Fullerenes, Nanotubes and Carbon Nanostructures

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Fullerenes, Nanotubes and Carbon Nanostructures

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Tight-Binding Simulation of Cubane C8H8, Methylcubane C9H10 and Cubane-Based Nanostructures M. M. Maslova a Moscow Engineering Physics Institute (State University), Moscow, Russia Online publication date: 03 December 2010

To cite this Article Maslov, M. M.(2011) 'Tight-Binding Simulation of Cubane C8H8, Methylcubane C9H10 and Cubane-

Based Nanostructures', Fullerenes, Nanotubes and Carbon Nanostructures, 19: 1, 127 — 132 To link to this Article: DOI: 10.1080/1536383X.2010.490132 URL: http://dx.doi.org/10.1080/1536383X.2010.490132

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Fullerenes, Nanotubes, and Carbon Nanostructures, 19: 127–132, 2011 Copyright © Taylor & Francis Group, LLC ISSN: 1536-383X print / 1536-4046 online DOI: 10.1080/1536383X.2010.490132

Tight-Binding Simulation of Cubane C8 H8 , Methylcubane C9 H10 and Cubane-Based Nanostructures M. M. MASLOV

Downloaded By: [Mikhail] At: 18:33 3 December 2010

Moscow Engineering Physics Institute (State University), Moscow, Russia We have carried out quantum-mechanical calculations of the cubane C8 H8 , methylcubane C9 H10 and various cubane-based oligomers with the original nonorthogonal tight-binding potential. The temperature dependence of cubane and methylcubane lifetimes to the decomposition moment was determined. The activation energies and frequency factors of the Arrhenius equation were found. Also, geometries and energetic properties of the cubane-based oligomers were calculated. Keywords Cubane C8 H8 , cubane-based oligomers, methylcubane C9 H10 , tightbinding simulation

Introduction Cubane C8 H8 (Figure 1) was first synthesized in 1964 (1). Carbon atoms in the cubane molecule are situated in cube vertices, and the C–C–C bond angle is 90◦ , as distinct from sp3 hybrid carbon orbitals with the angle 109.5◦ . High energy content of cubane makes it a promising material for fuel elements, and the possibility of replacing the hydrogen atoms with various functional groups opens the way to the synthesis of new compounds with unique properties (2). Cubane derivative, methylcubane C9 H10 (Figure 2) (3), in which a hydrogen atom is replaced by the CH3 group, is liquid at room temperature and is thus of interest as a liquid fuel (4). Cubane-based oligomers (linear and zig-zag chains, networks and supercubane structure; see Figure 3) attract a special interest. All of these structures were built up using different cubane-based clusters (dehydrogenated cubanes) C8 Hn , where n = 0, 4, 5, 6, 7, as the building blocks, coupled to each other with strong covalent bonds. These materials have been proposed as elementary units for systems with unique novel properties (2,5,6). Also, the supercubane structure is suggested to be a “superdense” polymorph with density greater than that of diamonds (7). The main purpose of this work was to numerically simulate the cubane and methylcubane dynamics over a wide temperature range and determine their activation energies, frequency factors of the Arrhenius equation and products of their decomposition. Also we obtained geometric and energy characteristics of the different cubane-based nanostructures. Address correspondence to M. M. Maslov, Moscow Engineering Physics Institute (State University), Kashirskoe Sh. 31, Moscow 115409, Russia. E-mail: [email protected]

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Figure 1. Cubane C8 H8.

Figure 2. Methylcubane C9 H10.

Method of Analysis All calculations were performed using the nonorthogonal tight-binding total energy model (8). The decisive advantage of the tight-binding model is that the cluster evolution over a comparatively long time (on an atomic scale) of ∼1 µs can be simulated. Total potential energy of the system Epot in this model can be decomposed into the electronic orbital energy and ionic repulsive energy. The electronic orbital energy is defined as the sum of one-electron energies for the occupied states. Energy spectrum is determined from the stationary Schrödinger equation. 1S orbitals for hydrogen atoms and 2S, 2Px , 2Py , 2Pz orbitals for carbon atoms are considered. This model gives values for interatomic bonds and binding energies, that agree with the experimental data and ab initio results for different clusters and molecules Cn Hm (8). We use the method of structural relaxation for obtaining the equilibrium structures. In the context of this method, initial configuration relaxes to the local or global minimum


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129

Figure 3. Supercubane structure.

of energy under the influence of intramolecular forces only. The force acting on the atom with index k is defined as: Fk = −2

− εn ∇k ψn ∇k H S ψn − ∇k U

(1)

n

is the tight-binding Hamiltonian, where U is the classical part of the potential energy, H S is the overlap matrix, |ψn and εn are the eigenstates and eigenenergies of the tight-binding Hamiltonian, respectively. To study the evolution of the excited cubane and methylcubane molecules, we used the method of molecular dynamics with the same tight-binding potential (see (9,10) for details).

