Abstract
By means of density functional theory computations, we demonstrated that C_{2}H_{4} is the ideal terminal group for zigzag graphene nanoribbons (zGNRs) in terms of preserving the edge magnetism with experimental feasibility. The C_{2}H_{4} terminated zGNRs (C_{2}H_{4}zGNRs) with pure sp^{2} coordinated edges can be stabilized at rather mild experimental conditions, and meanwhile reproduce the electronic and magnetic properties of those hydrogen terminated zGNRs. Interestingly, the electronic structures and relative stability of C_{2}H_{4}zGNRs with different edge configurations can be well interpreted by employing the Clar's rule. The multiple edge hyperconjugation interactions are responsible for the enhanced stability of the sp^{2} coordinated edges of C_{2}H_{4}zGNRs. Moreover, we demonstrated that even pure sp^{2} termination is not a guarantee for edge magnetism, for example, C_{2}H_{2} termination can couple to the πelectron system of zGNRs, and destroy the magnetism. Our studies would pave the way for the application of zGNRs in spintronics.
Introduction
Since its experimental realization in 2004^{1,2}, graphene, the first strict twodimensional (2D) crystal with oneatomic thickness, has been a subject of great interest due to its excellent properties and promising applications^{3,4,5}. Interestingly, one dimensional (1D) graphene nanoribbons (GNRs) can also be yielded by cutting graphene in the nanoscaled width. Depending on the cutting direction, two unique types of edges can be obtained: zigzag and armchair. Different from graphene which is actually semimetal, both zigzag and armchair GNRs have a nonzero band gap, which has been confirmed both theoretically^{6,7} and experimentally^{8,9}. Moreover, the edge geometry also makes a huge difference in the πelectron structure at the edges. As early as in 1996, Fujita et al.^{10} revealed that zigzag GNRs (zGNRs) have peculiar localized edge states (completely absent in the armchair edge), which give rise to the quite flat bands near the Fermi level^{11}. By employing the Hubbard model with the unrestricted HartreeFock approximation, Fujita et al.^{10,12} also deduced that the edge states of zGNRs are ferromagnetically (FM) coupled on each edge but antiferromagnetically (AFM) coupled between two edges. In 2006, Son et al.^{13} found that the edge states of zGNRs in different spin channels response oppositely to the transverse external electric field, and thus zGNRs can be halfmetallic (metallic for one spin channel and insulating for the other) under a critical value of electric field. Later theoretical studies demonstrated that selective edge modification^{14,15} can also tune zGNRs into halfmetallic. Therefore, zGNRs have very promising applications in future spintronics.
However, there is a large gap between theoretical prediction and experimental realization. The edge states of zGNRs are very reactive^{16}, and thus cause instability, whereas armchair edges are more stable^{17,18,19}. As a consequence, most synthesized nanographenes have armchair peripheries^{20,21}, and the synthesis of GNRs with consecutive zigzag edges has been rather difficult for a long time. Encouragingly, experimental peers have achieved great progress recently in fabricating GNRs with smooth zigzag edges^{22,23,24,25,26}, and the localized edge states have been vigorously confirmed by scanning tunneling microscopy (STM) and spectroscopy^{27,28,29,30,31}. However, the edge magnetism of zGNRs has been scarcely detected experimentally^{32,33}, because, to preserve the edge magnetism, the edge sites of zGNRs should have the pure sp^{2} coordination. Unfortunately, density functional theory (DFT) computations by Wassmann et al.^{34} demonstrated that the pure sp^{2} coordinated edges of hydrogen terminated zGNRs (HzGNRs) can be stabilized only at extremely low hydrogen concentration, which is rather challenging experimentally. Under normal conditions, the edge sites tend to be fully saturated by hydrogen, which directly suppresses the edge magnetism. More seriously, zGNRs are also characterized by the nonmagnetic nature in presence of some typical atmospheric molecules, such as O_{2}, H_{2}O, NH_{3}, and CO_{2}^{35}.
Therefore, to preserve the edge magnetism of zGNRs, the first urgent thing is to find a suitable termination group for zGNRs. Recently, Chai et al.^{36} have suggested that large bulky ligands (i.e. tertiarybutyl, C_{4}H_{9}) terminated zGNRs favor the pure sp^{2} termination across a broader range of thermodynamic conditions due to the strong steric effect of ligands. Though not mentioned explicitly, the hyperconjugation between the large bulky ligands and the edge states (can be seen as radicals)^{16,37} also contributes to the enhanced stability of the edge. Then, an interesting question arises: can we use some more simple terminal groups to stabilize sp^{2} coordinated edges of zGNRs by taking advantage of hyperconjugation interaction?
