Metallic BSi3 Silicene and Its One-Dimensional Derivatives: Unusual

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Metallic BSi3 Silicene and Its One-Dimensional Derivatives: Unusual Nanomaterials with Planar Aromatic D6h Six-Membered Silicon Rings Xin Tan, Fengyu Li, and Zhongfang Chen* Department of Chemistry, Institute for Functional Nanomaterials, University of Puerto Rico, Rio Piedras Campus, San Juan 00931, Puerto Rico S Supporting Information *

ABSTRACT: Achieving two-dimensional (2D) aromatic compounds with planar cyclic six-membered silicon rings (c-Si6) is a grand challenge. By means of density functional theory (DFT) computations, we predicted that c-BSi3 silicene, the global minimum of the BSi3 monolayer, contains planar aromatic D6h c-Si6. In cBSi3 silicene, the strong π−p conjugation between c-Si6 and B atoms is responsible for the planar geometry of the aromatic D6h c-Si6, which is in stark contrast to the conventional bonding motifs of silicon (sp3-bonding). Interestingly, the 2D c-BSi3 silicene and its one-dimensional (1D) derivatives (c-BSi3 nanotubes and nanoribbons) are metallic, regardless of the charity, tube diameter, or ribbon width, and the metallic behavior of c-BSi3 silicene is very robust to mechanical strain and surface chemical functionalization. The high stabilities of these systems strongly suggest the feasibility for their experimental realizations.

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INTRODUCTION Although silicon is a heavier congener of carbon, its structures and bonding motifs differ remarkably from carbon. The carbon π systems are usually stable and ubiquitous.1−3 However, silicon is reluctant to form unsaturated compounds, and its π-bonding ability is rather weak compared to carbon.4−10 This substantial difference leads to the grand challenge of synthesis and isolation of stable unsaturated silicon compounds. It was not until 1981 that West et al.4 achieved the big breakthrough in unsaturated silicon chemistry by isolating a stable compound containing a SiSi double bond, tetramesityldisilene. Since then, a number of other interesting stable unsaturated silicon compounds have been reported,11−17 and a few compounds with stable SiSi triple bonds have been ultimately achieved.16,18,19 Benzene20 and graphene,21 both with planar aromatic D6h cyclic six-membered carbon ring(s) (c-C6), are the paradigms of Hückel-aromatic compounds and two-dimensional (2D) aromatic compounds, respectively. Their silicon analogues with planar aromatic D6h cyclic six-membered silicon rings (c-Si6), such as hexasilabenzene and planar graphene-like structure of silicon, have been intriguing chemists but remain elusive.22,23 The planar D6h c-Si6 unit in hexasilabenzene is unstable due to the pseudo Jahn−Teller effect, and the chairlike structures were established for hexasilabenzene.24,25 Experimentally, only three isomers with cluster-like Si6 have been synthesized so far, namely, hexasilaprismane,26 a tricyclic aromatic isomer,12 and a cage isomer of hexasilabenzene.27,28 The compounds composed solely of planar cyclic silicon are limited to persila-analogues of the cyclopropenium cation29 and cyclobutadiene dianion.30 Several methods were proposed to approach planar D6h c-Si6: © XXXX American Chemical Society

substituting Si atoms by C atoms in silabenzenes can lead to the planar benzene-like structures;31 anionic systems c-Si62−, cSi64−, and c-Si66− are planar;32−34 and further studies suggested that reduction of the c-Si66− anion in the presence of lithium leads to Si6Li6 with symmetry group D2h.35 Silicene, the silicon analogue of graphene, has recently attracted significant attention because of its honeycomb structure, unique electronic and magnetic properties,36−39 and its compatibility with mature Si-based electronics. Experimentally the epitaxial silicene has been successfully synthesized on Ag,40,41 Ir,42 and ZrB2 substrates,43 but freestanding silicene has not been achieved so far. Similar to the case of hexasilabenzene, the silicene sheet is not planar, and various theoretical studies fully established the low-buckled honeycomb structure with a buckling distance Δ = 0.44 Å.36−38 It has also been theoretically proposed that a planar silicene sheet could be obtained by adsorption of Li+ on buckled silicene38 and intercalation of K atoms between silicene and the metal substrate.44,45 Currently, the synthesis of 2D aromatic compounds with planar c-Si6 rings is still a grand challenge. Several questions thus arise naturally: Is there any stable compound, especially 2D compound, containing planar aromatic D6h c-Si6? If yes, what properties will be associated with such unique structures? How can we realize these stable 2D materials? How about the stabilities and physicochemical properties of their one-dimensional (1D) derivatives such as nanotubes and nanoribbons? Addressing these issues will not Received: July 14, 2014 Revised: August 22, 2014

