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May 14, 2012 - The concept of planar tetracoordinated carbon (ptC) was first put forth by Hoffman et al.(1) in the 1970s and attracted much interest b...
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Tri-Wing Graphene Nano-Paddle-Wheel with a Single-File Metal Joint: Formation of Multi-Planar Tetracoordinated-Carbon (ptC) Strips Menghao Wu,†,‡ Yong Pei,*,§ Jun Dai,† Hui Li,† and Xiao Cheng Zeng*,†,‡ †

Department of Chemistry, University of NebraskaLincoln, Lincoln, Nebraska 68588, United States Department of Physics and Astronomy, University of NebraskaLincoln, Lincoln, Nebraska 68588, United States § Department of Chemistry, Key Laboratory of Environmentally Friendly Chemistry and Applications of Ministry of Education, Xiangtan University, Hunan Province, China, 411105 ‡

S Supporting Information *

ABSTRACT: Using density-functional theory (DFT), we show that edge-passivated zigzag graphene nanoribbons by a metal ligand M (ZGNR-M) can form various nanostructures through a single-file metal-chain joint. We have investigated structural properties of ZGNR-M (M = Al, Sc, Ti, V, Cr, Mn, Fe, or Co) based bi-wing nanostructures and tri-wing “nanopaddle-wheels”, named as bi-ZGNR and tri-ZGNR, respectively. In particular, we explore whether one or more wings in bi-ZGNR or tri-ZGNR nanostructures can entail a strip of planar tetracoordinated carbon (ptC), a concept originally proposed by Hoffman et al. (J. Am. Chem. Soc. 1970, 92, 4992) for molecular species. We find that although the ptC is energetically less favorable than nonplanar tetracoordinated carbon in bi-ZGNR nanostructures (M = Al, Sc, Ti, V, Cr, Mn, Fe, or Co), surprisingly, the ptC strip can be fully stabilized in two wings of tri-ZGNR and in all three wings of tri-ZGNR “nano-paddle-wheel”. We also show that tri-ZGNR can be a structural unit for building a three-dimensional (3D) titanium-graphene framework (TiGF), the first predicted 3D porous material with segments of ptC strips.

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The first successful synthesis of ptC molecular species was reported in 1977, in which the ptC is coordinated by two vanadium (V) atoms.18 To date, most of the synthesized ptC compounds have been transition-metal-containing organometallic species. For instance, the group-IVB transition-metalbased bent metallocenes, i.e., titanocene, zirconocene, and hafnocene, are especially valuable for making carbon compounds with unusual coordinate structures.19 The simplest molecules with ptC are composed of five atoms, and they were first predicted by Schleyer and Boldyrev.16 These ptCcontaining molecules are planar due to the occupied molecule orbital that is nonbonding with respect to the central atom− ligand interactions but bonding with respect to ligand−ligand interactions. The orbital shows maximum overlap in the planar square structure. Stimulated by the theoretical prediction, a series of ptC molecules were later identified in gas-phase photoelectron spectroscopy experiments.17 Beyond the ptC, the notion of planar hyper-coordinated carbon was also proposed on the basis of high-level ab initio calculations. A number of metastable planar hyper-coordinated carbon molecular species have been theoretically predicted.20

INTRODUCTION The concept of planar tetracoordinated carbon (ptC) was first put forth by Hoffman et al.1 in the 1970s and attracted much interest by chemists over the past two decades.2 It is known that saturated carbon atoms in the majority of organic compounds are tetracoordinated (Kekulé, 1857)3 and favor (near)-tetrahedral geometries (van’t Hoff and Le Bel, 1874).4 The ptC is apparently contrary to the tetrahedral geometries and is thus expected to be highly unstable. Over the past two decades, many research efforts have been made to seek energetically stable ptC systems5 in view of the fact that realization of the “anti-van’t Hoff/LeBel” compounds in the laboratory is a very challenging task. The chemical mechanism underlying Hoffmann et al.’s proposal is that introduction of the σ-donating/π-accepting substituent or incorporation of the ptC lone pair into the π-electron delocalization systems can efficiently stabilize the ptC center, known as the electronic stabilization mechanism.3,6 On the basis of the electronic stabilization mechanism, numerous ptC species have been predicted theoretically.7−9 Besides the electronic stabilization mechanism, an alternative mechanism to stabilize the planar tetracoordinate carbon is to incorporate a ptC unit such as the “CC4” or “CB4” into rigid steric systems.10−17 The ptC center is stabilized by the strain of the molecular skeleton. © 2012 American Chemical Society

