Quantum chemical density-functional theory calculations of the structures of defect C60 with four vacancies

Quantum chemical density-functional theory (DFT) calculations have been carried out for the six isomers obtained by removing four adjacent atoms from C60. The most stable isomer consists of twelve 5-member and eighteen 6-member rings, indicating that the removal of some atoms from C60, which contains twelve 5-member rings and twenty 6-member rings, does not always generate larger holes. Each of the other five isomers contains at least one 4-member ring and one larger ring (7-, 8-, 9-, or 10-member ring) besides the 5- and 6-member rings. All isomers have similar structures for singlet and triplet spin multiplicities but with different stabilities. The ground states for two of the isomers are triplets, whereas the ground states for the other isomers are singlets. Furthermore, a comparison between the various isomers allowed one to examine the effect of the structure on the stability of fullerene cages.     

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.     

Synthesis and structural characterization of highly chlorinated C70, C70Cl28

Chlorination of [70]fullerene with SbCl(5), VCl(4) or PCl(5) yielded C(70)Cl(28) comprising three isomers, all containing four isolated benzenoid rings in the fullerene cage. This demonstrates, for the first time for C(70) derivatives, a stabilization effect due to planar aromaticity.     

Structure and stability of B5C and C5B clusters

Geometry optimizations and vibrational frequencies of B5C and C5B clusters were calculated with the Becke-3LYP method using the 6-311+G(d) basis set and some stable configurations of B5C and C5B clusters have been found. The most stable structure of B5C is a planar six-membered ring. However, for C5B clusters, the most stable structure is linear with a boron atom in position 3. Various configurations of B5C clusters containing three-membered boron rings have predominance in energy, whereas various configurations of C5B clusters containing three-membered carbon rings are disadvantageous in energy. In B5C clusters, isomer2 can be converted into isomer1 by surmounting an energy barrier of 43.83 kJ.mol(-1). In C5B clusters, the conversions of isomer5 into isomer2 and isomer7 into isomer2 have energy barriers of 19.66 and 20.57 kJ.mol(-1), respectively.     

The conversion among various B4C clusters: a density functional theoretical study

Geometry optimizations and vibration frequencies of B4C clusters were performed with Becke-3LYP method using 6-31G(d) basis set. We have found 14 stable isomers, and the most stable structure among them is the five-member ring containing two three-member boron rings. We also analyzed these stable isomers in detail, and the results show that the structures containing three-member boron rings are predominant in energy for B4C clusters. In terms of MO and NBO analysis, the three-centered bond and the pi-electron delocalization play an important role in stabilizing the planar five-member rings of these B4C clusters. Our calculations suggest that isomer4 can be converted into isomer7 with only an energy barrier of 0.31 kJ mol(-1) at the B3LYP/6-311G+(3df) level. Although the planar structures of the five-member rings (isomers12-14) can be converted with each other, the conversions of isomer14 to isomer13 and isomer13 to isomer12 have high-energy barriers of 70.99 and 68.51 kJ mol(-1) at the B3LYP/6-31G(d) level, respectively.     

The reaction of fullerene C(60) with 4,6-dimethyl-1,2,3-triazine: formation of an open-cage fullerene derivative.

A thermal reaction of fullerene C(60) with 4,6-dimethyl-1,2,3-triazine (4) in o-dichlorobenzene gave azacyclohexadiene-fused fullerene derivative 5, by the reaction with intermediate azete 11, and then, after flash chromatography over SiO(2), open-cage fullerene derivative 6 having an eight-membered ring orifice on the C(60) cage. Compound 6 is assumed to be formed via addition of diradical intermediate 13 to C(60). Compound 6 underwent a further photochemical reaction with singlet oxygen with the cleavage of one of the double bonds at the rim of the orifice to afford triketone derivative 8 having a 12-membered ring orifice.     