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dx.doi.org/10.1021/jp507011p | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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Figure 1. Top (upper) and side (lower) views of optimized structure of (a) B6Si18H12 and (b) Si24H12 molecules with a c-Si6 ring center. The yellow, light magenta, and white spheres denote the Si, B, and H atoms, respectively. The Si atoms, which are composed of the center c-Si6 ring, are denoted with larger yellow spheres. (c) Schematic representation and the heat of reaction (ΔH) for Si24H12 + 6XSi5H6 = X6Si18H12 + 6Si6H6 (X = B, Al, and C).

Figure 2. (a) Top (upper) and side (lower) views of 2D c-BSi3 silicene. (b) Top (upper) and side (lower) views of 2D g-BSi3 predicted by Dai et al.50 The unit cells of BSi3 sheets are indicated by dashed lines in (a) and (b). The yellow and light magenta spheres denote the Si and B atoms, respectively.

only contribute to the basic understanding of planar D6h c-Si6 but also provide some guidelines to the synthesis of nanomaterials with planar D6h c-Si6 units. In this work, by means of density functional theory (DFT) computations, we found that replacing Si atoms adjacent to the central c-Si6 by B atoms in the silicon analogue of coronene can significantly reduce the buckling of the central c-Si6 ring due to the strong π−p conjugation between c-Si6 and B atoms (Figure 1a). Extending this molecular model to 2D materials led to cBSi3 silicene (Figure 2a),46 which was recently constructed based on the experimentally synthesized BC3 nanosheet.47−49 We found that this stable 2D monolayer with planar aromatic D6h c-Si6 is lower in energy than the previously predicted global minimum of BSi3 compounds,50 and the planar geometry of the aromatic D6h c-Si6 in c-BSi3 silicene, in stark contrast to the conventional bonding motifs of silicon (sp3-bonding), is due to the strong π−p conjugation between c-Si6 and B atoms. Interestingly, the 2D c-BSi3 silicene and its 1D derivatives (c-

BSi3 nanotubes and nanoribbons) are metallic, regardless of the charity, tube diameter, or ribbon width, and the metallic behavior of c-BSi3 silicene is very robust to mechanical strain and surface chemical functionlization.

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COMPUTATIONAL DETAILS For the X (X = B, Al, and C) substituted silicon analogue of coronene (X6Si18H12, Figure 1a and Figure S1 in Supporting Information), full geometry optimizations and frequency analyses were performed at the PW9151/6-311+G(d) level of theory using the Gaussian 09 package.52 Our spin-polarized DFT calculations on 2D c-BSi3 silicene and its 1D derivatives (c-BSi3 nanotubes and nanoribbons) were carried out using the Dmol3 package.53 The generalized gradient approximation (GGA) in the PW91 functional form together with an all-electron double numerical basis set with polarization function (DNP) were adopted. It is well-known that the standard PW91 function is incapable of giving an B



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Figure 3. (a) Calculated electronic band structure and DOS of the 2D c-BSi3 silicene. (b) Iso-surface (0.05 e/au) of deformation electronic density of c-BSi3 silicene. Blue and yellow regions refer to the electron-rich and -deficient regions, respectively. (c) Total electronic density projected on the c-BSi3 silicene surface. The red circles in (b) and (c) represent the aromatic c-Si6 ring. Electronic profile of (d) HOSE and (e) LUSE of c-BSi3 silicene at the Γ point. The iso-surface value is 0.04 e/au.

