Tb3N@C84: an improbable, egg-shaped endohedral fullerene that violates the isolated pentagon rule

The structure of isomer 2 of Tb3N@C84 has been determined through single-crystal X-ray diffraction on Tb3N@C84.NiII(OEP).2(C6H6). The carbon cage has a distinct egg shape due to the presence of a single pair of fused pentagons at one apex of the molecule. Thus, although 24 IPR structures are available to the C84 cage, Nature utilizes one of the 51 568 isomeric structures that do not conform to the IPR for this unusual molecule. The Tb3N portion of isomer 2 of Tb3N@C84 is strictly planar. One Tb atom is nestled within the fold of the fused pentagons, while the other Tb atoms are disordered over four pairs of sites.     

Unusual pentagon and hexagon geometry of three isomers (no 1, 20, and 23) of fullerene C84

Three isomers 23 (D_2d), 1 (D₂), and 20 (T_d) of fullerene C₈₄ have been investigated by PM3, HF/6‐31G*, and DFT methods with B3LYP functional at the 6‐31G and 6‐31G* levels. In this article we reveal for the first time that some distortion of hexagon (pentagon), measured as its maximal dihedral angles, caused by local molecular strains may serve as a new criterion of stability of fullerenes with closed shell. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

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.     

Electronic structures of some of C84 fullerene isomers and the structures of their perfluoroalkyl derivatives

The electronic structures of the pristine fullerene molecules have been shown for the first time to be is the most important factor affecting the distribution of addends in the addition reactions of perfluoroalkyl radicals R^F to C₈₄ fullerene, and most likely positions of addends on the fullerene core are hexagons with delocalized π-bonds.     

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     

Isolated pentagon rule violating endohedral metallofullerenes explained using the Hückel rule: A statistical mechanical study of the C84 Isomeric Set

Fullerenes and their structure and stability have been a major topic of discussion and research since their discovery nearly 30 years ago. The isolated pentagon rule (IPR) has long served as a guideline for predicting the most stable fullerene cages. More recently, endohedral metallofullerenes have been discovered that violate the IPR. This article presents a systematic, temperature dependent, statistical thermodynamic study of the 24 possible IPR isomers of C₈₄ as well as two of the experimentally known non‐IPR isomers (51365 and 51383), at several different charges (0, ?2, ?4, and ?6). From the results of this study, we conclude that the Hückel rule is a valid simpler explanation for the stability of fused pentagons in endohedral metallofullerenes. © 2014 Wiley Periodicals, Inc.     

Isolated pentagon rule in buckybowls: a computational study on thermodynamic stabilities and bowl-to-bowl inversion barriers

Computations on a series of sumanene and pinakene isomers reveal that the isolated pentagon species are found to be more stable than non-isolated pentagon structures. However, the present study indicates that there is no correlation between the bowl-to-bowl inversion barrier and the relative stability. Unexpectedly, the least stable isomer has the lowest bowl-to-bowl inversion barrier in pinakene isomers. Thus, curvature cannot be taken as a measure to evaluate the stability of buckybowls. The relative energy ordering and HOMO-LUMO gap correlate well in the series of pinakene isomers considered.     

Violating the isolated pentagon rule (IPR): endohedral non-IPR C98 cages of Gd2@C98

The geometric, electronic structure, and thermodynamic stability of large gadolinium-containing endohedral metallofullerenes, Gd(2)@C(98), have been systematically investigated by comprehensive density functional theory calculations combined with statistical mechanics treatments. The Gd(2)@C(2)(230924)-C(98) structure, which satisfies the isolated-pentagon rule (IPR), is determined to possess the lowest energy followed with some stable non-IPR isomers. In order to clarify the relative stabilities at elevated temperatures, entropy contributions are taken into account on the basis of the Gibbs energy at the B3LYP level for the first time. Interestingly, a novel non-IPR Gd(2)@C(1)(168785)-C(98) isomer which has one pair of pentagon adjacency is more thermodynamically stable than the lowest energy IPR species within a wide temperature interval related to fullerene formation. Therefore, the Gd(2)@C(1)(168785)-C(98) is predicted to be the most proper isomer obtained experimentally, which is the largest non-IPR carbon cage found so far. Our findings demonstrate that interaction between metals and carbon cages could stabilize the fused pentagons effectively, and thus, the non-IPR isomers should not be ignored in some cases of endohedral metallofullerenes. The IR features of Gd(2)@C(98) are simulated to assist its future experimental characterization.     

