Relative isomer abundance of fullerenes and carbon nanotubes correlates with kinetic stability

ZZ Polynomials for Isomers of (5,6)-Fullerenes Cn with n = 20–50

A compilation of ZZ polynomials (aka Zhang–Zhang polynomials or Clar covering polynomials) for all isomers of small (5,6)-fullerenes Cn with n = 20–50 is presented. The ZZ polynomials concisely summarize the most important topological invariants of the fullerene isomers: the number of Kekulé structures K, the Clar number Cl, the first Herndon number h1, the total number of Clar covers C, and the number of Clar structures. The presented results should be useful as benchmark data for designing algorithms and computer programs aiming at topological analysis of fullerenes and at generation of resonance structures for valence-bond quantum-chemical calculations.

Fullerene Thermochemical Stability: Accurate Heats of Formation for Small Fullerenes, the Importance of Structural Deformation on Reactivity, and the Special Stability of C60

We have used quantum chemistry computations, in conjunction with isodesmic-type reactions, to obtain accurate heats of formation (HoFs) for the small fullerenes C₂₀ (2358.2 ± 8.0 kJ mol^-1), C₂₄ (2566.2 ± 7.6), and the lowest-energy isomers of C₃₂ (2461.1 ± 15.4), C₄₂ (2629.0 ± 20.5), and C₅₄ (2686.2 ± 25.3). As part of this endeavor, we have also obtained accurate HoFs for several medium-sized molecules, namely 216.6 ± 1.4 for fulvene, 375.5 ± 1.5 for pentalene, 670.8 ± 2.9 for acepentalene, and 262.7 ± 2.5 for acenaphthylene. We combine the energies of the small fullerenes and previously obtained energies for larger fullerenes (from C₆₀ to C₆₀₀₀) into a full picture of fullerene thermochemical stability. In general, the per-carbon energies can be reasonably approximated by the "R+D" model that we have previously developed [Chan et al. J. Chem. Theory Comput. 2019, 15, 1255-1264], which takes into account Resonance and structural Deformation factors. In a case study on C₅₄, we find that most of the high-deformation-energy atoms correspond to the sites of the C-Cl bond in the experimentally captured C₅₄Cl₈. In another case study, we find that C₆₀ has the lowest value for the maximum local-deformation energy when compared with similar-sized fullerenes, which is consistent with its "special stability". These results are indicative of structural deformation playing an important role in the reactivity of fullerenes.

Estimation of the thermal and photochemical stabilities of pheromones

The correlation between the kinetic stability of molecules against temperature and variations in their geometric structure under optical excitation is investigated by the example of different organic pheromone molecules sensitive to temperature or ultraviolet radiation using the density functional theory. The kinetic stability is determined by the previously developed method based on the calculation of the probability of extension of any structural bond by a value exceeding the limit value L_мах corresponding to the breaking of the bond under temperature excitation. The kinetic stability calculation only requires the eigenfrequencies and vibrational mode vectors in the molecule ground state to be calculated, without determining the transition states. The weakest bonds in molecules determined by the kinetic stability method are compared with the bond length variations in molecules in the excited state upon absorption of light by a molecule. Good agreement between the results obtained is demonstrated and the difference between them is discussed. The universality of formulations within both approaches used to estimate the stability of different pheromone molecules containing strained cycles and conjugated, double, and single bonds allows these approaches to be applied for studying other molecules. Graphical Abstract Estimation of the thermal and photochemical stabilities of pheromones.

Identification of Four C40 Isomers by Means of a Theoretical XPS/NEXAFS Spectra Study

XPS and NEXAFS spectra of four stable C₄₀ isomers [29( C₂), 31( C _s), 38( D₂), and 39( D_{5 d})] have been investigated theoretically. We combined density functional theory and the full core hole potential method to simulate C 1s XPS and NEXAFS spectra for nonequivalent carbon atoms of four stable C₄₀ fullerene isomers. The NEXAFS showed obvious dependence on the four C₄₀ isomers, and XPS spectra are distinct for all four isomers, which can be employed to identify the four stable structures of C₄₀. Furthermore, the individual components of the spectra according to different categories have been investigated, and the relationship between the spectra and the local structures of C atoms was also explored.