Received: March 4, 2012 Revised: April 28, 2012 Published: May 14, 2012 11378

dx.doi.org/10.1021/jp302115n | J. Phys. Chem. C 2012, 116, 11378−11385

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Figure 1. The geometric structures of (a) H-ZGNR-M (M = Al or Co), (b) H-ZGNR>M (M = Sc, Ti, V, Cr, Mn, or Fe), and (c) bi-ZGNR. (d) Realization of bi-ZGNR by fusing the unpassivated edge of an H-ZGNR to the M edge of an H-ZGNR>M. Green, white, and pink (or dark blue) balls represent carbon, hydrogen, and M atoms, respectively.

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COMPUTATIONAL METHODS For computing structural and electronic properties of ptC strips, bi-wing nanostructures Bi-ZGNR, and tri-wing nano-paddle-wheels tri-ZGNR, density function theory (DFT) calculations are carried out using the DMol3 4.1 package.23 The generalized gradient approximation (GGA) in the Perdew−Burke−Ernzerhof (PBE) form and an all-electron double numerical basis set (DNP) with polarized function are selected for the spin-unrestricted DFT computation.24 The real-space global cutoff radius is set to be 4.5 Å. The supercell is a rectangle prism with spatial dimensions of 36 × 4.94 × 26 Å3. For ptC strips, each supercell contains 32 carbon atoms (or 8 zigzag chains), 2 metal atoms, and 2 hydrogen atoms, while, for bi-wing nanostructures, each supercell also contains 32 carbon atoms, 2 metal atoms, and 4 hydrogen atoms. For tri-wing nano-paddle-wheels, each supercell contains 48 carbon atoms, 2 metal atoms, and 6 hydrogen atoms. For geometric optimization, the Brillouin zone is sampled by 1 × 20 × 1 k points using the Monkhorst−Pack scheme.25 After optimization, the force on each atom is less than 0.0002 Ha/Å. To examine the thermal stability of the nano-paddle-wheels (at 1000 K), we have also performed a Born−Oppenheimer quantum molecular dynamic (BOMD) simulation (using the BOMD program implemented in the DMol3 4.1 package). The canonical ensemble is chosen for which the Nosé−Hoover chain method26 is used to control the temperature (1000 K) of the system. The Nosé Q ratio is set to be 2.0, and the Nosé chain length is 2. For computing the electronic properties of the 3D periodic hexagonal titanium-graphene framework (TiGF), the supercell is a rhomboid prism with a spatial dimension of 22.6 × 22.6 × 5.1 Å3, which contains 16 metal atoms and 96 carbon atoms. To examine the structural stability of the Ti-GF, we have computed phonon band structure using the GGA/PBE method implemented in the Quantum-Espresso package.27 The valence electron−ion interaction is described by an ultrasoft pseudopotential,28 which allows a relatively low cutoff energy

