Adjacent Pentagons Research Articles

Theoretical study of ionization potentials and dissociation energies of Cnq+ fullerenes (n=50–60, q=0, 1 and 2)

We have evaluated electronic energies of neutral, singly charged and doubly charged fullerenes with sizes n=50–60 using density functional (DFT) theory. For each value of the cluster charge, we have considered around 40 possible structures. We have found that, except for C522+, the most stable isomer always has the minimum possible number of C2 units between adjacent pentagons. We have evaluated adiabatic dissociation energies corresponding to the various dissociation channels leading to the emission of carbon dimers with different charges. Our findings for dissociation leading to C2 emission are in reasonable agreement with the latest experimental values. As a byproduct of our calculations, we have also evaluated the first and second adiabatic ionization potentials. Both dissociation energies and ionization potential are useful data to interpret fragmentation of fullerenes by impact of energetic photons, electrons and ions.

Structural and electronic properties of coiled and curled carbon nanotubes having a large number of pentagon–heptagon pairs

A family of Haeckelite nanotubes is generated by rolling up a two-dimensional threefold coordinated carbon network composed of pentagon-heptagon pairs and hexagons in proportion 2:3. The corresponding two-dimensional network is highly strained due to the presence of adjacent pentagons and heptagons. When the sheet is folded into a cylinder, part of the strain is released by having the pentagons protrude outward, and sometimes inward the tube. Due to that property, a large variety of structures can be generated such as coiled, screwlike, curled, and pearl-necklace-like nanotubes. All the Haeckelite nanotubes obtained in this work are semiconductors, some having a small band gap. Scanning-tunneling microscopy images, computed for a few Haeckelite nanotubes, show salient topographic protrusions at the location of the pentagon pairs.

Scratching the surface of buckminsterfullerene: the barriers for Stone-Wales transformation through symmetric and asymmetric transition states.

General-gradient approximation (PBE) and hybrid Hartree-Fock density functional theories (B3LYP) in conjunction with basis sets of up to polarized triple-zeta quality have been applied to study the Stone-Wales transformation of buckminsterfullerene (BF) to yield a C(60) isomer of C(2)(v) symmetry with two adjacent pentagons (#1809). In agreement with earlier investigations, two different transition states and reaction pathways could be identified for the rearrangement from BF to C(60)-C(2)(v) on the C(60) potential energy surface (PES). One has C(2) molecular point group symmetry with the two migrating carbon atoms remaining close to the fullerene surface. The other one has a high-energy carbene-like (sp(3)) structure where a single carbon atom is significantly moved away from the C(60) surface. The carbene intermediate and the second transition state along the stepwise reaction path characterized previously at lower levels of theory do not exist as stationary points with the density functionals utilized here. The classical barriers of both mechanisms are essentially identical, 6.9 eV using PBE and 7.3 eV with B3LYP.

Oxygen Atom Reactions with Circumtrindene and Related Molecules: Analogues for the Oxidation of Nanotube Caps

Circumtrindene, a C 3 6 H 1 2 open geodesic dome with alternating five- and six-membered rings, is of interest as a vesicle for carrying out chemical reactions and also as a model for certain carbon nanotube caps. Here theaddition of an oxygen atom to circumtrindene is examined by means of density functional calculations. O-atom addition to a C-C bond shared between the central and adjacent hexagons gives an epoxide structure while O-atom addition to a C-C bond shared by the central hexagon and an adjacent pentagon results in cleavage of the C-C bond and an R-O-R insertion product. Despite their structural dissimilarity, the two oxidation products are predicted to be of comparable stability (with binding energies of -74.9 and -78.7 kcal/mol, respectively), and to have a large (55.7 kcal/mol) barrier for interconversion.

Kinetic stability of carbon cages in non-classical metallofullerenes

Charged carbon cages in isolable metallofullerenes are kinetically stable with a minimum bond resonance energy ( min BRE )>−0.100 | β| . Charged carbon cages with adjacent pentagons in recently isolated non-classical metallofullerenes, Sc 2@C 66 and Sc 3N@C 68, are not exceptions. In fact, many molecular anions of fullerenes with adjacent pentagons have a large negative min BRE. Nature seems to choose carbon cages from among a small number of kinetically stable fullerene molecular anions with adjacent pentagons to design isolable non-classical metallofullerenes. There is no doubt that the isolated pentagon rule cannot be applied to charged fullerenes.

