Stable configurations of carbon clusters: Chains, rings, and fullerenes

Electronic Structure, Aromaticity, and Magnetism of Minimum-Sized Regular Dodecahedral Endohedral Metallofullerenes Encapsulating Rare Earth Atoms

A series of minimally sized regular dodecahedron-embedded metallofullerene REC20 clusters (RE = Sc, Y, La, Ce, Pr, Nd, Pm, Sm, Eu, and Gd) as basic units of nanoassembled materials with tunable magnetism and UV sensitivity have been explored using density functional theory (DFT). The contribution of the 4f orbital of the rare earth atom at the center of the C20 cage to the frontier molecular orbital of REC20 gives the REC20 cluster additional stability. The AdNDP orbitals of the four REC20 superatoms that conform to the spherical jellium model indicate that through natural population analysis and spin density diagrams, we observe a monotonic increase in the magnetic moment from Ce to Gd. This is attributed to the increased number of unpaired electrons in the 4f orbitals of lanthanide rare earth atoms. The UV-visible spectrum of REC20 clusters shows strong absorption in the mid-UV and near-UV bands. REC20 clusters encapsulating lanthanide rare earth atoms stand out for their tunable magnetism, UV sensitivity, and stability, making them potential new self-assembly materials.

Ring Structures of Metal Atom Doped C9, C11, and C13 Clusters from Ab Initio Calculations-The Finding of a Gd@C13 Magnetic Superatom Ring

Pure C9 clusters have a linear chain structure. However, here, we report using ab initio calculations the transformation of a chain into a cyclic ring structure with the capping of Ca, Sr, and Ba atoms. Further calculations on neutral and charged clusters doped with Sc, Y, and La atoms show stabilization of a cation C9 isoelectronic cyclic ring capped with the metal (M) atom, but anion clusters doped with these trivalent atoms form a C10 like MC9 ring, which deforms to a necklace structure. Both the ring structures correspond to electronic shell closing with 20 delocalized valence electrons in a disk jellium model and have a large highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap. Calculations of IR and Raman spectra show no imaginary frequency, suggesting that the structures are stable. Addition of two C atoms to the ring structure of LaC9 leads to a capped ring structure of the cation LaC11 and an open ring structure of the LaC11 anion. Further addition of two C atoms leads to a La@C13 cation as well as Ca@C13 and Sr@C13 neutral wheel-shaped rings with endohedral doping of the M atom. These novel ring structures have a large HOMO-LUMO gap of more than 4 eV and are magic with electronic shell closing corresponding to 28 delocalized valence electrons in a disk jellium model. There is π aromaticity in this ring satisfying 4n+2 (n = 3) Hückel's rule with 14 valence electrons. Interestingly, when the dopant is a Gd atom, there is a formation of a magnetic superatom ring Gd@C13 + with 7 μB magnetic moments due to seven 4f up-spin states of Gd being fully occupied. Bonding in these novel ring structures is discussed.

Introducing hafnium to atomically small- and medium-sized tin clusters (HfSnn0/-/2- (n = 4-17)): A computational investigation of geometrical and growth behavior, spectral properties, electronic configuration and thermochemistry

The global and local minimum configurations of single Hf atom doped Sn clusters are conducted via density function theory (DFT) combined with artificial bee colony algorithm (ABCluster). Furthermore, DFT method is also used to systematically investigate on their structural growth evolution, spectral and electronic information, thermochemical properties following the size of tin clusters doped Hf atom. Structurally, the ground-state geometries of neutral, anion and di-anion are discovered that, from n = 4, the number of Sn atoms in cluster, HfSnn0/-/2- adsorb additional Sn atom on the prior architecture one by one until forming n = 17 for HfSnn-10/-, as well as forming n = 16 for HfSnn-12-. And for the HfSn110/- and HfSn102- as beginning the species veritably develop sealed architectures. The strongest vibrational modes of sealed nanoclusters are stretching modes of Hf atom with infrared actives and breathing modes of the Sn cage framework with Raman actives, respectively. The natural population analysis (NPA) elucidates the stronger relationship between the Hf atoms and the tin frameworks in sealed clusters than that in unsealed clusters. The results of thermochemical properties, molecular orbital shell (MOs), adaptive natural density partitioning (AdNDP) and ultraviolet visible absorption spectrum (UV-Vis) indicate that, the HfSn16 with high symmetry of Td exhibits thermochemical stability and optoelectronic properties, which is utilized potentially as zero-dimensional unit of self-assembling fluorescent nanomaterials.

