4480
J. Phys. Chem. C 2008, 112, 4480-4485
Cycloadditions to Control Bond Breaking in Naphthalenes, Fullerenes, and Carbon Nanotubes: A First-Principles Study Young-Su Lee*,† and Nicola Marzari Department of Materials Science and Engineering, and Institute for Soldier Nanotechnologies, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 ReceiVed: April 20, 2007; In Final Form: December 15, 2007
Covalent functionalizations represent a very promising avenue to engineer or manipulate carbon nanotubes. However, in metallic tubes the electrical conductance can drop by several orders of magnitude following functionalization, due to sp3 rehybridization of the sidewall carbons that strongly disrupts the conjugated π-network. First-principles calculations have predicted that some divalent functional groups, carbenes or nitrenes, can instead recover the original sp2 hybridization and perfect metallic conductance of the pristine tubes. In these cycloaddition reactions, the extra bond added by the functional group with each of the bridgehead carbons is compensated by a breaking of the sidewall bond between them, restoring in the process the original sp2 environment. We characterize this bond-breaking chemistry with extensive first-principles calculations and highlight its sensitivity to the orientation of the π-electron system of the chosen addend. Using dinitrocarbene as a model case, we show that the bridgehead carbon atoms can reversibly rehybridize from sp2 to sp3 in response to the π orientation of the addends. These results suggest a novel route to modulating the electronic properties of carbon nanotubes that is based on orbital rehybridization and that can be directed with optical or electrochemical means.
Introduction For fullerenes1 and carbon nanotubes2 alike, covalent functionalizations have been an indispensable tool for manipulation and an avenue to tailor their electronic, optical, and electrochemical properties. Similarities in bonding allow these carbon allotropes to share many of the functionalization routes proposed.3,4 Although the bonding structure and its correlation to physical properties have been discussed extensively for the case of functionalized fullerenes, an experimental identification of the bonding structure for functionalized carbon nanotubes is still in its early stages, partly because of the relatively short history of nanotube functionalizations but also because of the difficulties in making pure and homogeneous samples. Recent theoretical studies5-7 have predicted that the local bonding configuration can significantly affect the electronic structure of functionalized carbon nanotubes. Most notably, the cyclopropane ring structure introduced by [2 + 1] cycloadditions of carbenes or nitrenes can either remain intact, or, as nanotube curvature increases, can lead to cleavage of the sidewall bond, leading to two valence tautomeric forms that display distinct electronic characteristics and markedly different transport properties in metallic tubes.7 In fact, the electronic properties of functionalized products closely resemble those of the pristine tube when the bond between the two bridgehead atoms is broken. The rationale offered is that the two sidewall carbons revert to sp2 hybridization once the bond between themselves is broken, thus recovering the original π-electron system. This is in marked contrast with the sp3 rehybridization and loss of π electrons found upon addition of monovalent chemical groups * Corresponding author. E-mail:
[email protected]. † Current address: Materials Science and Technology Research Division, Korea Institute of Science and Technology, Seoul 136-791, Republic of Korea.
in other functionalization schemes, where all sidewall bonds remain intact8 and lead to a several orders-of-magnitude decrease in conductance for metallic tubes.9 This characteristic behavior of cycloadditions has been studied extensively in organofullerenes: [5,6]-open adducts retain the original 60 π electrons, whereas [6,6]-closed adducts are left with 58 π electrons.10,11 Such connections between hybridizations and conductance emphasizes the importance of identifying or controlling the local bonding structure to understand or engineer the physical properties of functionalized carbon nanostructures, from carbon nanotubes to graphene nanoribbons. Although experimental identification of the bonding structure in [2 + 1] cycloaddition products has not yet been achieved, recent electrical transport measurement on chemically modified carbon nanotubes12 detected only a small decrease in electrical conductivity upon redox cycling, attributed to the formation of an oxygen bridge (ether structure) that resembles the carbene bridges discussed in ref 7. In this work, we characterize the structure and electronic structure of cycloaddition functionalizations on model carbon compounds, from annulenes to fullerenes to nanotubes, using extensive first-principles calculations, and we demonstrate that the orientation of the unsaturated π-system of the addend is the key factor that determines the valence tautomeric equilibrium between the bond-open and the bond-closed configurations. In fact, it will be seen that when the plane of the π system bisects the bond between two bridgehead carbons the interaction with the Walsh orbitals in the cyclopropane ring is strengthened, stabilizing the bond-closed configuration.13,14 The role of π orientation is demonstrated taking dinitrocarbene as a test case. Although this is by no means a unique choice, it is optimally suited to the problem studied because π orientation can be changed by rotating the nitro groups without changing the chemical nature of the addend; the rotation effect is also
10.1021/jp073067i CCC: $40.75 © 2008 American Chemical Society Published on Web 02/29/2008
Cycloadditions to Control Bond Breaking
J. Phys. Chem. C, Vol. 112, No. 12, 2008 4481
Figure 1. Left: molecular structure of a 11,11-dinitro-1,6-methano[10]annulene with the two NO2 groups in their equilibrium positions (henceforth labeled 1a). The molecule has C2V symmetry, and the four N-O bonds are equivalent. Right: structure obtained when the two NO2 groups are forced to rotate and placed in the xz plane (henceforth labeled 1b).
