C100 IPR fullerenes: temperature-dependent relative stabilities based on the Gibbs function

Continuous symmetry and chirality measures: approximate algorithms for large molecular structures

Quantifying imperfect symmetry of molecules can help explore the sources, roles and extent of structural distortion. Based on the established methodology of continuous symmetry and chirality measures, we develop a set of three-dimensional molecular descriptors to estimate distortion of large structures. These three-dimensional geometrical descriptors quantify the gap between the desirable symmetry (or chirality) and the actual one. They are global parameters of the molecular geometry, intuitively defined, and have the ability to detect even minute structural changes of a given molecule across chemistry, including organic, inorganic, and biochemical systems. Application of these methods to large structures is challenging due to countless permutations that are involved in the symmetry operations and have to be accounted for. Our approach focuses on iteratively finding the approximate direction of the symmetry element in the three-dimensional space, and the relevant permutation. Major algorithmic improvements over previous versions are described, showing increased accuracy, reliability and structure preservation. The new algorithms are tested for three sets of molecular structures including pillar[5]arene complexes with Li+, C100 fullerenes, and large unit cells of metal organic frameworks. These developments complement our recent algorithms for calculating continuous symmetry and chirality measures for small molecules as well as protein homomers, and simplify the usage of the full set of measures for various research goals, in molecular modeling, QSAR and cheminformatics.

Vibrational anatomy of C90, C96, and C100 fullertubes: probing Frankenstein's skeletal structures of fullerene head endcaps and nanotube belt midsection

Fullertubes are tubular fullerenes with nanotube-like middle section and fullerene-like endcaps. To understand how this intermediate form between spherical fullerenes and nanotubes is reflected in the vibrational modes, we performed comprehensive studies of IR and Raman spectra of fullertubes C₉₀-D_5h, C₉₆-D_3d, and C₁₀₀-D_5d. An excellent agreement between experimental and DFT-computed spectra enabled a detailed vibrational assignment and allowed an analysis of the localization degree of the vibrational modes in different parts of fullertubes. Projection analysis was performed to establish an exact numerical correspondence between vibrations of the belt midsection and fullerene headcaps to the modes of nanotubes and fullerene C₆₀-I_h. As a result, we could not only identify fullerene-like and CNT-like vibrations of fullertubes, but also trace their origin in specific vibrational modes of CNT and C₆₀-I_h. IR spectra were found to be dominated by vibrations of fullerene-like caps resembling IR-active modes of C₆₀-I_h, whereas in Raman spectra both caps and belt vibrations are found to be equally active. Unlike the resonance Raman spectra of CNTs, in which only two single-phonon bands are detected, the Raman spectra of fullertubes exhibit several CNT-like vibrations and thus provide additional information on nanotube phonons.

Structural Studies of Giant Empty and Endohedral Fullerenes

Structure elucidations of giant fullerenes composed of 100 or more carbon atoms are severely hampered by their extremely low yield, poor solubility and huge numbers of possible cage isomers. High-temperature exohedral chlorination followed by X-ray single crystal diffraction studies of the chloro derivatives offers a practical solution for structure elucidations of giant fullerenes. Various isomers of giant fullerenes have been determined by this method, specially, non-classical giant fullerenes containing heptagons generated by the skeletal transformations of carbon cages. Alternatively, giant fullerenes can be also stabilized by encapsulating metal atoms or clusters through intramolecular electron transfer from the encapsulated species to the outer fullerene cage. In this review, we present a comprehensive overview on synthesis, separation and structural elucidation of giant fullerenes. The isomer structures, chlorination patterns of a series of giant fullerenes C_2n (2n = 100-108) and heptagon-containing non-classical fullerenes derived from giant fullerenes are summarized. On the other hand, giant endohedral fullerenes bearing different endohedral species are also discussed. At the end, we propose an outlook on the future development of giant fullerenes.

Probing the structure of giant fullerenes by high resolution trapped ion mobility spectrometry

We present high-resolution trapped ion mobility spectrometry (TIMS) measurements for fullerene ions in molecular nitrogen.