Geometric and electronic structures of metal-substitutional fullerene C59Sm and metal-exohedral fullerenes C60Sm

The geometric and electronic structures of metal-substituted fullerene C59Sm and exohedral fullerenes C60Sm are studied using the density-functional theory. The geometric optimization shows that the replacement of a C atom with a Sm in C60 yields a stable substitutionally doped fullerene C59Sm, and among the five possible optimized geometries for C60Sm, the most favorable exohedral sites are above the center of a hexagon and a pentagon ring. The calculations for electronic structures show that the magnetic moment of Sm is preserved for all the stable structures as tiny hybridization takes place between the orbitals of the Sm atom and those of their neighboring carbons. Because of the small energy gaps and the half occupation of the highest occupied molecular orbitals, all the stable C60Sm isomers are inferred to be conductors.     

Theoretical investigation of C56 fullerene isomers and related compounds

All the 924 classical isomers of fullerene C(56) have been investigated by PM3, and some most stable isomers are refined with HCTH/3-21G and B3LYP6-31G(d) methods. D(2):003 with the least number of adjacent pentagons is predicted to be the most stable isomer at B3LYP/6-31G(d) level, while C(s):022 and C(2):049 possess nearly degenerate energies with relative energies of 0.03 and 3.90 kcal/mol, respectively. However, as to dianionic C(56)(2-) fullerene, C(2v):011 is predicted to be the most stable isomer. Investigations also show that the encapsulation of Ca atom in C(56) fullerene is exothermic and the metallofullerenes Ca@C(56) can be described as Ca(2+)@C(56)(2-). The computed relative stabilities show that the D(2):003 behaves more thermodynamically stable than other isomers in a wide temperature interval, and C(2v):011 should also be an important component. The electronic isomerization of C(56) (C(2v):011) and C(50) (D(5h):002) indicates that this phenomenon might be rather general in fullerenes and causes different properties, thus bringing about new possible applications of fullerenes. The static second-order hyperpolarizabilities of the three most stable isomers are slightly larger than that of C(60).     

Structures, stabilities, electronic, and optical properties of C64 fullerene isomers, anions (C64(2-) and C64(4-)), metallofullerene Sc2@C64, and Sc2C2@C64

The 3465 classical isomers of C(64) fullerene have been investigated by quantum chemical methods PM3, and the most stable isomers have been refined with HCTH/3-21G//SVWN/STO-3G, B3LYP/6-31G(d)//HCTH/3-21G, and B3LYP/6-311G(d)//B3LYP/6-31G(d) level. C(64)(D(2):0003) with the lowest e(55) (e(55) = 2), the number of pentagon-pentagon fusions, is predicted to be the most stable isomer and it is followed by the C(64)(C(s):0077) and C(64)(C(2):0103) isomers within relative energy of 20.0 kcal/mol. C(64)(D(2):0003) prevails in a wide temperature range according to energy analysis with entropy contribution at B3LYP/6-31G(d) level. The simulated IR spectra and electronic spectra help to identify different fullerene isomers. All the hexagons in the isomers with e(55) = 2 display local aromaticity. The relative stabilities of C(64) isomers change with charging in ionic states. Doping also affects the relative stabilities of fullerene isomers as demonstrated by Sc(2)@C(64)(D(2):0003) and Sc(2)@C(64)(C(s):0077). The bonding of Sc atoms with C(64) elongates the C-C bond of two adjacent pentagons and enhances the local aromaticity of the fullerene cages. Charging, doping, and derativization can be utilized to isolate C(64) isomers through differentiating the electronic and steric effects.     

C_(59)F_(2n)HN(n=1,2)异构体的结构与稳定性的理论研究

分别用MNDO和AM1两种半经验方法,对C59F2nHN (n = 1, 2) 的异构体进行几何构型全优化,结合频率分析及HF/6-31G单点能计算,确定了各异构体的基态结构及其相对稳定性。计算结果表明,C59HN的F加成物的立体选择性规律与C60的不同,最稳定异构体不是1-2加成物。C59F2HN的最稳定异构体是1-4加成的6, 18-或12, 15-异构体; C59F4HN的最稳定异构体是1-4,1-4加成的6, 18; 12, 15-异构体,其能量远小于其它各异构体的能量。N原子取代碳笼骨架C原子后,改变了碳笼F加成物的立体选择性规律。     

Thermodynamic rearrangement synthesis and NMR structures of C1, C3, and T isomers of C60H36

The structures of three C60H36 isomers, produced by high-temperature transfer hydrogenation of C(60) in a 9,10-dihydroanthracene melt, was accomplished by 2D (1)H-detected NMR experiments, recorded at 800 MHz. The unsymmetrical C(1) isomer is found to be the most abundant one (60-70%), followed by the C(3) isomer (25-30%) and the least abundant T isomer (2-5%). All three isomers are closely related in structure and have three vicinal hydrogens located on each of the 12 pentagons. Facile hydrogen migration on the fullerene surface during annealing at elevated temperatures is believed to be responsible for the preferential formation of these thermodynamically most stable C60H36 isomers. This hypothesis was further supported by thermal conversion of C60H36 isomers to a single C(3v) isomer of C60H18.     

