Stone-Wales Rearrangement Pathways from the Hinge-Opened [2+2] C60 Dimer to Ipr C120 Fullerenes. Vibrational Analysis of Intermediates

Possibility of the previously proposed hinge-opened product 2 of [2+2] C₆₀, dimer 1 transforming itself into IPR C₁₂₀ fullerenes by a series of generalized Stone-Wales (GSW) rearrangements has been tested by seeking all topologically acceptable pathways with the help of a graphical search program. the first IPR isomer 4 appeared after 20 GSW steps from the wide-bridged dumb-bell shaped precursor 3. More than 1,000 C₁₂₀ fullerene structures were generated during subsequent ten GSW steps, but the outstanding T_dC₁₂₀ global minimum 5 was not reached. Semiempirical vibrational calculations predict characteristic transition in the vibrational spectra in the course of rearrangement pathway.     

A Computational Treatment of 35 IPR Isomers of C88

Abstract

The complete sets of 35 isolated-pentagon-rule (IPR) isomers of C₈₈ is described by the SAM1 (Semi-Ab-initio Model 1) quantum-chemical method. The separation energetics is also computed at the HF/STO-3G, HF/3-21G, and HF/4-31G levels. The SAM1 and HF/4-31G data mostly agree within a few kJ/mol. As the SAM1 energetics does not reproduce the recent NMR observations, entropy contributions are included, too, being based on the harmonic-oscillator and rigid-rotator model. Considerable temperature effects on the relative stabilities in the system are found. The ground-state structure of C₈₈ is a C ₃ isomer, however, with an increase of temperature a C ₂ structure becomes important. At still higher temperatures a near C ₂ species is dominant. The results can be viewed as a good agreement with the available observations, and they further expand the family of the IPR sets where the thermodynamic equilibrium treatment allows for a satisfactory support of observations.     

Analysis of the Growth Mechanism of Carbon Nanotubes by C2 Ingestion

Abstract

Cap structures capable of sustaining infinite growth by ingestion of C₂ fragments to give a carbon nanotube were screened systematically. For this purpose a total of 23,296 IPR cap structures having characteristic tubule vectors of (5～20, 0～10) were generated by the use of net algorithm. Eighteen recurring patterns were found which involve 50 cap structures having tubule vectors (6～11, 5).     

C60 Dimers Revisited

Abstract

Several dimers: C₁₂₀, C₁₄₀, C₁₃₀ and their oxygen‐containing derivatives as well as some oligomers or polymers of the well known spherical fullerenes have been synthesized so far. Some of the formulas attributed to such compounds represent the first steps in a more complex fate leading to trivalent capped tubulenes. Such a way could even be followed by functionalized fullerenes. A detailed network transformation is given for C₆₀ and its mono‐ and di‐epoxy derivatives. Semiempirical calculations support the presented findings.     

Eu@C86 isomers: Calculated relative populations

Abstract

Relative populations of four energy-lowest IPR (isolated-pentagon-rule) isomers of Eu@C₈₆ are computed using the Gibbs energy based on characteristics from density functional theory calculations (M06-2X/3-21G?～?SDD entropy term, M06-2X/6-31G*～SDD or B2PLYP(D)/6-31G*～SDD energetics). The calculations confirm that the recently isolated Eu@C₁(7)-C₈₆ species is a major isomer in a relevant temperature region. Relationship to the empty C₈₆ cages is discussed, too.     

Calculated Relative Stabilities of C84

C₈₄ is treated as a system composed of 24 local minima whose energies, geometries, and vibrational frequencies are obtained from MNDO calculations. The predicted global minimum of D_2d symmetry remains the most abundant species in the equilibrium isomeric mixture only till 276 K, being replaced by a D₂ species beyond that point. However, a C ₁ structure is prevalent in the high temperature limit. The calculated composition around a temperature of 1000 K is consistent with very recent NMR observations.     