Most ptC systems reported so far involve a single or a few ptC centers. A question that naturally arises is how multiple ptC units can be assembled into condensed matter. A strategy proposed recently is to use ptC as a basic structural unit to create an extended (periodic) system. On the basis of this strategy, a number of prototype one- or two-dimensional (2D) materials built upon known molecular ptC motifs, such as CAl42−, C52−, CSi4, or CB4, have been predicted theoretically.21 In particular, a global search of optimal structures of 2D network materials BxCy (B1−3,5C, BC1−3,5) shows that the ptCbased 2D networks are likely the most stable periodic structures among the B2C, B3C, and B5C sheets.21j To stabilize a ptC center in a molecular system, a known challenge is how to overcome atomic exchange between the ptC and surrounding ligand atoms. If a molecular ptC species is a local minimum but not the global minimum, a carbon atom can migrate to any peripheral position to lower the coordination number (M, H-ZGNR-M, and biZGNR Nanostructures M

Al

out-of-plane angle, θ (deg) C−M bond length (Å) M−M bond length (Å) out-of-plane angle (deg) C−M bond length (Å) M−M bond length (Å)

Sc

0 2.02 2.46

24.9 2.2 3.1

13.6 2.1 2.66

21.1 2.25 3.04

Ti

V

H-ZGNR>M&-M 17.5 15.3 2.11 2.21 2.81 2.77 Bi-ZGNR 10.6 8.4 2.16 2.15 2.64 2.56

Cr

Mn

Fe

Co

20.5 2.16 2.83

15.1 2.09 2.65

13.7 2.05 2.65

0 1.85 2.46

16.8 2.12 2.53

8.28 2.12 2.54

6.74 2.09 2.52

7.6 2.04 2.59

Table 2. Computed Binding Energy (Eb) of M to the Edge of H-ZGNR>M, H-ZGNR-M, bi-ZGNR, and tri-ZGNR Nanostructures, Bulk Cohesive Energy Ec(M(bulk)), Eb′ with Respect to Reference Bulk Metal, and the Largest Bent Anglea M

Al

Sc

Ti

V

Cr

Mn

Fe

Co

Eb of M in H-ZGNR>M or H-ZGNR-M (eV) Eb of M in bi-ZGNR (eV) Eb of M in tri-ZGNR (eV) Ec(M(bulk)) (eV) Eb′ of M in bi-ZGNR (eV) Eb′ of M in tri-ZGNR (eV) the largest bent angle of a wing of tri-ZGNR, T (deg)

4.51 6.36 9.75 3.73 2.63 6.02 0

5.48 9.25 11.55 4.79 4.46 6.76 8.4

4.93 8.46 11.67 5.38 3.08 6.29 0

4.82 7.99 11.12 5.42 2.57 5.7 20.0

3.53 6.61 9.26 4.03 2.58 5.23 4.3

3.73 6.76 9.27 4.02 2.74 5.25 8.9

4.05 7.08 9.68 4.44 2.64 5.24 8.0

4.19 6.79 9.57 4.3 2.49 5.17 7.0

As a comparison, the calculated binding energy of hydrogen Eb on the edge of H-ZGNR-H is 5.05 eV, and that with respect to hydrogen gas Eb′ is 2.68 eV. The highest binding energies of various nanostructures are highlighted in bold. a

(here 40 Ry) for the plane-wave expansion. A 4 × 4 × 12 kpoint mesh generated within the Monkhorst−Pack scheme25 is selected for Brillouin zone integration, and a 2 × 2 × 2 q-point mesh and a Gaussian smearing of 0.05 Ry are used for dynamical matrix and phonon mode calculations.

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E b = −(E(H‐ZGNR>M or ‐M) − E(H‐ZGNR) − 2E(M(gas)))/2

