Structures, stabilities, and electronic and optical properties of C62 fullerene isomers

The 2385 classical isomers and four nonclassical isomers of fullerene C62 have been studied by PM3, HCTH/3-21G//SVWN/STO-3G, B3LYP/6-31G(d)//HCTH/3-21G, and B3LYP/6-31G(d)//B3LYP/6-31G(d). The Cs:7mbr isomer, with a chain of four adjacent pentagons surrounding a heptagon, is predicted to be the most stable isomer, followed by C2v:4mbr which is 3.15 kcal/mol higher in energy. C2:0032 with three pairs of adjacent pentagons is the most stable isomer in the classical framework. To clarify the relative stabilities of C62 isomers at high temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP/6-31G(d) level. Analyses reveal that Cs:7mbr prevails in a wide temperature range. The vibrational frequencies of the five most stable C62 fullerene isomers are also predicted at the B3LYP/6-31G(d) level, and the simulated IR spectra show important differences in positions and intensities of the vibrational modes for different isomers. The nucleus-independent chemical shift and the density of states of the three most stable isomers show that the square in C2v:4mbr and the adjacent pentagons in Cs:7mbr and C2:0032 possess high chemical reactivity. In addition, the electronic spectra and second-order hyperpolarizabilities are determined by means of ZINDO and the sum-over-states mode. The intensity-dependent refractive index gamma(-omega; omega, omega, -omega) at omega = 2.3305 eV of Cs:7mbr is very large because of resonance with the external field. The second-order hyperpolarizabilities of the five most stable isomers of C62 are predicted to be larger than those of C60.     

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.     

Theoretical Studies on Structures,Stabilities, NMR Spectra and Designing Methods of Dihedral Fullerenes of C3 Series

Using bowl shaped carbon intermediates to construct dihedral fullerenes is an advisable method. Assu- ming that cap shaped C21 extends the size through building pentagons and hexagons at the U and V clefts of the brims, a series of homologous carbon intermediates was generated, in which most of the members have been unknown up to now. The joins between these homologous intermediates gave the C3 dihedral series under the restriction of C3 sym- metrical axis. The investigations point out that the stabilities of these fullerenes not only relate to the shapes of cages and the co-planarities of polygons, but also associate with the equalizations of bond lengths and the pentagonal dis- tributions. The stabilities reveal that the pentagonal distribution in cages is not negligible to the Jr delocalization, be- sides the co-planarities of hexagons and pentagons. Analyzing the possible Stone-Wales（SW） rearrangements in those fullerenes with dehydrogenated pyracyclene units（DPUs） can help us to find out the highly stable isomers. Based on the geometrical optimizations, the calculations provided the theoretical chemical shifts of unknown fullerenes and the data reconfirmed the existence of members C78 and C84. The symmetry adaptation analyses for the frontier orbitals support the formative mechanism of consecutive pentagonal and hexagonal fusions, but the simulated routes are more complicated than the pentagon road（PR） mechanism, which include not only C2 but also C3 additive reactions.     

Structure and Electronic Properties of Fullerenes C52q+: Is C522+ an Exception to the Pentagon Adjacency Penalty Rule?

The structure, vibrational spectra and electronic properties of the neutral, singly and doubly charged C52 fullerenes were studied by means of the Hartree-Fock method and density functional theory. Different isomers were considered, in particular those with the lowest possible number (five or six) of adjacent pentagons, and an isomer with a four-atom ring. For neutral and singly charged species, the most stable isomer is that with the lowest number of adjacent pentagons, namely five. However, for C(52)2+, the most stable structure has six adjacent pentagons. This finding, which contradicts the pentagon adjacency penalty rule, is a consequence of complete filling of the HOMO pi shell and the near-perfect sphericity of the most stable isomer. The simulated vibrational spectra show important differences in the positions and intensities of the vibrations for the different isomers.     