Thermal Transformation of Ring-Opened [2+2] C60 Dimer into a Wide-Bridged C120 Isomer. A Computational Evaluation of Fulvalene-Naphthalene Rearrangements

Abstract

As a continuation of the studies on thermal transformation of the [2+2] C₆₀ dimer (1), the consequence of the pyracylene-rearrangement-like valence isomerization of the fulvalene partial structure at the bridge of the ring-opened product from 1, namely 2, was searched by dynamic reaction coordinate /AM1 semiempirical MO calculations. It is predicted that the fulvalene bridge of 2 rearranges into naphthalene partial structure by the concerted ‘in-plane’ mechanism to give a wide-bridged C₁₂₀ intermediate having twenty five-membered rings and two ten-membered rings (3). The computed energy of activation (145 kcal/mol) is 40 kcal/mol lower than those computed for pyracylene rearrangements. In contrast, the recently reported analogous rearrangement of indigo (13) to dibenzonaphthyridindione (14) is computed to occur by the stepwise ‘sp³’ mechanism.     

Diphenylmethane Fulleroid C73H10: AM1 Computational Study

Diphenylmethane fulleroid C₇₃H₁₀ is studied by means of the AM1 quantum-chemical method. Full geometry optimization of its C _2v structure is performed together with vibrational harmonic analysis. The computed length of the C-C bond between two cage-hexagons bridged by the tetra-hedral C atom is 1.565 Å. Vibrational frequencies with a substantial IR intensity are reported.     

High-pressure behavior of the crystal structure of the fullerene molecular complex with ferrocene C60·{Fe(C5H5)2}2

Abstract

The crystal structure of the molecular complex C₆₀·{Fe(C₅H₅)₂}₂ was studied by single crystal X-ray diffraction (XRD) analysis at pressures up to 5?GPa using the diamond anvil cell (DAC) technique. The XRD data and subsequent structural analysis clearly show that there is no pressure-induced polymerization in fullerene layers in pressure range studied. The reciprocal unit cell volume V₀/V is a smooth and monotonous function of pressure and fits well to the Murnaghan equation of state (V₀/V) ^B'=?{1?+?P·(B'/B₀)}, where V₀ is the volume at ambient pressure, B₀=8.7?GPa and B'=10.5 are the bulk modulus and its derivative, respectively. Pressure dependence of the shortest distance between the C₅H₅ ring of the ferrocene molecule and the center of the nearest fullerene molecule is linear, while the slope changes at 2.2?GPa indicating on the intermolecular interactions crossover. Other relevant parameter, the Fe-C bond lengths of ferrocene, sensitive to iron charge state, gradually increases. This peculiarity can a sign of pressure-induced partial charge transfer between the donor ferrocene and acceptor fullerene molecules.     

On the Limitation of Net Algorithm for Enumerating Isomeric Structures of Giant Fullerenes

Abstract

Application of our net algorithm to the generation of all possible IPR isomers for giant fullerenes C_n, n=102 to 120, missed nine out of 39,621 possible structures. Analysis revealed that the omission of too small and too large cap triangles was the reason. Within the range of fullerenes studied, the missed structures are of high-energy and do not affect the distribution of significantly low-energy isomers.     

C60(NO2)2: Quantum-Chemical Evaluations of Structure,Energetics, and Vibrational Spectra

Abstract

The complete PM3 structural optimizations are reported for all 23 positional isomers of C₆₀(NO₂)₂ and interesting symmetry reductions are found. There are two low energy structures while all the remaining species are separated by more than 10 kcal/mol from the computed ground state. In the ground state the two nitro groups are placed in para position on one hexagon. The next lowest structure is produced by addition to one 6/6 (double) bond of the cage. The species highest in energy are separated by more than 50 kcal/mol from the ground state. IR vibrational spectra are also predicted for the low-energy structures.     