where H-ZGNR denotes ZGNR with one carbon edge passivated by H atoms and the other carbon edge unpassivated and E(M(gas)) represents the total energy of a single metal atom (in gas phase). As shown in Table 2, the binding energy for M = Al or Sc is much greater than the cohesive energy of the corresponding bulk phase Ec(M(bulk). In contrast, for M = Ti, Cr, Mn, Fe, or Co, the binding energy of M is less than the corresponding cohesive energy (with the energy difference being less than 0.6 eV) but much greater than the binding energy of M on the surface of a graphene or ZGNR.29,30 In addition, we consider the ZGNR with both edges decorated by metal element Sc or by Ti. The computed binding energies of Sc and Ti are still 5.48 and 4.93 eV, respectively, the same as those shown in Table 2. As a comparison, the calculated binding energy of H for the same ZGNR with both edges passivated by H is 5.05 eV. Here, the binding energy of H is computed based on the formula Eb = −(E(H-ZGNR-H) − 2E(H-ZGNR) − 2E(H(gas, radical)))/2, where E(H(gas,radical)) represents the total energy of a single hydrogen atom (in gas phase). Even if the entropic contribution is included, the binding energy of Sc atom is still slightly greater than that of hydrogen atom (up to about 850 K). Given that the experimentally produced carbon nanoribbons can be passivated by hydrogen and that the binding energy of hydrogen atom is comparable to that of Sc and Ti, it is plausible that bare edges of carbon nanoribbons can be passivated by Sc or Ti as well through chemical vapor deposition or other chemical means. Bi-ZGNR. As an edge of H-ZGNR>M or H-ZGNR-M structure, the metal (M) line is capable of binding with additional ZGNRs. First, we have studied a new nanostructure, namely, bi-ZGNR, in which two ZGNR wings are joined together by a single-file metal chain. Here, each metal atom

RESULTS AND DISCUSSION

H-ZGNR>M or H-ZGNR-M. We first consider ZGNRs with one edge decorated by H and another edge passivated by a metal element M (M = Al, Sc, Ti, V, Cr, Mn, Fe, or Co). When each metal atom M is bonded with only one carbon atom at the edge, the carbon atom is in the sp2 hybridization (Figure 1a). We define this configuration as H-ZGNR-M. When each metal atom is bonded with two carbon atoms, the carbon atoms are in the sp3 hybridization (Figure 1b). We define this configuration as H-ZGNR>M. Among eight edge-decorated ZGNRs considered in this study, the edge-decorated ZGNRs by Al or Co adopt the H-ZGNR-M configuration, while other six edgedecorated ZGNRs adopt the H-ZGNR>M configurations, all exhibiting nonplanar structures (Figure 1b). For both the HZGNR-M and H-ZGNR>M configurations, we define an outof-plane angle (θ) between the ZGNR plane and the plane formed by M and their adjacent edge carbon atoms. Any HZGNR>M structure with θ = 0 indicates that the structure itself is a perfect ptC strip (for example, CuCu22a). In Table 1, we summarize the computed bond lengths of C−M and M−M and the out-of-plane angle (θ) in various H-ZGNRM and H-ZGNR>M systems. It can be seen that θ angles of the six H-ZGNR>M structures are all nonzero, indicating that none of these edge-decorated ZGNRs adopt the structure of the ptC strip. The computed cohesive energy of bulk metal in the solid state and the binding energy of a metal atom to the ZGNR edge for all H-ZGNR>M and H-ZGNR-M structures are presented in Table 2. Here the binding energy per metal atom is defined as 11380

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Figure 2. Optimized geometric structures of three-winged graphene “nano-paddle-wheel”: a tri-ZGNR is composed of (a) three H-ZGNR>M wings (M = Sc or Ti) and (b) two H-ZGNR>M and one H-ZGNR-M wings (M = Al, V, Cr, Mn, Fe, or Co). (c) A top view of the three-winged graphene “nano-paddle-wheel along the axial direction, where the bent angle of a wing (T) is defined. Green, white, and pink (or dark blue) balls represent carbon, hydrogen, and M atoms.

