer a more promising candidate for specific application in mechanical devices. No doubt, the negative Poisson’s ratio of Be_{5}C_{2} monolayer should be originated from its intriguing structural properties, especially the uniquely oriented chemical bonds. Our results could provide some guidelines for designing materials with a negative Poisson ’s ratio.
With so many fascinating properties, it is desirable to synthesize Be_{5}C_{2} monolayer in the laboratory. Considering that there is no layered structure of Be_{5}C_{2} in nature, a promising approach is to grow Be_{5}C_{2} monolayer on the surface of metal or metal oxide via chemical vapour deposition with accurately controlled Be/C ratio, just similar to the growth of silicene^{47,48}. It is noteworthy that Be has toxic properties and the chemical vapour deposition synthesis usually requires high temperature; hence, special caution should be given during the experimental realization.
To summarize, inspired by the bonding characters of a ppCcontaining molecule, Be_{9}C_{2}^{4−}, we designed a ppCcontaining 2D inorganic material with a Be_{5}C_{2} stoichiometry. Our DFT computations demonstrated that ppCs in Be_{5}C_{2} monolayer are essentially stabilized by the charge transfer from Be ligands. The moderate cohesive energy, absence of imaginary modes in phonon spectrum and high melting point evaluated from FPMD simulations indicated that Be_{5}C_{2} monolayer is experimentally viable. Especially, a global minimum search revealed that Be_{5}C_{2} monolayer is the lowestenergy structure for the Be_{5}C_{2} stoichiometry in 2D space, which endows Be_{5}C_{2} monolayer great possibility to be realized experimentally. Our computations demonstrated that Be_{5}C_{2} monolayer is semimetallic with a zero band gap in the electronic band structure. More interestingly, Be_{5}C_{2} monolayer has rather intriguing mechanical properties featured with a negative Poisson’s ratio. Therefore, Be_{5}C_{2} monolayer is expected to have wide applications in electronics and mechanics. We hope our theoretical studies will promote the experimental realization of this novel material and attract more attentions on investigating nanomaterials with novel chemical bonding.
Methods
DFT computations
For the Be_{9}C_{2}^{4−} molecule, geometry optimizations, frequency analyses and electronic structure computations were performed at the B3LYP^{61,62} level of theory with the 6–311+G*(d, p) basis set as implemented in Gaussian 03 package^{63}. For 2D Be_{5}C_{2} monolayer, DFT computations were performed using the planewave technique implemented in Vienna ab initio simulation package^{64}. The ion–electron interaction was described using the projectoraugmented plane wave approach^{65,66}. The generalized gradient approximation expressed by PBE functional^{67} and a 500eV cutoff for the planewave basis set were adopted in all the computations. The convergence threshold was set as 10^{−4} eV in energy and 10^{−3} eV Å^{−1} in force. We set the x and y directions parallel and the z direction perpendicular to the layer plane, and adopted a supercell length of 15 Å in the z direction. The Brillouin zones was sampled with an 8 × 6 × 1 Γ centred k points grid. The phonon spectrum was computed using finite displacement method as implemented in CASTEP code^{68}. The elastic constants were also computed using the CASTEP code. The chemical bonding analysis of Be_{5}C_{2} monolayer was done using the SSAdNDP method^{46}, which can well interpret the chemical bonding in terms of classical lone pairs, twocentre bonds, as well as multicentre delocalized bonds in bulk solids, surfaces and nanostructures.
Molecular dynamics simulations
The thermal stability of Be_{5}C_{2} monolayer was evaluated by means of firstprinciples molecular dynamics simulations. The groundstate structure of Be_{2}C monolayer was annealed at different temperatures. At each temperature, MD simulation in NVT ensemble lasts for 10 ps with a time step of 1.0 fs. The temperature was controlled by using the NoséHoover method^{69}.
Global minimum structure searches
The PSO method within the evolutionary scheme as implemented in the CALYPSO code^{70} was employed to find the lowenergy structures of 2D Be_{5}C_{2} monolayer. In our PSO simulation, the number of generation was maintained at 30. Unit cells containing total atoms of 7, 14 and 28 were considered. The structure relaxations during the PSO simulation were performed using Vienna ab initio simulation package at PBE level of theory.
Data availability
All relevant data are available from the authors.
Additional information
How to cite this article: Wang, Y. et al. Semimetallic Be_{5}C_{2} monolayer global minimum with quasiplanar pentacoordinate carbons and negative Poisson’s ratio. Nat. Commun. 7:11488 doi: 10.1038/ncomms11488 (2016).
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Acknowledgements
Support in China by Natural Science Foundation of China (numbers 21403115 and 21522305) and the NSF of Jiangsu Province of China (number BK20150045), and in the United States by National Science Foundation (Grant EPS1010094) and Department of Defense (Grant W911NF1210083) is gratefully acknowledged. The computational resources used in this research were provided by Shanghai Supercomputer Center.
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Y.L. and Z.C. conceived the initial idea of this research. Y.W. and F.L. demonstrated the initial idea and collected all the data. Y.W., Y.L. and Z.C. wrote the paper and all authors commented on it.
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Wang, Y., Li, F., Li, Y. et al. Semimetallic Be_{5}C_{2} monolayer global minimum with quasiplanar pentacoordinate carbons and negative Poisson’s ratio. Nat Commun 7, 11488 (2016). https://doi.org/10.1038/ncomms11488
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DOI: https://doi.org/10.1038/ncomms11488
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