The First Experimentally Confirmed Isolated Pentagon Rule (IPR) Isomers of Higher Fullerene C98 Captured as Chlorides, C98(248)Cl22 and C98(116)Cl20

High-temperature chlorination of pristine C98 fullerene isomers separated by HPLC from the fullerene soot afforded crystals of C98Cl22 and C98Cl20. An X-ray structure elucidation revealed, respectively, the presence of carbon cages of the most stable C2-C98(248) and rather unstable C1-C98(116), which represent the first isolated pentagon rule (IPR) isomers of fullerene C98 confirmed experimentally. The chlorination patterns of the chlorides are discussed in terms of the formation of isolated C=C bonds and aromatic substructures on the fullerene cages.

New Isolated-Pentagon-Rule and Skeletally Transformed Isomers of C100 Fullerene Identified by Structure Elucidation of their Chloro Derivatives

High-temperature chlorination of C100 fullerene followed by X-ray structure determination of the chloro derivatives enabled the identification of three isomers of C100 from the fullerene soot, specifically numbers 18, 425, and 417, which obey the isolated pentagon rule (IPR). Among them, isomers C1-C100 (425) and C2-C100 (18) afforded C1-C100 (425)Cl22 and C2-C100 (18)Cl28/30 compounds, respectively, which retain their IPR cage connectivities. In contrast, isomer C2v -C100 (417) gives Cs -C100 (417)Cl28 which undergoes a skeletal transformation by the loss of a C2  fragment, resulting in the formation of a nonclassical (NC) C1-C98 (NC)Cl26 with a heptagon in the carbon cage. Most probably, two nonclassical C1-C100 (NC)Cl18/22 chloro derivatives originate from the IPR isomer C1-C100 (382), although both C1-C100 (344) and even nonclassical C1-C100 (NC) can be also considered as the starting isomers.

Unusual Chlorination Patterns of Three IPR Isomers of C88 Fullerene in C88 (7)Cl12/24 , C88 (17)Cl22 , and C88 (33)Cl12/14

High-temperature chlorination of three IPR isomers of fullerene C88 , C2 -C88 (7), Cs -C88 (17), and C2 -C88 (33), resulted in the isolation and X-ray structural characterization of C88 (7)Cl12 , C88 (7)Cl24 , C88 (17)Cl22 , and C88 (33)Cl12/14 . Chlorination patterns of C88 (7) and C88 (33) isomers are unusual in that one or more pentagons remain free from chlorination while some other pentagons are occupied by two or three Cl atoms. The addition patterns of the isolated chlorides are discussed in terms of the distribution of twelve pentagons on the carbon cages and the formation of stabilizing isolated C=C bonds and benzenoid rings.

Capturing an unstable C100 fullerene as chloride, C100(1)Cl12, with a nanotubular carbon cage

The chlorination of a HPLC C100 fraction afforded C100(1)Cl12 with an unprecedented nanotubular carbon cage of a highly unstable D5d-C100 fullerene.

C100 is Converted into C94 Cl22 by Three Chlorination-Promoted C2 Losses under Formation and Elimination of Cage Heptagons

Chlorination of the C100 (18) fullerene with a mixture of VCl4 and SbCl5 gives rise to branched skeletal transformations affording non-classical (NC) C94 (NC1)Cl22 with one heptagon in the carbon cage together with the previously reported C96 (NC3)Cl20 with three heptagons. The three-step pathway to C94 (NC1)Cl22 starts with two successive C2 losses of 5:6 CC bonds to give two cage heptagons, whereas the third C2 loss of the 5:5 CC bond from a pentalene fragment eliminates one of the heptagons. Quantum-chemical calculations demonstrate that the two unusual skeletal transformations-creation of a heptagon in C96 (NC3)Cl20 through a Stone-Wales rearrangement and the presently reported elimination of a heptagon through C2 loss-are both characterized by relatively low activation energy.

Chlorination of IPR C100 fullerene affords unconventional C96 Cl20 with a nonclassical cage containing three heptagons

Chlorination of C100 fullerene with a mixture of VCl4 and SbCl5 afforded C96Cl20 with a strongly unconventional structure. In contrast to the classical fullerenes containing only hexagonal and pentagonal rings, the C96 cage contains three heptagonal rings and, therefore, should be classified as a fullerene with a nonclassical cage (NCC). There are several types of pentagon fusions in the C96 cage including pentagon pairs and pentagon triples. The three-step pathway from isolated-pentagon-rule (IPR) C100 to C96(NCC-3hp) includes two C2 losses, which create two cage heptagons, and one Stone-Wales rotation under formation of the third heptagon. Structural reconstruction established C100 isomer no. 18 from 450 topologically possible IPR isomers as the starting C100 fullerene. Until now, no pristine C100 isomers have been confirmed based on the experimental results.