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     

C64H4: production, isolation, and structural characterizations of a stable unconventional fulleride

Unconventional fullerenes are those smaller than C(60) or those intermediate between C(60) and C(70), which are not stable in structure as none of the unconventional fullerene isomers satisfying the "isolated-pentagon-rule" (IPR). Below we report the synthesis of a stable unconventional fullerene derivative C(64)H(4) by introducing methane in the fullerene productions with the normal Kr?tschmer-Huffman method. We also applied various spectroscopic measurements such as mass spectrometry, (13)C NMR, IR, UV-vis absorption spectrometry, etc. to characterize the structural and electronic properties of this molecule, revealing an unprecedented fullerene cage with a triplet of directly fused pentagons in the framework of C(64)H(4). Four hydrogen atoms are added to the carbons at vertexes of fused pentagons to allow the bond angles at these sites close to the sp(3) tetrahedral angle, which essentially release the sp(2) bond strains on the abutting-pentagon sites of C(64). Ab initio calculations were performed to explore the electronic property and simulate the (13)C NMR and IR spectra of this fulleride, which reproduced well the experimental results and confirmed the structural assignment of the C(64)H(4).     

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.     

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.     

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.     

Structures, stabilities, and electronic and optical properties of C52 fullerene, ions, and metallofullerenes

The 437 classical isomers of fullerene C52 have been studied by PM3, HCTH/3-21G, and B3LYP6-31G(d). C(2):029 with the least number of adjacent pentagons is predicted to be the most stable isomer. The investigations show that both the number of adjacent pentagons and the degree of aromaticity play important roles in the relative stabilities of fullerene isomers. To clarify the relative stabilities of the C52 isomers in a wide range of temperatures, the entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP6-31G(d) level. C(2):029 prevails in a wide temperature range. In addition, the electronic spectra and second-order hyperpolarizabilities are determined by means of ZINDO and sum-over-states model. The static second-order hyperpolarizability of C(2):029 is 51% larger than that of C60. Furthermore, intensity-dependent refractive index gamma (-omega;omega,omega,-omega) (omega=1.1653 eV) of C(2):029 is 13 times larger than that of C60. The encapsulation of Ca atom in C52 fullerene is exothermic and the metallofullerene Ca-C52 is described as Ca2+-C52(2-).     

Deformation and thermodynamic instability of a C84 fullerene cage

Quantum chemical calculations of electronic and geometric structures were performed for molecules of 24 isomers of C₈₄ fullerenes obeying the isolated pentagons rule. The reasons for the instability of isomers not obtained experimentally were established, and the possibility of obtaining some of them was proven. It was shown that the deformation of hexagons and pentagons is the most important geometric parameter directly connected with the thermodynamic instability of fullerenes having closed shells, reflecting the local strain of the molecules.     

Strain Release of Fused Pentagons in Fullerene Cages by Chemical Functionalization

According to the isolated pentagon rule (IPR), for stable fullerenes, the 12 pentagons should be isolated from one another by hexagons, otherwise the fused pentagons will result in an increase in the local steric strain of the fullerene cage. However, the successful isolation of more than 100 endohedral and exohedral fullerenes containing fused pentagons over the past 20 years has shown that strain release of fused pentagons in fullerene cages is feasible. Herein, we present a general overview on fused‐pentagon‐containing (i.e. non‐IPR) fullerenes through an exhaustive review of all the types of fused‐pentagon‐containing fullerenes reported to date. We clarify how the strain of fused pentagons can be released in different manners, and provide an in‐depth understanding of the role of fused pentagons in the stability, electronic properties, and chemical reactivity of fullerene cages.     

Structures,stabilities, and IR and 13C-NMR spectra of dihedral fullerenes: A density functional theory study

