Rippled nanocarbons from periodic arrangements of reordered bivacancies in graphene or nanotubes

We report on various nanocarbons formed from a unique structural pattern containing two pentagons, three hexagons, and two heptagons, resulting from local rearrangements around a divacancy in pristine graphene, or nanotubes. This defect can be inserted in sheets or tubes either individually or as extended defect lines. Sheets or tubes containing only this defect as a pattern can also be obtained. These fully defective sheets, and most of the tubes, present a very pronounced rippled (wavy) structure and their energies are lower than other structures based on pentagons and heptagons published so far. Another particularity of these rippled carbon sheets is their ability to fold themselves into a two-dimensional porous network of interconnected tubes upon heat treatment as shown by hybrid Monte Carlo simulations. Finally, contrary to the common belief that pentagon/heptagon based structures are metallic, this work shows that this defect pattern should give rise to semimetallic conduction.     

Why alkali metals preferably bind on structural defects of carbon nanotubes: a theoretical study by first principles

By using ab initio calculations we investigated the interaction of alkali metal atoms and alkali metal cations with perfect and defective carbon nanotubes. Our results show that the alkali metals prefer to interact with the pentagons and heptagons that appear on the defective site of the carbon nanotube rather than with the hexagons. The alkali metals remain always positively charged not depending on their charge state (neutral, cation) or the different carbon ring that they interact with. The molecular orbital energy level splitting from a defect creation on the carbon nanotube along with the localization of charge-electron density on the defect, results in binding the alkali metals more efficient. More interestingly, metallic sodium appears to bind very weak on the nanotube compared to the rest of alkali metals. The Na anomaly is attributed to the fact that unlike the K case, sodium's inner p shell falls energetically lower than carbon nanotube's p molecular orbitals. As a result, the Na p shell is practically excluded from any binding energy contribution. In the alkali metal cation case the electronegativity trend is followed.     

Dicyclohepta[ijkl,uvwx]rubicene with Two Pentagons and Two Heptagons as a Stable and Planar Non-benzenoid Nanographene

Polycyclic aromatic hydrocarbons with hexagons/pentagons or hexagons/heptagons have been intensively investigated in recent years, but those with simultaneous presence of hexagons, pentagons and heptagons remain rare. In this paper, we report dicyclohepta[ijkl,uvwx]rubicene ( DHR ), a non-benzenoid isomer of dibenzo[bc,kl]coronene with two pentagons and two heptagons. We developed an efficient and scalable synthetic method for DHR by using Scholl reaction and dehydrogenation. Crystal structure of DHR shows that the benzenoid rings, two pentagons and two heptagons are coplanar. The bond lengths analysis and the ICSS(1)zz and LOL-π calculations indicate that the incorporation of two formal azulene moieties has an effect on the conjugated structure. The π-electrons of benzenoid and pentagon rings are more delocalized. Cyclic voltammetry studies indicate that DHR shows multiple oxidation and reduction potentials. Interestingly, DHR exhibits unusual S₀ to S₂ absorption and abnormal anti-Kasha S₂ to S₀ emission. Moreover, crystals of DHR exhibit semiconducting behaviour with hole mobility up to 0.082 cm² V⁻¹ s⁻¹.     

Dicyclohepta[ijkl,uvwx]rubicene with Two Pentagons and Two Heptagons as a Stable and Planar Non‐benzenoid Nanographene

Polycyclic aromatic hydrocarbons with hexagons/pentagons or hexagons/heptagons have been intensively investigated in recent years, but those with simultaneous presence of hexagons, pentagons and heptagons remain rare. In this paper, we report dicyclohepta[ijkl,uvwx]rubicene ( DHR ), a non‐benzenoid isomer of dibenzo[bc,kl]coronene with two pentagons and two heptagons. We developed an efficient and scalable synthetic method for DHR by using Scholl reaction and dehydrogenation. Crystal structure of DHR shows that the benzenoid rings, two pentagons and two heptagons are coplanar. The bond lengths analysis and the ICSS(1)zz and LOL‐π calculations indicate that the incorporation of two formal azulene moieties has an effect on the conjugated structure. The π‐electrons of benzenoid and pentagon rings are more delocalized. Cyclic voltammetry studies indicate that DHR shows multiple oxidation and reduction potentials. Interestingly, DHR exhibits unusual S₀ to S₂ absorption and abnormal anti‐Kasha S₂ to S₀ emission. Moreover, crystals of DHR exhibit semiconducting behaviour with hole mobility up to 0.082 cm² V^?1 s^?1.     

