Quantum molecular dynamics simulations of fullerenes and graphitic microtubules

We describe the results of extensiveab initio molecular dynamics calculations of the properties of fullerenes and microtubules. Our finite temperature quantum MD simulations for solid C₆₀ are in excellent agreement with NMR, photoemission and neutron scattering data. The C₆₀ isomer containing two pairs of adjacent five-fold rings has a binding energy only 1.6 eV smaller than that of perfect C₆₀, but the transformation between these two structures is hindered by a 5.4 eV barrier. It thus requires high temperatures and long annealing times. High temperatures are also needed for the transformation of the lowest energy C₂₀ isomer, a dodecahedron, to a corannulene structure, which can be thought of as a fragment of C₆₀. The corannulene structure is a natural precursor for the formation of C₆₀. Simulations of reactions show that C₂ can insert into C₅₈, perfect C₆₀, and defect C₆₀ fullerenes without an activation barrier, while C₃ attaches only to their surfaces. Evaporative fragmentation of carbon clusters during annealing is unlikely, but atom and fragment exchange during collision favor "locally" most stable structures, such as C₆₀. These results may explain the large increase in the abundance of C₆₀ and C₇₀ when carbon clusters are annealed at high density. We have also carried out calculations for paradigmatic microtubules, both reflection-symmetric and chiral. We find that the optimized geometries of the tubules are close to the ideal ones. It is possible to fabricate tubules with direct band gaps away from the Γ point by exploiting the similarities between the projected band structure of graphite and that of the tubule. The semiconducting tubules can be doped n- and p-type by substitutional N and B, respectively.     

A Computational NICS and 13C NMR Characterization of C60−n Si n Heterofullerenes (n = 1, 2, 6, 12, 20, 24, 30)

Density functional theory (DFT) calculations are performed for a representative set of low-energy structures of C_60-n Si _n heterofullerenes (n = 1, 2, 6, 12, 20, 24, 30) to investigate the effect of silicon doping on the electron structure of fullerene. The results show that chemical shielding (CS) parameters are so sensitive to the structural distortion made by outwardly relaxing silicon doped atoms from the fullerene surface which results in puckered Si-doped rings. As a result, the chemical shifts of the nearest carbon sites of silicon atoms considerably shift to downfield. Our survey shows that those first neighbors of silicon atoms which have minor ¹³C chemical shift belong to normal (un-puckered) rings. Meanwhile, the chemical shielding anisotropy (Δσ) parameter detects the effects of dopant so that Δσ values of the carbon atoms which are contributed to the Si–C bond are mainly larger than the others. Compensation between diatropic and paratropic ring currents lead to less negative NICS values at cage centers of Si-doped fullerenes than that of C₆₀ except C₅₈Si₂-b and C₅₄Si₆-b in which more negative NICS values may be attributed to more spherical geometries of their carbon cages.     

Theoretical Investigation of Mono and Multiply Oxygenated C70 Fullerenes

We have applied DFT calculations to investigate atomic arrangements of fullerene oxides, C₇₀O _n with n = 1, 5, 15, 20, and 25. The oxidation reaction energies are generally exothermic. In the case of C₇₀O, the most stable configuration is the one in which the oxygen atom is chemisorbed on the C–C bond at the equatorial belt of fullerene with oxidoannulene like structure. In highly oxygenated fullerenes, the addition of oxygen atoms on the [6, 6] bonds near the pole area of the C₇₀ leads to lower values of reaction energies. Among these, C₇₀O₂₀ with three oxygen atoms adsorbed on a benzenoid ring yields the most energetically favorable configuration. Different positions of the oxygen atoms on the surface of the mono oxygenated fullerenes lead to significant differences in their ¹⁷O NQR parameters. Meanwhile, the ¹⁷O NQR parameters of the highly oxygenated fullerenes divide their oxygen nuclei into a few groups. For example, the electric field gradient tensor for oxygen atoms chemisorbed on the [6, 5] bonds with larger η values becomes considerably asymmetric in comparison to those chemisorbed on the [6, 6] bonds. These are also reflected in the calculated natural charges of oxygen atoms.     

