Molecular Mechanics Calculations of Giant- and Hyperfullerenes with Eicosahedral Symmetry

Yoshida, Mitsuho; Ōsawa, Eiji

doi:10.1080/15363839308015516

Cited by 88 publications

(33 citation statements)

References 16 publications

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“…Nevertheless, and as verified in Ref. 8, the interlayer interaction is mainly between adjacent shells. Each singleshell fullerene is now assumed to be in its ground (lowest energy) state and here we focus on its HOMO.…”

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confidence: 52%

Electronic structure of single- and multiple-shell carbon fullerenes

Lin¹,

Nori²

1994

Phys. Rev. B

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We study the electronic states of giant single-shell and the recently discovered nested multishell carbon fullerenes within the tight-binding approximation. We use two different approaches, one based on iterations and the other on symmetry, to obtain the π-state energy spectra of large fullerene cages: C240, C540, C960, C1500, C2160 and C2940. Our iteration technique reduces the dimensionality of the problem by more than one order of magnitude (factors of ∼ 12 and 20), while the symmetry-based approach reduces it by a factor of 10. We also find formulae for the highest occupied and lowest unoccupied molecular orbital (HOMO and LUMO) energies of C 60·n 2 fullerenes as a function of n, demonstrating a tendency towards metallic regime for increasing n. For multi-shell fullerenes, we analytically obtain the eigenvalues of the intershell interaction.PACS numbers: 31.15.+q, 02.90.+pIntroduction.-The discovery of a new simple technique 1 for the production in bulk quantities of fullerenes has triggered intensive research on these new all-carbon molecules and the search for other novel forms of carbon. Subsequently, a new type of carbon structure composed of multilayered needle-like tubes has been discovered by high-resolution transmission electron microscopy 2 . Quite recently, giant nested shells of onion-like fullerenes (also called hyperfullerenes 3 ) have been synthesized by intense electron-beam irradiation 4 . Essentially they consist of a composition of concentric spherical fullerene cages. The innermost cage is a C 60 molecule which is encapsulated by giant fullerenes C 240 , C 540 , · · ·, one following the other 4,5 . The interlayer spacing coincides with that for bulk graphite (3.34Å). A recent investigation 6 on the stability of these brand-new diverse forms of carbon shows that multi-sh Specifically, a very recent letter 7 shows that a stability transition from single to multilayer fullerenes occurs when the number of atoms exceeds ∼ 6000. Moreover, the concentric carbon onion structure containing no dangling bonds provides a challenge to graphite (comprising flat sheets of carbon hexagons) for the most stable form of pure carbon.The structures and energies for several carbon "onions" have recently been carried out by using realistic atomic potentials 7 and molecular mechanics calculations 8 . As yet there has been little spectroscopic information available regarding the electronic properties of the multi-shell fullerenes, besides total energy calculations. The exact diagonalization of a local orbital matrix scales as N 3 (for a N −dimensional matrix). The orthonormalization step in plane-wave methods also scales as N 3 . These two examples illustrate typical bottlenecks encountered when studying one of the central thrusts of condensed matter theory: to compute the energetics of very large systems. Different suggestions on how to minimize this formidable problem have recently attracted a lot of attention (see, e.g., Ref. 9). Here, we explore different ways to reduce this difficulty by using two very dissim...

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confidence: 52%

Electronic structure of single- and multiple-shell carbon fullerenes

Lin¹,

Nori²

1994

Phys. Rev. B

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“…Experimentally, all BOs are found to belong to the C 60 N 2 icosahedral family with N = 1, 2, … (i.e. their shells are consecutive elements of the icosahedral C 60 N 2 fullerene family, with C 60 being the smallest shell 8 and the intershell distance being very close to the interplanar separation in graphite, often taken to be 3.55 Å, the C 60 radius; Yoshida & Osawa 1993; Ruiz, Bretón & Gomez Llorente 2004). So far, all the experimentally generated and analysed BOs are in the nanometer size range (∼3–15 nm in diameter; see de Heer & Ugarte 1993; Cabioc'h et al 1997; Chhowalla et al 2003).…”

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confidence: 99%

On buckyonions as an interstellar grain component

Chen

et al. 2008

Monthly Notices of the Royal Astronomical Society: Letters

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The carrier of the 2175 Å interstellar extinction feature remains unidentified since its first detection over 40 yr ago. In recent years, carbon buckyonions have been proposed as a carrier of this feature, based on the close similarity between the electronic transition spectra of buckyonions and the 2175 Å interstellar feature. We examine this hypothesis by modelling the interstellar extinction with buckyonions as a dust component. It is found that dust models containing buckyonions (in addition to amorphous silicates, polycyclic aromatic hydrocarbon molecules, graphite) can closely reproduce the observed interstellar extinction curve. To further test this hypothesis, we call for experimental measurements and/or theoretical calculations of the infrared vibrational spectra of hydrogenated buckyonions. By comparing the infrared emission spectra predicted for buckyonions vibrationally excited by the interstellar radiation with the observed emission spectra of the diffuse interstellar medium, we will be able to derive (or place an upper limit on) the abundance of interstellar buckyonions.

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“…Even if we consider the Van der Waals radius of carbon with 1.415 Å, there is enough space inside C 720 to encapsulate other fullerenes such as C 60 , thus forming what is known as a hyper-fullerene. [89,90] We briefly mention that we can take any combination of LFT and HS of C 20 to generate I h -fullerenes, that is, fullerenes with number of vertices 3 n (ijkl) 2 n v with n, i, j, k, l being any positive integer. In general, the Goldberg-Coxeter transformation T GC k;l [C 20 ] gives icosahedral structures for n v ¼ 20(k 2 þ kl þ l 2 ), of which the HS l ¼ 0 and the general LFTs (k ¼ l) lead to I h symmetry, and to chiral I symmetry otherwise.…”

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confidence: 99%

Program Fullerene: A software package for constructing and analyzing structures of regular fullerenes

2013

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Fullerene (Version 4.4) is a general purpose open-source program that can generate any fullerene isomer, perform topological and graph theoretical analysis, as well as calculate a number of physical and chemical properties. The program creates symmetric planar drawings of the fullerene graph and generates accurate molecular 3D geometries by way of force-field optimization, serving as a good starting point for further quantum theoretical treatments. It includes a number of fullerene-to-fullerene transformations, such as Goldberg-Coxeter transforms, Stone-Wales transforms, Endo-Kroto, Yoshida-Fowler, and Brinkmann-Fowler vertex insertions. The program is written in standard Fortran and C++ and can easily be installed in a Linux or UNIX environment.

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Molecular Mechanics Calculations of Giant- and Hyperfullerenes with Eicosahedral Symmetry

Cited by 88 publications

References 16 publications

Electronic structure of single- and multiple-shell carbon fullerenes

Electronic structure of single- and multiple-shell carbon fullerenes

On buckyonions as an interstellar grain component

Program Fullerene: A software package for constructing and analyzing structures of regular fullerenes

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