Generalized structural motif model for studying the thermodynamic stability of fullerenes: from C60to graphene passing through giant fullerenes

A generalized motif model to describe the stability of neutral fullerenes, covering the full range of cage sizes, starting from C₆₀, going through giant fullerenes, and ultimately leading to graphene.

Theoretical Investigation of Molecular and Electronic Structures of Buckminsterfullerene-Silicon Quantum Dot Systems

Density functional theory (DFT) and density functional tight binding (DFTB) molecular dynamics (DFTB/MD) simulations of embedding and relaxation of buckminsterfullerene C₆₀ molecules chemisorbed on (001) and (111) surfaces and inside bulk silicon lattice were performed. DFT calculations of chemisorbed fullerenes on both surfaces show that the C₆₀ molecule deformation was very small and the C₆₀ binding energies were roughly ∼4 eV. The charge analysis shows that the C₆₀ molecule charges on (001) and (111) surfaces were between -2 and -3.5 electrons, respectively, that correlates well with the number of C-Si bonds linking the fullerene molecule and the silicon surface. DFT calculations of the C₆₀ molecule inside bulk silicon confirm that the C₆₀ molecule remains stable with the deformation energy values of between 11 and 15 eV for geometries with different C₆₀ configurations. The formation of some C-Si bonds causes local silicon amorphization and corresponding electronic charge uptake on the embedded fullerene cages. Charge analysis confirms that a single C₆₀ molecule can accept up to 20 excessive electrons that can be used in practice, wherein the main charge contribution is located on the fullerene's carbon atoms bonded to silicon atoms. These DFT calculations correlate well with DFTB/MD simulations of the embedding process. In this process, the C₆₀ molecule was placed on the top of the Si(111) surface, and it was further exposed by a stream of silicon dimers, resulting in subsequent overgrowth by silicon.

Self-assembly of endohedral metallofullerenes: a decisive role of cooling gas and metal-carbon bonding

The endohedral metallofullerene (EMF) self-assembly process in Sc/carbon vapor in the presence and absence of an inert cooling gas (helium) is systematically investigated using quantum chemical molecular dynamics simulations. It is revealed that the presence of He atoms accelerates the formation of pentagons and hexagons and reduces the size of the self-assembled carbon cages in comparison with analogous He-free simulations. As a result, the Sc/C/He system simulations produce a larger number of successful trajectories (i.e. leading to Sc-EMFs) with more realistic cage-size distribution than simulations of the Sc/C system. The main Sc encapsulation mechanism involves nucleation of several hexagons and pentagons with Sc atoms already at the early stages of carbon vapor condensation. In such proto-cages, both Sc-C σ-bonds and coordination bonds between Sc atoms and the π-system of the carbon network are present. Sc atoms are thus rather labile and can move along the carbon network, but the overall bonding is sufficiently strong to prevent dissociation even at temperatures around 2000 kelvin. Further growth of the fullerene cage results in the encapsulation of one or two Sc atoms within the fullerene. In agreement with experimental studies, an extension of the simulations to Fe and Ti as the metal component showed that Fe-EMFs are not formed at all, whereas Ti is prone to form Ti-EMFs with small cage sizes, including Ti@C28-Td and Ti@C30-C2v(3).

Top-down formation of fullerenes in the interstellar medium

Fullerenes have been recently detected in various circumstellar and interstellar environments, raising the question of their formation pathway. It has been proposed that they can form at the low densities found in the interstellar medium by the photo-chemical processing of large polycyclic aromatic hydrocarbons (PAHs). Following our previous work on the evolution of PAHs in the NGC 7023 reflection nebula, we evaluate, using photochemical modeling, the possibility that the PAH C66H20 (i.e. circumovalene) can lead to the formation of C60 upon irradiation by ultraviolet photons. The chemical pathway involves full dehydrogenation of C66H20, folding into a floppy closed cage and shrinking of the cage by loss of C2 units until it reaches the symmetric C60 molecule. At 10" from the illuminating star and with realistic molecular parameters, the model predicts that 100% of C66H20 is converted into C60 in ~ 105 years, a timescale comparable to the age of the nebula. Shrinking appears to be the kinetically limiting step of the whole process. Hence, PAHs larger than C66H20 are unlikely to contribute significantly to the formation of C60, while PAHs containing between 60 and 66 C atoms should contribute to the formation of C60 with shorter timescales, and PAHs containing less than 60 C atoms will be destroyed. Assuming a classical size distribution for the PAH precursors, our model predicts absolute abundances of C60 are up to several 10-4 of the elemental carbon, i.e. less than a percent of the typical interstellar PAH abundance, which is consistent with observational studies. According to our model, once formed, C60 can survive much longer (> 107 years for radiation fields below G0 = 104) than other fullerenes because of the remarkable stability of the C60 molecule at high internal energies. Hence, a natural consequence is that C60 is more abundant than other fullerenes in highly irradiated environments.