Dihedral fullerenes are thermodynamically stable molecules with D nd or D nh symmetry.Based on experimental findings,two series of dihedral fullerenes with five-fold(C5) and six-fold(C6) symmetry have been studied using density functional theory(DFT).The DFT calculations showed that for both series the stabilities increased with increasing fullerene size.Structural analyses indicated that the stabilities are related to specific local geometries.In the case of the more abundant C5 series,the presence of approximately planar pentagons and hexagons on the top bowl favors their formation.That is to say,those fullerenes with small dihedral angles within the polygons are readily formed,because planar hexagons lead to strengthened conjugation which lowers average bonding energies(ABE) and increases thermodynamic stabilities.Non-planar hexagons at equatorial positions in tube-shaped fullerenes have an adverse effect on the conjugation and inhibit their formation.Calculations also demonstrated that fullerenes in the two series,including C 50(D 5h),C 60(D 6h),C 80(D 5d),C 96(D 6d),C 110(D 5h),and C 120(D 5d),have thermodynamically stable triplet structures with strong conjugation.The calculated IR and 13 C NMR spectra of the fullerenes show some similarities and regular trends due to their homogenous structures.The electronic structures indicate that short double bonds in hexagons with high electron occupancies are readily attacked by electrophilic agents and can also be coordinated by transition metals.Mechanistic discussions suggested that C 2 additions and C 2 losses constitute reversible processes at high temperature and C 2 additions in pentagonal fusions are crucial to the kinetics of the curvature of structures.C 3 additions lead to the formation of large fullerenes of other types.     

Nonclassical fullerenes with a heptagon violating the pentagon adjacency penalty rule

Nonclassical fullerenes with heptagon(s) and their derivatives have attracted increasing attention, and the studies on them are performing to enrich the chemistry of carbon. Density functional theory calculations are performed on nonclassical fullerenes C_n (n = 46, 48, 50, and 52) to give insight into their structures and stability. The calculated results demonstrate that the classical isomers generally satisfy the pentagon adjacency penalty rule. However, the nonclassical isomers with a heptagon are more energetically favorable than the classical ones with the same number of pentagon–pentagon bonds (B₅₅ bonds), and many of them are even more stable than some classical isomers with fewer B₅₅ bonds. The nonclassical isomers with the lowest energy are higher in energy than the classical ones with the lowest energy, because they have more B₅₅ bonds. Generally, the HOMO–LUMO gaps of the former are larger than those of the latter. The sphericity and asphericity are unable to rationalize the unique stability of the nonclassical fullerenes with a heptagon. The pyramidization angles of the vertices shared by two pentagons and one heptagon are smaller than those of the vertices shared by two pentagons and one hexagon. It is concluded that the strain in the fused pentagons can be released by the adjacent heptagons partly, and consequently, it is a common phenomenon for nonclassical fullerenes to violate the pentagon adjacent penalty rule. These findings are heuristic and conducive to search energetically favorable isomers of C_n, especially as n is 62, 64, 66, and 68, respectively. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2010     

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).     

Crystallographic characterization of the structure of the endohedral fullerene [Er2@C82 isomer I] with C(s) cage symmetry and multiple sites for erbium along a band of ten contiguous hexagons

The structure of one of the three previously separated isomers of {Er2@C82} has been determined through a single-crystal X-ray structure determination of the noncovalent adduct, {Er2@C82 Isomer I}.{CoII(OEP)}.1.4(C6H6).0.3(CHCl3). The C82 cage is identified specificlly as the Cs(82:6) isomer (one of nine possible isolated pentagon isomers) from the crystallographic data. The carbon atoms of the C82 cage were individually identified and refined with only a constraint that required the two halves of the cage to possess similar bond lengths. Although the carbon cage is well ordered at 113 K, the erbium atoms are disordered. The electron density within the cage of {Er2@C82 Isomer I} has been modeled with two major sites with occupancies of 0.35 and 21 other individual erbium sites with occupancies ranging from 0.138 to 0.011. These erbium sites all reside near the walls of the fullerence and cluster near a band of ten contiguous hexagons that encircles the carbon cage. Since two other isomers of C82 (C3v(82:8) and C2v(82:9)) have a similar band of ten contiguous hexagons, it is tempting to speculate that the other two known isomers of {Er2@C82} have these cage structures.     