In geometry optimizations, all the atomic coordinates were fully relaxed until the residual atomic forces were smaller than 0.001 Ha/Å, and the total energy was converged to 10−5 Ha. The Brillouin zone was sampled by k-points with 0.02 Å−1 spacing using the Monkhorst−Pack scheme55 for 2D and 1D systems. To estimate the stability of different BSi3 structures, we evaluated the binding energy (Eb), which is defined as Eb = [3E(Si) + E(B) − E(BSi3)]/4, where E(Si), E(B), and E(BSi3) are the total energies of the silicon atom, boron atom, and BSi3 sheet with different atomic structures, respectively. According to this scheme, those with more positive binding energies are more favorable energetically. In order to investigate the binding strength of the 2D c-BSi3 silicene monolayer to the Ag(111) surface, we calculated the adhesion energy Ead of the c-BSi3 silicene monolayer on the Ag(111) surface. Ead is defined as Ead = [E(M) + E(Ag) − E(M/Ag)]/N, where E(M), E(Ag), and E(M/Ag) are the total energies of the freestanding c-BSi3 silicene monolayer, bare

accurate description of weak interactions. Therefore, for c-BSi3 silicene adsorption on the Ag(111) surface, we adopted a DFT +D (D stands for dispersion) approach with the Ortmann− Bechstedt−Schmidt (OBS) vdW correction.54 The real-space global cutoff radius was set to be 5.1 Å. For c-BSi3 silicene, a 1 × 1 unit cell with periodic boundary conditions in the x−y plane was employed (Figure 2a). The vacuum space was set to larger than 20 Å in the z direction to avoid interactions between periodic images. For c-BSi3 nanotubes and nanoribbons, 1D periodic boundary conditions were applied along the z direction to simulate their infinitely long systems. The minimum distance between two tubes (ribbons) is larger than 15 Å, which can safely avoid the interaction between two tubes (ribbons). For the c-BSi3 silicene monolayer on the Ag(111) surface, we put one layer of (2 × 2) c-BSi3 silicene on top of four layers of (5 × 5) the Ag(111) surface and optimized the structure by fixing the bottom two Ag layers at the bulk Ag parameter (aAg = 4.171 Å), which includes the 0.7% lattice mismatch. C



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Figure 4. Top and side view of a snapshot of the 2D infinite c-BSi3 silicene at (a) 2000 K, 10 ps, and (b) 2250 K, 5 ps of the ab initio MD simulations in the NVT ensemble. The estimated melting temperature is between 2000 and 2250 K.

Ag(111) surface, and c-BSi3 silicene monolayer on the Ag(111) surface, respectively. N is the number of atoms in the c-BSi3 silicene monolayer. According to this definition, a more positive adhesion energy indicates a stronger binding of the c-BSi3 silicene monolayer to the Ag(111) surface. To assess the thermal stability of c-BSi3 silicene, we performed ab initio molecular dynamics (MD) simulations. The PW91 functional and DNP basis set, as implemented in the DMol3 code,53 were used. The initial structure of the c-BSi3 silicene sheet was annealed at different temperatures. At each temperature, MD simulation in the NVT ensemble lasted for 10 ps with a time step of 1.0 fs. The temperature was controlled by using the Nose−Hoover method.56 To search for the global minimum structure of the 2D BSi3 silicene system, we employed the particle swarm optimization (PSO) method within the evolutionary algorithm, as implemented in the CALYPSO (Crystal structure AnaLYsis by Particle Swarm Optimization) code.57,58 This method has successfully predicted new highly stable 2D nanostructures,59 such as BxCy compounds,60 SiC2 siligraphene,61 nitrogengraphene alloys,62 boron monolayers,63 the Be2C monolayer,64 and AlxC (x = 1/3, 1, and 3) monolayers.65 In our calculations, the population size was set to be 50, and the number of formula units per simulation cell was considered from 1 to 3. The most stable 2D structure of BSi3 was successfully predicted by only one generation. The required structure relaxations were performed using the VASP code.66