Spectral identification of fullerene C82 isomers

Ultraviolet photoelectron spectra (UPS) of C(82) isomers have been calculated using hybrid density functional theory in combination with the Gelius model [Proceedings of the International Conference on Electron spectroscopy, edited by D. A. Shirley (North-Holland, Amsterdam, 1972), p. 311; J. Electron Spectrosc. Relat. Phenom. 5, 985 (1974)]. The calculated UPS spectra are found to be isomer dependent and in good agreement with the experimental counterparts. Near-edge x-ray absorption fine structure (NEXAFS), x-ray photoelectron spectroscopy (XPS), x-ray emission spectroscopy, and the resonant inelastic x-ray scattering (RIXS) spectra of three important isomers [3(C(2)), 6(C(s)), and 9(C(2v))] have also been simulated. Strong isomer dependence has also been found for NEXAFS, XPS, and RIXS spectra.     

Sc2S@C(s)(10528)-C72: a dimetallic sulfide endohedral fullerene with a non isolated pentagon rule cage

A non isolated pentagon rule metallic sulfide clusterfullerene, Sc(2)S@C(s)(10528)-C(72), has been isolated from a raw mixture of Sc(2)S@C(2n) (n = 35-50) obtained by arc-discharging graphite rods packed with Sc(2)O(3) and graphite powder under an atmosphere of SO(2) and helium. Multistage HPLC methods were utilized to isolate and purify the Sc(2)S@C(72). The purified Sc(2)S@C(s)(10528)-C(72) was characterized by mass spectrometry, UV-vis-NIR absorption spectroscopy, cyclic voltammetry, and single-crystal X-ray diffraction. The crystallographic analysis unambiguously elucidated that the C(72) fullerene cage violates the isolated pentagon rule, and the cage symmetry was assigned to C(s)(10528)-C(72). The electrochemical behavior of Sc(2)S@C(s)(10528)-C(72) shows a major difference from those of Sc(2)S@C(s)(6)-C(82) and Sc(2)S@C(3v)(8)-C(82) as well as the other metallic clusterfullerenes. Computational studies show that the Sc(2)S cluster transfers four electrons to the C(72) cage and C(s)(10528)-C(72) is the most stable cage isomer for both empty C(72)(4-) and Sc(2)S@C(72), among the many possibilities. The structural differences between the reported fullerenes with C(72) cages are discussed, and it is concluded that both the transfer of four electrons to the cage and the geometrical requirements of the encaged Sc(2)S cluster play important roles in the stabilization of the C(s)(10528)-C(72) cage.     

Capturing C84 isomers as chlorides and pentafluoroethyl derivatives: C84Cl22 and C84(C2F5)12

A mixture of higher fullerenes C(76)-C(96) was pentafluoroethylated with C(2)F(5)I at 250 °C affording a mixture of C(2)F(5) derivatives. After separation with high-performance liquid chromatography, the second C(2)F(5) derivative of C(84)(16), C(84)(C(2)F(5))(12), was investigated by X-ray crystallography and compared with the known isomer in terms of addition patterns and formation energies. Chlorination of a C(84) isomeric mixture with VCl(4) at 350-400 °C resulted in the formation of C(84)Cl(22). X-ray diffraction study revealed the superposition of several C(84)Cl(22) molecules with different isomeric C(84) cages but the same chlorination pattern.     

Thermodynamic and kinetic stabilities of complementary double helices utilizing amidinium-carboxylate salt bridges

A series of dimer strands consisting of m-terphenyl backbones bearing complementary chiral or achiral amidines and achiral carboxylic acid residues connected by various types of linkers, such as diacetylene, Pt(II)-acetylide, and p-diethynylbenzene linkages, were synthesized by a modular strategy, and their chiroptical properties on the complementary double helix formations were investigated by absorption, circular dichroism (CD), and (1)H NMR spectroscopies. The thermodynamic and kinetic stabilities of the complementary double helices assisted by amidinium-carboxylate salt bridges are highly dependent on their linkages, and the thermodynamic analyses of the dimer duplexes revealed that the association constants increased in the order: Pt(II)-acetylide linker < p-diethynylbenzene linker < diacetylene linker, which is in agreement with the reverse order of their bulkiness. The substituents on the amidine groups were also found to affect the stabilities on the duplexes and the association constants increased in the order: isopropyl < (R)-1-phenylethyl < cyclohexyl. In addition, the introduction of electron-donating and/or electron-withdrawing substituents at the phenyl groups of the p-diethynylbenzene linkers connecting the amidine and carboxylic acid units, respectively, tends to stabilize the complementary double helices, especially in polar solvents, such as DMSO, due to the attractive charge-transfer interactions between the aromatic linkers, although the salt bridge formation is hampered in DMSO. Furthermore, the kinetic analyses of the chain exchange reactions for the duplexes bearing diacetylene and p-diethynylbenzene linkages showed that these were slow processes with negative ΔS([symbol: see text]) values, meaning that the chain exchange reactions proceed via direct exchange pathways. In contrast, those for the duplexes bearing Pt(II)-acetylide linkages were fast processes supported by positive ΔS([symbol: see text]) values, suggesting that the chain exchange reactions proceed via dissociation-exchange ones. The helix-inversion kinetics investigated for the racemic dimer duplexes composed of achiral amidines based on variable-temperature (1)H NMR measurements indicated that the barriers for the helix-inversion increased in the order: Pt(II)-acetylide linker, p-diethynylbenzene linker < diacetylene linker.     