Cyclo[n]carbons and catenanes from different perspectives: disentangling the molecular thread

All-carbon atomic rings, cyclo[n]carbons, have recently attracted vivid attention of experimentalists and theoreticians. Among them, cyclo[18]carbon is the most studied system. In this paper, we summarize and review various properties of cyclo[n]carbons, emphasising the aspects of their aromaticity/antiaromaticity. In the first part, the trends in bonding patterns and selected aromaticity indices with the increasing size of the rings are discussed. In the second part we explore the properties of catenane models based on interlocked cyclo[18]carbon rings from different perspectives and investigate their behaviour under the action of external force using computational experiments.

Odd-Number Cyclo[n]Carbons Sustaining Alternating Aromaticity

Cyclo[n]carbons (n = 5, 7, 9, ..., 29) composed from an odd number of carbon atoms are studied computationally at density functional theory (DFT) and ab initio complete active space self-consistent field (CASSCF) levels of theory to get insight into their electronic structure and aromaticity. DFT calculations predict a strongly delocalized carbene structure of the cyclo[n]carbons and an aromatic character for all of them. In contrast, calculations at the CASSCF level yield geometrically bent and electronically localized carbene structures leading to an alternating double aromaticity of the odd-number cyclo[n]carbons. CASSCF calculations yield a singlet electronic ground state for the studied cyclo[n]carbons except for C₂₅, whereas at the DFT level the energy difference between the lowest singlet and triplet states depends on the employed functional. The BHandHLYP functional predicts a triplet ground state of the larger odd-number cyclo[n]carbons starting from n = 13. Current-density calculations at the BHandHLYP level using the CASSCF-optimized molecular structures show that there is a through-space delocalization in the cyclo[n]carbons. The current density avoids the carbene carbon atom, leading to an alternating double aromaticity of the odd-number cyclo[n]carbons satisfying the antiaromatic [4k+1] and aromatic [4k+3] rules. C₁₁, C₁₅, and C₁₉ are aromatic and can be prioritized in future synthesis. We predict a bond-shift phenomenon for the triplet state of the cyclo[n]carbons leading to resonance structures that have different reactivity toward dimerization.

Radiative relaxation in isolated large carbon clusters: Vibrational emission versus recurrent fluorescence

Recurrent fluorescence (RF) from isolated carbon clusters containing between 24 and 60 atoms is theoretically investigated as a function of internal energy, cluster size, and structural features. The vibrational relaxation kinetics and the associated IR emission spectra are determined by means of a Monte Carlo approach with vibrational density of states computed in the harmonic approximation. RF is generally found to be highly competitive with vibrational emission. The behaviors predicted for clusters of various sizes and archetypal structures indicate that the IR emission spectra are strongly influenced by RF, an energy gap law being obtained for the evolution of the RF rate constant depending on the electronic excitation state. The present results are relevant to the photophysics of the interstellar medium and could contribute to elucidating the carriers of the extended red emission bands and the continuum emission lying below the aromatic infrared bands believed to originate from mixed aromatic–aliphatic compounds.

TAO-DFT investigation of electronic properties of linear and cyclic carbon chains

It has been challenging to adequately investigate the properties of nanosystems with radical nature using conventional electronic structure methods. We address this challenge by calculating the electronic properties of linear carbon chains (l-CC[n]) and cyclic carbon chains (c-CC[n]) with n = 10-100 carbon atoms, using thermally-assisted-occupation density functional theory (TAO-DFT). For all the cases investigated, l-CC[n]/c-CC[n] are ground-state singlets, and c-CC[n] are energetically more stable than l-CC[n]. The electronic properties of l-CC[n]/c-CC[n] reveal certain oscillation patterns for smaller n, followed by monotonic changes for larger n. For the smaller carbon chains, odd-numbered l-CC[n] are more stable than the adjacent even-numbered ones; c-CC[[Formula: see text]]/c-CC[4m] are more/less stable than the adjacent odd-numbered ones, where m are positive integers. As n increases, l-CC[n]/c-CC[n] possess increasing polyradical nature in their ground states, where the active orbitals are delocalized over the entire length of l-CC[n] or the whole circumference of c-CC[n].