In this work, by means of systematic DFT computations, we explored the possibility of using ethylene (C_{2}H_{4}), a very simple and common organic molecule, as the terminal group for zGNRs to preserve the edge magnetism. C_{2}H_{4} was chosen due to two reasons: (1) experimentally C_{2}H_{4} is an important carbon resource for graphene growth^{38,39}, and thus technically it would be rather practical to use C_{2}H_{4} as terminal group for zGNRs; (2) after bonding to edges sites, the C–H bonds of C_{2}H_{4} can have hyperconjugation interaction with edge states. Our computations demonstrated that due to the multiple edge hyperconjugation interactions, sp^{2} coordinated edges of C_{2}H_{4} terminated zGNRs (C_{2}H_{4}zGNRs) can be realized at rather mild experimental conditions, and C_{2}H_{4}zGNRs can well reproduce the electronic and magnetic properties of HzGNRs.
Results
To ascertain whether the edge magnetism of zGRNs can be preserved by C_{2}H_{4 }termination, we need to determine the most stable edge configuration for C_{2}H_{4}zGNRs firstly. In our computations, C_{2}H_{4}zGNR with a width parameter of 8 (8C_{2}H_{4}zGNR) was chosen as a representative (Figure 1). For simplicity, two edges of 8C_{2}H_{4}zGNR were set to have the same configuration. Following the previous convention^{34,35,36}, the edge configurations are denoted with , where n_{i} = 1, 2 stands for the number of C_{2}H_{4} molecules bonded to the ith edge site, and x is the number of edge sites in a unit cell. Six edge configurations, including z_{11}, z_{121}, z_{11121}, z_{22}, z_{1122}, and z_{111122} were considered. Here note that different from H, one C_{2}H_{4} can bond to two edge sites, thus some edge configurations consisting of odd number of sp^{2} edge sites, such as z_{12} and z_{1112}, are only available for H termination but not available for C_{2}H_{4} termination. Moreover, we also considered the reconstructed zigzag edge, in which two hexagons transform into a pentagon and a heptagon, denoted as z(57)^{19}. This haeckelite edge structure has been observed experimentally^{40}. For z(57), two possible edge configurations, including z(57)_{11} and z(57)_{22}, were investigated.
To compare the stability of these edge configurations, we first computed the edge formation energy () for each configuration, which is defined as: where , , and are the total energies of the nanoribbon, one carbon atom of graphene, and one C_{2}H_{4} molecule, respectively. and are the numbers of carbon atoms and C_{2}H_{4} groups in the supercell, respectively. L is the length of one unit cell. According to this definition, the edge configurations with lower values are more favorable energetically at 0 K. For comparison, the of 8HzGNR with pure sp^{2} termination (z(H)_{1}) was also computed. The computed of all the considered edge configurations and their corresponding ground states are summarized in Table 1. According to our computations, for C_{2}H_{4}zGNRs, the nonmagnetic edge configuration z_{111122} has the lowest value of , tightly followed by the pure sp^{2} coordinated edge configuration z_{11}. Especially, the of z_{11} is lower than z(H)_{1}, implying that C_{2}H_{4} termination could produce more stable sp^{2} coordinated edge than hydrogen termination.
However, the content of C_{2}H_{4} changes under real experimental conditions, and the chemical potential of C_{2}H_{4} should be taken into account. Thus, we evaluated the relative stability of different edge configurations for 8C_{2}H_{4}zGNR under real experimental conditions by comparing their respective Gibbs formation energy (), which is defined as: where is a function of the temperature T and the partial C_{2}H_{4} gas pressure P, and can be expressed as: and are the enthalpy and entropy at the pressure = 1 bar, respectively, the values of which at T = 298 K are obtained from the textbook^{41}. Then, we plotted the curve of for 8C_{2}H_{4}zGNR with different edge configurations as a function of in Figure 2. According to the above definition, the most stable edge configuration should have the lowest value of within a given value of .