joint: (1) tri-ZGNR structure which is composed of three H-ZGNR>M wings (M = Sc or Ti), as shown in Figure 2a, where each wing entails a ptC strip. (2) tri-ZGNR structure which is composed of two H-ZGNR>M wings and one H-ZGNR-M wing (M = Al, V, Cr, Mn, Fe, or Co), as shown in Figure 2b, where each of the two H-ZGNR>M wings entails a ptC strip. Top views of optimized structures of tri-ZGNR nanopaddle-wheels in the direction of metal chain are shown in Supporting Information Figure S1. For most tri-ZGNR (M = Sc, V, Cr, Mn, Fe, and Co), it can be seen that one or two H-ZGNR>M wings are not perfectly flat as the ZGNRs are slightly bent with respect to the plane formed by edge carbon atoms and the metal chain. We refer to carbon in this type of edge as quasi-ptCs. Interestingly, tri-ZGNR and triZGNR possess, respectively, two and three perfect ptC strips (cf. Supporting Information Figure S1 and Table 2). Compared to a single ZGNR-M, the binding behaviors of Al and Co in bi-ZGNR and tri-ZGNR are markedly different (Table 2). When the second and third ZGNRs are anchored to the metal edge of ZGNR-Al or ZGNR-Co, each Al or Co atom tends to bind more edge carbon atoms, yielding either ptC or quasi-ptC structure. In Figure 2c, the bent angle (T) of a nonplanar wing is defined as the angle between the ZGNR plane and the plane formed by the edge carbon atoms and the metal chain. The bent-angle reflects the degree of outof-plane bending of the quasi-ptC strip. As shown in Table 2, tri-ZGNR and tri-ZGNR possess two and three perfect ptC strips, respectively. For other metal elements, the bent-angles are nonzero, leading to the quasi-ptC structures. For M = Sc, the bent-angles of the three wings are 4.5, 3.7, and 8.4°, respectively, while, for M = V, the bent-angles of the two H-ZGNR>V wings are 8.3 and 20.0°, respectively. The computed binding energies of M to tri-ZGNR nano-paddle-wheels are shown in Table 2, where the binding energy per metal atom is defined as

(M) is bonded with four edge carbon atoms in the biZGNR. As shown in Figure 1c, DFT structural optimizations indicate that, for M = Al, Co, Sc, Ti, V, Cr, Mn, or Fe, the single-file metal chain is not a straight line but exhibits periodically puckered structure, and all the metal atoms in H-ZGNR>M and H-ZGNR-M structures are located either above or below the ZGNR plane in a periodical fashion. The second out-of-plane angle (see Table 1) is defined as the angle between the ZGNR plane and the plane formed by an M atom and its two adjacent edge carbon atoms on one wing. The second out-of-plane angle ranges from 6.74 to 21.1° for M = Al, Co, Sc, Ti, V, Cr, Mn, and Fe. Hence, no ptC strips are formed among the eight bi-ZGNR nanostructures. The binding energies of a metal atom onto the biZGNR nanostructures are further evaluated and listed in Table 2. Here the binding energy per metal atom is defined as E b = −(E(bi‐ZGNR) − 2E(H‐ZGNR) − 2E(M(gas)))/2

It is found that the binding energy per M atom for biZGNR is much greater than that for the corresponding HZGNR>M and H-ZGNR-M nanostructures. Moreover, stability of the bi-ZGNR nanostructures can be assessed by computing the binding energy Eb′ with respect to reference bulk metal M, Eb′ = −(E(bi-ZGNR) − 2E(M(bulk)))/2 = Eb − Ec(M(bulk)), where Ec(M(bulk) = E(M(gas)) − E(M(bulk)) is the cohesive energy of the bulk metal (Table 2). The calculated Eb′ values for Sc and Ti are notably greater than that (2.68 eV) for the hydrogen passivated system, computed according to Eb′ = −[E(H-ZGNR-H) − E(HZGNR) − E(H2(gas))]/2. Therefore, the bi-ZGNR nanostructures (M = Sc and Ti) are energetically most favorable, and may be realized by fusing the bare carbon edge of an H-ZGNR with the M edge of an H-ZGNR>M (M = Sc or Ti) (see Figure 1d for illustration). Tri-ZGNR. In addition to bi-ZGNR nanostructures, we further investigate the binding of the third ZGNR to the single-file metal-chain joint in a bi-ZGNR nanostructure, in the direction normal to the plane of the bi-ZGNR nanostructure. Upon geometric optimization, remarkably, the periodically puckered metal chain may turn into a straight line for certain metal elements. The tri-wing graphene nano-paddlewheels can be classified into two groups based on the coordination between edge carbon atoms with the metal