Results The calculated binding energy of atoms in cubane is Eb = 4.42 eV/atom (experimental value is Eb = 4.47 eV/atom (4)). In the methylcubane molecule, the binding energy equals to Eb = 4.37 eV/atom (we are not aware of experimental data for methylcubane). Bond lengths in the cubane are lC-C = 1.570 Å and lC-H = 1.082 Å. The bond lengths in the cubic frame of the methylcubane molecule are lC-C = 1.566; 1.571; 1.585 Å, the intercarbon bond length between the cubic frame and the methyl-radical equals to lC-C = 1.469 Å, the C-H bond length in the cubic frame is lC-H = 1.082 Å, and the C-H bond length in the attached methyl-radical is lC-H = 1.105 Å.

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The cubane decomposition starts with the transformation into the sinTricyclooctadiene (STCO) isomer and then to the fast (0.1–1 ps) conversion of STCO into the cyclooctatetraene (COT) molecule or into the bicyclooctatriene (BCT) isomer. Finally, BCT transforms into the COT or decomposes into the benzene (BEN) and acetylene. Methylcubane decomposition scheme runs in the following way. At first, the methylcubane molecule transforms to one of two isomers of methyl-STCO, and then each of them decomposes into the various isomers of methyl-BCT. Final product of the methylcubane decomposition is the methyl-COT molecule, and sometimes we can see the combinations of the BEN and propyne or the toluene and acetylene. The obtained results allow one to suggest the direction in the search for new ways of synthesis of cubane and methylcubane. Direct calculations of the cubane and methylcubane lifetimes τ at different temperatures T allowed us to find the values of the activation energy Ea and the frequency factor A in the Arrhenius equation: Ea (2) τ −1 (T) = A exp − kB T where kB is the Boltzmann constant. For the cubane these values are Ea = (1.9 ± 0.1) eV and A = 1016.03 ± 0.36 s−1 , and for the methylcubane they are Ea = (1.7 ± 0.2) eV and A = 1015.63 ± 0.53 s−1 . The values of activation energies and frequency factors found can be used to determine cubane and methylcubane lifetimes at both very high and comparatively low temperatures, where the experimental data are unavailable. Knowledge of τ (T) is vitally needed for optimization of the synthesis conditions for these clusters and the structures derived from them. We also analyzed geometries and energetics of different cubane-based structures. The binding energy Eb of linear and zig-zag chains was defined as Eb =

1 {(Ncluster − 2) E (C8 H6 ) + 2E (C8 H7 ) − Etot (chain)} Ncluster

(3)

where Ncluster is the number of clusters in the chain, Etot (chain) is the total energy of the chain, E(C8 H7 ) and E(C8 H7 ) are the energies of isolated C8 H6 and C8 H7 clusters, respectively. The binding energy Eb of the two-dimensional network was defined as Eb =

1 Ncluster

√ 2 [E1 (C8 H6 ) + E2 (C8 H6 )] + 4 Ncluster − 2 E (C8 H5 ) + 2

√ + Ncluster − 2 E (C8 H4 ) − Etot (network)

(4)

where Ncluster is the number of clusters in the network, E1 (C8 H6 ) and E2 (C8 H6 ) are the energies of isolated isomers C8 H6 , differing in positions of H atoms, E (C8 H4 ) and E (C8 H5 ) are the energies of isolated C8 H4 and C8 H5 clusters, respectively. The maximal investigated network size was 5 × 5. Figure 4 displays binding energies of linear and zig-zag chains Eb as a function of inverse number of clusters 1/Ncluster in the structure; Eb depends linearly on 1/Ncluster . By extrapolation, we obtained the binding energies and intermolecular bond lengths of the macroscopic structures (Ncluster >> 1). The values are the following 4.58; 4.89; 8.62 eV/cluster and 1.454; 1.458; 1.456 Å for linear chain, zig-zag chain and two-dimensional

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131

5.2

Eb, eV/cluster

4.8 4.4 4 3.6 3.2

0

0.1

0.2 1/Ncluster

0.3

0.4


Figure 4. Binding energies Eb of the linear (circles) and zig-zag (squares) chains versus 1/N cluster.

network, respectively. We also simulated the fragment of bulk supercubane structure. We made hydrogen passivation in order to avoid the interfacial effects. The calculated density of supercubane is only 2.7 g/cm3 (to be compared with ≈3.6 g/cm3 in diamond). Obtained value is in good agreement with ab initio calculations 2.9 g/cm3 (7). We found that supercubane is not a “superdense” polymorph. The intermolecular covalent bond in such a structure equals 1.460 Å. Note, that the intramolecular C-C bond in C8 cluster equals 1.600 Å (to be compared with 1.570 Å intramolecular C-C bond in the isolated cubane C8 H8 cluster in the context of the same model). Later we plan to make the detailed investigations of the decomposition of the 1D and 2D cubane-based oligomers.

Acknowledgments The author thanks L.A. Openov and A.I. Podlivaev for help with preparation of this work.

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8. Maslov, M. M., Podlivaev, A. I., and Openov, L. A. (2009) Nonorthogonal tight-binding model for hydrocarbons. Phys. Lett. A., 373: 1653–1657. 9. Maslov, M. M., Lobanov, D. A., Podlivaev, A. I., and Openov, L. A. (2009) Thermal stability of cubane C8 H8 . Physics of the Solid State, 51: 645–648. 10. Maslov, M. M. (2009) Simulation of the thermal decomposition of the C9 H10 methylcubane molecule. Russian Journal of Physical Chemistry B, 3: 211–215.