Theoretical investigation on bond and spectrum of cyclo[18] carbon (C18) with sp-hybridized

In an experiment, cyclo[18]carbon (C₁₈), prepared with low-temperature STM-AFM (scanning tunneling microscopy-atomic force microscopy) from C₂₄O₆, C₂₂O₄, and C₂₀O₂ molecules, have been confirmed being alternating single and triple bonds structure. Nevertheless, the stability of C₁₈ is weak at room temperature in gas. Thus, it is difficult to study the spectrum, orbital, and bonds characters of the C₁₈ molecule in the experiment. In this paper, we have obtained absorption spectrum, orbital, and bonding characters of the C₁₈ molecule in theory. Besides, bonds and spectra of C₂₄O₆, C₂₂O₄, C₂₀O₂, B₉N₉, C₆, C₁₂, C₁₆, and C₂₀ molecules have been investigated to further confirm the structure and the characters of the C₁₈ molecule. The results show that carbon-carbon bonds of C₂₄O₆, C₂₂O₄, and C₂₀O₂ molecules in ring are alternating single and triple bonds except those connected with CO group. B₉N₉ molecule as the isoelectronic structure of C₁₈ has a larger bandgap and shorter wavelength of absorption spectra than those of the C₁₈ molecule. Moreover, all bonds between boron and nitrogen in B₉N₉ molecule are single one. Study bonding characters for C₆, C₁₂, C₁₆, and C₂₀ molecules have confirmed that carbon-carbon bonds of cyclo[n]carbon changed gradually from double bonds to alternating single and triple bonds with increasing n value. The data from theory would give help for future research on C₁₈ and B₉N₉ molecules in experiment. Graphical abstract Theoretical investigation for bond and spectra characters of cyclo[18]carbon (C₁₈), prepared with low-temperature STM-AFM (scanning tunneling microscopy-atomic force microscopy) from C₂₄O₆, C₂₂O₄, and C₂₀O₂ molecules, which have been confirmed being alternating single and triple bonds structure.

Electric-field-induced spin switch of endohedral dodecahedrane heterodimers H@C20Hn-C20Hn@M (M= Cu, Ag and Au, n = 15, 18, and 19): a theoretical study

We designed nine endohedral dodecahedrane heterodimers H@C₂₀H_n-C₂₀H_n@M (M = Cu, Ag, and Au, n = 15, 18, and 19) that may act as single-molecule spin switches, and we predicted theoretically that the ground states of the dimmers shift from low-spin states (S = 0) to the high-spin states (S = 1) under an external electric field applied parallel or perpendicular to the molecular symmetry axes, consisting well with the analyses of Stark effect. Molecular orbitals analyses provide an intuitive insight into the spin crossover behavior. This study expands the application of endohedral chemistry and provides new molecules for designing single-molecule spin switch.

The formation of the smallest fullerene-like carbon cages on metal surfaces

The nucleation and growth of carbon on catalytically active metal surfaces is one of the most important techniques to produce nanomaterials such as graphene or nanotubes. Here it is shown by in situ electron microscopy that fullerene-like spherical clusters with diameters down to 0.4 nm and thus much smaller than C60 grow in a polymerized state on Co, Fe, or Ru surfaces. The cages appear on the surface of metallic islands in contact with graphene under heating to at least 650 °C and successively cooling to less than 500 °C. The formation of the small cages is explained by the segregation of carbon on a supersaturated metal, driven by kinetics. First principles energy calculations show that the clusters polymerize and can be attached to defects in graphene. Under compression, the polymerized cages appear in a crystalline structure.