E b = −(E(tri‐ZGNR) − 3E(H‐ZGNR) − 2E(M(gas)))/2

In addition, the stability of the tri-ZGNR nanostructures can be assessed by computing the binding energy Eb′ with respect to reference bulk metal M, Eb′ = −(E(tri-ZGNR) − 3E(H-ZGNR) − 2E(M(bulk)))/2 = Eb − Ec(M(bulk)) (see Table 2). We find that binding energies of an M atom are 11381

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Table 3. Hirshfeld Charge on M and Adjacent Edge Carbon Atoms, and Magnetic Moment on M in tri-ZGNR Systemsa M charge (e), M C1 C2 magnetic moment (μB) on M a

Al 0.96 −0.27 −0.34 0

Sc

Ti

0.31

0.29

−0.12 0.016

−0.12 0

V

Cr

Mn

Fe

Co

0.23 −0.077 −0.1 0.96

0.39 −0.091 −0.14 2.07

0.15 −0.041 −0.061 1.59

0.089 −0.026 −0.03 0.14

0.11 −0.003 −0.051 0.019

C1 and C2 represent the edge carbon atoms connecting to M in H-ZGNR-M and H-ZGNR>M wings, respectively.

Figure 3. (a) Iso-surface (0.1 e/au) of the deformation electronic density of tri-ZGNR and tri-ZGNR. Blue and yellow color indicate electron rich and deficient region, respectively. (b) The highest occupied electronic state and (c) lowest unoccupied electronic state of the triZGNR and tri-ZGNR at the Γ point.

(Table 3). For tri-ZGNR, a highly delocalized deltaorbital is contributed by the central Cr atoms. In both cases, LUES is mainly contributed by the 2pz atomic orbitals of carbon. The computed spin density, electronic band structure, and partial density of states contributed by M and C1 + C2 in triZGNR and tri-ZGNR are shown in Figure 4a and b, respectively. The calculations suggest that Cr metal chain is spin-polarized. The three outmost zigzag edges of the wings are ferromagnetically coupled. For tri-ZGNR, little spin density is distributed on the Ti metal chain and the adjacent C2 strips in the center. However, in tri-ZGNR, the Cr metal chain in the center is antiferromagnetically coupled. To examine the thermal stability of the nano-paddle-wheels at a high temperature (1000 K), we have performed a BOMD simulation. Snapshots of the tri-ZGNR and triZGNR structures at the end of 5 ps BOMD simulations are displayed in Figure 4c. Despite significant structural distortion of the whole structure, either the ptC or the quasiptC structure is still intact even at 1000 K. To gain more insights into the chemical bonding nature of ptC and quasi-ptC within the tri-ZGNR nanostructure, we investigate the chemical properties of two relevant organometallic molecules, namely, C38H20Co2 and C50H23Co3 (see Figure 5); both can be viewed as molecular segments of triZGNR. The two molecular structures are optimized at the B3LYP/6-311++(2df,2dp) level of theory, implemented in the Gaussian 03 package.32 The metal element Co is selected