Several conclusions can be drawn from Figure 2. First, the of z_{121}, z_{11121}, z(57)_{11}, or z(57)_{22} could never be the lowest at any given value of , indicating that these four edge configurations have no chance to be realized under real experimental conditions. Especially, the unfavorability of z(57)_{11} and z(57)_{22} suggests that the reconstruction of zigzag edge can be suppressed under the C_{2}H_{4} environment. Second, the of z_{22} is the lowest when is larger than 2.03 eV, indicating that z_{22} can be stabilized only at extremely high C_{2}H_{4} concentration. When is in the range of [0.44, 2.03] eV, z_{1122} becomes stable. z_{111122}, which has the lowest value of , is stable only in a rather narrow range of [−0.11, 0.44]. When < −0.11 eV, z_{11} becomes the most stable edge configuration. At room temperature, −0.11 eV of corresponds to a C_{2}H_{4} pressure (P) of 2.45 bar. In other words, if the C_{2}H_{4} pressure can be controlled to be lower than 2.45 bar at room temperature, which is experimentally rather feasible, the pure sp^{2} coordinated edges can be stabilized. In sharp contrast, pure sp^{2} coordinated edges of HzGNRs can be stabilized only at extremely low hydrogen concentration and thus unlikely to be realized. Therefore, C_{2}H_{4} is superior to hydrogen as a terminal group for zGNRs in terms of generating pure sp^{2} coordinated edges and preserving the edge magnetism. Experimentally, C_{2}H_{4}zGNRs can be synthesized via lithographic patterning of graphene under the C_{2}H_{4} atmosphere, or by etching the edges of preobtained zGNRs using C_{2}H_{4} gas.
After establishing that pure sp^{2} coordinated edges of zGNRs, namely, z_{11}, can be produced by C_{2}H_{4} termination at mild experimental conditions, we quite wonder the magnetic and electronic properties of C_{2}H_{4}zGNRs with z_{11} edge configuration. The same as HzGNRs, our computations also revealed an AFM ground state for C_{2}H_{4}8zGNRs, which is 2 and 24 meV/edge atom lower in energy than the FM and NM states, respectively. For comparison, the AFM state of 8HzGNR is 2 and 26 meV/edge atom lower in energy than the FM and NM states, respectively.
Figure 3a presents the spatial distribution of the charge difference between αspin and βspin for 8C_{2}H_{4}zGNR. The magnetization per edge atom of C_{2}H_{4}8zGNR is 0.13 μB (0.15 μB for 8HzGNR), decaying gradually from two edges to the inner. Therefore, the stability and magnitude of edge magnetism of C_{2}H_{4}zGNRs are comparable to those of HzGNRs.
Then, we computed the band structure of 8C_{2}H_{4}zGNR in the AFM state. As shown in Figure 3b, 8C_{2}H_{4}zGNR has a 0.42 eV (0.45 eV for 8HzGNR) band gap for both spin channels. Especially, the spinpolarized π and π* bands are also quite flat near the Fermi level, a known symbol of edge states.
In lights of the above results, we conclude that C_{2}HzGNRs can well reproduce the electronic and magnetic properties of those HzGNRs. Therefore, C_{2}H_{4}zGNRs may realize many fancy properties previously predicted for HzGNRs, such as halfmetallicity^{13}. Our computations demonstrated that under a 0.7 V/Å transverse electric field, 8C_{2}HzGNR with z_{11} edge configuration can be tuned into halfmetallic. Here note that generalized gradient approximation (GGA) usually predicts a much higher critical value of electric filed than local density approximation (LDA)^{42}.
Discussion
Although we have determined that pure sp^{2} coordinated edges of zGNRs, namely, z_{11}, can be produced by C_{2}H_{4} termination at rather mild experimental conditions, there is an obvious question to be explained: why does z_{121} have a relatively large value of and is unfavorable on the whole range of thermodynamics conditions? As revealed by Wassmann et al.^{34}, z_{121} has the lowest value of among all the edge configurations of HzGNRs, and is stable in a rather boarder range of thermodynamic conditions. Then, what makes the difference for C_{2}H_{4} and hydrogen terminations? Actually this difference is simply due to the steric effect of C_{2}H_{4} molecules. As shown in Figure 1, in a unit cell of z_{121}, two C_{2}H_{4} molecules bond to an edge site of zGNR together to generate a sp^{3} edge site, and the rest two carbon atoms of C_{2}H_{4} molecules bond to two edge sites of zGNR to generate two sp^{2} edge sites. Due to the strong steric effect, two C_{2}H_{4} molecules are pushed up and down, respectively, at the sp^{3} edge sites. Thus, the strain imposed on two sp^{2} edge sites causes a serious edge distortion (Figure S1 of supplementary information) and consequently increases the . Here note that for z_{111122} and z_{1122}, in which continuous two sp^{3} coordinated edge sites are present, the edge distortion is absent. Since z_{121} has the same C_{2}H_{4} density () as z_{111122} but a higher than z_{111122}, z_{121} could never be the most stable edge configuration in any given value of according to equation (2), and is hence excluded from the phase diagram.