Search for lowest-energy fullerenes: C98 to C110

By combining the semiempirical density-functional based tight-binding optimization with density-functional theory single-point energy calculation at the PBE1PBE/6-311G level, we propose an efficient computational approach to determine lowest-energy structures of large-sized carbon fullerenes. Our studies show that C(92) (D(3): 28) and C(94) (C(2): 43) are the new leading candidates for the lowest-energy structures of C(92) and C(94). Moreover, for the first time, the lowest-energy structures of C(98)-C(110) are identified on the basis of the density-functional theory calculation. The lowest-energy isomers C(102) (C(1): 603) and C(108) (D(2): 1771) are readily isolated experimentally because they are much lower in energy than their other low-lying IPR isomers.

Prediction of low-energy isomers of large fullerenes from C132 to C160

To predict energetically favored isomers, we used a topological scheme as a prescreening tool to select candidate isomers for each fullerene from C(106) to C(160). Comparison with the PM3 and tight-binding (TB) potential calculated results and few published data for the low-energy isomers of C(106) to C(130) indicates that the prescreening approach is feasible. For each fullerene from C(132) up to C(160), the selected 1000 candidate isomers were further optimized by PM3 and TB potential. The analysis of the semiempirical PM3 and TB results of C(106) to C(160) provides some qualitative features of the large fullerenes. Furthermore, calculations at the B3LYP/6-31G*//B3LYP/3-21G level of theory were carried out on the top ten PM3 and TB low-energy isomers of C(132) to C(160) to accurately predict the stable isomers, and the HOMO-LUMO gap, the ionization energy, and electron affinity of the lowest-energy isomers were also investigated at the same level.

An efficient approach for theoretical study on the low-energy isomers of large fullerenes C90-C140

An approach that consists of a molecular mechanics method based on the second generation reactive empirical bond order (REBO) potential and the more accurate semiempirical method PM3 (Parametric Method No. 3) was proposed to predict the energetically favored isomers of the fullerenes from C90 to C140 at the semiempirical level. All the 578,701 isolated-pentagon-rule isomers of fullerenes from C90 to C140 were enumerated from topological structures and systematically searched using an energy minimization method to select the best 100 low-energy isomers based on the REBO potential for each fullerene. Then these candidate isomers were further optimized by PM3 and ranked again to determine the top low-energy isomers. This approach was applied to calculate the energetically favored isomers of C90-C140. The results of C90-C120 are in good agreement with the published results by quantum-chemical methods. Furthermore, the top five low-energy isomers of C90-C120, as well as C122-C140 which have scarcely been systematically studied before, are also predicted with the approach. The analysis of the structures showed that the hexagon-neighbor rule is an important factor to the stability of C90-C140. The time cost for the systematical search based on the REBO potential was also discussed. It indicates that the approach proposed is efficient for predicting the energetically favored isomers of large fullerenes at the semiempirical level.

Search for suitable approximation methods for fullerene structure and relative stability studies: Case study with C50

Local density approximation (LDA), several popular general gradient approximation (GGA), hybrid module based density functional theoretical methods: SVWN, BLYP, PBE, HCTH, B3LYP, PBE1PBE, B1LYP, and BHandHLYP, and some nonstandard hybrid methods are applied in geometry prediction for C60 and C70. HCTH with 3-21G basis set is found to be one of the best methods for fullerene structural prediction. In the predictions of relative stability of C50 isomers, PM3 is an efficient method in the first step for sorting out the most stable isomers. HCTH with 3-21G predicts very good geometries for C50, similar to the performance of B3LYP6-31G(d). The gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital from the predictions of all the density functional theory methods has the following descending order: E(gap)(half-and-half hybrid)>E(gap)(B3LYP)>E(gap)(HCTH)(GGA)>E(gap)(SVWN)(LDA).

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.