Structures, stabilities, and electronic and optical properties of c(58) fullerene isomers, ions, and metallofullerenes.

The 1205 classical isomers of fullerene C58, as well as one quasi-fullerene C58 isomer with a heptagonal ring (labeled as Cs:hept) have been investigated by the quantum chemical methods PM3, HCTH/3-21G, and B3LYP/6-31G(d). Isomer C3v:0001, which has the lowest number of adjacent pentagons, is predicted to be the most stable isomer, but the quasi-fullerene isomer Cs:hept is only 2.50 kcal mol-1 higher in energy. Systematic investigations of the electronic properties of C3v:0001 and Cs:hept find that the C3v:0001 isomer has high vertical electron affinity (3.19 eV). The nucleus-independent chemical shifts (NICS) value at the center of Cs:hept (-5.1 ppm) is more negative than that of C60 (-2.8 ppm). The NICS value at the center of the heptagonal ring in Cs:hept (-2.5 ppm) indicates weakly aromatic character. In contrast, the C58(6-) and C58(8-) ions of the C3v:0001 and Cs:hept geometries possess large aromatic character, with NICS values between -14.0 and -26.2 ppm. To clarify the thermodynamic stabilities of C58 isomers at different temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP/6-31G(d) level. The C3v:0001 isomer prevails in a wide range of temperatures, and the Cs:hept isomer is also an important component around 2800 K. The IR spectra of C58 isomers are simulated to facilitate experimental identification of different isomers. In addition, the electronic spectra and the second-order hyperpolarizabilities are predicted by ZINDO and the sum-over-states model. The static second-order hyperpolarizability of the C3v:0001 isomer is 96.5 % larger than that of C60, and its second-order hyperpolarizabilities at external field frequencies are at least nine times larger than those of C60.     

异质富勒烯C58BN的结构与光谱研究

用AM1、MNDO和INDO半经验方法研究了异质富勒烯C₅₈BN各异构体的结构、稳定性和电子光谱.所有这些半经验方法给出了相似的稳定性顺序.结果表明,在6-6位置取代的异构体是最稳定的,异构体的稳定性随杂原子间距离的增加而降低;与C₆₀相比,硼氮杂富勒烯C₅₈BN具有较低的前线轨道能级差、较小的电离势和较低的稳定化能.C₅₈BN很可能具有与C₆₀分子相似的反应活性,易发生亲核反应,但比C₆₀更易失去电子形成正离子.以AM₁优化构型为基础,利用INDO/CIS方法计算了各异构体的电子光谱.     

CCSD calculations on C(14), C(18), and C(22) carbon clusters

The structure and energetics of the ring isomers of C(4n+2) (n=3-5) carbon clusters were studied by using coupled-cluster singles and doubles excitation theory to overcome the vast differences existing in the literature. The results obtained in the present study clearly indicate that C(14), C(18), and C(22) carbon rings have bond-length and bond-angle alternated acetylenic minimum energy structures. Contrarily, density functional theory calculations were unable to predict these acetylenic-type structures and they ended up with the cumulenic structures. It is found from the coupled-cluster studies that the lowest-energy ring isomer for the first two members of C(4n+2) series is a bond-angle alternated cumulenic D((2n+1)h) symmetry structure while the same for the remaining members is a bond-length and bond-angle alternated C((2n+1)h) symmetry structure. In C(4n+2) carbon rings, Peierls-type distortion, transformation from bond-angle alternated to bond-length alternated minimum energy structures, occurs at C(14) carbon ring.     

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.     

Structural and electronic properties of S-doped fullerene C58: where is the S atom situated?