Besides the unstability problem of z_{121}, there are still some concerns to be addressed. For example, for these stable edge configurations on the whole range of thermodynamic conditions, why are z_{11} and z_{22} magnetic while z_{1111122} and z_{1122} are nonmagnetic? Moreover, why does z_{11 }have a rather low , while z_{22} has a higher than other stable edge configurations? Why does z_{111122} has an even lower than z_{11}?
The above concerns can be satisfactorily understood by the Clar's rule^{43,44}, which has been successfully applied for accounting the π electron distribution and reactivity of polycyclic aromatic hydrocarbons (PAH)^{45,46,47} and many carbon nanomaterials^{48,49,50,51,52,53}. According to the Clar's rule, the sp^{2} coordinated carbon atoms of a closeshell PAH can be formulated into two structural units that are linked by single bonds, benzenoid aromatic ring and olefinic double bond, wherever necessary. A PAH is the most stable when it has the greatest number of benzenoid rings. The unusual stability of graphene can be understood as all carbon atoms are benzenoid with a maxima density of benzenoid rings of 1/3. Without considering the steric effect of termination groups (as for Hterminated zGNRs), z_{121} should be the most stable edge configuration for zGNRs since it enables that zGNRs have the same density of benzenoid rings as graphene (Figure S2 of supplementary information). However, for C_{2}H_{4}terminated zGNRs, the enhanced stabilization from aromaticity is overwhelmed by the steric effect; thus the z_{121} configuration is not favored anymore.
For zGNRs with density of benzenoid rings lower than 1/3, there is a competition between maximizing the density of benzenoid rings for the bulk and imposing unsaturated carbon atoms on the edges. Taking z_{11} of 8C_{2}H_{4}zGNR as an example, if we assume that all its carbon atoms are saturated with four chemical bonds with neighboring atoms, z_{11} will form the quinonoid structure with two double bonds in each hexagon (Figure S3 of supplementary information), and the formation of benzenoid ring in z_{11} is completely forbidden. However, the quinonoid structure is quite unstable. In this case, z_{11} would impose two unpaired electrons on each edge in a 1×1×3 supercell, and the resulted nanoribbon has the same density of benzenoid rings (1/3) as graphene (Figure 4a). The energy gain from the resonance favors this electronic structure as the ground state. Therefore, z_{11} has a magnetic ground state with unpaired electrons on the edges. Moreover, the unpaired electrons of z_{11} have subtle hyperconjugation interactions with neighboring C = C bonds and C–H bonds of C_{2}H_{4}, which could stabilize the unpaired electrons (thus stabilizing the edge). Besides, there is also hyperconjugation interaction between C = C bonds and C–H bonds, which could also contribute to the stability of the edge. Thus, the multiple hyperconjugation interactions on the edge should be responsible for the rather favorable of z_{11}. In contrast, in HzGNRs, there only exists the hyperconjugation interaction between unpaired electrons and C = C bonds, resulting in a larger for z(H)_{1} than z_{11}.
Similarly, by imposing four unpaired electrons to the outer sp^{2} carbon atoms on each edge in a 1×1×3 supercell, the interior carbon atoms of z_{22} can also maximize the density of benzenoid rings (Figure 4b). In contrast to z_{11}, only half of the unpaired electrons of z_{22} can have hyperconjugation interaction with C = C double bonds while the rest are localized. Such densely localized unpaired electrons on the edges result in a very high for z_{22}. These analyses can also explain why the magnetization of fully saturated edges of zGNRs is larger than the sp^{2} coordinated edges^{54}.
In contrast to z_{11} and z_{22}, z_{111122} can achieve the maximum density of benzenoid rings without imposing unpaired electron on the edge (Figure 4c). Moreover, z_{111122} can be further stabilized by the conjugation interaction between edge C = C double bonds. It is known that generally conjugation stabilization is stronger than hyperconjugation stabilization^{55,56}. As a result, z_{111122} favors the nonmagnetic ground state and has a lower than z_{11}. For z_{1122}, when the edge carbon atoms are all saturated, the inner carbon atoms can only be partially benzenoid (Figure 4d). However, imposing unpaired electron on edge cannot increase the number of benzenoid rings. Therefore, z_{1122} also favors the nonmagnetic ground state.
Finally, an interesting question arises: is pure sp^{2} termination a guarantee for edge magnetism? Taking an example, like hydrogen and C_{2}H_{4}, C_{2}H_{2} can only form single bonds with edge carbon atoms, and intuitively may not disturb the π electron system of zGNR. Then, is C_{2}H_{2}, the dehydrogenation product of C_{2}H_{4}, also an ideal terminal group for zGNRs?