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.     

The geometric structure of deformed nanotubes and the topological coordinates

After summarizing the harmonic approach to topological coordinates and the null space embedding of graphs, three-coordinated tiling of the plane by hexagons, pentagons, and heptagons are presented and used for the construction of tubular, toroidal, and helical carbon structures. Physically realistic 3D geometries are formed from the corresponding adjacency matrices, and the final structure was obtained with the help of Brenner-potential based molecular mechanics methods.     

Double Negatively Curved C70 Growth through a Heptagon‐Involving Pathway

All previously reported C₇₀ isomers have positive curvature and contain 12 pentagons in addition to hexagons. Herein, we report a new C₇₀ species with two negatively curved heptagon moieties and 14 pentagons. This unconventional heptafullerene[70] containing two symmetric heptagons, referred to as dihept‐C₇₀, grows in the carbon arc by a theoretically supported pathway in which the carbon cluster of a previously reported C₆₆ species undergoes successive C₂ insertion via a known heptafullerene[68] intermediate with low energy barriers. As identified by X‐ray crystallography, the occurrence of heptagons facilitates a reduction in the angle of the π‐orbital axis vector in the fused pentagons to stabilize dihept‐C₇₀. Chlorination at the intersection of a heptagon and two adjacent pentagons can greatly enlarge the HOMO–LUMO gap, which makes dihept‐C₇₀Cl₆ isolable by chromatography. The synthesis of dihept‐C₇₀Cl₆ offers precious clues with respect to the fullerene formation mechanism in the carbon‐clustering process.     

Topology and electronic structure of nanotube junctions of tetrapod shape

We propose a series of carbon nanostructures in the shape of tetrapod as a kind of three-dimensional junction for carbon nanotubes. The tetrapod junctions are such open networks that are made of sp² carbon atoms only, have negative Gaussian curvature, and connect four nanotubes together. We define the structure of standard tetrapod junctions, the simplest one, that have 12 heptagons other than hexagons and have the T_d symmetry.Our tight-binding energy-band calculations for the standard tetrapod junctions of smaller sizes show that their electronic property mainly depends on one particular topological factor: the junctions having a carbon atom in the center of each triangular face of tetrahedron exhibit metallic band structure while the junctions having a benzene ring in the center of the faces are semiconductors. We also find that tetrapod junctions connecting (6,0) nanotubes exhibit a flat band near the Fermi energy in a particular momentum region. The origin of the flat band states can be figured out from the wavefunction distribution. We also show the possibility to extend the standard tetrapod junctions to some non-standard ones that can connect nanotubes of different kinds and/or radii.     

Super face d-antimagic labeling for disjoint union of toroidal fullerenes

The discovery of the fullerene molecules and related forms of carbon such as nanotubes has generated an explosion of activity in chemistry, physics, and materials science. Classical fullerene is an all-carbon molecule in which the atoms are arranged on a pseudospherical framework made up entirely of pentagons and hexagons. A toroidal fullerene (toroidal polyhex) is a cubic bipartite graph embedded on the torus such that each face is a hexagon. In this paper we examine the existence of entire labeling, where face-weights of all 6-sided faces of disjoint union of toroidal fullerenes form an arithmetic progression with common difference \(\hbox {d}\in \{1,2,3\}\).     

Three-stage transformation pathway from nanodiamonds to fullerenes

The dynamics of structure evolution of nanodiamonds ranging from 22 to 318 atoms of various shapes is studied by density functional tight-binding molecular dynamics. The spherical and cubic nanodiamonds can be transformed into fullerene-like structures upon heating. A number of the transformed fullerenes consist of pentagons and hexagons only. Others contain squares, heptagons, and octagons. One simulated fullerene is an isomer of C(60). The temperature of the transformation depends on the size, shape, and orientation of initial cluster. To be transformed into onion-like fullerenes, the spherical nanodiamonds should have 200 atoms or more, while the cubic ones require 302 atoms or more. The time-resolved energy profiles of all the transformations clearly reveal three-stage transformation character. During the first stage, the energy reduces quickly due to converting sp(3) carbon with dangling bond at the surface into sp(2) one, and the formation of partial sp(2) envelope wrapping the cluster. For the second stage, energy decreases slowly. The remaining interior carbon atoms come to the surface through the hole in the sp(2) envelope, and similar amount of sp(3) and sp(2) atoms coexist. The third stage involves the closure of holes, accompanied by the detachment of C(2) molecules and carbon chains from the edges. The energy decreases relatively fast in this stage. The proposed three-stage transformation pathway holds for all the simulations performed in this work, including those with the instant heating.     