amplified by the strong electron-withdrawing nature of the nitro group.13 We thus characterize and compare the geometry, energy, and electronic structure of dinitrocarbene-functionalized naphthalenes, fullerenes, and armchair carbon nanotubes in the two possible conformations: the energetically stable one and that obtained by rotating the nitro groups. Computational Details All of our electronic structure calculations and structural optimizations are performed within density-functional theory in the Perdew-Burke-Ernzerhof generalized-gradient approximation (PBE-GGA).15 We use ultrasoft pseudopotentials16 with a planewave basis set and a cutoff energy of 30 Ry for the wavefunctions and 240 Ry for the charge density, as implemented in the Quantum-ESPRESSO distribution.17 The Wannier function analysis18 is performed using the Wannier90 package.19 Annulenes and methanofullerenes are placed in simple cubic supercells with sides of 15.88 and 21.17 Å , respectively. For functionalized (n,n) armchair carbon nanotubes, the supercell used contains 12 n carbon atoms plus one carbene group. A 1 × 1 × 4 regular mesh of k points is used for structural optimizations, and a denser 1 × 1 × 8 mesh is used for singlepoint energy calculations in the optimized structures, using in both cases the cold smearing technique with a temperature of 0.03 Ry.20 Results and Discussion 1,6-Methano[10]annulenes. In its most stable configuration 1a, 11,11-dinitro-1,6-methano[10]annulene displays a bond-open form, with four oxygen atoms positioned at the symmetrically equivalent sites (C2V point group), as shown in the left panel of Figure 1. If the two NO2 groups are forced to rotate such that all atoms lie in the xz plane (1b), then the bisnorcaradiene form is stabilized, as shown in the right panel of Figure 1 (throughout the text, a indicates the NO2 groups in their equilibrium configuration, always parallel to the carbon rings, and b indicates the NO2 groups forced in the rotated configuration). Configuration b is unstable; once the NO2 groups are allowed to move out of the xz plane, they rotate back to the a position. The potential energy surfaces as a function of the C1-C6 bond length (d1,6) for these two isomers are shown in Figure 2.7 The molecular structure at each point is obtained by fully relaxing all of the atomic coordinates at any given d1,6 under the
Figure 2. Potential energy surface of 1a (solid circle) and 1b (open circle) as a function of d1,6. A rotation of the NO2 groups can shift the equilibrium configuration from the annulene to the bisnorcaradiene form. The zero-energy point is the 1a energy minimum; the 1b minimum is 1.21 eV above the 1a minimum.
constraint of preserving C2V symmetry (e.g., this ensures that for 1b the NO2 groups remain in the xz plane during the structural optimizations.). We note that the equilibrium configuration of 1b is 1.21 eV higher in energy than that of 1a. The structural parameters are summarized in Table 1. It is immediately evident that the equilibrium d1,6 undergoes a dramatic change upon reorientation of the π system, from 2.29 to 1.52 Å : this corresponds to an unambiguous switch from a bond-open to a bond-closed form. The C-C distances in 1a show a minor deviation from those in naphthalene, suggesting aromatic character for 1a; on the contrary, alternating single and double bond character is more obvious in 1b. Although dicyanocarbene is one of the well-known chemical groups that stabilizes a closed form,21 the calculations above show that the stabilization induced by rotating the dinitrocarbene groups is even stronger. In fact, although a double minimum is found theoretically for dicyanocarbene with only a small energy difference between the open and the closed forms (