The topology of fullerenes

Fullerenes are carbon molecules that form polyhedral cages. Their bond structures are exactly the planar cubic graphs that have only pentagon and hexagon faces. Strikingly, a number of chemical properties of a fullerene can be derived from its graph structure. A rich mathematics of cubic planar graphs and fullerene graphs has grown since they were studied by Goldberg, Coxeter, and others in the early 20th century, and many mathematical properties of fullerenes have found simple and beautiful solutions. Yet many interesting chemical and mathematical problems in the field remain open. In this paper, we present a general overview of recent topological and graph theoretical developments in fullerene research over the past two decades, describing both solved and open problems. WIREs Comput Mol Sci 2015, 5:96-145. doi: 10.1002/wcms.1207 Conflict of interest: The authors have declared no conflicts of interest for this article. For further resources related to this article, please visit the WIREs website.

Small endohedral metallofullerenes: exploration of the structure and growth mechanism in the Ti@C2n (2n = 26-50) family

Analysis of the structure and the bottom-up growth mechanism in the family of small endohedral metallofullerenes Ti@C_2n (2n = 26–50).

The formation of the smallest fullerene, C₂₈, was recently reported using gas phase experiments combined with high-resolution FT-ICR mass spectrometry. An internally located group IV metal stabilizes the highly strained non-IPR C₂₈ cage by charge transfer (IPR = isolated pentagon rule). Ti@C₄₄ also appeared as a prominent peak in the mass spectra, and U@C₂₈ was demonstrated to form by a bottom-up growth mechanism. We report here a computational analysis using standard DFT calculations and Car–Parrinello MD simulations for the family of the titled compounds, aiming to identify the optimal cage for each endohedral fullerene and to unravel key aspects of the intriguing growth mechanisms of fullerenes. We show that all the optimal isomers from C₂₆ to C₅₀ are linked by a simple C₂ insertion, with the exception of a few carbon cages that require an additional C₂ rearrangement. The ingestion of a C₂ unit is always an exergonic/exothermic process that can occur through a rather simple mechanism, with the most energetically demanding step corresponding to the closure of the carbon cage. The large formation abundance observed in mass spectra for Ti@C₂₈ and Ti@C₄₄ can be explained by the special electronic properties of these cages and their higher relative stabilities with respect to C₂ reactivity. We further verify that extrusion of C atoms from an already closed fullerene is much more energetically demanding than forming the fullerene by a bottom-up mechanism. Independent of the formation mechanism, the present investigations strongly support that, among all the possible isomers, the most stable, smaller non-IPR carbon cages are formed, a conclusion that is also valid for medium and large cages.

Single-walled carbon nanotube growth from chiral carbon nanorings: prediction of chirality and diameter influence on growth rates

Catalyst-free, chirality-controlled growth of chiral and zigzag single-walled carbon nanotubes (SWCNTs) from organic precursors is demonstrated using quantum chemical simulations. Growth of (4,3), (6,5), (6,1), (10,1) and (8,0) SWCNTs was induced by ethynyl radical (C(2)H) addition to organic precursors. These simulations show a strong dependence of the SWCNT growth rate on the chiral angle, θ. The SWCNT diameter however does not influence the SWCNT growth rate under these conditions. This agreement with a previously proposed screw-dislocation-like model of transition metal-catalyzed SWCNT growth rates [Ding, F.; Proc. Natl. Acad. Sci. 2009, 106, 2506] indicates that the SWCNT growth rate is an intrinsic property of the SWCNT edge itself. Conversely, we predict that the rate of SWCNT growth via Diels-Alder cycloaddition of C(2)H(2) is strongly influenced by the diameter of the SWCNT. We therefore predict the existence of a maximum growth rate for an optimum diameter/chirality combination at a given C(2)H/C(2)H(2) ratio. We also find that the ability of a SWCNT to avoid defect formation during growth is an intrinsic quality of the SWCNT edge.