Crystal structure, spectroscopic studies and quantum mechanical calculations of 2-[((3-iodo-4-methyl)phenylimino)methyl]-5-nitrothiophene

The title compound, 2-[((3-iodo-4-methyl)phenylimino)methyl]-5-nitrothiophene, C12H9O2N2I1S1, was synthesized and characterized by IR, UV-Vis and single-crystal X-ray diffraction technique. The molecular structure was optimized at the B3LYP, B3PW91 and PBEPBE levels of the density functional method (DFT) with the 6-311G+(d,p) basis set. Using the TD-DFT method, the electronic absorption spectra of the title compound was computed in both the gas phase and ethanol solvent. The harmonic vibrational frequencies of the title compound were calculated using the same methods with the 6-311G+(d,p) basis set. The calculated results were compared with the experimental determination results of the compound. The energetic behavior such as the total energy, atomic charges, dipole moment of the title compound in solvent media were examined using the B3LYP, B3PW91 and PBEPBE methods with the 6-311G+(d,p) basis set by applying the Onsager and the polarizable continuum model (PCM). The molecular orbitals (FMOs) analysis, the molecular electrostatic potential map (MEP) and the nonlinear optical properties (NLO) for the title compound were obtained with the same levels of theory. And then thermodynamic properties for the title compound were obtained using the same methods with the 6-311G(d,p) basis set.

Molecular structure of tetraaqua adenosine 5'-triphosphate aluminium(III) complex: a study involving Raman spectroscopy, theoretical DFT and potentiometry

The Alzheimer's disease is one of the most common neurodegenerative diseases that affect elderly population, due to the formation of β-amyloid protein aggregate and several symptoms, especially progressive cognitive decline. The result is a decrease in capture of glucose by cells leading to obliteration, meddling in the Krebs cycle, the principal biochemical route to the energy production leading to a decline in the levels of adenosine 5'-triphosphate. Aluminium(III) is connected to Alzheimer's and its ion provides raise fluidity of the plasma membrane, decrease cell viability and aggregation of amyloid plaques. Studies reveal that AlATP complex promotes the formation of reactive fibrils of β-amyloid protein and independent amyloidogenic peptides, suggesting the action of the complex as a chaperone in the role pathogenic process. In this research, one of complexes formed by Al(III) and adenosine 5'-triphosphate in aqueous solution is analyzed by potentiometry, Raman spectroscopy and ab initio calculations. The value of the logK(AlATP) found was 9.21±0.01 and adenosine 5'-triphosphate should act as a bidentate ligand in the complex. Raman spectroscopy and potentiometry indicate that donor atoms are the oxygen of the phosphate β and the oxygen of the phosphate γ, the terminal phosphates. Computational calculations using Density Functional Theory, with hybrid functions B3LYP and 6-311++G(d,p) basis set regarding water solvent effects, have confirmed the results. Frontier molecular orbitals, electrostatic potential contour surface, electrostatic potential mapped and Mulliken charges of the title molecule were also investigated.

Experimental and quantum chemical computational study of (E)-1-[5-(3,4-dimethylphenyldiazenyl)-2-hydroxyphenyl]ethanone

In this work, the azo dye, (E)-1-[5-(3,4-dimethylphenyldiazenyl)-2-hydroxyphenyl]ethanone, has been synthesized and characterized by IR, and X-ray single-crystal determination. In the theoretical calculations, the stable structure geometry of the isolated molecule in gas phase was investigated under the framework of the density functional theory (B3LYP) with 6-31G (d, p). To designate lowest energy molecular conformation of the title molecule, the selected torsion angle was varied every 10° and the molecular energy profile was calculated from -180° to +180°. Besides, molecular electrostatic potential (MEP), frontier molecular orbitals (FMO) analysis, and thermodynamic properties were described from the computational process. In addition to these calculations, we were investigated solvent effects on the nonlinear optical properties (NLO) of the title compound.

The smallest stable fullerene, M@C28 (m = Ti, Zr, U): stabilization and growth from carbon vapor

The smallest fullerene to form in condensing carbon vapor has received considerable interest since the discovery of Buckminsterfullerene, C(60). Smaller fullerenes remain a largely unexplored class of all-carbon molecules that are predicted to exhibit fascinating properties due to the large degree of curvature and resulting highly pyramidalized carbon atoms in their structures. However, that curvature also renders the smallest fullerenes highly reactive, making them difficult to detect experimentally. Gas-phase attempts to investigate the smallest fullerene by stabilization through cage encapsulation of a metal have been hindered by the complexity of mass spectra that result from vaporization experiments which include non-fullerene clusters, empty cages, and metallofullerenes. We use high-resolution FT-ICR mass spectrometry to overcome that problem and investigate formation of the smallest fullerene by use of a pulsed laser vaporization cluster source. Here, we report that the C(28) fullerene stabilized by encapsulation with an appropriate metal forms directly from carbon vapor as the smallest fullerene under our conditions. Its stabilization is investigated, and we show that M@C(28) is formed by a bottom-up growth mechanism and is a precursor to larger metallofullerenes. In fact, it appears that the encapsulating metal species may catalyze or nucleate endohedral fullerene formation.

