Defining rules of aromaticity: a unified approach to the Hückel, Clar and Randić concepts

The molecular structure of any system may be unambiguously described by its adjacency matrix, A, in which bonds are assigned entry a(ij) = 1 and non-bonded pairs of atoms entry a(ij) = 0. For π-electron-containing conjugated hydrocarbons, this matrix may be modified in order to represent one of the possible Kekulé structures by assigning entry 1 to double bonds and entry 0 to single bonds, leading to the Kekulé matrix K which can be obtained from the A matrix by subtracting 1 from elements a(pq) that represent single bonds in the Kekulé structure. The A and K matrices are the boundary cases of a general matrix A(ε), named perturbation matrix, in which from elements a(pq) that represent single bonds is subtracted a value ε∈<0,1> representing the magnitude of the perturbation. The determinant of the A(ε) matrix is unambiguously represented by an appropriate polynomial that, in turn, can be written in a form containing terms ±(1-ε)(N/2) that identify types of π-electron conjugated cycles (N is the corresponding number of π-electrons). If the sign before the term is (+), then the contribution is stabilizing, but if it is (-) the contribution is destabilizing. The approach shows why and how the Hückel rule works, how the Randi? conjugated circuits result from the analysis of canonical structures, and also how the Clar rule may be extended to include aromatic cycles larger than six-membered (aromatic sextet).     

Effect on ring current of the Kekulé vibration in aromatic and antiaromatic rings

Derivative current-density maps are used to follow the changes in ring-current (and hence, on the magnetic criterion, the changes in aromaticity) with the Kekulé vibrations of the prototypical aromatic, antiaromatic, and nonaromatic systems of benzene, cyclooctatetraene (COT), and borazine. Maps are computed at the ipsocentric CHF/6-31G**//RHF/6-31G** level. The first-derivative map for benzene shows a growing-in of localized bond currents, and the second-derivative map shows a pure, paratropic "antiring-current", leading to the conclusion that vibrational motion along the Kekulé mode will reduce the net aromaticity of benzene, on average. For planar-constrained D(4h) COT, the Kekulé mode (positive for reduction of bond-length alternation) increases paratropicity at both first and second order, indicating an average increase in antiaromaticity with zero-point motion along this mode. On the ring-current criterion, breathing expansions of benzene and D(4h) COT reduce aromaticity and increase antiaromaticity, respectively.     

Algebraic Kekulé structures of benzenoid hydrocarbons

An algebraic Kekulé structure of a benzenoid hydrocarbon is obtained from an ordinary Kekulé structure by inscribing into each hexagon the number of pi-electrons which (according to this Kekulé structure) belong to this hexagon. We show that in the case of catafusenes, there is a one-to-one correspondence between ordinary and algebraic Kekulé structures. On the other hand, in the case of perifusenes, one algebraic Kekulé structure may correspond to several ordinary Kekulé structures.     

Generation of Kekulé valence structures and the corresponding valence bond wave function

A new scheme, called "list of nonredundant bonds", is presented to record the number of bonds and their positions for the atoms involved in Kekulé valence structures of (poly)cyclic conjugated systems. Based on this scheme, a recursive algorithm for generating Kekulé valence structures has been developed and implemented. The method is general and applicable for all kinds of (poly)cyclic conjugated systems including fullerenes. The application of the algorithm in generating Valence Bond (VB) wave functions, in terms of Kekulé valence structures, is discussed and illustrated in actual VB calculations. Two types of VBSCF calculations, one involving Kekulé valence structures only and the second one involving all covalent VB structures, were performed for benzene, pentalene, benzocyclobutadiene, and naphthalene. Both strictly local and delocalised p-orbitals were used in these calculations. Our results show that, when the orbitals are restricted to their own atoms, other VB structures (Dewar structures) also have a significant contribution in the VB wave function. When removing this restriction, the other VB structures (Dewar and also the ionic structures) are accommodated in the Kekulé valence structures, automatically. Therefore, at VBSCF delocal level, the ground states of these systems can be described almost quantitatively by considering Kekulé valence structures only at a considerable saving of time.     

Resonance energy in graphite

According to Zhu et al. the resonance energy/electron (REPE) in infinite graphite sheets is equal to 0.17 eV. In the present work the REPE was calculated for parallelogram-shaped graphite sheets (PSGSs). The number of Kekulé structures and contributions of benzene-like and naphthalene-like conjugated circuits were taken into account. Analogously to polyacenes, it was found that REPE = 0.00 eV in PSGSs. The convergence is slow. These results indicate that PSGS is less "aromatic" than its infinite counterpart. Therefore addition reactions are expected to be less difficult to carry out in PSGSs than in infinite or rectangular graphite sheets.     