significantly increased for tri-ZGNR, compared to those of corresponding bi-ZGNR. In other words, the anchor of the third ZGNR to the metal chain in bi-ZGNR is energetically favorable. In Table 3, computed Hirshfeld charges and spin densities on metal atoms (M) and edge carbon atoms in tri-ZGNR are listed, where C1 and C2 represent the edge carbon atoms connecting to M in H-ZGNR-M and H-ZGNR>M wing, respectively. As shown in Table 3, significant charge transfer from M (M = Al, Sc, Ti, V, Cr, or Mn) to C2 and C1 (except Sc and V) is found. The absolute value of charge on C1 is always less than that on C2 because C2 is in sp3 hybridization (bonded with two M atoms) while C1 is in sp2 hybridization (bonded with one M atom). On the basis of spin analysis, it is found that the 3d transition metals prefer to be in the low-spin state (M = V, Cr, or Mn) or zero-spin state (M = Sc, Ti, Fe, or Co). Next, we treat tri-ZGNR and tri-ZGNR as two benchmark systems for further analysis. Figure 3a displays the computed deformation electronic density31 which shows that the edge ptC atoms form multicenter electron-deficient covalent bonds (regions in blue in Figure 3a) with metal atoms. The highest occupied electronic state (HOES) and the lowest unoccupied electronic state (LUES) at the gamma (Γ) point are displayed in Figure 3b and c, respectively. The HOES of tri-ZGNR and tri-ZGNR show multicenter bond character between ptC and metal atoms. For tri-ZGNR, the HOES is mainly contributed by the 3dz2 atomic orbitals of Ti atoms, which are known to give zero magnetic moment 11382

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molecular structures based on natural bonding orbital (NBO) calculation.33 As shown in Figure 5, the Co−C bonds are weakened with the increase the number of ptC centers from molecule (a) to (b), as reflected by the smaller WBIs for the Co−C bonds. However, the total WBI for the ptC remains at 3.69 and 3.74, respectively; both values are close to 4.0. The NPA analysis suggests that Co atoms are positively charged while ptC is negatively charged, consistent with the Hirshfeld analysis for the periodic tri-ZGNR>Co system. Hexagonal Metal-Graphene Framework. Lastly, we point out that the tri-ZGNR nano-paddle-wheel can be viewed as a building block for 3D metal−carbon networks (MCF).34 An example of such an MCF is the hexagonal titanium-graphene framework (TiGF) with Ti wires as junctions, as shown in Figure 6a. In the hexagonal TiGF, the graphene side walls around the Ti wires still retain the same structural features as the building unit. To examine the structural stability of the hexagonal TiGF, we have computed the phonon band structure of a TiGF (see Computational Methods for details). The computed phonon spectrum is shown in Figure 6b. One can see that no dynamical instabilities (negative frequencies) are seen in the phonon spectrum, indicating that the TiGF structure is dynamically stable and no charge-density-wave instabilities occur in the system. In addition, the computed electronic band structure suggests that the hexagonal TiGF is metallic (see Figure 6c). The hexagonal TiGF is a porous structure whose pore size is at the low-end limit. Hence, the hexagonal TiGFs shown in Figure 6a can be categorized as lightweight materials, since their mass densities are less than 1.44 g/cm3, compared to the mass density (3.54 g/cm3) of cubic diamond. Moreover, the hexagonal TiGFs possess fairly large surface area per mass; the one shown in Figure 6 has a surface area of ∼2380 m2/g and a large surface area per volume, ∼3.4 × 109 m2/m3, which is much larger than the internal surface area per volume (5000−50 000 m2/m3) of common carbon foams.35 Thus, not only the hexagonal TiGFs are of fundamental interest due to their novel ptC-containing features, but also their large surface area, low mass-density, and high structural integrity render the materials potentially valuable for applications such as gas storages.

Figure 4. Computed spin density, electronic band structure, and the partial density of states contributed by M and C1 + C2 in triZGNR where (a) M = Ti and (b) M = Cr. For spin density, blue and yellow represent spin-up and spin-down; the range of the isosurface values of spin density is [−0.03, 0.03]. In band structure, black represents the spin-up channel and red represents the spin-down channel; in PDOS plots, black represents PDOS distributed by M and red represents the PDOS distributed by C1 + C2. (c) A snapshot of the equilibrium structure of tri-ZGNR (M = Ti, Cr) at 1000 K, at the end of 5 ps BOMD simulations.