Structures of Pb(n) (n = 21-30) clusters from first-principles calculations

Neutral lead clusters Pb(n) (n = 21-30) were studied using a genetic algorithm (GA)/tight-binding (TB) search combined with density functional theory (DFT)-Perdew-Burke-Ernzerhof (PBE) calculations. The calculated results show that the Pb(n) (22 ≤ n ≤ 30) clusters favor endohedral cage structures with two (Pb(22 - 26)) or three (Pb(27 - 30)) endohedral atoms. The binding energies, stabilities, and highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gaps of the Pb(n) clusters were also discussed. The results from our calculations also indicate that Pb(24) and Pb(28) are especially stable clusters compared with their neighbors.

Architecture of clathrin fullerene cages reflects a geometric constraint--the head-to-tail exclusion rule--and a preference for asymmetry

Fullerene cages have n trivalent vertices, 12 pentagonal faces, and (n-20)/2 hexagonal faces. The smallest cage in which all of the pentagons are surrounded by hexagons and thus isolated from each other has 60 vertices and is shaped like a soccer ball. The protein clathrin self-assembles into fullerene cages of a variety of sizes and shapes, including smaller ones with adjacent pentagons as well as larger ones, but the variety is limited. To explain the range of clathrin architecture and how these fullerene cages self-assemble, we proposed a hypothesis, the "head-to-tail exclusion rule" (the "Rule"). Of the 5769 small clathrin cage isomers with n< or =60 vertices and adjacent pentagons, the Rule permits just 15, three identified in 1976 and 12 others. A "weak version" of the Rule permits another 99. Based on cryo-electron tomography, Cheng et al. reported six raw clathrin fullerene cages. One was among the three identified in 1976. Here, (1) we identify the remaining five. (2) Four are new and are among the 12 others permitted by the Rule. (3) One, also new, is among the 99 weak version cages. (4) Of particular note, none of the remaining 5565 excluded cages has been identified. These findings provide powerful experimental confirmation of the Rule and the principle on which it is based. (5) Surprisingly, the newly identified clathrin cages are among the least symmetric of those permitted. (6) By devising a method for counting assembly paths, (7) we show that asymmetric cages can be assembled by larger numbers of paths, thus providing a kinetic explanation for the prevalence of asymmetric cages. (8) Finally, we show that operation during cage growth of the Rule greatly increases the likelihood of producing a closed fullerene cage, specifically one of those permitted, but efficient assembly still appears to require internal remodeling.

A geometric constraint, the head-to-tail exclusion rule, may be the basis for the isolated-pentagon rule in fullerenes with more than 60 vertices

Carbon atoms self-assemble into the famous soccer-ball shaped Buckminsterfullerene (C(60)), the smallest fullerene cage that obeys the isolated-pentagon rule (IPR). Carbon atoms self-assemble into larger (n > 60 vertices) empty cages as well-but only the few that obey the IPR-and at least 1 small fullerene (n <or= 60) with adjacent pentagons. Clathrin protein also self-assembles into small fullerene cages with adjacent pentagons, but just a few of those. We asked why carbon atoms and clathrin proteins self-assembled into just those IPR and small cage isomers. In answer, we described a geometric constraint-the head-to-tail exclusion rule-that permits self-assembly of just the following fullerene cages: among the 5,769 possible small cages (n <or= 60 vertices) with adjacent pentagons, only 15; the soccer ball (n = 60); and among the 216,739 large cages with 60 < n <or= 84 vertices, only the 50 IPR ones. The last finding was a complete surprise. Here, by showing that the largest permitted fullerene with adjacent pentagons is one with 60 vertices and a ring of interleaved hexagons and pentagon pairs, we prove that for all n > 60, the head-to-tail exclusion rule permits only (and all) fullerene cages and nanotubes that obey the IPR. We therefore suggest that self-assembly that obeys the IPR may be explained by the head-to-tail exclusion rule, a geometric constraint.