Figure 5. (a) Top and (b) side views of the 2D c-BSi3 silicene monolayer on Ag(111). The yellow, light magenta, larger blue, and larger gray spheres denote Si, B, surface Ag layer, and bottom three Ag layer atoms, respectively. The average distance between the c-BSi3 silicene monolayer and the Ag(111) is given in units of Å. (c) Calculated electronic band structure of c-BSi3 silicene on Ag(111).

Si 6 ring, indicated by the well-delocalized π electron distribution (see Figure S2 in Supporting Information). In addition, the calculated heat of reaction is −1.64 eV, which indicates the strong π−p conjugation in B6Si18H12 lead to the high stability of B6Si18H12 compared to Si24H12. For comparison, we also studied the structural property of Al6Si18H12 and C6Si18H12 and the relative stability of Al6Si18H12 and C6Si18H12 with respect to Si24H12. The center c-Si6 ring in Al6Si18H12 is planar, while the center c-Si6 ring in C6Si18H12 is buckled (see Figure S1 in Supporting Information). The heats of reaction involving Al6Si18H12 and C6Si18H12 are −1.97 and 2.43 eV, respectively, indicating that the stability is Al6Si18H12 > B6Si18H12 > Si24H12 > C6Si18H12. Note that the π−p conjugation in Al6Si18H12 is even stronger than B6Si18H12. Global Minimum Structure of the 2D BSi3 Monolayer in Comparison with AlSi 3 and CSi 3 Monolayers. Encouraged by the above finding that the π−p conjugation is able to stabilize a planar center c-Si6 ring in the cluster model, we extended our study to the 2D c-BSi3 silicene,46 where the cSi6 rings are isolated by B atoms. Compared with the previously predicted global minimum of BSi3 compounds (g-BSi3),50 the binding energy of c-BSi3 silicene is 0.04 eV/atom higher than that of g-BSi3. In order to identify the lowest-energy structure of BSi3, we calculated the total energies of seven possible 2D BSi3 structures with hexagonal and rectangular symmetry, inspired

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RESULTS AND DISCUSSION Molecular Model Containing a Planar c-Si6 Ring. Our very recent work noticed the strong π conjugation through the vacant p orbital of the B atom in the BC3 monolayers.67 Actually, such π−p conjugations may help stabilize a planar geometry of the c-Si6 ring. To confirm this idea, we investigated the structural property of the B6Si18H12 molecule with a c-Si6 ring center (Figure 1a) and the relative stability of B6Si18H12 with respect to Si24H12, in comparison with the relative stability of Al6Si18H12 and C6Si18H12 with respect to Si24H12. Here, we used the scheme Si24H12 + 6XSi5H6 = X6Si18H12 + 6Si6H6 (X = B, Al, and C) (Figure 1c) to evaluate the relative stability of X6Si18H12 (X = B, Al, and C) with respect to Si24H12. After geometry optimization, the center c-Si6 ring in B6Si18H12 relaxed to a planar geometry (Figure 1a), while the center c-Si6 ring in Si24H12 is buckled (Figure 1b). The planar geometry of the center c-Si6 ring in B6Si18H12 originates from the strong π−p conjugation between B atoms and the center cD



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Figure 6. Top (upper) and side (lower) views of optimized geometric structures of 2D c-BSi3 silicene with tensile strain of (a) 10% and compressive strain of (b) −3%.

Figure 7. Top (upper) and side (lower) views of optimized structures and corresponding band structures of the fully (a) hydrogenated and (b) fluorinated c-BSi3 silicene with the chair conformation. The yellow, light magenta, white, and light blue spheres denote Si, B, H, and F atoms, respectively.