Pentaheptite modifications of the graphite sheet

Pentaheptites (three-coordinate tilings of the plane by pentagons and heptagons only) are classified under the chemically motivated restriction that all pentagons occur in isolated pairs and all heptagons have three heptagonal neighbors. They span a continuum between the two lattices exemplified by the boron nets in ThMoB4 (cmm) and YCrB4 (pgg), in analogy with the crossover from cubic-close-packed to hexagonal-close-packed packings in 3D. Symmetries realizable for these pentaheptite layers are three strip groups (periodic in one dimension), p1a1, p112, and p111, and five Fedorov groups (periodic in two dimensions), cmm, pgg, pg, p2, and p1. All can be constructed by simultaneous rotation of the central bonds of pyrene tilings of the graphite sheet. The unique lattice of cmm symmetry corresponds to the previously proposed pentaheptite carbon metal. Analogous pentagon-heptagon tilings on other surfaces including the torus, Klein bottle, and cylinder, face-regular tilings of pentagons and b-gons, and a full characterization of tilings involving isolated pairs and/or triples of pentagons are presented. The Kelvin paradigm of a continuum of structures arising from propagation of two original motifs has many potential applications in 2D and 3D.     

Pentagon-Embedded Cycloarylenes with Cylindrical Shapes

Cylinder-shaped graphitic networks in carbon nanotubes have attracted interest from scientists in various disciplines. The chemical synthesis of segments thereof is considered as a challenging and appealing subject in chemistry, and deepens our understanding of curved and conjugated arrays of hexagons. We herein report the synthesis of cylinder-shaped molecules containing non-hexagon bridges in their conjugated systems. Multiple pentagon units were embedded in the cylinder-shaped discrete molecules, and the stereoisomerism originating from their helical carbon arrangements was studied. Structural analysis by NMR, UV/Vis absorption spectroscopy, and single-crystal X-ray diffraction provided fundamental experimental information on the curved systems with conjugation across the pentagons. This study provides the first experimental guide for further explorations of anomalous non-hexagon arrays of graphitic carbon materials with cylindrical shapes.     

Pentagon‐Embedded Cycloarylenes with Cylindrical Shapes

Cylinder‐shaped graphitic networks in carbon nanotubes have attracted interest from scientists in various disciplines. The chemical synthesis of segments thereof is considered as a challenging and appealing subject in chemistry, and deepens our understanding of curved and conjugated arrays of hexagons. We herein report the synthesis of cylinder‐shaped molecules containing non‐hexagon bridges in their conjugated systems. Multiple pentagon units were embedded in the cylinder‐shaped discrete molecules, and the stereoisomerism originating from their helical carbon arrangements was studied. Structural analysis by NMR, UV/Vis absorption spectroscopy, and single‐crystal X‐ray diffraction provided fundamental experimental information on the curved systems with conjugation across the pentagons. This study provides the first experimental guide for further explorations of anomalous non‐hexagon arrays of graphitic carbon materials with cylindrical shapes.     

First-principles calculations on the curvature evolution and cross-linkage in carbon nitride

First-principles calculations were utilized to study the formation mechanisms and structural features of fullerene-like carbon nitride (FL CN_x). Cohesive energy comparisons reveal the energy cost for different defects arising from substitution of C for N as a function of the nitrogen concentration. In FL CN_x, combinations of pentagons and heptagons compete in causing graphene sheet curvature during the addition of CN-precursors and single species. Also, cross-linkage between graphene layers in FL CN_x can be explained by the bond rotation due to incorporated N atoms. The computational results agree with recent experimental observations from the growth of FL CN_x thin films.     