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.     

C3H4: Theoretical study of structures and stabilities of isomers

The various isomers including stable structures, carbenes, and diradicals on the C₃H₄ surface have been investigated. The two carbenes propenylidene and cyclopropylidene have been found to have singlet ground states. Vinylmethylene is predicted to have a triplet ground state with a planar diradical type of structure. The syn and anti forms of this state are degenerate. This is in agreement with the observation of two triplet states in the electron spin resonance (ESR ) spectra. The π electrons are found to be delocalized over the three carbons. The singlet diradical structures are found to be more stable than the carbene structures, which retain the CH₂ (DOUBLE BOND) CH allylic structures. The orbital compositions of the frontier orbitals of all systems have been determined to examine the nature of these orbitals. © 1996 John Wiley & Sons, Inc.     

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).     

Electronic structure and stability of fullerene C82 isolated-pentagon-rule isomers

All nine isolated-pentagon-rule isomers of fullerene C(82) were investigated by the DFT method with the B3LYP functional at the 6-31G, 6-31G*, and 6-31+G* levels. The distribution of single, double, and delocalized π-bonds in the molecules of these isomers is shown for the first time. The obtained results are fully supported by DFT quantum-chemical calculations of electronic and geometrical structures of these isomers. The molecules of isomers 7 (C(3v)), 8 (C(3v)), and 9 (C(2v)) contain some radical substructures (such as the phenalenyl-radical substructure), which indicates that they are unstable and cannot be obtained as empty molecules. Thus, there is a possibility of obtaining them only as endohedral metallofullerenes or exohedral derivatives. Isomers 1 (C(2)), 2 (C(s)), 4 (C(s)), 5 (C(2)), and 6 (C(s)) with closed electronic shell are supposed to be stable, resembling isomer 3 (C(2)), which has just been extracted experimentally as an empty fullerene. We assume they can be produced as empty molecules.     

A facile route to the non-IPR fullerene Sc3N@C68: synthesis, spectroscopic characterization, and density functional theory computations (IPR=isolated pentagon rule)

Owing to the unique feature of the non-IPR D3 (isomer 6140) C68 cage (IPR=isolated pentagon rule), Sc3N@C68 has been attracting great interest in the fullerene community. Herein we report the first high-yield synthesis of Sc3N@C68 by the "reactive gas atmosphere" method and its facile isolation by single-step HPLC to a high purity (>or=99 %). Thus, Sc3N@C68 is isolated in sufficient quantities for its further spectroscopic characterization, while the high purity of the sample ensures the reliability of the spectroscopic data obtained. In particular, the electronic and vibrational structures of Sc3N@C68 were studied in detail experimentally and by theoretical computations. The assignment of the observed absorption bands to particular electronic transitions is given in detail on the basis of time-dependent DFT computations. Vibrational spectroscopy of Sc3N@C68 reveals good agreement between the measured spectra and the theoretically calculated spectra. A detailed assignment of the vibrational modes, including the Sc3N cluster modes, cage modes, and vibrations of the adjacent pentagons are discussed. This study reveals that the effect of Sc3N encapsulation in the cage is much more complicated than just a formal transfer of six electrons. Consequently the electronic and vibrational spectra of the carbon cage in Sc3N@C68 cannot be adequately understood on the basis of a C68 (6-) cage alone.     

Theoretical studies of structures and stabilities of a new odd-numbered fullerene dimer: C141

The possible isomers of a newly synthesized C(141) molecule are calculated using MNDO, AM1, PM3, B3LYP/3-21G, and B3LYP/6-31G(d) methods. The geometry optimizations showed that the isomer 8-8 has the lowest total energy in all 64 possible structures of C(141). Unlike those of C(130), C(140), etc., the C(141) 8-8 shows a new structure: two C(70) side cages open [6.6] ring junctions located at the equator (instead of cap) area to create new chemical bonds for the bridge atom. Theoretical measurements of the average length of the long and short axes of C(70) side cages in the C(141) molecule reveal that when two C(70) cages are connected with each other at the equators, their geometric shapes become more spherical compared with the pristine C(70); this leads to a reduction of the molecular polarizability. Analysis of the local and global strain indicates that the global strain of C(70) monomer in the C(141) 8-8 is greatly reduced compared to the pristine C(70). The stable C(70) derivatives that are formed with reacted C-C bonds in the equator area may put new insights into fullerene chemistry, in particular, for C(70) to react with a large molecule. The results are discussed together with the experimental data.