ChemInform Abstract: Stabilization of Pentagon Adjacencies in the Lower Fullerenes by Functionalization.

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Mg@C 72 MNDO/d evaluation of the isomeric composition

Temperature development of the relative stabilities of isomers of Mg@C 72 (which has not yet been isolated) is computed using the recently introduced MNDO/d method. Four isomers originally considered for the Ca@C 72 case are treated: one isolated-pentagon-rule (IPR) structure, two structures with a pair of adjacent pentagons, and one cage with a heptagon. The IPR structure comes as the lowest in MNDO/d potential energy, being rather closely followed by the two structures with a pentagon–pentagon pair. On the other hand, the structure with a heptagon is located too high in potential energy to be of any experimental significance. The entropy contributions are evaluated by the MNDO/d-based partition functions so that the relative concentrations can be treated accordingly. The computations suggest that if Mg@C 72 is isolated, it should be a mixture of either two or three isomers. The prediction depends on temperature prehistory. If preparation takes place at temperatures of approximately 1000 K, two isomers should be produced. If temperatures are increased to approximately 2000 K, there will already be three isomers with significant relative concentrations. The study supplies a further interesting example of the profound role of enthalpy–entropy interplay in stabilities of isomeric fullerenic structures. © 2001 by Elsevier Science Inc.

Some 4-fluorophenyl derivatives of [60]fullerene; spontaneous oxidation and oxide-induced fragmentation to C58

The main products from the reaction of C60Cl6 with fluorobenzene–FeCl3 are C60(4-FC6H4)5Cl, 1,4-(4-FC6H4)2C60 (both of Cs symmetry) and asymmetric C60(4-FC6H4)4, accompanied by a small amount of C60(4-FC6H4)4H2. Exposure of the product to light and air before processing gives other components, including C60(4-FC6H4)4(4-FC6H3)O2, C60(4-FC6H4)5OH, and C60(4-FC6H4)6 (each of Cs symmetry), C60(4-FC6H4)4O2, C60(4-FC6H4)6O2, C60(4-FC6H4)7H, and C60(4-FC6H4)5H(OH)2/C60(4-FC6H4)5H. The formation of the oxides from air-exposed reaction products emphasises the need for atmospheric protection of fullerene derivatives. Fragmentation of the oxides during EI mass spectrometry occurs readily to give C58 and derivatives which must contain adjacent pentagons, stabilisation being derived from the presence of a heptagon.

Stabilisation of pentagon adjacencies in the lower fullerenes by functionalisation

Relative stabilities are calculated with the density-functional based tight-binding method for all isomers C36H2x (x = 1, 2, 3) based on the two C36 classical fullerenes with minimal pentagon adjacencies. Preferential addition at pentagon junctions leads to low-energy candidates for C36H4 and C36H6 based on the sixfold-symmetric cylindrical C36 fullerene cage, 36 ∶ 15.

A stable non-classical metallofullerene family

In the evolving field of fullerenes, nanotubes and endohedral metallofullerenes, the isolated-pentagon rule (IPR)1 is sacrosanct — exceptions have been predicted2,3, but no bare carbon cages with adjacent pentagons have been characterized. Small organic molecules with metal-stabilized fused five-membered rings (pentalenes) have been created4, however, and here we describe a family of non-classical endohedral metallofullerenes with the general structure AxSc3−xN@C68 (where x = 0–2, A is a rare-earth metal, Sc is scandium and N is nitrogen) that has a non-IPR cage of only 68 carbon atoms containing annelated five-membered rings. This internal ring network is metal-stabilized and is accessible for external organic reaction chemistry.

