On the Limitation of Net Algorithm for Enumerating Isomeric Structures of Giant Fullerenes

Abstract

Application of our net algorithm to the generation of all possible IPR isomers for giant fullerenes C_n, n=102 to 120, missed nine out of 39,621 possible structures. Analysis revealed that the omission of too small and too large cap triangles was the reason. Within the range of fullerenes studied, the missed structures are of high-energy and do not affect the distribution of significantly low-energy isomers.     

Modeling the structure of fulleranes and their endohedral complexes involving small molecules with nontrivial topological properties

'In' and 'out' isomers of perhydrogenated fullerenes and endohedral fullerene complexes have only recently been incorporated into the realm of topological chemistry. The 'in' isomers are, until now, purely hypothetical while for the latter group mostly studied are the complexes with metal ions that can be obtained during the fullerenes manufacturing. Much more difficult to obtain are the complexes with small molecules buried inside fullerene cages produced by laborious synthesis involving opening the cage, inserting the guest into it, and closing the cage chemically. This complicated procedure has only recently been accomplished for a hydrogen molecule put in the C60. Two H2 molecules inside the opened C70 cage and H2O in the opened C60 have been also reported recently. Model calculations, when carefully applied, allow one to predict the possibility of obtaining endohedral fullerene complexes with small molecules and 'in' isomers of perhydrogenated fullerenes. However, such systems are too large to be reliably handled by quantum calculations. Interestingly, such a simple method as molecular mechanics seems much more trustworthy.     

Correlation Between Strain Energies of Proper Fullerenes and Their Topological Invariants. Part II. Fullerenes with Isolated Pentagons

By selecting 5 or 6 parameters from the 14 possible topological parameters referring to the disposition of the 5- and 6-membered rings around each edge in a proper fullerene with isolated pentagons, it is possible to obtain good correlations with calculated (MM+) energies of fullerenes. The correlations were tested on all isomers of IPR fullerenes with 94 to 100 carbon atoms, and standard deviations around 2.5 kcal/mol were obtained.     

Structural transformations, reactions, and electronic properties of fullerenes, onions, and buckytubes

We describe the results of extensive quantum molecular dynamics calculations of the properties of fullerenes and microtubules. The topics to be discussed include: (i) stability of C₆₀ isomers and barriers to isomerization; (ii) reactivity of C₆₀ and C₅₈ with C₂ and C₃, and its implications on the formation and growth of fullerenes; and (iii) atomic and electronic structure and doping of semiconducting microtubules. We also discuss the structures, stabilities and atomic transformations of large multishell fullerenes and offer an explanation for the formation of spheroidal “onions” under high fluence electron irradiation conditions. The last results, which involved calculations for up to 15 000 atoms, were obtained using classical three-body potentials.     

内包金属富勒烯C_(66)-C_(84)团簇的结构特征

从富勒烯笼五六元环的分布情况评述了内包单金属、双金属、三金属以及三金属氮化物(M_3N)和碳化物(M_2C_2)富勒烯C_(66)～C_(84)团簇的结构特征.富勒烯满足五元环最大分离规则,内包不同类型的金属团簇不仅改变了笼的稳定性顺序,也使C_(66)、C_(68)、C_(70)、C_(72)、C_(74)、C_(78)和C_(84)的部分异构体违背五元环最大分离规则 .     

Computational Study of Structure and Thermochemistry of Some Endo‐ and Exohedral Fullerene Derivatives

Abstract

DFT calculations were applied to the problem of fullerene isomerism. Two classes of thermally stable fullerene derivatives are considered: endohedral metallofullerenes, which in some cases reveal carbon cage topology different from that observed in the empty fullerenes of the same size, and fullerene fluorides, which have uniquely rich number of theoretically possible isomers.     

Enumeration of stereo,position and chiral isomers of polysubstituted giant fullerenes: applications to C180 and C240

Abstract

We have developed combinatorial generation function methods that combine M?bius inversion and character cycle indices for the enumeration of stereo, position and chiral isomers of icosahedral giant fullerenes C₁₈₀ and C₂₄₀. Techniques are also developed for the machine perception of symmetries of especially giant fullerenes. The techniques yield, symmetries, position, stereo and chiral isomers of giant fullerenes which we illustrate with applications to icosahedral C₁₈₀(I_h), and C₂₄₀(I_h). We have obtained combinatorial tables for the isomers of C₁₈₀X_k and C₂₄₀X_k. Our results point to errors in previous computations on C₂₄₀ permutations. We have also outlined applications to NMR and ESR spectroscopy.     