Nanotubes: number of Kekulé structures and aromaticity

Carbon nanotubes (CNTs) are composed of cylindrical graphite sheets consisting of sp(2) carbons. Due to their structure CNTs are considered to be aromatic systems. In this work the number of Kekulé structures (K) in "armchair" CNTs was estimated by using the transfer matrix technique. All Kekulé structures of the cyclic variants of naphthalene and benzo[c]phenanthrene have been generated and the basic patterns have been obtained. From this information the elements of the transfer matrix were derived. The results obtained indicate that K (and the resonance energy) is greater if tubulenes are extended in the vertical than in the horizontal direction. Tubulenes are therefore more stabile than cyclic strips. An illustration, obtained by using scanning probe microscope, has been attached to affirm the existence of thin CNTs.     

Valence-bond determination of bond lengths of polycyclic aromatic hydrocarbons: comparisons with recent experimental and ab initio results

Pauling's valence-bond (VB) method for determining bond lengths is compared to ten recent literature experimental and theoretical results and is shown to give comparable results. His method only requires computation of the number of Kekulé (K) and Dewar structures (DS) of conjugated hydrocarbons. Both K and DS are obtained from the last two coefficients of the matching polynomial which is also used to obtain topological resonance energy (TRE). A molecular fragmentation method is given for determining DS of essentially disconnected polycyclic aromatic hydrocarbons (PAHs). Both Kekuléan alternant and nonalternant PAHs, including essentially disconnected and non-Kekuléan systems, have bond lengths that are easily determined by this method.     

Numerical Kekulé structures of fullerenes and partitioning of pi-electrons to pentagonal and hexagonal rings

We calculated the partitioning of pi-electrons within individual pentagonal and hexagonal rings of fullerenes for a collection of fullerenes from C20 to C72 by constructing their Kekulé valence structures and averaging the pi-electron content of individual rings over all Kekulé valence structures. The resulting information is collected in Table 2, which when combined with the Schlegel diagram of fullerenes (illustrated in Figure 7) uniquely characterizes each of the 19 fullerenes considered. The results are interpreted as the basic information on the distributions (variation) of the local (ring) pi-electron density.     

Growth of conical carbon nanotubes by chemical reduction of MgCO3

Carbon nanotubes were synthesized by chemical reduction of magnesium carbonate with metallic lithium at 600 degrees C. The nanotubes with an average length of 13 microm and diameter of 60 nm are made of short coaxial conical cylinder tubular graphite sheets with their cone axis parallel to the tube axis, different from the ordinary carbon nanotubes, composed of concentric cylindrical graphite layers with their normal perpendicular to the tube axis. It is suggested that nanoscale rough surface of lithium formed at the interface between supercritical carbon dioxide and liquid lithium takes the roles of both the reductant for reduction of carbon dioxide to carbon and the template for growth of carbon nanotubes.     

Corannulene and corazulene tiling of nanostructures

Tiling modification in nanostructure modeling can be achieved by map operations, as well as the well-known Stone-Wales bond rotation. In this respect, sequences of classical operations, or single generalized operations, were used to obtain corannulenic flowers and corannulene-like azulenic patterns. The first "corazulenic" tessellation is reported. The aromaticity of some cages tessellated by the above supra-faces is discussed in terms of several different criteria. The covering was given as a pi-electron partition within some Kekulé valence structures.The well-known geometric index of aromaticity HOMA (harmonic oscillator model of aromaticity) enabled the evaluation of local aromaticity of the discussed supra-faces and brought evidence for several dominant Kekulé valence structures. The most intriguing is the "Kekulé-Dewar" valence structure of the cage C(192) having a disjoint corazulenic tessellation.     

Molecules-in-molecule estimation of the extent of localization of Kekuléan substructures in polycyclic aromatic hydrocarbons

This article first revises graph-theoretical (local aromaticity and overall molecular) indices, introduced by M. Randi? in 1975, for benzenoid hydrocarbons and somewhat improves them for computer enumeration. This goes beyond total Kekulé structure enumeration, yielding an index calculation useful for the quantitative estimation of localization of different Kekuléan substructures (including ethylene-, benzene-, annulene-, and radialene-units). This may be viewed as a "molecules-in molecule" approach to polycyclic aromatic hydrocarbons within the context of graph theoretical partitioning.     