2‐Aminoethanol Extraction as a Method for Purifying Sc3N@C80 and for Differentiating Classes of Endohedral Fullerenes on the Basis of Reactivity

Extraction with 2‐aminoethanol is an inexpensive method for removing empty cage fullerenes from the soluble extract from electric‐arc‐generated fullerene soot that contains endohedral metallofullerenes of the type Sc₃N@C_2n (n=34, 39, 40). Our method of separation exploits the fact that C₆₀, C₇₀, and other larger, empty cage fullerenes are more susceptible to nucleophilic attack than endohedral fullerenes and that these adducts can be readily extracted into 2‐aminoethanol. This methodology has also been employed to examine the reactivity of the mixture of soluble endohedral fullerenes that result from doping graphite rods used in the Krätschmer–Huffman electric‐arc generator with the oxides of Y, Lu, Dy, Tb, and Gd. For example, with Y₂O₃, we were able to detect by mass spectrometry several new families of endohedral fullerenes, namely Y₃C₁₀₈ to Y₃C₁₂₆, Y₃C₁₀₇ to Y₃C₁₂₅, Y₄C₁₂₈ to Y₄C₁₄₆, that resisted reactivity with 2‐aminoethanol more than the empty cage fullerenes and the mono‐ and dimetallo fullerenes. The discovery of the family Y₃C₁₀₇ to Y₃C₁₂₅ with odd numbers of carbon atoms is remarkable, since fullerene cages must involve even numbers of carbon atoms. The newly discovered families of endohedral fullerenes with the composition M₄C_2n (M=Y, Lu, Dy, Tb, and Gd) are unusually resistant to reaction with 2‐aminoethanol. Additionally, the individual endohedrals, Y₃C₁₁₂ and M₃C₁₀₂ (M=Lu, Dy, Tb and Gd), were remarkably less reactive toward 2‐aminoethanol.     

Carbon clusters in a storage ring

Anions of fullerenes and small carbon clusters C _n ^- have been stored in the storage ring ASTRID and observed decays on a millisecond time scale are interpreted as electron emission from metastable excited states. For the fullerenes, the fast decay is caused by thermionic emission, quenched by radiative cooling. The observed decay times are longest for the magic numbers n = 50, 60, reflecting a reduction of the thermal radiation due to the electronic shell structure. This statistical interpretation is supported by experiments on thermionic emission from C ₆₀ ^- molecules heated by a Nd:YAG laser pulse. For anions of small carbon clusters (n = 2 - 9) there is a metastable component for n = 2 and for odd n but no metastability on a millisecond time scale for even n. The excited states are suggested to be quartet states decaying by Auger emission.     

Towards the selective formation of specific isomers of fullerenes: T - and p-dependence in the yield of various isomers of fullerenes C60–C84

Systematic fractional change in the yield of various isomers of fullerenes was revealed to strongly depend on temperature of a buffer gas. A new kinetic consideration is proposed for understanding the observed temperature- and pressure-dependence of yield of fullerenes. The model consists of three competitive reactions in consideration of plausible behaviors of a precursor, (1) decomposition into smaller fragments, (2) isomerization leading to formation of a stable fullerene cage, and (3) growth into a larger carbon cluster. Arrhenius activation energy of formation of stable fullerenes was determined to be 0.8 eV for both C₆₀ and C₇₀, while a higher energy of 2.0?3.3 eV for seven different isomers of higher fullerenes ranging from C₇₆ to C₈₄. Correlation in the activation energy is noted for a series of higher fullerenes with different sizes, suggesting the existence of a specific precursor in their formation processes.     

Theoretical Study of Structural Relationships and Electrochemical Properties of Supramolecular [14-MR Macrolides]@Cn Complexes

Macrolides are a broad spectrum of antibiotics that are commonly used in human pathologies as well as in veterinary medicine. The electrochemical detection of macrolide antibiotics were studied at various methods using amperometric and coulometric detectors. Since the discovery of fullerenes (C_n), one of the main classes of carbon compounds, the unusual structures and physiochemical properties of these molecules have been discovered, and many potential applications and physicochemical properties have been introduced. Up to now, various empty carbon fullerenes with different numbers “n,” such as C₆₀, C₇₀, C₇₆, C₈₂, and C₈₆, have been obtained. Topological indices are digital values that are assigned based on chemical composition. These values are purported to correlate chemical structures with various chemical and physical properties. They have been successfully used to construct effective and useful mathematical methods to establish clear relationships between structural data and the physical properties of these materials. In this study, the number of carbon atoms in the fullerenes was used as an index to establish a relationship between the structures of Erythromycin-A (EA), Erythromycin-A enol ether (EMEN), Olendomycin (OM), and Anhydroerythromycin-A (AEA), 1-4 and fullerenes C_n (n = 60, 70, 76, 82 and 86), which create [Tetracyclines]@C_n, A-1 to A-5 ([EA]@C_n), B-1 to B-5 ([EMEN]@C_n), C-1 to C-5 ([OM]@C_n), and D-1 to D-5 ([AEA]@C_n). The relationship between the number of carbon atoms and the free energies of electron transfer (ΔG_et(1) to ΔG_et(4)) is assessed using the Rehm-Weller equation for A-1 to A-5, B1 to B-5, C-1 to C-5, and D-1 to D-5 supramolecular [14-MR Macrolides]@C_n complexes 5-24. Calculations are presented for the four reduction potentials (^Red.E₁ to ^Red.E₄) of fullerenes C _n . The results were used to calculate the four free-energies of electron transfer (ΔG_et(1) to ΔG_et(4)) of supramolecular complexes A-1 to A-18 to B-1 to B-18, C-1 to C-18, and D-1 to D-18 (5-76) for fullerenes C₆₀ to C₃₀₀.     