BSi3 silicene and R-I are also the same. Moreover, using the CALYPSO structure prediction method,57,58 we also obtained c-BSi3 silicene and R-I as the global minima of BSi3. In comparison, c-AlSi3 silicene is the global minimum, and it is 0.02 eV/atom lower in energy than the second lowest-energy structure R-I, while the energetically most favored structure of CSi3 is R-I, which is 0.01 eV/atom lower in energy than c-CSi3 silicene and H-II. Note that the relative stabilities of 2D XSi3 (X = B, Al, C) isomers are consistent with our cluster models: the system with stronger π−p conjugation favors the structure with c-Si6 units.

by the previous investigations to explore the global minimum of BC3 and NC3,68−70 which have the same stoichiometry as BSi3 (see Figure S3 in Supporting Information). Here, we use H and R to label the hexagonal and rectangular symmetry, respectively. Similar investigations have been performed for AlSi3 and CSi3 to search their global minima (see Figures S4 and S5 in Supporting Information). Among all the seven possible structures, c-BSi3 silicene and R-I have the lowest and the same total energies, indicating these two isoenergetic structures are the global minima of BSi3. Note that we also calculated the two lowest-energy structures of BSi3 using the hybrid HSE06 functional, and the total energies of cE



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Since the global minimum of AlSi3, the c-AlSi3 silicene, is semiconductor,46 which is similar to BC3 and NC3,68,69 and the most stable structure of CSi3, R-I, does not contain the c-Si6 rings and is semimetallic (see Figure S6 in Supporting Information), we will not further discuss these two 2D materials in this work. Considering the metallic R-I BSi3 (see Figure S7 in Supporting Information) does not have a c-Si6 ring, we will discuss the R-I BSi3 structure elsewhere. In this paper, we only focus on c-BSi3 silicene with c-Si6 rings which has unique metallic electronic property as discussed below. Structural and Electronic Properties of 2D c-BSi3 Silicene. The structure of c-BSi3 silicene, optimized without any symmetry constraint, is strictly planar, and in the hexagonal space group, P6/mmm (no. 191), with aBSi3 = 7.308 Å. The unit cell of c-BSi3 silicene contains two B atoms and six Si atoms. The most remarkable structural property of c-BSi3 silicene is the presence of planar D6h c-Si6 rings with six equal Si−Si bonds, which are separated from each other by B atoms. The Si−Si bond length (2.279 Å) is equal to those in silicene36−38 and only slightly longer than those in silabenzene (2.238 Å),25 indicating the aromaticity of the c-Si6 rings, while the B−Si bond length (1.941 Å) is in the standard range between the B− Si bond (2.01 Å) and BSi bond (1.85 Å) and is shorter than the B−Si bond in the hexagonal Si−B sheet (1.99 Å).71 In general, these structural parameters agree well with the previous calculations.46 The unique feature of Si−Si and B−Si bond lengths of c-BSi3 silicene is a good indication of the significant π conjugation through the vacant p orbital of the B atom, which is also found in many other organoboron compounds.72−78 Analyzing the electronic band structure and density of states (DOS) of c-BSi3 silicene (Figure 3a) revealed that this planar nanostructure shows metallic features, and the states at the Fermi level originate mainly from Si-3p and B-2p, which are consistent with previous calculations,46 because GGA typically underestimates the band gap and the hybrid functionals such as HSE06 can predict more accurate band gaps close to experimental measurements.79,80 We also computed the band structure of the c-BSi3 silicene by the HSE06 functional as implemented in VASP code81 (see Figure S8 in Supporting Information). The dispersion of electronic band structure computed with the HSE06 functional is rather similar to that of the PW91 functional, which confirms the metallic character of the c-BSi3 silicene. To elucidate the nature of chemical bonding, we plotted the deformation and total electron density of c-BSi3 silicene (Figure 3b, c). The deformation electron density is defined as the total

Figure 8. Side (left upper) and top (left lower) views of optimized structures and corresponding electronic band structures for (a) (8, 8) and (b) (12, 0) c-BSi3 nanotubes. (c) Variation of the strain energy of (n, n) (4 ≤ n ≤ 10) and (n, 0) (6 ≤ n ≤ 16) c-BSi3 nanotubes as a function of n. In (a) and (b), the unit-cell lengths parallel to the tube axis and the diameter of the tubes are given in unit of Å.