Molecular vibrations of [n]oligoacenes (n=2-5 and 10) and phonon dispersion relations of polyacene

As model compounds for nanosize carbon clusters, the phonon dispersion curves of polyacene are constructed based on density functional theory calculations for [n]oligoacenes (n=2-5, 10, and 15). Complete vibrational assignments are given for the observed Fourier-transform infrared and Raman spectra of [n]oligoacenes (n=2-5). Raman intensity distributions by the 1064-nm excitation are well reproduced by the polarizability-approximation calculations for naphthalene and anthracene, whereas several bands of naphthacene and pentacene at 1700-1100 cm(-1) are calculated to be enhanced by the resonance Raman effect. It is found from vibronic calculations that the coupled a(g) modes between the Kekulé deformation and joint CC stretching give rise to the Raman enhancements of the Franck-Condon type, and that the b(3g) mode corresponding to the graphite G mode is enhanced by vibronic coupling between the (1)L(a)((1)B(1u)) and (1)B(b)((1)B(2u)) states. The phonon dispersion curves of polyacene provide a uniform foundation for understanding molecular vibrations of the oligoacenes in terms of the phase difference. The mode correlated with the defect-sensitive D mode of the bulk carbon networks is also found for the present one-dimensional system.     

Fabrication of carbon nanotube sheets and their bilirubin adsorption capacity

Bilirubin adsorption on carbon nanotube surfaces has been studied to develop a new adsorbent in the plasma apheresis. Powder-like carbon nanotubes were first examined under various adsorption conditions such as temperatures and initial concentrations of bilirubin solutions. The adsorption capacity was measured from the residual concentrations of bilirubin in the solution after the adsorption process using a visible absorption spectroscopy. We found that multi-walled carbon nanotubes (MWCNTs) exhibit greater adsorption capacity for bilirubin molecules than that of single-walled carbon nanotubes (SWCNTs). To guarantee the safety of the adsorbents, we fabricated carbon nanotube sheets in which leakage of CNTs to the plasma is suppressed. Since SWCNTs are more suitable for robust sheets, a complex sheet consisting of SWCNTs as the scaffolds and MWCNTs as the efficient adsorbents. CNT/polyaniline complex sheets were also fabricated. Bilirubin adsorption capacity of CNTs has been found to be much larger than that of the conventional materials because of their large surface areas and large adsorption capability for polycyclic compound molecules due to their surface structure similar to graphite.     

Applying the conjugated circuits method to Clar structures of [n]phenylenes for determining resonance energies

We consider the aromaticity of biphenylene and structurally related linear or angular [n]phenylenes for which the direct application of the model of conjugated circuits does not offer valid expressions for resonance energy and aromaticity. We located the cause of this problem as being due to Kekulé valence structures in which neighboring benzenoid rings are connected by two CC double bonds. By restricting the selection of Kekulé valence structures to those that contribute to Clar structures of such systems, we were able to show that linear and angular [n]phenylenes have approximately similar resonance energies, with angular [n]phenylenes being slightly more stable due to second order contributions arising from disjoint conjugated circuits. Expressions for resonance energies of [n]phenylenes up to n = 8 are listed and recursion expressions for higher n values are outlined.     

基于从头计算法的三维碳同素异形体结构设计

由于独特的成键特性,在不同温度和压强下,碳具有丰富的结构特性。除了实验上已发现各种同素异形体,理论计算也预言了丰富的新结构。在本文中,我们对第一性原理计算预言的三维碳同素异形体做了综述,特别地,我们着重关注了泡沫状的碳结构。碳泡沫主要由石墨片断以各种碳键连接而成,具体多孔结构及较大的表面积。另外,针对由低维碳结构,如碳富勒烯、纳米芽、纳米管及石墨烯等组成的三维碳超结构以及其他三维碳晶体我们也做了概述。这些新型碳结构有的由混杂的sp-sp²碳或者纯sp²碳组成(H-6, bct-4, C-20, K₄等),有的质量密度比金刚石还大(C₈, hP3, tl12, tp12等),有的可以由石墨在室温高压下转化而成(M碳, bct-4碳, W碳, Z碳等)。在这些预言的碳同素异形体中,有些在将来可能在实验室合成。     

Micro-Raman and Tip-Enhanced Raman Spectroscopy of Carbon Allotropes

Summary: Raman spectroscopic data are obtained on various carbon allotropes like diamond, amorphous carbon, graphite, graphene and single wall carbon nanotubes by micro-Raman spectroscopy, tip-enhanced Raman spectroscopy and tip-enhanced Raman spectroscopy imaging, and the potentials of these techniques for advanced analysis of carbon structures are discussed. Depending on the local organisation of carbon the characteristic Raman bands can be found at different wavenumber positions, and e.g. quality or dimensions of structures of the samples quantitatively can be calculated. In particular tip-enhanced Raman spectroscopy allows the investigation of individual single wall carbon nanotubes and graphene sheets and imaging of e.g. local defects with nanometer lateral resolution. Raman spectra of all carbon allotropes are presented and discussed.     