Nonclassical fullerenes with a heptagon violating the pentagon adjacency penalty rule

Nonclassical fullerenes with heptagon(s) and their derivatives have attracted increasing attention, and the studies on them are performing to enrich the chemistry of carbon. Density functional theory calculations are performed on nonclassical fullerenes C_n (n = 46, 48, 50, and 52) to give insight into their structures and stability. The calculated results demonstrate that the classical isomers generally satisfy the pentagon adjacency penalty rule. However, the nonclassical isomers with a heptagon are more energetically favorable than the classical ones with the same number of pentagon–pentagon bonds (B₅₅ bonds), and many of them are even more stable than some classical isomers with fewer B₅₅ bonds. The nonclassical isomers with the lowest energy are higher in energy than the classical ones with the lowest energy, because they have more B₅₅ bonds. Generally, the HOMO–LUMO gaps of the former are larger than those of the latter. The sphericity and asphericity are unable to rationalize the unique stability of the nonclassical fullerenes with a heptagon. The pyramidization angles of the vertices shared by two pentagons and one heptagon are smaller than those of the vertices shared by two pentagons and one hexagon. It is concluded that the strain in the fused pentagons can be released by the adjacent heptagons partly, and consequently, it is a common phenomenon for nonclassical fullerenes to violate the pentagon adjacent penalty rule. These findings are heuristic and conducive to search energetically favorable isomers of C_n, especially as n is 62, 64, 66, and 68, respectively. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

Stability of hollow spheroidal silicon clusters Sin and SinHn

The structures of Si_n and Si_nH_n fullerenes with 20 ≶n ≶60 are calculated in the MINDO/3 approximation using the Monte Carlo technique for geometry optimization. The calculations show that spheroidal silicon clusters consisting of more than 36 atoms are stable and the bond energy increases with their size. This increase is not noticed for compact clusters calculated as an alternative. For n ≥40-50, the latter have lower bond energies compared to fullerenes. The geometry optimization of the tetrahedral cluster Si₄₅ results in a structure close to spheroidal, which gains in bond energy. The addition of hydrogen atoms to small deformed fullerenes and their geometry optimization make it possible to obtain stable spheroidal structures Si_nH_n whose bond energy is greater than that of alternative compact silicon hydride clusters. When the size of spheroidal clusters Si_nH_n increases, i. e., when n > 36, the hydrogen elimination barriers decrease abruptly; the Si_nH_n diamond structure of the cluster is more advantageous when n ≥50.     

Synthesis and some aspects of the formation mechanism of carbon structures under hydrothermal conditions

The formation of carbon structures upon the reactions of organic compounds with strong mineral acids under hydrothermal conditions was studied. The reactions were found to give amorphous carbon, microcrystalline graphite, nanodiamonds, diamond-like carbon, diamonds, C₆₀ and C₇₀ fullerenes, and carbolite. Hydrocarbons of various compositions including aromatics and naphthenes were detected among the reaction products. A possible mechanism of the formation of carbon structures with sp ² bond hybridization under hydrothermal conditions was proposed.     

Thermal behaviour of carbon clusters and small fullerenes

The structural and thermal properties of small carbon clusters (C _N , N = 13, 20, and 32) are investigated by constant energy Molecular Dynamics simulations over a wide range of temperatures, i.e., from T = 0K to above the melting point of graphitic carbon. The Tersoff interatomic potential [6] is used to mimic the covalent bond between the carbon atoms in the cluster. We find that small carbon clusters start to fragment or to evaporate atoms or C₂ or C₃ units before fully developing a liquidlike phase. As a consequence, some relevant isomers (such as rings, bowls, hollow cages) are thermally isolated from each other i.e., there are no thermally activated isomerization transitions between them. Possible implications of our results on the growth mechanism of fullerenes are discussed.     