Structural and electronic properties of S-doped fullerene C58 were calculated systematically via Hartree-Fock self-consistent field (SCF) and density functional B3LYP levels of theory with 6-31G(d) basis set. The most stable C58S represents an open cage structure with a nine-member ring orifice, which provides a large hole for large atoms or small molecules to pass through into the cage. The most stable endohedral S@C58 has the S atom seated near the center of the C58 cage. The calculated highest occupied molecular orbital-lowest unoccupied molecular orbital energy gaps of the isomers lie in the range of 1.42-2.50 eV. The electron affinity and the ionization potential were also presented as an indicator of the kinetic stability. Our results may aid in the design of experimental methods for controlling the nature of fullerene cages (for example, doping, opening, and reclosing them).     

The synthesis,characterization, and structure solution of SSZ-58: a novel two-dimensional 10-ring pore zeolite with previously unseen double 5-ring subunits

The synthesis, structure solution, and characterization of the novel zeolite SSZ-58 are described. SSZ-58 was synthesized under hydrothermal conditions using 1-butyl-1-cyclooctylpyrrolidinium cation as a structure-directing agent. The framework topology of SSZ-58 was determined with the FOCUS Fourier recycling method. SSZ-58 possesses 12 tetrahedral atoms in the asymmetric unit of its highest topological symmetry, and to date it is the most complex zeolite structure solved from powder data. Rietveld refinement of synchrotron powder X-ray diffraction data in space group Pmma confirmed the proposed model. SSZ-58 contains layers of atoms that are linked together by double five-membered rings (D5R), or 5(2)4(5) subunits, that have not been observed before in any zeolite or zeotype structures. SSZ-58 possesses a two-dimensional channel system consisting of 10-membered ring pores that intersect to form large cavities circumscribed by 12- and 16-membered ring pores.     

A DFT study on the dimerization of C62, H2-C62, and F2-C62

On the basis of calculations using the density functional theory, we show that C(62), a recently synthesized nonclassical fullerene, will presumably undergo dimerization with various isomers at elevated temperatures. This is shown by calculating the dimerization energy and the activation barrier of the dimerization. Eight possible isomers of the dimer were identified, all of which are more stable than the two isolated monomers. The relative stability of various isomers depends upon the kind of C=C bonds within the four-membered carbon ring involved in the dimerization. In addition, similar calculations were performed for the monomers and dimers of H(2)-C(62) and F(2)-C(62). Six isomers were identified for each of the dimers. Although less pronounced than the case of the C(62) dimer, all isomers of the H(2)-C(62) dimer are appreciably more stable than the individual monomers. Although a large steric repulsion due to F atoms significantly reduces the stability of F(2)-C(62) dimer, its two isomers are still more stable than separate monomers.     

Stability,structures and a hypothetical growth mechanism of carbon 5/6 network

A novel picture of growth of fullerene and fullerene-like structures is proposed. The ring stacking model have been studied in detail in connection with the stability, structures and growth mechanism of carbon 5-and 6-membered ring network. Combining the model with energetic considerations, the selective formation of sizes and isomers of large fullerenes has successfully been described.     

On the structure and relative stability of C50 fullerenes

The complete set of 271 classical fullerene isomers of C50 has been studied by full geometry optimizations at the SAM1, PM3, AM1, and MNDO quantum-chemical levels, and their lower energy structures have also been partially computed at the ab initio levels of theory. A D(5h) species, with the least number of pentagon adjacency, is predicted by all semiempirical methods and the HF/4-31G calculations as the lowest energy structure, but the B3LYP/6-31G* geometry optimizations favor a D3 structure (with the largest HOMO-LUMO gap and the second least number of adjacent pentagons) energetically lower (-2 kcal/mol) than the D(5h) isomer. To clarify the relative stabilities at elevated temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the HF/4-31G level for the first time. The computed relative-stability interchanges show that the D3 isomer behaves more thermodynamically stable than the D(5h) species within a wide temperature interval related to fullerene formation. According to a newly reported experimental observation, the structural/energetic properties and relative stabilities of both critical isomers (D(5h) and D3) are analyzed along with the experimentally identified decachlorofullerene C50Cl10 of D(5h) symmetry. Some features of higher symmetry C50 nanotube-type isomers are also discussed.