Theoretical Investigations of Carbon Nanotube Growth

The growth of carbon nanotubes was investigated using a variety of complementary simulation techniques. Currently, a number of experimental methods are used to synthesize carbon nanotubes suggesting that different mechanisms play a role in their formation. However, it has been shown that growth of nanotubes takes place primarily at the open-ended tips of nanotubes. Ab initio simulations show that the high electric fields present at the nanotube tips in carbon arc discharges cannot be responsible for keeping the tubes open. Rather, the opening and closing of tubes is controlled by the formation of curvature-inducing defects such as adjacent pentagon pairs. On narrow tubes, the formation of such defects is favored leading to the rapid closure of the tubes. By contrast, the formation of hexagons, which lead to straight open-ended growth is favored on large-diameter tubes, with an estimated crossover radius of about 3 nm. Large-scale molecular dynamics and kinetic Monte Carle simulations have been used to verify these ideas. We have also explored the role of the so-called lip–lip interactions during growth. Such an interaction is important in producing multiwalled nanotubes, where the interaction between two open nanotube tips leads to the formation of a network of bonds. Simulations show that such an interaction is indeed significant, but does not provide the additional stabilization required for straight, open-ended, multiwalled nanotube growth. Finally, we consider the formation of nanotubes in the presence of large and small catalytic particles. In the former case, growth is believed to take place via a root-growth mechanism, while the direct adsorption and extrusion of carbon from the vapor dominates the latter. Both mechanisms lead to the formation of small-diameter, single-wall nanotubes.

C 36, a hexavalent building block for fullerene compounds and solids

Structures and energies are calculated at the DFTB level for C 36-based fullerenes, hydrides, oligomers and solids. The two fullerenes with minimal pentagon adjacencies are isoenergetic. The isomer implicated in recent experiments has C 6 v broken symmetry, a small HOMO–LUMO gap and can gain or lose up to six electrons. C 36 forms stronger inter-cage bonds than larger fullerenes. A favoured σ-bonding pattern rationalises a dimer with ten times the stabilisation of (C 60) 2, a linear polymer, a ‘superbenzene’ oligomer, a ‘supergraphite’ layer and a hexagonal close-packed solid with a monomer stabilisation of 522 kJ mol −1 and a d-spacing (6.82 Å) compatible with the experiments.

Pentagon adjacency as a determinant of fullerene stability

Optimisation of geometries of all 40 fullerene isomers of C40, using methods from molecular mechanics and tight-binding to full abinitio SCF and DFT approaches, confirms minimisation of pentagon adjacency as a major factor in relative stability. The consensus predictions of 11 out of 12 methods are that the isomer of lowest total energy is the D2 cage with the smallest possible adjacency count, and that energies rise linearly with the number of adjacencies. Quantum mechanical methods predict a slope of 80–100 kJ mol-1 per adjacency. Molecular mechanics methods are outliers, with the Tersoff potential giving a different minimum and its Brenner modification a poor correlation and much smaller penalty.

The structures of fullerene C 40 and its derivatives

In this paper, the three possible fullerene isomers of C 40 and their derivatives are investigated employing ab initio methods with using 3 Gauss type orbitals instead of one Slater type orbital (STO-3G). Of the three structures, two have D 5 d symmetry [ D 5 d ( I) and D 5 d ( II)], the other has T d symmetry. Through the full optimized calculation, the predicted order of stability for isomers is found to be D 5 d ( I) > T d > D 5 d ( II). Energies and properties of the negative ion and positive ions of different kinds of C 40 are calculated. Generally, the stability of negative ions is better than positive ions. The hydrogenated C 40 has also been studied. It can be concluded that the most active center for adding hydrogen is the vertex of three adjacent pentagons.

New growing modes for carbon: Modelization of lattice defects, structure of tubules and onions

Topological defects and tubule-to-tubule connections on single-walled carbon nanotubes are examined in the frame of dislocations and Burgers vectors concepts. A tubule is defined by its Burgers vector on the graphene triangular Bravais lattice. The ‘adjacent pentagon + heptagon defect’, in short ‘5 ⊕ 7’, is identified with a dislocation with a lattice primitive vector as Burgers vector, i.e. a high-energy-highly-mobile defect. It acts as an elementary translational operator on the triangular array, allowing the description of the set of transformations undergone by a tubule through a single 5 ⊕ 7 in terms of nearest neighbours jumps. The standard labelling system in use for tubules is extended into a unified system for tubules and for chiral and non-chiral icosahedral fullerenes, allowing easy relations between a tubule and the either flat or hemispherical caps able to match it. Interest of these ideas in onions and multi-walled nanotubes is emphasized.