A MODEL STUDY OF NARROW NANOTUBES RELATED TO C36, C32, C20, AND C16: SEMIEMPIRICAL AND NONEMPIRICAL TREATMENTS

ABSTRACT

Very recently, narrow nanotubes have been observed with diameters of 5 or even 4?Å. In this report we perform calculations of narrow model nanotubes capped by fragments of D _2d and D _6h C₃₆ fullerene cages or by fragments of C₃₂ and C₁₆ quasi-fullerene cages with two four-membered rings, or finally by a fragment of dodecahedral C₂₀. The computations can reproduce the observed diameters of the narrow nanotubes. The results also indicate that fragments of C₃₂, used as caps instead of C₃₆, can lead to quite competitive energetics. Thus, a novel possibility that some of the narrow nanotubes can contain four-membered rings at their tips is suggested.     

Quantum Chemical ab initio Investigations of Non-Covalent Bonding Derivatives of Fullerene C60 and Li Atom or Cs2, C6H6 Molecules

Abstract

Quantum chemical ab initio investigations of the stability of the non-covalent fullerene complexes: C₆₀ molecule + Li atom, two C₆₀, two C₆₀ + CS₂, C₆₀ + CS₂, C₆₀ + C₆H₆ were performed using Hartree-Fock (HF) and Density Functional Theory (DFT) methods in various basis sets. The inclusion of electron correlation effect calculated by using DFT B3PW91 model during the optimization of Li atom position above hexagonal of C₆₀ gives the smaller distance from the centre of C₆₀ equal to 7.75 Å and large positive energy of formation equal to 4.452 kcal/mol in comparison with HF calculated distance 8.39 Å and energy of formation 1.810 kcal/mol. The positive energy of formation equal to 0.483 kcal/mol for optimized complex two C₆₀ + one CS₂ was found by HF. The presence of CS₂ molecule stabilises this complex with the energy equal to 0.281 kcal/mol. Complexes: C₆₀ + CS₂, C₆₀ + C₆H₆ do not possess the positive energy of formation.     

Penultimate Intermediates to C60 and C70

Abstract

Penultimate intermediates leading to C₆₀ and C₇₀ fullerenes contain one or two pairs of pentalene units and 32 to 55 kcal/mol less stable than the final products. Energy barriers of pyracylene rearrangements from these intermediates to the final products are computed to be 118 to 125 kcal/mol in height by MOPAC/AM1, which are comparable to those of preceding steps in the Stone-Wales rearrangement cascade.     

Infrared Spectra and Structure of C60 Heterocyclic Derivatives

Abstract

Infrared spectra of a number of C₆₀ cycloaddition products, namely, fullerenopyrroline and fullerenopyrazolines with the substituents in the heterocyclic fragments have been studied experimentally and employing DFT calculations. Complete vibrational assignment is proposed.     

On the study of phase formation and critical current density in superconducting MgB2

Superconducting bulk MgB₂ samples have been synthesized by employing sintering technique without using any additional process steps, generally undertaken in view of the substantial loss of magnesium, during heat treatment. Starting with Mg rich powders having different atomic ratios of Mg : B, as against the nominally required Mg : B = 1:2 ratio, we have obtained superconducting MgB₂ samples of different characteristics. The effect of excess Mg in the starting mixture and processing temperature on the phase-formation, transition temperature (T _C) and critical current density (J _C) have been investigated by electrical transport and a.c. susceptibility measurements. The X-ray diffraction and X-ray photoelectron spectroscopic analyses of MgB₂ bulk samples have been carried out to understand the role of excess Mg and the effect of processing temperature. It is established that MgB₂ samples with high critical current density can be synthesized from a Mg rich powder having Mg : B in 2:2 ratio, at temperatures around 790°C. Critical current density has been found to vary systematically with processing temperature.     