Prospects of the use of fullerenes for the orientation of liquid-crystalline compositions

The dynamic characteristics of liquid crystal (LC) structures containing fullerenes C₆₀ and C₇₀ were studied, and the effect of fullerenes on the reorientation capacity of liquid crystal molecules was assessed. It is established that fullerenes C₆₀ and C₇₀ influence the operation time of polymer-dispersed LC cells containing photosensitive 2-cyclooctylamine-5-nitropyridine molecules. A possible mechanism of reorientation in the system is considered, and it is shown that fullerenes can provide for effective switching of the electrooptical response in such LC cells. Fullerenes have good prospects for use in orienting coatings of various types employed in the LC technology.     

Modifying the buckyball

Structural and electronic properties of carbon clusters, in particular the C₆₀ “buckyball” molecule as well as structurally and chemically modified fullerenes, are calculated using a combination of predictive ab initio techniques and parametrized total energy schemes. These calculations indicate that single- and multi-shell fullerenes are the most stable C_n isomers at T = 0 for n < 20. More open structures are favored by entropy at higher temperatures. Upon interaction with donor elements, C₆₀ molecules form stable M@C₆₀ endohedral complexes; analogous acceptor-based complexes are unstable. Solid C₆₀ reacts with alkali metals and forms a stable intercalation compound which shows superconducting behavior. The relatively high value of the critical temperature for superconductivity can be explained quantitatively within the Bardeen-Cooper-Schrieffer formalism.     

Weighted Homo-Lumo Energy Separations for the Polyene References of Fullerenes with Up to 100 Carbon Atoms

The T value represents the HOMO-LUMO energy separation of a ε-electronic system weighted with the number of conjugated atoms. We found that this value is kept almost constant for the polyene references defined graph-theoretically for isolated-pentagon isomers of fullerenes with up to 100 carbon atoms. on this numerical basis, the T value can safely be considered as a realistic index of kinetic stability or chemical inertness for all fullerenes without abutting pentagons.     

Comparative investigation of derivatives of C60 and its isomers

To provide insight into the derivatization of fullerenes, extensive density functional theory calculations were performed on their hydrides and fluorides of several isomers of C60. The calculated results demonstrate that the hydrides and fluorides of isolated pentagon rule (IPR) C60 are less stable than those of non-IPR C60. These results indicate that derivatization may cause structural transformation of a fullerene; and that many more non-IPR fullerenes may be captured in the forms of derivatives.     

Weighted Homo-Lumo Energy Separations for the Polyene References of Fullerenes with Up to 100 Carbon Atoms

Abstract

The T value represents the HOMO-LUMO energy separation of a ?-electronic system weighted with the number of conjugated atoms. We found that this value is kept almost constant for the polyene references defined graph-theoretically for isolated-pentagon isomers of fullerenes with up to 100 carbon atoms. on this numerical basis, the T value can safely be considered as a realistic index of kinetic stability or chemical inertness for all fullerenes without abutting pentagons.     

Double-Toroid,Almost-Polyhex Fullerenes

Abstract

This study presents examples of double-toroid fullerenes comprised entirely of hexagonal faces except as required by Euler's polyhedron closure rule. Kekulé structure counts give a rough idea of stability of these structures relative to each other and to other types of fullerenes with the same carbon number (C₁₂₀). Electronic constraints demanded by the various atomic arrangements are discussed, along with possible applications.     

Systematic search for energetically favored isomers of large fullerenes C122–C130 and C162–C180

Based on the methodology by Cioslowski et al. [J. Cioslowski, N. Rao, D. Moncrieff, J. Am. Chem. Soc. 122 (2000) 8265–8270], two empirical fit equations to predict the standard enthalpy of formation are obtained over large number of calculation results at B3LYP/6-31G* theory level for fullerene isomers, which can be used as a preliminary and second-level screening tool, respectively, for large fullerenes. By applying these equations in screening the whole isolated pentagon rule (IPR) isomers, the energetically favored isomers of large fullerenes C₁₂₂–C₁₃₀ and C₁₆₂–C₁₈₀ were predicted at the B3LYP/6-31G* density functional theory level for the first time. Our results show that the lowest energy isomers of C₁₇₄ (2473259: C_3v) and C₁₈₀ (4071832: I_h) possess much lower relative energy and larger HOMO–LUMO gaps. Moreover, the ionization energy and electron affinity of the lowest energy isomers were also investigated.     