Table 1. Diameter of the Nanotube (D), the Unit-Cell Length of the Supercell Parallel to the Tube Axis (c), the Average B−Si (lB−Si) and Si−Si (lSi−Si) Bond Lengths, Energy Gap (Eg), and the Average Net Hirshfeld Charge on Si and B Atoms of the (n, n) (4 ≤ n ≤ 10) and (n, 0) (6 ≤ n ≤ 16) c-BSi3 Nanotubes nanotube

D (Å)

c (Å)

lB−Si (Å)

lSi−Si (Å)

HSi (e)

HB (e)

Eg (eV)

(4, 4) (6, 6) (8, 8) (10, 10) (6, 0) (8, 0) (10, 0) (12, 0) (14, 0) (16, 0)

8.052 12.032 16.255 20.020 6.838 9.267 11.613 13.953 16.312 18.624

7.336 7.334 7.333 7.332 12.810 12.771 12.739 12.737 12.711 12.699

1.943 1.940 1.941 1.942 1.935 1.940 1.947 1.947 1.943 1.944

2.277 2.288 2.287 2.281 2.308 2.298 2.282 2.283 2.288 2.286

0.065 0.066 0.066 0.066 0.064 0.065 0.065 0.065 0.066 0.066

−0.197 −0.198 −0.198 −0.198 −0.193 −0.196 −0.197 −0.197 −0.198 −0.198

0 0 0 0 0 0 0 0 0 0

F



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Figure 9. Optimized structures and the corresponding band structures of (a) Arm-I-3, (b) Arm-II-4, (c) Zig-I-3, and (d) Zig-II-2 c-BSi3 nanoribbons. Each edge atom is passivated with a hydrogen atom (white spheres). I and II denote the edge termination with Si/B atoms or pure Si atoms, respectively, and the numbers indicate the number of c-Si6 rings.

more precisely, viable? The answer is yes. First, the vibration frequency calculation at the Γ point does not find any imaginary frequency, suggesting that the c-BSi3 silicene is a local minimum on the potential energy surface. Second, the binding energy of the c-BSi3 silicene (4.10 eV/atom) is relatively large, even higher than that of the experimentally synthesized low-buckled silicene sheet (3.93 eV/atom).82 Third, the thermal stability of c-BSi3 silicene is considerably high, as indicated by our ab initio MD simulations at 1750, 2000, 2250, and 2500 K for 10 ps. As shown in Figure 4, at 2000 K, the geometry of c-BSi3 silicene is well kept for 10 ps, while at 2250 K, the structure of c-BSi3 silicene seriously folds and melts; many Si−B and Si−Si bonds are broken, and hexagonal rings are destroyed. These MD simulations suggest that the c-BSi3 silicene likely melts at a temperature between 2000 and 2250 K. Moreover, to further test the thermodynamic stability of c-BSi3 silicene, we performed optimizations starting from the distorted structures after MD simulations. After full atomic relaxation, the distorted structures from 1750 and 2000 K can easily recover the planar structure, while that annealed at 2250 and 2500 K cannot. Accordingly, once formed, c-BSi3 silicene can maintain its structural integrity at least up to 2000 K. Fourth, the elastic constants (C11 = 91 N/m and C12 = 37 N/m)46 satisfy the Born criteria, indicating that the c-BSi3 silicene is mechanically stable. Thus, we concluded that c-BSi3