Ab initio calculation of carbon clusters. II. Relative stabilities of fullerene and nonfullerene C24

Chemical stabilities of six low-energy isomers of C24 derived from global-minimum search are investigated. The six isomers include one classical fullerene (isomer 1) whose cage is composed of only five- and six-membered rings (56-MRs), three nonclassical fullerene structures whose cages contain at least one four-membered ring (4-MR), one plate, and one monocyclic ring. Chemical and electronic properties of the six C24 isomers are calculated based on a density-functional theory method (hybrid PBE1PBE functional and cc-pVTZ basis set). The properties include the nucleus-independent chemical shifts (NICS), singlet-triplet splitting, electron affinity, ionization potential, and gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital (HOMO-LUMO) gap. The calculation suggests that the neutral isomer 2, a nonclassical fullerene with two 4-MRs, may be more chemically stable than the classical fullerene (isomer 1). Analyses of molecular orbital NICS show that the incorporations of 4-MRs into the cage considerably reduce paratropic contributions from HOMO, HOMO-1, and HOMO-2, which are mainly responsible for the sign change in NICS from positive for isomer 1 (42) to negative (-19) for isomer 2, although C24 clusters satisfy neither 4N+2 nor 2(N+1)2 aromaticity rule. Anion photoelectron spectra of four cage isomers, one plate, one monocyclic ring, and one tadpole isomer, as well as three bicyclic ring isomers are calculated. The simulated photoelectron spectra of mono- and bicyclic rings (with C1 symmetry) appear to match the measured HOMO-LUMO gap (between the first and second band in the experimental spectra) [S. Yang et al., Chem. Phys. Lett. 144, 431 (1988)]. Nevertheless, the nonclassical fullerene isomers 3 and 4 apparently also match the measured vertical detachment energy (2.90 eV) reasonably well. These results suggest possible coexistence of nonclassical fullerene isomers with the mono- and bicyclic ring isomers of C24(-) under the experimental conditions.

A geometric principle may guide self-assembly of fullerene cages from clathrin triskelia and from carbon atoms

Clathrin triskelia and carbon atoms alike self-assemble into a limited selection of fullerene cages (with n three connected vertices, 3n/2 edges, 12 pentagonal faces, and (n-20)/2 hexagonal faces). We show that a geometric constraint-exclusion of head-to-tail dihedral angle discrepancies (DADs)-explains this limited selection as well as successful assembly into such closed cages in the first place. An edge running from a pentagon to a hexagon has a DAD, since the dihedral angles about the edge broaden from its pentagon (tail) end to its hexagon (head) end. Of the 21 configurations of a central face and surrounding faces, six have such DAD vectors arranged head-to-tail. Of the 5770 mathematically possible fullerene cages for n <or= 60, excluding those with any of the six configurations leaves just 15 cages plus buckminsterfullerene (n = 60), among them the known clathrin cages. Of the 216,739 mathematically possible cages for 60 < n <or= 84, just the 50 that obey the isolated-pentagon rule, among them known carbon cages, pass. The absence of likely fullerenes for some n (30,34,46,48,52-58,62-68) explains the abundance of certain cages, including buckminsterfullerene. These principles also suggest a "probable roads" path to self-assembly in place of pentagon-road and fullerene-road hypotheses.

Comparison of Geometric, Electronic, and Vibrational Properties for Isomers of Small Fullerenes C20−C36

We employ the self-consistent-charge density-functional tight-binding (SCC-DFTB) method for computing geometric, electronic, and vibrational properties for various topological isomers of small fullerenes. We consider all 35 five- and six-member rings containing isomers of small fullerenes, C20, C24, C26, C28, C30, C32, C34, and C36, as first part of a larger effort to catalog CC distance distributions, valence CCC angle distributions, electronic densities of states (DOSs), vibrational densities of states (VDOSs), and infrared (IR) and Raman spectra for fullerenes C20-C180. Common features among the fullerenes are identified and properties characteristic for each specific fullerene isomer are discussed.

