Quantum-Chemical Simulation of New Hybrid Nanostructures: Small Fullerenes C20 and C28 in Single-Walled Boron-Nitrogen Nanotubes

A quantum-chemical simulation of new hybrid nanostructures consisting of regular chains of the small fullerenes C₂₀ and C₂₈ encapsulated into the bulk of achiral zigzag single-walled boron-nitrogen nanotubes [(C₂₀,C₂₈)@BN-NT]. The electronic properties and the nature of interatomic bonds in these nanostructures are analyzed as a function of the fullerene and the distances between fullerenes in the chain and between fullerenes and tube walls. The electronic characteristics of hybrid nanostructures are compared with those of "isolated" fullerenes and nanotubes, and (C20,C28) + BN-NT structures simulating fullerene adsorption on tube surface as the initial stage of (C₂₀,C₂₈)@BN-NT formation.     

Selective extraction of higher fullerenes using cyclic dimers of zinc porphyrins

Higher fullerenes (>/=C76) were selectively extracted from a fullerene mixture obtained from a combustion-based industrial production source by cyclic dimers of beta-unsubstituted porphyrin zinc complexes 2C5-2C7 with C5-C7 alkylene spacers as host molecules. Results of single extraction of the fullerene mixture with 2C5-2C7 together with a beta-substituted analogue of 2C6 (1C6) and spectroscopic titration of 2C6 and 1C6 with C60, C70, and C96 indicated that the host selectivity toward higher fullerenes is much dependent on the structure of the porphyrin units and the size of the host cavity. Sequential three-stage extraction of the fullerene mixture with the best-behaved 2C6 resulted in considerable enrichment in very rare fullerenes C102-C110 (<0.1 abs %) up to 82 abs % (C76-C114, 99 abs %) (356 nm) of total fullerenes.     

Nonbonding orbitals in fullerenes: nuts and cores in singular polyhedral graphs

A zero eigenvalue in the spectrum of the adjacency matrix of the graph representing an unsaturated carbon framework indicates the presence of a nonbonding pi orbital (NBO). A graph with at least one zero in the spectrum is singular; nonzero entries in the corresponding zero-eigenvalue eigenvector(s) (kernel eigenvectors) identify the core vertices. A nut graph has a single zero in its adjacency spectrum with a corresponding eigenvector for which all vertices lie in the core. Balanced and uniform trivalent (cubic) nut graphs are defined in terms of (-2, +1, +1) patterns of eigenvector entries around all vertices. In balanced nut graphs all vertices have such a pattern up to a scale factor; uniform nut graphs are balanced with scale factor one for every vertex. Nut graphs are rare among small fullerenes (41 of the 10 190 782 fullerene isomers on up to 120 vertices) but common among the small trivalent polyhedra (62 043 of the 398 383 nonbipartite polyhedra on up to 24 vertices). Two constructions are described, one that is conjectured to yield an infinite series of uniform nut fullerenes, and another that is conjectured to yield an infinite series of cubic polyhedral nut graphs. All hypothetical nut fullerenes found so far have some pentagon adjacencies: it is proved that all uniform nut fullerenes must have such adjacencies and that the NBO is totally symmetric in all balanced nut fullerenes. A single electron placed in the NBO of a uniform nut fullerene gives a spin density distribution with the smallest possible (4:1) ratio between most and least populated sites for an NBO. It is observed that, in all nut-fullerene graphs found so far, occupation of the NBO would require the fullerene to carry at least 3 negative charges, whereas in most carbon cages based on small nut cubic polyhedra, the NBO would be the highest occupied molecular orbital (HOMO) for the uncharged system.     

A C78 fullerene precursor: toward the direct synthesis of higher fullerenes

A C78 fullerene related structure (of C78:1 and C78:4, the last undiscovered C78 IPR isomer) has been synthesized and investigated as a pyrolytic precursor. The pyrolysis of precursor containing all 78 carbon atoms in the required positions and 93 of the 117 C-C bonds, needed for fullerene formation, showed selectivity for C78 fullerene formation. In independent experiments it has been shown that the flash pyrolysis of C78 fullerene is not affected by Stone-Wales rearrangement and loss of C2 fragments and, thus, is very promising for the synthesis of individual isomers of higher fullerenes.     