electron density of c-BSi3 silicene subtracting those of isolated atoms from the sheet. Obviously, some electrons are extracted from the 3p orbital of the Si atoms to the vacant p orbital of B atoms (0.070 |e| electron transfer according to Hirshfeld charge analysis), and the B atoms form multicenter electron-deficient covalent bonds with three neighboring Si atoms (the blue regions near B atoms in Figure 3b), which indicated the Bcentered covalent bonds should be hybrid sp2 in nature. Such a strong hybridization between Si-3p and B-2p indicates that there is a strong π−p conjugation between B atoms and aromatic c-Si6 rings, which is responsible for the high stability and the planar geometry of the c-BSi3 silicene. In addition, the π electrons are distributed evenly within the entire layer (Figure 3c), which leads to the metallic behavior of the c-BSi3 silicene. In order to study the aromatic properties of the c-Si6 ring in c-BSi3 silicene, we present the highest occupied state edge (HOSE) and the lowest unoccupied state edge (LUSE) of cBSi3 silicene at the Γ point (Figure 3d, e). Impressively, both the HOSE and LUSE are almost identical to the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of benzene and hexalithiosilabenzene.22 Thus, with all the theoretical proofs discussed above, we concluded that the c-BSi3 silicene is a 2D aromatic compound with planar c-Si6 rings. Stability of 2D c-BSi3 Silicene and the Feasibility for Experimental Realization. Is the 2D c-BSi3 silicene stable or, G



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atoms to H (F) atoms. The charge transfer from B and Si atoms to H (F) atoms is 0.049 (0.123) and 0.063 (0.163) |e|, respectively, according to Hirshfeld charge analysis. Structural and Electronic Properties as Well as Stability of c-BSi3 Nanotubes. Similar to the case of the single-walled carbon nanotube (CNT), a series of single-walled c-BSi3 nanotubes can be built by rolling the c-BSi3 silicene sheet along specific directions according to a well-established method.89 Both (n, n) armchair and (n, 0) zigzag c-BSi3 nanotubes were considered. First we computed two representative c-BSi3 nanotubes, namely, (8, 8) and (12, 0) (Figure 8a and b). In the optimized structures, the unit-cell lengths are 7.333 and 12.737 Å for (8, 8) and (12, 0) nanotubes, respectively. The Si−Si bond lengths (2.287 and 2.283 Å for (8, 8) and (12, 0) tube, respectively) and the BSi bond lengths (1.941 and 1.947 Å for (8, 8) and (12, 0) tube, respectively) are quite close to those in the c-BSi3 silicene sheet. The charge transfer from Si (0.066 and 0.065 |e| for (8, 8) and (12, 0) tube, respectively) to B is slightly less than that in the c-BSi3 silicene sheet (0.070 |e|). The same as their 2D analogues, both (8, 8) and (12, 0) c-BSi3 nanotubes are metallic, as indicated by the computed band structures (Figure 8a and b). In addition, we also computed a series of (n, n) (4 ≤ n ≤ 10) and (n, 0) (6 ≤ n ≤ 16) c-BSi3 nanotubes (Table 1). For all the (n, n) and (n, 0) c-BSi3 tubes, the optimized bond lengths are very close to those in the c-BSi3 silicene sheet, and the charge transfer from Si to B is also similar to the value for the 2D sheet. Especially, independent of the charity and diameter, all cBSi3 nanotubes are metallic. This interesting results are similar to SiB nanotubes71 and pt-SiC2 nanotubes82 but in stark contrast to the buckled Si nanotubes,90 carbon nanotubes,91 BC3 nanotubes,92 SiC nanotubes,93 and g-SiC2 nanotubes.94 The stability of c-BSi3 nanotubes is evaluated by the strain energy, which is defined as the cohesive energy difference between a tube and a sheet. The strain energies of (n, n) (4 ≤ n ≤ 10) and (n, 0) (6 ≤ n ≤ 16) c-BSi3 tubes are presented in Figure 8c. In general, (n, n) nanotubes have lower strain energies than (n, 0) nanotubes and are thus more stable. For both types, the strain energy decreases with increasing the tube diameter. The tubes wider than 11 Å in diameter have very small stain energies (

Metallic BSi3 Silicene and Its One-Dimensional Derivatives: Unusual

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