Molecular structures of the open-shell IPR isomers of fullerene C90

Fifteen open-shell isomers off the forty six IPR isomers of fullerene C₉₀ were found and investigated: 5 (C_s), 7 (C₁), 9 (C₁), 10 (C_s), 11 (C₁), 20 (C₁), 21 (C₁), 22 (C₁), 23 (C₂), 24 (C₁), 25 (C_2v), 41 (C₂), 42 (C₂), 43 (C₂), and 44 (C₂). According to developed by us approach the positions of single, double, and delocalized π-bonds in the molecules of these isomers are shown for the first time. The obtained results of electronic and geometrical structures are fully supported by DFT method with the B3LYP functional at the 6-31G and 6-31G* levels. Molecules of these open-shell isomers contain different radical substructures (mainly the phenalenyl-radical substructures), they should be unstable and could not be obtained as empty molecules. Nevertheless, there is a possibility of obtaining them in polymeric forms or as endohedral or exohedral derivatives.     

Bromination of [60]Fullerene. II. Crystal and Molecular Structure of [60]Fullerene Bromides,C60Br6, C60Br8, and C60Br24

Abstract

The crystal and molecular structures of the bromofullerene solvates C₆₀Br₆·0.5C₆H₅Cl·0.5Br₂, C₆₀Br₈·1.5(o‐C₆H₄Cl₂), C₆₀Br₈·Br₂, C₆₀Br₈·0.5C₆H₅Br·0.5Br₂, and C₆₀Br₂₄·2Br₂ have been determined by single crystal X‐ray diffraction. The molecular species C₆₀Br₆, C₆₀Br₈, and C₆₀Br₂₄ which have idealized C _s , C _2v  , and T _h symmetries, respectively, have several different types of C?Br and C?C bonds. A comparison between different solvates of the same bromofullerenes revealed a larger stability of the packing modes for the C₆₀Br₆ and C₆₀Br₂₄ solvates, whereas the C₆₀Br₈ solvates showed different packing motifs dependent on the nature and amount of the solvent molecules.     

On the Size Dependence of Standing Waves in Tubular Fullerenes

Summary

We present an analysis of principal vibrational modes whose propagation creates the standing waves along the lateral surfaces of the elongated fullerenes.

We deduce the recurrence rules determining the possibility of resonances between the skew and vertical modes, as well as the appearance of isolated standing waves with nodes in the elongated fullerenes C_N with N = 50 + 10k, k= 1,2,3….

We discuss briefly the influence of different vibrational spectra on the mechanical stability of C_N-elongated fullerenes, and its impact on the relative rate of their production.

     

A Robust Molecular Porous Material for C2H2/CO2 Separation

A molecular porous material, MPM-2, comprised of cationic [Ni₂(AlF₆)(pzH)₈(H₂O)₂] and anionic [Ni₂Al₂F₁₁(pzH)₈(H₂O)₂] complexes that generate a charge-assisted hydrogen-bonded network with pcu topology is reported. The packing in MPM-2 is sustained by multiple interionic hydrogen bonding interactions that afford ultramicroporous channels between dense layers of anionic units. MPM-2 is found to exhibit excellent stability in water (>1 year). Unlike most hydrogen-bonded organic frameworks which typically show poor stability in organic solvents, MPM-2 exhibited excellent stability with respect to various organic solvents for at least two days. MPM-2 is found to be permanently porous with gas sorption isotherms at 298 K revealing a strong affinity for C₂H₂ over CO₂ thanks to a high (ΔQ_st)_AC [Q_st (C₂H₂) − Q_st (CO₂)] of 13.7 kJ mol⁻¹ at low coverage. Dynamic column breakthrough experiments on MPM-2 demonstrated the separation of C₂H₂ from a 1:1 C₂H₂/CO₂ mixture at 298 K with effluent CO₂ purity of 99.995% and C₂H₂ purity of >95% after temperature-programmed desorption. C-H···F interactions between C₂H₂ molecules and F atoms of AlF₆³⁻ are found to enable high selectivity toward C₂H₂, as determined by density functional theory simulations.