Version of zones and zigzag structure in icosahedral fullerenes and icosadeltahedra

A circuit of faces in a polyhedron is called a zone if each face is attached to its two neighbors by opposite edges. (For odd-sized faces, each edge has a left and a right opposite partner.) Zones are called alternating if, when odd faces (if any) are encountered, left and right opposite edges are chosen alternately. Zigzag (Petrie) circuits in cubic (= trivalent) polyhedra correspond to alternating zones in their deltahedral duals. With these definitions, a full analysis of the zone and zigzag structure is made for icosahedral centrosymmetric fullerenes and their duals. The zone structure provides hypercube embeddings of these classes of polyhedra which preserve all graph distances (subject to a scale factor of 2) up to a limit that depends on the vertex count. These embeddings may have applications in nomenclature, atom/vertex numbering schemes, and in calculation of distance invariants for this subclass of highly symmetric fullerenes and their deltahedral duals.     

Non-IPR fullerenes with properly closed shells

Fullerenes with properly closed shells (having exactly half their adjacency eigenvalues strictly positive) are rare. All reported examples obey the isolated-pentagon rule (IPR), usually considered a necessary condition of overall stability, and fall into three series (leapfrogs, carbon cylinders and sporadic closed shells). It is shown here that there also exist fullerenes with properly closed shells that violate the IPR ('super-sporadic' fullerenes). All have negative LUMO eigenvalues of small magnitude. Exhaustive search finds four examples with 160 or fewer vertices: one isomer of C(120), two of C(156) and one of C(160). The first three contain single pentagon pairs and the fourth, a linear triple of fused pentagons. Larger examples can be found. A capping construction gives a series of properly closed shell fullerenes of C(3)/C(3v) symmetry, each with a single fully fused triple of pentagons and ≥632 vertices. Tubular extension of the C(120) example leads a series of C(1)/C(s) isomer pairs with ≥168 vertices, retaining the single pentagon adjacency and approaching isospectrality with increasing size. Both constructions are conjectured to lead to an infinite number of super-sporadic fullerenes.     

Comparison of geometric, electronic, and vibrational properties for isomers of small fullerenes C20-C36

We employ the self-consistent-charge density-functional tight-binding (SCC-DFTB) method for computing geometric, electronic, and vibrational properties for various topological isomers of small fullerenes. We consider all 35 five- and six-member rings containing isomers of small fullerenes, C20, C24, C26, C28, C30, C32, C34, and C36, as first part of a larger effort to catalog CC distance distributions, valence CCC angle distributions, electronic densities of states (DOSs), vibrational densities of states (VDOSs), and infrared (IR) and Raman spectra for fullerenes C20-C180. Common features among the fullerenes are identified and properties characteristic for each specific fullerene isomer are discussed.     

Fullerene Graphs with Exponentially Many Perfect Matchings

We show that for all sufficiently large even p there is a fullerene graph on p vertices that has exponentially many perfect matchings in terms of the number of vertices. Further, we show that all fullerenes with full icosahedral symmetry group have exponentially many perfect matchings and indicate how such results could be extended to the fullerenes with lower symmetry.     

Fullerene black: Structure, properties and possible applications

This review concerns the fullerene black, a poorly known nano-sized carbon material, the insoluble residue after extraction of fullerenes from fullerene soot obtained by arc vaporization of carbon material (usually graphite) in a helium atmosphere. This by-product of the production of fullerenes, whose yield reaches 80 wt %, is a finely dispersed material with a particle size of 40–50 nm. It includes amorphous carbon, graphitized particles, and graphite. Test reactions showed the presence in the structure of fullerene black of curved surfaces, and, like fullerenes, of alternating nonconjugated ordinary and double bonds. In addition to the double bonds, its structure includes dangling bonds in the concentration not higher than one per 1200 carbon atoms. Fullerene black absorbs oxygen from the atmosphere and water, and enters into the reactions of nucleophilic addition. The fullerene black cannot be graphitized, and its application is extremely important. The fullerene black was shown to activate hydrogen and thus to undergo a hydrogenolysis in the absence of a catalyst and to catalyze the dehydrogenation and dehydrocyclization of alkanes. This carbon nanomaterial can be used as a sorbent and a catalyst carrier, a tribotechnical additive; it can interact with carbide-forming metals and harden their surface.     