Fullerene Desymmetrization as a Means to Achieve Single‐Enantiomer Electron Acceptors with Maximized Chiroptical Responsiveness

Solubilized fullerene derivatives have revolutionized the development of organic photovoltaic devices, acting as excellent electron acceptors. The addition of solubilizing addends to the fullerene cage results in a large number of isomers, which are generally employed as isomeric mixtures. Moreover, a significant number of these isomers are chiral, which further adds to the isomeric complexity. The opportunities presented by single‐isomer, and particularly single‐enantiomer, fullerenes in organic electronic materials and devices are poorly understood however. Here, ten pairs of enantiomers are separated from the 19 structural isomers of bis[60]phenyl‐C61‐butyric acid methyl ester, using them to elucidate important chiroptical relationships and demonstrating their application to a circularly polarized light (CPL)‐detecting device. Larger chiroptical responses are found, occurring through the inherent chirality of the fullerene. When used in a single‐enantiomer organic field‐effect transistor, the potential to discriminate CPL with a fast light response time and with a very high photocurrent dissymmetry factor (g_ph = 1.27 ± 0.06) is demonstrated. This study thus provides key strategies to design fullerenes with large chiroptical responses for use as chiral components of organic electronic devices. It is anticipated that this data will position chiral fullerenes as an exciting material class for the growing field of chiral electronic technologies.     

Structural and electronic properties of C and BN nanotubes based on periodic fullerenes: A density functional theory study

The structural and electronic properties of C and BN nanotubes based on periodic fullerenes were studied using density functional theory. It was shown that these tubular structures are stable. The electronic band structures and density of states indicated that the C nanotubes based on periodic fullerenes are metals. The energy band gap was appeared by substitution of C atoms with B and N atoms. The BN nanotubes based on periodic fullerenes show semiconducting properties. Our results suggest that the nanotubes based on periodic fullerenes can be used to design of nanoelectronic devices.     

Fullerenes with Non-Positive Gaussian Curvature: Holey-Balls and Holey-Tubes

Classical fullerenes such as C₆₀ and C₇₀ need 12 pentagonal rings of carbon for the closure of the cage. These pentagons produce the positive Gaussian curvature which gives the characteristic spherical shape. In this paper we propose a new family of fullerene-like structures which do not have pentagonal rings (no positive Gaussian curvature), no dangling bonds, possesing hexagons and heptagons only. The topology of this new family of perforated fullerenes (holey-balls) and nanotubes (holey-tubes) is higher than classical fullerenes presenting genus 5, 11 up to 21. Holey balls can be icosahedral (I_h) and cubic (O_h). The geometry, elastic stabilities and possible applications of holey-balls and holey-tubes are studied.     

电弧法制备洋葱状富勒烯的工艺研究

运用纳米Bi2O3微粒作催化剂，在电弧放电条件下，进行了纳米洋葱状富勒烯大量合成的研究。并用透射电镜对产物的形貌、结构进行了观察与分析。结果表明：纳米洋葱状富勒烯的石墨化程度很高，且直径均匀(约为25nm)，结构较完善；同时伴有单核纳米洋葱状富勒烯向多核纳米洋葱状富勒烯的转变。为洋葱状富勒烯的宏量制备提供了有利线索。     

Synthesis of C60-NBN and C70-NBN(N=L, 2) by DC arc Burning Method

Macroscopic quantities of boron-doped fullerenes, such as C_60-nB_n and C_70-nB_n(n = 1, 2), were successfully synthesized by DC arc burning method, extracted by CS₂, and characterized by field desorption mass spectra. Among them C₅₈B₂ and C₆₈B₂ were extracted for the first time. The boron-doped fullerenes were found to be less stable than their pristine fullerene analogs. When the electric current becomes too high, no boron doped fullerene, but more higher fullerenes, were formed.     

Gas phase sorting of fullerenes, polypeptides and carbon nanotubes

We discuss the Stark deflectometry of micro-modulated molecular beams for the enrichment of biomolecular isomers as well as single-wall carbon nanotubes, and we demonstrate the working principle of this idea with fullerenes. The sorting is based on the species-dependent susceptibility-to-mass ratio χ/m. The device is compatible with a high molecular throughput, and the spatial micro-modulation of the beam permits one to obtain a fine spatial resolution and a high sorting sensitivity.