Ab initio calculation of bowl, cage, and ring isomers of C20 and C20-

High-level ab initio calculations have been carried out to reexamine relative stability of bowl, cage, and ring isomers of C(20) and C(20)(-). The total electronic energies of the three isomers show different energy orderings, strongly depending on the hybrid functionals selected. It is found that among three popular hybrid density-functional (DF) methods B3LYP, B3PW91, PBE1PBE, and a new hybrid-meta-DF method TPSSKCIS, only the PBE1PBE method (with cc-pVTZ basis set) gives qualitatively correct energy ordering as that predicted from ab initio CCSD(T)/cc-pVDZ [CCSD(T)-coupled-cluster method including singles, doubles, and noniterative perturbative triples; cc-pVDZ-correlation consistent polarized valence double zeta] as well as from MP4(SDQ)/cc-pVTZ [MP4-fourth-order Moller-Plesset; cc-pVTZ-correlation consistent polarized valence triple zeta] calculations. Both CCSD(T) and MP4 calculations indicate that the bowl is most likely the global minimum of neutral C(20) isomers, followed by the fullerene cage and ring. For the anionic counterparts, the PBE1PBE calculation also agrees with MP4/cc-pVTZ calculation, both predicting that the bowl is still the lowest-energy structure of C(20)(-) at T=0 K, followed by the ring and the cage. In contrast, both B3LYP/cc-pVTZ and B3PW91/cc-pVTZ calculations predict that the ring is the lowest-energy structure of C(20)(-). Apparently, this good reliability in predicting the energy ordering renders the hybrid PBE method a leading choice for predicting relative stability among large-sized carbon clusters and other carbon nanostructures (e.g., finite-size carbon nanotubes, nano-onions, or nanohorns). The relative stabilities derived from total energy with Gibbs free-energy corrections demonstrate a changing ordering in which ring becomes more favorable for both C(20) and C(20)(-) at high temperatures. Finally, photoelectron spectra (PES) for the anionic C(20)(-) isomers have been computed. With binding energies up to 7 eV, the simulated PES show ample spectral features to distinguish the three competitive C(20)(-) isomers.

C20 Carbon Clusters: Fullerene–Boat–Sheet Generation, Mass Selection, Photoelectron Characterization

Electron-impact ionization in a time-of-flight mass spectrometer of C(20)H(0-3)Br(14-12) probes-secured from C(20)H(20) dodecahedrane by a "brute-force" bromination protocol-provided bromine-free C(20)H(0-2(3)) anions in amounts that allowed the clean mass-separation of the hydrogen-free C(20) (-) ions and the photoelectron (PE) spectroscopic characterization as C(20) fullerene (electron affinity (EA)=2.25+/-0.03 eV, vibrational progressions of 730+/-70). The extremely strained C(20) fullerene ions surfaced as kinetically rather stable entities (lifetime of at least the total flight time of 0.4 ms); they only very sluggishly expel a C(2) unit. The HOMO and LUMO are suggested to be almost degenerate (DeltaE=0.27 eV). The assignment as a fullerene was corroborated by the PE characterization of the C(20) bowl (EA=2.17+/-0.03 eV, vibrational progression of 2060+/-50 cm(-1)) analogously generated from C(20)H(10) corannulene (C(20)H(1-3)Br(9-8) samples) and comparably stable. Highly resolved low-temperature PE spectra of the known C(20) ring (EA=2.49+/-0.03 eV, vibrational progressions 2022+/-45 and 455+/-30 cm(-1)), obtained from graphite, display an admixture of, most probably, a bicyclic isomer (EA=3.40+/-0.03 eV, vibrational progression 455+/-30 cm(-1)). The C(20) (+(-)) and C(20)H(2) (+(-)) cluster ions generated from polybrominated perylene (C(20)H(0-2)Br(12-10)) have (most probably) retained the planar perylene-type skeleton (sheet, EA=2.47+/-0.03 eV, vibrational progressions of 2089+/-30 and 492+/-30 cm(-1) and EA=2.18+/-0.03 eV, vibrational progressions of 2105+/-30 and 468+/-30 cm(-1)).

Conversion pathways between a fullerene and a ring among C20 clusters by a sphere contracting walk method: Remarkable difference in local potential energy landscapes around the fullerene and the ring

Conversion pathways from a fullerene to a ring and vice versa among C(20) clusters have been explored. A new technique has been developed for discovering multistep reaction pathways, which can be searched by finding constrained energy minima on spheres whose surfaces are contracting from the starting point to the terminal. Local landscapes that appeared on the pathways were found to be considerably different around the fullerene and the ring, from which one can make a new interpretation for no generation of the C(20) fullerene in laser vaporization of graphite.