多氯代菲分子结构和热力学性质的密度泛函理论研究

采用密度泛函理论方法在B3LYP/6-311G(d, p)水平上对527个多氯代菲分子的几何结构进行了全优化并计算得到它们的热力学性质(等容热容( )、熵(S$)、标准生成焓(ΔfH$)和标准生成Gibbs自由能(ΔfG$)), 研究了这些性质与取代的氯原子数目和位置的关系, 根据各异构体的相对标准生成Gibbs自由能(Δr,fG$)的大小, 得到它们的热力学稳定性顺序. 计算结果表明: 绝大多数多氯代菲分子具有非平面的几何构型, 在多氯代菲分子中存在三种类型的分子内弱相互作用(H…H、C—H…Cl和Cl…Cl相互作用), 随着分子中取代的氯原子数目的增加, 多氯代菲最稳定异构体的ΔfH$和ΔfG$开始时逐渐减小, 然后又快速增加. 具有相同数目氯原子的多氯代菲异构体的ΔfH$和ΔfG$与氯原子的取代位置有很大的关系. 多氯代菲异构体的相对热力学稳定性主要由分子内的离域π键和Cl…Cl核排斥作用的强弱决定.     

Single crystal X-ray structure of tetrahedral C60F36: the most aromatic and distorted fullerene

Tetrahedral C60F36 is shown by its single-crystal X-ray structure to be the most aromatic (and distorted) fullerene derivative, having four planar hexagons with almost equal bond lengths, the average of which (1.373 A) is the same as in C60F18; one exceptionally long FC-CF bond (1.665 A) corresponds to the similarly long bond in C60F18 (a motif of T C60F36) and is likely to be the site of oxygen insertion in C60F36O.     

Structure, stability, and cluster-cage interactions in nitride clusterfullerenes M3N@C2n (M = Sc, Y; 2n = 68-98): a density functional theory study

Extensive semiempirical calculations of the hexaanions of IPR (isolated pentagon rule) and non-IPR isomers of C(68)-C(88) and IPR isomers of C(90)-C(98) followed by DFT calculations of the lowest energy structures were performed to find the carbon cages that can provide the most stable isomers of M(3)N@C(2n) clusterfullerenes (M = Sc, Y) with Y as a model for rare earth ions. DFT calculations of isomers of M(3)N@C(2n) (M = Sc, Y; 2n = 68-98) based on the most stable C(2n)(6-) cages were also performed. The lowest energy isomers found by this methodology for Sc(3)N@C(68), Sc(3)N@C(78), Sc(3)N@C(80), Y(3)N@C(78), Y(3)N@C(80), Y(3)N@C(84), Y(3)N@C(86), and Y(3)N@C(88) are those that have been shown to exist by single-crystal X-ray studies as Sc(3)N@C(2n) (2n = 68, 78, 80), Dy(3)N@C(80), and Tb(3)N@C(2n) (2n = 80, 84, 86, 88) clusterfullerenes. Reassignment of the carbon cage of Sc(2)@C(76) to the non-IPR Cs: 17490 isomer is also proposed. The stability of nitride clusterfullerenes was found to correlate well with the stability of the empty 6-fold charged cages. However, the dimensions of the cage in terms of its ability to encapsulate M(3)N clusters were also found to be an important factor, especially for the medium size cages and the large Y(3)N cluster. In some cases the most stable structures are based on the different cage isomers for Sc(3)N and Y(3)N clusters. Up to the cage size of C(84), non-IPR isomers of C(2n)(6-) and M(3)N@C(2n) were found to compete with or to be even more stable than IPR isomers. However, the number of adjacent pentagon pairs in the most stable non-IPR isomers decreases as cage size increases: the most stable M(3)N@C(2n) isomers have three such pairs for 2n = 68-72, two pairs for n = 74-80, and only one pair for n = 82, 84. For C(86) and C(88) the lowest energy IPR isomers are much more stable than any non-IPR isomer. The trends in the stability of the fullerene isomers and the cluster-cage binding energies are discussed, and general rules for stability of clusterfullerenes are established. Finally, the high yield of M(3)N@C(80) (Ih) clusterfullerenes for any metal is explained by the exceptional stability of the C(80)(6-) (Ih: 31924) cage, rationalized by the optimum distribution of the pentagons leading to the minimization of the steric strain, and structural similarities of C(80) (Ih: 31924) with the lowest energy non-IPR isomers of C(760(6-), C(78)(6-), C(82)(6-), and C(84)(6-) pointed out.