To address this concern, we investigated two edge configurations for C_{2}H_{2} terminated 8zGNRs (8C_{2}H_{2}zGNR), including z_{11} and z_{111122}. In contrast to 8C_{2}H_{4}zGNR, z_{11} of 8C_{2}H_{2}zGNR (−0.205 eV/Å) has a lower than z_{111122} (−0.196 eV/Å). Moreover, our computations revealed that both z_{11} and z_{111122} of 8C_{2}H_{2}zGNR have a nonmagnetic ground state. At first glance, this is rather surprising. The nonmagnetic z_{111122} of 8C_{2}H_{2}zGNR can be understood in the same away as discussed above for 8C_{2}H_{4}zGNR. However, why is z_{11} of 8C_{2}H_{2}zGNR also nonmagnetic? This seemingly unexpected result can also be understood by the competition between hyperconjugation, conjugation and maximizing benzenoid rings.
In contrast to the general intuition, C_{2}H_{2} terminations significantly differ from C_{2}H_{4} terminations, since C_{2}H_{2} can couple to the π electron system of zGNR by forming double bonds with edge sites in the dominant resonance structure (Figure 5a): in a 1×1×3 supercell of z_{11} of 8C_{2}H_{2}zGNR, two C_{2}H_{2} molecules each form two CC single bonds with two edge sites in each edge, but the third C_{2}H_{2} molecule forms two C = C bonds with two edge sites. With the help of newly formed C = C bonds, the carbon atoms of 8C_{2}H_{2}zGNR can achieve a density of benzenoid rings of 2/7 without imposing unpaired electron on the edge.
We can also get the resonance structure (Figure 5b) by imposing two unpaired electrons on each edge, in which the density of benzenoid rings can be increased to the maximum (1/3), the same as z_{11} of 8C_{2}H_{4}zGNR. However, this magnetic state is not favorable energetically since the conjugation in the nonmagnetic state overwhelms the energy gain by maximizing the benzenoid rings. In the nonmagnetic state, the C = C bonds at edges have conjugation interaction along the zigzag direction; in the magnetic state, there exists hyperconjugation interaction between unpaired electrons and neighboring C = C bonds. The much stronger conjugation stabilization in the nonmagnetic state over the hyperconjugation stabilization in the magnetic state overcompensates the unfavorability of the nonmagnetic state with fewer benzenoid rings, which leads to a nonmagnetic ground state.
Another question is why z_{11 }8C_{2}H_{2}zGNR has a lower than z_{111122}. Note that z_{111122} has the same density of benzenoid rings as z_{11}, and it also has the conjugation stabilization among edge C = C bonds (Figure S4 of supplementary information). However, the conjugation interaction in z_{111122} is not continuous in the zigzag direction while the conjugation interaction in z_{11} is continuous. Therefore, z_{111122} has a slightly lower than z_{11}.
Overall, though C_{2}H_{2} termination can produce sp^{2} coordinated edges with energetically very favorable , C_{2}H_{2} can suppress the edge magnetism by coupling to the πelectron system of zGNR, which disqualifies C_{2}H_{2} as an ideal terminal group for zGNRs. Therefore, even pure sp^{2} termination is not a guarantee for edge magnetism.
To summarize, by means of DFT computations, we systemically studied the energetics and electronic properties of C_{2}H_{4}zGNRs with different edge configurations. The pure sp^{2} coordinated edges, namely z_{11}, can be stabilized at rather mild experimental conditions. Especially, such C_{2}H_{4}zGNRs with sp^{2} edges can well reproduce the magnetic and electronic properties of HzGNRs. Therefore, C_{2}H_{4} is an ideal terminal group for zGNRs in terms of preserving the edge magnetism. Interestingly, the edge electronic structures of C_{2}H_{4}zGNRs can be well interpreted by employing the Clar's rule. Further analysis identified multiple hyperconjugation interactions as the key factor responsible for enhanced stability of the sp^{2} coordinated edges. Moreover, we demonstrated that pure sp^{2} termination can not guarantee edge magnetism for zGNRs, for example, C_{2}H_{2} termination can couple to the πelectron system of zGNRs, and suppress the magnetism. These findings would deepen our basic knowledge of graphene electronics and provide a feasible way for realizing zGNRbased spintronics.