Table of periodic properties of fullerenes based on structural parameters

The periodic table (PT) of the elements suggests that hydrogen could be the origin of everything else. The construction principle is an evolutionary process that is formally similar to those of Darwin and Oparin. The Kekulé structure count and permanence of the adjacency matrix of fullerenes are related to structural parameters involving the presence of contiguous pentagons p, q and r. Let p be the number of edges common to two pentagons, q the number of vertices common to three pentagons, and r the number of pairs of nonadjacent pentagon edges shared between two other pentagons. Principal component analysis (PCA) of the structural parameters and cluster analysis (CA) of the fullerenes permit classifying them and agree. A PT of the fullerenes is built based on the structural parameters, PCA and CA. The periodic law does not have the rank of the laws of physics. (1) The properties of the fullerenes are not repeated; only, and perhaps, their chemical character. (2) The order relationships are repeated, although with exceptions. The proposed statement is the following: The relationships that any fullerene p has with its neighbor p + 1 are approximately repeated for each period.     

Structures,stabilities, and IR and 13C-NMR spectra of dihedral fullerenes: A density functional theory study

Dihedral fullerenes are thermodynamically stable molecules with D nd or D nh symmetry.Based on experimental findings,two series of dihedral fullerenes with five-fold(C5) and six-fold(C6) symmetry have been studied using density functional theory(DFT).The DFT calculations showed that for both series the stabilities increased with increasing fullerene size.Structural analyses indicated that the stabilities are related to specific local geometries.In the case of the more abundant C5 series,the presence of approximately planar pentagons and hexagons on the top bowl favors their formation.That is to say,those fullerenes with small dihedral angles within the polygons are readily formed,because planar hexagons lead to strengthened conjugation which lowers average bonding energies(ABE) and increases thermodynamic stabilities.Non-planar hexagons at equatorial positions in tube-shaped fullerenes have an adverse effect on the conjugation and inhibit their formation.Calculations also demonstrated that fullerenes in the two series,including C 50(D 5h),C 60(D 6h),C 80(D 5d),C 96(D 6d),C 110(D 5h),and C 120(D 5d),have thermodynamically stable triplet structures with strong conjugation.The calculated IR and 13 C NMR spectra of the fullerenes show some similarities and regular trends due to their homogenous structures.The electronic structures indicate that short double bonds in hexagons with high electron occupancies are readily attacked by electrophilic agents and can also be coordinated by transition metals.Mechanistic discussions suggested that C 2 additions and C 2 losses constitute reversible processes at high temperature and C 2 additions in pentagonal fusions are crucial to the kinetics of the curvature of structures.C 3 additions lead to the formation of large fullerenes of other types.     

New molecular complexes of fullerenes C60 and C70 with tetraphenylporphyrins [M(tpp)], in which M=H2, Mn, Co, Cu, Zn, and FeCl