Edge effects, electronic arrangement, and aromaticity patterns on finite-length carbon nanotubes

Previous investigations have revealed that even long carbon nanotubes (CNTs) retain bond patterns that are characterized by the localization of Clar rings. Even for CNTs with 10 nm length, an alternated, oscillating structure of Clar and Kekulé patterning was also found, indicating that these arrangements may possibly persist for even longer nanotubes, given that they are finite. In the present work, we perform a detailed and comprehensive theoretical study of this phenomenon, in order to find the causes that give rise to these patterns. A complete set of CNTs with different chiralities, diameters (up to 2 nm), lengths (up to 10 nm) and endings (capped, uncapped, and tailored endings) was considered for such purposes. The results indicate that the Clar patterning appears not only on armchair CNTs, but also on those with chiral angle values close to 30°, and this results in a stabilization of the structure, when compared with the uniform, zigzag CNTs. This stabilizing effect points to the causes that underlie the three Nakamura CNT types, resulting as the superposition of structures with a maximal number of Clar rings. Although there is a strict dependence on the border shape, the main cause of the bond patterning in long tubes is to be found in the intrinsic wrapping of each CNT, because the type and number of oscillations present in the longest structures do not depend on the particular length. Nevertheless, the three Nakamura types of armchair tubes appear to subsist beyond the appearance of oscillations, because each of these sets evolves in a different manner, and energy properties that link them together. Apart from the geometry, Clar patterning was investigated through NICS (Nucleus Independent Chemical Shifts) measures, which reveal a connection between the Clar rings and a local concentration of aromaticity.     

脉冲激光溅射下固液界面生长的碳纳米管及其机理初探

以脉冲激光束直接溅射浸在水中的单质碳样品，发现在固液界面也能产生的碳纳米管，实验还发现碳纳米管的形成与样品的结构有密切的关联：石墨的层状结构越完整，碳纳米管的形成越容易，而且石墨层面相对于激光束的取向也会显著地影响碳的生成。     

脉冲激光溅射下固液界面生长的碳纳米管及其机理初探

以脉冲激光束直接溅射浸在水中的单质碳样品，发现在固液界而也能产生碳纳米管．实验还发现碳纳米管的形成与样品的结构有密切的关联：石墨的层状结构越完整，碳纳米管的形成越容易，而且石墨层而相对于激光束的取向也会显著地影响碳纳米管的生成．通过对实验结果的分析，探讨了激光液相溅射产生碳纳米管的机理，认为激光溅射产生的碳蒸气被水束缚在固液的界而内，而完整的晶而使碳蒸气在界而内的分布具有准二维的性质，为碳纳米管的生长提供了较为理想的环境．     

Graphite-incorporated MoS2 nanotubes: a new coaxial binary system

Graphite-filled MoS2 nanotubes were synthesized by pyrolizing propylene inside MoS2 nanotubes prepared by a template-assisted technique. The large coaxial nanotubes were constituted of graphite sheets inserted between the MoS2 layers, forming the outer part, and coaxial multiwall carbon nanotubes intercalated with MoS2 inside. High-resolution electron microscopy (HREM) and electron energy loss spectroscopy techniques along with molecular dynamics simulation and quantum mechanical calculations were used to characterize the samples. The one-dimensional structures exhibit diverse morphologies such as long straight and twisted nanotubes with several structural irregularities. The interplanar spacing between the MoS2 layers was found to increase from 6.3 to 7.4 A due to intercalation with carbon. Simulated HREM images revealed the presence of mechanical strains in the carbon-intercalated MoS2 layers as the reason for obtaining these twisted nanostructures. The mechanism of formation of carbon-intercalated MoS2 tubular structures and their stability and electronic properties are discussed. Our results open up the possibility of using MoS2 nanotubes as templates for the synthesis of new one-dimensional binary-phase systems.