Methods
DFT computations were performed using the planewave technique implemented in Vienna ab initio simulation package (VASP)^{57}. The ionelectron interaction is described using the projectoraugmented plane wave (PAW) approach^{58,59}. GGA expressed by PBE functional^{60} and a 400 eV cutoff for the planewave basis set were adopted in all computations. Selfconsistent field (SCF) calculations were conducted with a convergence criterion of 10^{−4} eV on the total energy and the electron density. 1D periodic boundary condition (PBC) was applied along the z direction in order to simulate their infinitely long systems. The minimum distance between two ribbons is larger than 15 Å, which can safely avoid the interaction between two ribbons. The Brillouin zone was sampled with a 1×1×10 Γ centered k points. Based on the optimized geometric structures, 21 kpoints were used to obtain the band structures.
References
 1.
Novoselov, K. S. et al. Electric field effect in atomically thin carbon films. Science 306, 666–669 (2004).
 2.
Novoselov, K. S. et al. Twodimensional atomic crystals. Proc. Natl. Acad. Sci. U.S.A. 102, 10451–10453 (2005).
 3.
Novoselov, K. S. et al. A roadmap for graphene. Nature 490, 192–200 (2012).
 4.
Georgakilas, V. et al. Functionalization of graphene: covalent and noncovalent approaches, derivatives and applications. Chem. Rev. 112, 6156–6214 (2012).
 5.
Tang, Q., Zhou, Z. & Chen, Z. F. Graphenerelated nanomaterials: tuning properties by functionalization. Nanoscale 5, 4541–4583 (2013).
 6.
Son, Y.W., Cohen, M. L. & Louie, S. G. Energy gaps in graphene nanoribbons. Phys. Rev. Lett., 97, 216803 (2006).
 7.
Barone, V., Hod, O. & Scuseria, G. E. Electronic structure and stability of semiconducting graphene nanoribbons. Nano Lett. 6, 2748–2754 (2006).
 8.
Li, X. L., Wang, X. R., Zhang, L., Lee, S. W. & Dai, H. J. Chemically derived, ultrasmooth graphene nanoribbon semiconductors. Science 319, 1229–1232 (2008).
 9.
Han, M. Y., Özyilmaz, B., Zhang, Y. & Kim, P. Energy bandgap engineering of graphene nanoribbons. Phys. Rev. Lett. 98, 206805 (2007).
 10.
Fujita, M., Wakabayashi, K., Nakada, K. & Kusakabe, K. Peculiar localized state at zigzag graphite edge. J. Phys. Soc. Jpn. 65, 1920–1923 (1996).
 11.
Nakada, K., Fujita, M., Dresselhaus, G. & Dresselhaus, M. S. Edge state in graphene ribbons: nanometer size effect and edge shape dependence. Phys. Rev. B 54, 17954–17961 (1996).
 12.
Wakabayashi, K., Sigrist, M. & Fujita, M. Spin wave mode of edgelocalized magnetic states in nanographite zigzag ribbons. J. Phys. Soc. Jpn. 67, 2089–2093 (1998).
 13.
Son, Y.W., Cohen, M. L. & Louie, S. G. Halfmetallic graphene nanoribbons. Nature 444, 347–349 (2006).
 14.
Kan, E. J., Li, Z. Y., Yang, J. L. & Hou, J. G. Halfmetallicity in edgemodified zigzag gaphene nanoribbons. J. Am. Chem. Soc. 130, 4224–4225 (2008).
 15.
Li, Y. F., Zhou, Z., Shen, P. W. & Chen, Z. Spin gapless semiconductormetalhalfmetal properties in nitrogendoped zigzag graphene nanoribbons. ACS Nano, 3, 1952–1958 (2009).
 16.
Jiang, D. E., Sumpter, B. G. & Dai, S. Unique chemical reactivity of a graphene nanoribbon's zigzag edge. J. Chem. Phys. 126, 134701 (2007).
 17.
Okada, S. Energetics of nanoscale graphene ribbons: edge geometries and electronic structures. Phys. Rev. B 77, 041408 (2008).
 18.
Huang, B. et al. Quantum manifestations of graphene edge stress and edge instability: a firstprinciples study. Phys. Rev. Lett. 102, 166404 (2009).
 19.
Koshinen, P., Malola, S. & Häkkinen, H. Selfpassivating edge reconstructions of graphene. Phys. Rev. Lett. 101, 115502 (2008).
 20.
Kastler, M., Schmidt, J., Pisula, W., Sebastiani, D. & Müllen, K. From armchair to zigzag peripheries in nanographenes. J. Am. Chem. Soc. 128, 9526–9534 (2006).
 21.
Cai, J. M. et al. Atomically precise bottomup fabrication of graphene nanoribbons. Nature 466, 470–473 (2010).