The saturated hydrides of C<Subscript>60</Subscript>:F<Subscript>5</Subscript>F<Subscript>6</Subscript> PK F<Subscript>5</Subscript>F<Subscript>7</Subscript> isomers

The carbon cages composed of pentagons and heptagons (F₅F₇ isomers) are the analogs of fullerenes composed of pentagons and hexagons (F₅F₆ isomers). To provide insight into the structures and stability of the hydrides of F₅F₆ and F₅F₇ isomers, systematical density functional theory calculations are performed on all the 1,812 F₅F₆–C₆₀H₆₀ and 56 F₅F₇–C₆₀H₆₀. The calculated results demonstrate that the isomer with lowest/highest energy has most/fewest fused pentagons for both F₅F₆ and F₅F₇ hydrides and the stability of these hydrides increase with the number of fused pentagons roughly. The lowest energy F₅F₆–C₆₀H₆₀ and F₅F₇–C₆₀H₆₀ are 237.1 and 152.5 kcal/mol lower in energy than the isolated pentagon rule (IPR) C₆₀H₆₀, respectively; however, these two parent cages are 529.6 and 660.0 kcal/mol higher in energy than the IPR C₆₀. The calculations suggest that heptagon-containing cages, not only those violating the IPR can be the candidate cages for fullerene derivatives and the possible repulsion between the added atoms may play an important role in determining the structures and stability of the hydrides of carbon cages.     

Synthesis,Properties, and Packing Structures of Corannulene‐Based π‐Systems Containing Heptagons

Introduction of heptagons into hexagonal carbon lattices can generate negatively curved polycyclic aromatic hydrocarbons, which are of significant interest in the field of exotic molecular nanocarbons. We have successfully synthesized and characterized corannulene‐based π‐systems containing heptagons ( 4 and 5 ) as new negatively curved polycyclic aromatic hydrocarbons as well as possible intermediates in the synthesis of warped nanographene 1 . The formation of 4 and 5 represents the first example for which a heptagon is formed under Scholl reaction conditions before all hexagons are formed. Even more interestingly, we discovered that the mode and degree of solid‐phase intermolecular π–π interaction can be altered significantly by the degree of ring closure.     

24 IPR isomers of fullerene C84: Cage deformation as geometrical characteristic of local strains

The structures of 24 IPR‐isomers of C₈₄ fullerene with distributed single, double and delocalized bonds are presented. Obtained results are fully supported by DFT quantum‐chemical calculations of electronic and geometrical structures of these isomers. Two reasons of instability of fullerene molecules are their radical origin and/or high local strain. Distortion of pentagons as well as hexagons with alternating single and double bonds is the most significant geometrical parameter reflecting local strain of a molecule. These distortions are measured as maximal dihedral angles of those cycles and reach 20 degrees in mostly deformed hexagons and pentagons. In contrast high values of dihedral angles in hexagons with delocalized π‐bonds are typical for stable isomers. Other geometric parameters such as valence angles, sums of valence angles and dihedral angles between approximate planes of fused rings have no marked influence on stability. The development of strain‐related criteria for fullerene stability will be helpful in the prediction which isomers might potentially be observable in experiment. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

Strain energies due to nonplanar distortion of fullerenes and their dependence on structural motifs

Accurate strain energies due to nonplanar distortion of 114 isolated pentagon rule (IPR) fullerenes with 60-102 carbon atoms have been calculated based on B3LYP/6-31G(d) optimized structures. The calculated values of strain energy due to nonplanar distortion (Enp) are reproduced by three simple schemes based upon counts of 8, 16, and 30 distinct structural motifs composed of hexagons and pentagons. Using C180 (Ih) and CN (Ih) (N is very large) as test molecules, the intrinsic limitations of the motif model based on six-membered rings (6-MRs) as the central unit have been discussed. On the basis of the relationship between the contributions of motifs to Enp and the number of five-membered rings (5-MRs) in motifs, we found that IPR fullerenes with dispersed 5-MRs present smaller nonplanar distortions.     

Structure and reactivity of C54q+ (q = 0, 1, 2 and 4) fullerenes

Using density functional theory we have studied the structural properties of eleven C54 isomers that appear in the C60 fragmentation. We have evaluated the relative stability of the different isomers with respect the most stable one, which corresponds to the structure with the minimum number (four) of adjacent pentagons. On average, the length of a bond shared by pentagons and/or hexagons increases in the order hexagon-hexagon, hexagon-pentagon and pentagon-pentagon. However, we have found that the central bond in the confluence of four hexagons, i.e. a pyrene substructure, is anomalously large, becoming in some cases the largest one. We have also evaluated the nucleus-independent chemical shifts (NICS) at the center of every individual ring in the most stable isomers. For the chlorine derivatives, our calculations show that the favorite position for chlorine addition are the bonds shared by pentagons.