Figure 5. Optimized structures and computed WBI (in parentheses) of organometallic molecules.

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for this study because other metal elements such as Sc or Ti give rise to too strong intermetal repulsions to distort the overall molecular structures. The vibrational frequency computation shows that both C38H20Co2 and C50H23Co3 are stable local minima. The Wiberg bond index (WBI) analysis and natural population analysis (NPA) are performed for both

CONCLUSION In conclusion, we have performed density-functional calculations and quantum molecular dynamics simulation to study ZGNR-M (M = Al, Sc, Ti, V, Cr, Mn, Fe, or Co) based

Figure 6. (a) A schematic plot of the hexagonal Ti-graphene framework built from tri-ZGNR nano-paddle-wheels. Color code: C (gray) and Ti (orange). (b and c) Computed phonon spectrum and electronic band structures of the hexagonal Ti-graphene framework where Γ(0.0, 0.0, 0.0), A (0.0, 0.0, 0.5), H(−0.333, 0.667, 0.50), K(−0.333, 0.667, 0.0), M(0.0, 0.5, 0.0), and L(0.0, 0.5, 0.5) are k-space points in the first Brillouin zone. In part c, the Fermi level is set to be 0. 11383

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nanostructures joined through a single-file metal chain, where the metal chain copassivates one edge of two zigzag graphene nanoribbons (forming bi-ZGNR) or three ZGNRs (forming tri-ZGNR). Particular attention has been placed on structural properties of bi-wing nanostructures and tri-wing “nano-paddle-wheels”. We find that, although the ptC is energetically less favorable than nonplanar tetracoordinated carbon in bi-ZGNR nanostructures (M = Al, Sc, Ti, V, Cr, Mn, Fe, or Co), surprisingly, the ptC strip can be fully stabilized in two wings of the tri-ZGNR “nano-paddle-wheel” and in all three wings of the tri-ZGNR “nano-paddle-wheel”. The computed electronic band structure of tri-ZGNR suggests that this nano-paddle-wheel system is metallic. The Ti-ZGNRTi nanostructure and three-wing nano-paddle-wheel triZGNR are of particular interest because (1) the binding energy of Ti on the edges of both nanostructures is comparable to that of hydrogen and (2) the three-wing nano-paddle-wheel tri-ZGNR can be viewed as a building block for the 3D hexagonal Ti-graphene framework (or Ti−C nanofoam) with large surface area, low mass-density, and high structural integrity. Note that a controlled synthesis of ultranarrow GNRs has been achieved recently in the laboratory.36 Successful synthesis of ultranarrow GNRs will provide precursor carbon substrates for the edge decoration by Sc or Ti, whose binding energies to the edges of GNRs are greater or comparable to that of hydrogen. In a previous BOMD simulation study by us,37 we placed a Sc atom 4 Å away from an unpassivated edge of narrow ZGNR. We found that, at 300 K, the Sc atom can bind spontaneously with the edge in 0.2 ps, suggesting that, if ultranarrow ZGNRs are exposed to chemical vapor of Sc atoms, it is very likely the ZGNR edges would be quickly passivated by Sc atoms. If edge-decorated ultranarrow GNRs by Ti can be realized in the laboratory, the three-wing nano-paddle-wheel tri-ZGNR may be synthesized via attaching two edge-unpassivated ZGNRs to an edgepassivated Ti-ZGNR-Ti in view of highly favorable binding energies of Ti in tri-ZGNR (see Table 2).

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ASSOCIATED CONTENT

S Supporting Information *

The projected structures of all tri-ZGNR nano-paddlewheels are collected. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported by grants from the NSF (DMR0820521) and ARL (W911NF1020099) and by the University of Nebraska’s Holland Computing Center. Y.P. is partially supported by the Academic Leader Program in Xiangtan University (10QDZ34) and Natural Science Foundation of China (Grant No. 21103144).

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REFERENCES

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