 22.
Jiao, L. Y., Zhang, L., Wang, X. R., Diankov, G. & Dai, H. J. Narrow graphene nanoribbons from carbon nanotubes. Nature 458, 877–880 (2009).
 23.
Kosynkin, D. V. et al. Longitudinal unzipping of carbon nanotubes to form graphene nanoribbons. Nature 458, 872–876 (2009).
 24.
Jiao, L. Y., Wang, X. R., Diankov, G., Wang, H. & Dai, H. J. Facile synthesis of highquality graphene nanoribbons. Nature Nanotechnol. 5, 321–325 (2010).
 25.
CamposDelgado, J. et al. Bulk production of a new form of sp^{2} carbon: crystalline Ggraphene. Nano Lett. 8, 2773–2778 (2008).
 26.
MorelosGómez, A. et al. Clean nanotube unzipping by abrupt thermal expansion of molecular nitrogen: graphene nanoribbons with atomically smooth edges. ACS Nano. 6, 2261–2271 (2012).
 27.
Kobayashi, Y., Fukui, K., Enoki, T. & Kusakabe, K. Edge state on hydrogenterminated graphite edges investigated by scanning tunneling microscopy, Phys. Rev. B 73, 125415 (2006).
 28.
Riter, K. A. & Lyding, J. W. The influence of edge structure on the electronic properties of graphene quantum dots and nanoribbons. Nat. Mater. 8, 235–242 (2009).
 29.
Tao, C. et al. Spatially resolving edge states of chiral graphene nanoribbons. Nat. Phys. 7, 616–620 (2011).
 30.
Pan, M. et al. Topographic and spectroscopic characterization of electronic edge states in CVD grown graphene nanoribbons. Nano Lett. 12, 1928–1933 (2012).
 31.
Zhang, X. et al. Experimentally engineering the edge termination of graphene nanoribbons. ACS Nano. 7, 198–202 (2013).
 32.
Joseph Joly, V. L. et al. Observation of magnetic edge state in graphene nanoribbons. Phys. Rev. B 81, 245428 (2010).
 33.
Konishi, A. et al. J. Am. Chem. Soc. 135, 1430–1437 (2013).
 34.
Wassmann, T., Seitsonen, A. P., Saitta, A. M., Lazzeri, M. & Mauri, F. Structure, stability, edge states, and aromaticity of graphene ribbons. Phys. Rev. Lett. 101, 096402 (2008).
 35.
Seitsonen, A. P., Saitta, A. M., Wassmann, T., Lazzeri, M. & Mauri, F. Structure and stability of graphene nanoribbons in oxygen, carbon dioxide, water, and ammonia. Phys. Rev. B 82, 115425 (2010).
 36.
Chia, C.I. & Crespi, V. H. Stabilizing the zigzag edge: graphene nanoribbons with sterically constrained terminations. Phys. Rev. Lett. 109, 076802 (2012).
 37.
Plasser, F. et al. The multiradical character of one and twodimensional graphene nanoribbons. Angew. Chem. Int. Ed. 52, 2581–2584 (2013).
 38.
Gao, L., Guest, J. R. & Guisinger, N. P. Epitaxial graphene on Cu(111). Nano Lett. 10, 3512–3516 (2010).
 39.
MartinezGalera, A., Brihuega, I. & GómezRodríguez, J. M. Ethylene irradiation: a new route to grow graphene on low reactivity metals. Nano Lett. 11, 3576–3580 (2011).
 40.
Koskinen, P., Malola, S. & Häkkinen, H. Evidence for Graphene Edges Beyond Zigzag and Armchair. Phys. Rev B 80, 073401 (2009).
 41.
Lide, D. R. CRC Handbook of chemistry and physics. (CRC, Boca Raton, 2008).
 42.
Li, Y., Zhou, Z., Shen, P. & Chen, Z. Electronic and magnetic properties of hybrid graphene nanoribbons with zigzagarmchair heterojunctions. J. Phys. Chem. C 116, 208–213 (2012).
 43.
Clar, E. Polycyclic hydrocarbons. (Academic Press: New York, 1964).
 44.
Clar, E. The aromatic sextet. (Wiley: London, 1972).
 45.
Watson, M. D., Fechtenkötter, A. & Müllen, K. Big is beautiful−“aromaticity” revisited from the viewpoint of macromolecular and supramolecular benzene chemistry. Chem. Rev. 101, 1267–1300 (2001).
 46.
Randic, M. Aromaticity of polycyclic conjugated hydrocarbons. Chem. Rev. 103, 3449–3606 (2003).