Exohedral interaction in cationic lithium metallofullerenes

We present a density functional theory study on the exohedral interaction between a singly positively charged lithium atom and fullerenes: Li⁺?C _n , n = 70, 60 and 50. We have found that the interaction is of electrostatic nature: the cation polarizes the π electronic cloud of the fullerene in an ion-induced dipole attraction. We show that these systems present a shallow potential energy surface where the local minima correspond to the interaction of the cation on top of one pentagonal or one hexagonal face of the fullerene and transition states connect them through a movement of the cation over a C?C bond. The type of interaction and the shape of the potential energy surface give rise to the so-called planetary systems, where the alkali cation is revolving around the carbon cage in orbits. The studied systems present several pathways that are more likely than others to behave as potentially favorable orbits.     

Rehybridization and π-orbital alignment: the key to the existence of spheroidal carbon clusters

The rehybridization and bonding in large carbon spheroids (C_n) has been analyzed with POAV/3D HMO theory; larger clusters are shown to be favored, and the (lower) critical value of n for stable clusters is discussed. In the generic series of truncated icosahedral spheroids of I_h symmetry, C₂₄₀ is found to be significantly more stable than its lower homologue C₆₀.     

Synthetic Approaches toward Molecular and Polymeric Carbon Allotropes

Life on earth is based on compounds that have carbon frames and backbones. Today, chemists have added to the world of biomolecules and biopolymers approximately 10⁷ different synthetic molecules and polymers, the structures of which also depend on the formation of strong, stable carbon–carbon bonds. Although the stability of carbon–carbon bonds has been recognized for more than a century, the two natural modifications graphite and diamond were, until recently, the only allotropic forms of carbon on earth that were available in macroscopic quantities and were structurally well characterized. With the synthesis of macroscopic quantities of buckminsterfullerene (C₆₀) and the higher fullerenes (C₇₀, C₇₆, C₇₈, etc.) and the exploration of the fascinating properties of these all-carbon spheres, this situation has completely changed. In the coming decades, the design, preparation, and study of novel molecular and polymeric allotropic forms of carbon will be a central topic in chemistry. Research in this area will dramatically advance the fundamental knowledge on carbon-based matter and, as already illustrated by the ongoing work on C₆₀, generate unprecedented technological perspectives. This review surveys synthetic organic-chemical approaches toward the preparation and study of all-carbon molecules and polymers that differ from the familiar networks of graphite and diamond as well as from the fullerenes. We will also discuss the ongoing research on fullerenes with a particular focus on the synthetic approaches to these all-carbon spheres and their transition metal complexes.     

Some aspects of the symmetry and topology of possible carbon allotrope structures

Elemental carbon has recently been shown to form molecular polyhedral allotropes known as fullerenes in addition to the familiar graphite and diamond known since antiquity. Such fullerenes contain polyhedral carbon cages in which all vertices have degree 3 and all faces are either pentagons or hexagons. All known fullerenes are found to satisfy the isolated pentagon rule (IPR) in which all pentagonal faces are completely surrounded by hexagons so that no two pentagonal faces share an edge. The smallest fullerene structures satisfying the IPR are the known truncated icosahedral C₆₀ of I _h symmetry and ellipsoidal C₇₀ of D _5h symmetry. The multiple IPR isomers of families of larger fullerenes such as C₇₆, C₇₈, C₈₂ and C₈₄ can be classified into families related by the so-called pyracylene transformation based on the motion of two carbon atoms in a pyracylene unit containing two linked pentagons separated by two hexagons. Larger fullerenes with 3ν vertices can be generated from smaller fullerenes with ν vertices through a so‐called leapfrog transformation consisting of omnicapping followed by dualization. The energy levels of the bonding molecular orbitals of fullerenes having icosahedral symmetry and 60n ² carbon atoms can be approximated by spherical harmonics. If fullerenes are regarded as constructed from carbon networks of positive curvature, the corresponding carbon allotropes constructed from carbon networks of negative curvature are the polymeric schwarzites. The negative curvature in schwarzites is introduced through heptagons or octagons of carbon atoms and the schwarzites are constructed by placing such carbon networks on minimal surfaces with negative Gaussian curvature, particularly the so-called P and D surfaces with local cubic symmetry. The smallest unit cell of a viable schwarzite structure having only hexagons and heptagons contains 168 carbon atoms and is constructed by applying a leapfrog transformation to a genus 3 figure containing 24 heptagons and 56 vertices described by the German mathematician Klein in the 19th century analogous to the construction of the C₆₀ fullerene truncated icosahedron by applying a leapfrog transformation to the regular dodecahedron. Although this C₁₆₈ schwarzite unit cell has local O _h point group symmetry based on the cubic lattice of the D or P surface, its larger permutational symmetry group is the PSL(2,7) group of order 168 analogous to the icosahedral pure rotation group, I, of order 60 of the C₆₀ fullerene considered as the isomorphous PSL(2,5) group. The schwarzites, which are still unknown experimentally, are predicted to be unusually low density forms of elemental carbon because of the pores generated by the infinite periodicity in three dimensions of the underlying minimal surfaces. This revised version was published online in July 2006 with corrections to the Cover Date.     