New molecular complexes of fullerenes C60 and C70 with tetraphenylporphyrins [M(tpp)] in which M-H2, MnII, CoII, CuII, ZnII and Fe(III)Cl, have been synthesised. Crystal structures of two C60 complexes with H2TPP, which differ only in the number of benzene solvated molecules, and C60 and C70 complexes with [Cu(tpp)] have been studied. The fullerene molecules form a honeycomb motif in H2TPP.2C60. 3C6H6, puckered graphite-like layers in H2TPP.2C60.4C6H6, zigzag chains in [Cu(tpp)].C70.1.5C7H8.0.5C2HCl3 and columns in [Cu(tpp)]2.C60. H2TPP has van der Waals contacts with C60 through nitrogen atoms and phenyl groups. Copper atoms of the [Cu(tpp)] molecules are weakly coordinated with C70, but form no shortened contacts with C60. The formation of molecular complexes with fullerenes affects the ESR spectra of [M(tpp)] (M = Mn, Co and Cu). [Mn(tpp)] in the complex with C70 lowers its spin state from S = 5/2 to S = 1/2, whereas [Co(tpp)] and [Cu(tpp)] change the constants of hyperfine interaction. ESR, IR, UV-visible and X-ray photoelectron spectroscopic data show no noticeable charge transfer from the porphyrinate to the fullerene molecules.     

Stability of silicon-doped C60 dimers

A theoretical investigation on the structure, stability, and thermal behaviors of the smallest polymeric units, the dimers, formed from substitutionally Si-doped fullerenes is presented. A density functional based nonorthogonal tight-binding model has been employed for describing the interatomic interactions. The study focuses on those polymeric structures which involve Si-Si or Si-C interfullerene bonds. The binding energy of the dimers increases with their Si content from about 0.25 eV in C(60)-C(60) to about 4.5 eV in C(58)Si(2)-C(58)Si(2). Moreover, the C(59)SiC(59) dimer, linked through the sharing of the Si atom between the two fullerenes, has been also considered. Upon heating, the dimers eventually fragment into their constituent fullerene units. The fragmentation temperature correlates with the strength of the interfullerene bonds. C(58)Si(2)-C(58)Si(2) exhibits a higher thermal stability (fragmentation temperature of approximately 500 K) than the pure carbon C(60)-C(60) dimer (with a fragmentation temperature of approximately 325 K). Given the higher structural and thermal stabilities of the Si-doped fullerene dimers, the authors propose the use of substitutionally Si-doped fullerenes as the basic units for constructing new fullerene-based polymers.     

The way of stabilizing non-IPR fullerenes and structural elucidation of C(54)Cl(8)

Recently, a new non-IPR chlorofullerene C(54)Cl(8) was isolated experimentally (Science 2004, 304, 699). To explore the ways to stabilize non-IPR fullerenes, the authors studied all of the possible isomers of C(54) fullerene and some of the C(54)Cl(8) isomers at PM3, B3LYP/3-21G, and B3LYP/6-31G* levels. Combined with analysis of pentagon distributions, bond resonance energies, and steric strains, C(54):540 with the least number of 5/5 bonds was determined to be the thermodynamically best isomer for the C(54)Cl(8). Based on C(54):540, the most probable structure of the experimental C(54)Cl(8) was elucidated. The results suggested one of the necessary conditions of stabilizing non-IPR fullerenes: chemical derivatizations of either endohedral complexation or exohedral addition need to sufficiently stabilize all of the kinetically unstable 5/5 bonds of the cages.     

Ferromagnetic and half-metallic behaviors of fullerene-cobalt polymer chains

We present the results of first-principles calculations for polymers (C(60)-Co)(n) and (C(70)-Co)(n), which consist of alternating chains of fullerenes and cobalt. Both of them favor a ferromagnetic ground state. The latter one is a half-metal which will give rise to 100% spin polarization in the electronic transport, while the former is a semiconductor. Polymers (N@C(60)-Co)(n) and (N@C(70)-Co)(n), which encapsulate a nitrogen atom in each fullerene have magnetic moments four times larger than those without encapsulated nitrogen atoms. All these results can be explained in terms of pi(fullerene)-d(Co) and pi(fullerene)-p(N) hybridizations.     

DFT study of fullerene dimers.