 47.
Popov, I. A. & Bolydrev, A. I. Chemical Bonding in Coronene, Isocoronene, and Circumcoronene. Eur. J. Org. Chem. 3485–3491 (2012).
 48.
Wassmann, T., Seitsonen, A. P., Saitta, A. M., Lazzeri, M. & Mauri, F. Clar's theory, πelectron sistribution, and deometry of graphene nanoribbons. J. Am. Chem. Soc. 132, 3440–3451 (2010).
 49.
Gao, X. F., Zhao, Y. L., Liu, B., Xiang, H. J. & Zhang, S. B. πbond maximization of graphene in hydrogen addition reactions. Nanoscale. 4, 1171–1176 (2012).
 50.
Popov, I. A., Bozhenko, K. V. & Boldyrev, A. I. Is graphene aromatic? Nano Res. 5, 117–123 (2012).
 51.
Popov, I. A. & Boldyrev, A. I. Deciphering chemical bonding in a BC_{3} honeycomb epitaxial sheet. J. Phys. Chem. C 116, 3147–3152 (2012).
 52.
Popov, I. A. & Boldyrev, A. I. Chemical bonding in coronene, isocoronene, and circumcoronene. Eur. J. Org. Chem. 2012, 3485–3491 (2012).
 53.
Li, Y. & Chen, Z. Patterned partially hydrogenated graphene (C_{4}H) and its onedimensional analogues: a computational study. J. Phys. Chem. C. 116, 4526–4534 (2012).
 54.
Kudin, K. N. Zigzag graphene nanoribbons with saturated edges. ACS Nano 2, 516–522 (2008).
 55.
Jarowski, P. D., Wodrich, M. D., Wannere, C. S., Schleyer, P. v. R. & Houk, K. N. How large is the conjugative stabilization of diynes? J. Am. Chem. Soc. 126, 15036–15038 (2004).
 56.
Fernández, I. & Frenking, G. Direct estimate of the strength of conjugation and hyperconjugation by the energy decomposition analysis method. Chem.–Eur. J. 12, 3617–3629 (2006).
 57.
Kresse, G. & Hafner, J. Ab initio molecular dynamics for liquid metals. Phys. Rev. B 47, 558–561 (1993).
 58.
Blöchl, P. E. Projector augmentedwave method. Phys. Rev B 50, 17953–17979 (1994).
 59.
Kresse, G. & Joubert, D. From ultrasoft pseudopotentials to the projector augmentedwave method. Phys. Rev B 59, 1758–1775 (1999).
 60.
Perdew, J. P., Burke, L. & Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 77, 3865–3868 (1996).
Acknowledgements
Support by Department of Defense (Grant W911NF1210083) and NSF (Grant EPS1010094) in the US and the 111 Project (B12015) in China is gratefully acknowledged. CRC acknowledges the financial support of NSF NSEC Center for Hierarchical Manufacturing Grant No. CHM  CMMI – 0531171.
Author information
Affiliations
Department of Chemistry, Institute for Functional Nanomaterials, NASAURC Center for Advanced Nanoscale Materials, University of Puerto Rico, Rio Piedras Campus, San Juan, PR 00931
 Yafei Li
 , Carlos R. Cabrera
 & Zhongfang Chen
Computational Centre for Molecular Science, Key Laboratory of Advanced Energy Materials Chemistry (Ministry of Education), Institute of New Energy Material Chemistry, Nankai University, Tianjin 300071, China
 Zhen Zhou
Authors
Search for Yafei Li in:
Search for Zhen Zhou in:
Search for Carlos R. Cabrera in:
Search for Zhongfang Chen in:
Contributions
Z.C. conceived the initial idea of this research. Y.L. demonstrated the initial idea and collected all the data. Z.Z. and C.C. participated in the discussion. Y.L. and Z.C. drafted the paper, and all coauthors revised the manuscript. Z.C. guided the work.
Competing interests
The authors declare no competing financial interests.
Corresponding author
Correspondence to Zhongfang Chen.
Supplementary information
Word documents
 1.
Supplementary Information
Supplementary Information
Rights and permissions
This work is licensed under a Creative Commons AttributionNonCommercialNoDerivs 3.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/byncnd/3.0/
To obtain permission to reuse content from this article visit RightsLink.
About this article
Further reading

1.
Onsurface synthesis of graphene nanoribbons with zigzag edge topology
Nature (2016)

2.
Preserving the edge magnetism of graphene nanoribbons by iodine termination: a computational study
Theoretical Chemistry Accounts (2014)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.