96/04961 Surface fractal dimension of graphitized carbon black particles

Axonometric projections together with the corresponding graphs for fullerenes are constructed in the range from 32 to 60. The growth of fullerenes is studied on the basis of a mechanism according to which a carbon dimer embeds in a hexagon of an initial fullerene. This leads to stretching and breaking the covalent bonds which are parallel to arising tensile forces. In this case, instead of a hexagon adjoining two pentagons, two adjacent pentagons adjoining two hexagons are obtained. As a result, there arises a new atomic configuration and there is mass increase of two carbon atoms. We considered the direct descendants of fullerene C32; namely, C2n, where n = 17–30.

Increasing cost of pentagon adjacency for larger fullerenes

The cost of a pentagon adjacency in a fullerene cage grows linearly from 72 kJ mol −1 for C 30 to 111 kJ mol −1 for C 60, according to systematic QCFF/PI model calculations on a set of 2624 structural isomers.

Energetics of Fullerenes with Four-Membered Rings

The energetic cost of introducing square faces to fullerenes with adjacent pentagons is investigated theoretically. Relative energies of all 1735 hypothetical C40 cages that can be assembled from square, pentagonal, and hexagonal faces are calculated within two independent semiempirical models. All isomers are found to lie in local minima on the potential surface. The QCFF/PI (quantum consistent force field/π) and DFTB (density functional tight binding) approaches agree in predicting that no cage with one or more squares is of lower energy than the best classical C40 fullerene but that many such cages are more stable than many C40 fullerenes. Energy penalties of 160−200 kJ mol-1 per square are suggested by the DFTB calculations, and penalties of about twice this size by the QCFF/PI model. The energy variation across the range of fullerenes and pseudofullerenes is steric in origin and correlates well with the normalized second moment of the hexagon neighbor signature: aggregation of hexagons in one part of the cage surface is incompatible with even distribution of curvature and implies crowding of defects elsewhere. QCFF/PI calculations for selected isomers of C62 to C68 also show that though cages with squares may again be more stable than some fullerenes, they are all bettered in energy by the best classical fullerene at each nuclearity.

Propensity Rules for the Stability of Odd-Numbered Fullerenes: A Semiempirical Proposal

The structures of C119 and C129, the two lowest odd-numbered fullerenes, are investigated by semiempirical quantum chemical calculations. In the process, the use of a recently proposed parametrization for a tight-binding Extended-Huckel model is validated to study the relative stability of fullerenes. Three general routes for the generation of the structures of odd-numbered fullerenes are described and used to generate systems that can be loosely characterized as having either a four-membered ring or a patch of adjacent pentagons, or a set of multiple connections between the cages of the pristine fullerenes. The structures of the six isomers of C119 obtained in this manner are optimized and it is confirmed that the most stable isomer of C119 has C2 symmetry and forms three bonds between the C59 and the C60 moieties. By analogy with C119, 56 structures of C129 are generated and their geometries are optimized. As in the case of C119, it is found that the most stable isomer of C129 can be formed both from th...

Energetics of fullerenes with heptagonal rings

The energetic costs of widening the fullerene definition to include carbon cages with heptagonal as well as pentagonal and hexagonal faces are investigated theoretically. Relative energies of all 426 hypothetical C40 cages that can be assembled from pentagonal, hexagonal and heptagonal faces are calculated within two independent semi-empirical models. All isomers are found to lie in local minima on the potential surface. The QCFF/PI (quantum consistent force field/π) and DFTB (density functional tight binding) approaches agree in predicting that no cage with one or more heptagons is of lower energy than the best classical C40 fullerene, but that many such cases are more stable than many C40 fullerenes. All one-heptagon C40 cages are predicted to lie within the range of energies spanned by the classical fullerene isomers. Energy penalties of 90–150 kJ mol–1 per heptagon are suggested by the DFTB calculations, and penalties about half as large again by the QCFF/PI model. The energy variation across the range of fullerenes and pseudo-fullerenes is rationalised by an extension of the isolated-pentagon rule: when heptagons are present, structures of low energy are those that maximise the number of pentagon–heptagon contacts subject to prior minimisation of the number of pentagon–pentagon adjacencies.