Several [2+2] dimerization products of a fullerene Cn (n=50, 52, 54, 56, 58, 60) in its most stable form are presented and discussed. In total, 34 dimers are studied. Only symmetric Cn-Cn dimers (no mixed products) are reported, and only dimers of the fullerenes C50 to C58 with bonds between C atoms in adjacent pentagons are considered. Geometries were optimized within the framework of density functional theory using the Becke-Perdew exchange-correlation functional (BP86) in combination with an empirical dispersive energy correction, which contributes significantly to the binding energy. The results are discussed in the context of the reactivity of adjacent pentagon sites. The lateral interaction between fullerenes is found to be stronger for C50 to C58 than for C60, which is consistent with recent experimental observations. Further, the possibility of polymer formation based on the investigated [2+2] reaction is addressed.     

Synthesis of C59Hx and C58Hx fullerenes stabilized by hydrogen

Prolonged hydrogenation of C(60) molecules by reaction with H(2) at elevated temperature and pressure results in fragmentation and collapse of the fullerene cage structure. However, fragments can be preserved by immediate termination of dangling bonds by hydrogen. Here we demonstrate that not only fullerene fragments but also hydrogenated fragmented fullerenes (e.g., C(58)H(40) and C(59)H(40)) can be synthesized in bulk amount by high-temperature hydrogenation of C(60). We confirm successful synthesis of these species by matrix-assisted laser desorption ionization time-of-flight mass spectrometry and complete speciation of the resultant complex fullerene mixtures by high-resolution field desorption/ionization Fourier transform ion cyclotron resonance mass spectrometry.     

Dendronized molecular knots: selective synthesis of various generations,enantiomer separation,circular dichroism

For the first time, knot molecules (of the amide type) are synthesized, which bear one to three dendritic units of various generations at their periphery. They were obtained through two different routes: i) attachment of dendritic wedges to new mono-, di- and trihydroxy functionalized dodecaamide knots that have been obtained by selective debenzylation of oligobenzyloxy substituted knots, or ii) cyclization of already dendron substituted pyridine-2,6-dicarbonyl dichlorides with an "extended diamine" to directly yield the "tri-dendroknots". The derivatization of knot molecules by functional substituents and even large dendritic units is an important advance in the synthesis and property variation of molecular knots. This holds true in particular for substitution of the pyridine units of the knots, whereas the isophthalic acid units seem not to tolerate larger substitutents, as reflected in lower knot yields. These syntheses also demonstrate knots to be accessible indirectly by substitution of the corresponding mono-, di- and tri-functionalized knot skeleton. An advantage of dendritic "decoration" is the control of solubility and chromatographic behaviour of the molecular knots (knotanes). Suggestions are made about the threading mechanism by supramolecular template effects leading to the formation of amide-based molecular knots. The topological chirality of the new "dendroknots" is shown by efficient enantioseparations (separation factor alpha between 1.22 and 1.48). For this purpose (commercially unavailable) chiral column material of the Chiralpak type was used, in which the chiral component is covalently bonded to the silica gel support. The racemate splittings provide additional evidence for the knotted structure, as all other conceivable isomers such as macromonocyclic or catenated dodecaamides would not be chiral. The pure enantiomers obtained exhibit pronounced Cotton effects in their circular dichroism spectra. By comparison with the unsubstituted knot, the absolute configuration (Lambda, Delta) of all new knots is derived.     

Microfluidics made of yarns and knots: from fundamental properties to simple networks and operations

We present and characterize cotton yarn and knots as building blocks for making microfluidic circuits from the bottom up. The yarn used is made up of 200-300 fibres, each with a lumen. Liquid applied at the extremity of the yarn spontaneously wets the yarn, and the wetted length increases linearly over time in untreated yarn, but progresses according to a square root relationship as described by Washburn's equation upon plasma activation of the yarn. Knots are proposed for combining, mixing and splitting streams of fluids. Interestingly, the topology of the knot controls the mixing ratio of two inlet streams into two outlet yarns, and thus the ratio can be adjusted by choosing a specific knot. The flow resistance of a knot is shown to depend on the force used to tighten it and the flow resistance rapidly increases for single-stranded knots, but remains low for double-stranded knots. Finally, a serial dilutor is made with a web made of yarns and double-stranded overhand knots. These results suggest that yarn and knots may be used to build low cost microfluidic circuits.