Computational Studies on Non‐covalent Interactions of Carbon and Boron Fullerenes with Graphene

First‐principles DFT calculations are carried out to study the changes in structures and electronic properties of two‐dimensional single‐layer graphene in the presence of non‐covalent interactions induced by carbon and boron fullerenes (C₆₀, C₇₀, C₈₀ and B₈₀). Our study shows that larger carbon fullerene interacts more strongly than the smaller fullerene, and boron fullerene interacts more strongly than that of its carbon analogue with the same nuclearity. We find that van der Waals interactions play a major role in governing non‐covalent interactions between the adsorbed fullerenes and graphene. Moreover, a greater extent of van der Waals interactions found for the larger fullerenes, C₈₀ and B₈₀, relative to smaller C₆₀, and consequently, results in higher stabilisation. We find a small amount of electron transfer from graphene to fullerene, which gives rise to a hole‐doped material. We also find changes in the graphene electronic band structures in the presence of these surface‐decorated fullerenes. The Dirac cone picture, such as that found in pristine graphene, is significantly modified due to the re‐hybridisation of graphene carbon orbitals with fullerenes orbitals near the Fermi energy. However, all of the composites exhibit perfect conducting behaviour. The simulated absorption spectra for all of the graphene–fullerene hybrids do not exhibit a significant change in the absorption peak positions with respect to the pristine graphene absorption spectrum. Additionally, we find that the hole‐transfer integral between graphene and C₆₀ is larger than the electron‐transfer integrals and the extent of these transfer integrals can be significantly tuned by graphene edge functionalisation with carboxylic acid groups. Our understanding of the non‐covalent functionalisation of graphene with various fullerenes would promote experimentalists to explore these systems, for their possible applications in electronic and opto‐electronic devices.     

Gas dynamics in an arc discharge chamber as a factor governing the isolation of C60 and other “magic” fullerenes

A joint analysis of fullerene assembly kinetics and gas flow dynamics in an arc chamber for the production of fullerenes showed that the effective annealing of fullerenes and the evident dominance of “magic” fullerenes C₆₀ and C₇₀ were mainly explained by the difference between the thermal dissociation rates of these and less stable C₆₂ and C₆₈ fullerenes. The percent of “nonmagic” fullerenes was also shown to depend on the structure of the gas flows formed in the arc discharge chamber. The majority of newly formed fullerenes were not immediately removed from the chamber, bur were trapped by closed gas flows. Back in the hot region of the chamber, fullerenes were simultaneously annealed and dissociated under the action of high temperature and, partially, UV radiation. The “nonmagic” fullerenes were most actively suppressed in a non-pumpable discharge chamber.     

Polythermal solubility of light fullerenes in valeric and caproic acids in the temperature range 20–80°C

The polythermal solubility of fullerene C₆₀ and a fullerene mixture (60 wt % C₆₀ + 39 wt % C₇₀ + 1 wt % higher fullerenes C _n , n = 76, 78, 84, 90...) in valeric and caproic acids was studied in the temperature range 20–80°C. The solubility diagrams are presented and characterized.     

Stable Non‐IPR C60 and C70 Fullerenes Containing a Uniform Distribution of Pyrenes and Adjacent Pentagons

The most abundant fullerenes, C₆₀ and C₇₀, and all the pure carbon fullerenes larger than C₇₀, follow the isolated‐pentagon rule (IPR). Non‐IPR fullerenes containing adjacent pentagons (APs) have been stabilized experimentally in cases where, according to Euler’s theorem, it is topologically impossible to isolate all the pentagons from each other. Surprisingly, recent experiments have shown that a few endohedral fullerenes, for which IPR structures are possible, are stabilized in non‐IPR cages. We show that, apart from strain, the physical property that governs the relative stabilities of fullerenes is the charge distribution in the cage. This charge distribution is controlled by the number and location of APs and pyrene motifs. We show that, when these motifs are uniformly distributed in the cage and well‐separated from one other, stabilization of non‐IPR endohedral and exohedral derivatives, as well as pure carbon fullerene anions and cations, is the rule, rather than the exception. This suggests that non‐IPR derivatives might be even more common than IPR ones.