Cyclic and Linear Structures of C13: A Computational Study

Recently, a linear structure of C₁₃ was observed and its infrared spectrum recorded. Computations of the linear and cyclic structures of C₁₃ are thus presented. The computations are performed at ab initio level using the standard 6-31G* basis set. Electron correlation is treated by density functional theory (Becke3LYP) and perturbation treatment (MP2=FC). With the density-functional approach the standard 6-311G* and 6-311G(2d,p) basis sets are applied, too. In all the treatments the cyclic structure (C_2v symmetry) is located about 90 kJ/mol below the linear form (D_∞h symmetry), while a tricyclic structure is considerably higher in energy (about 280 kJ/mol above the monocyclic species). Even at high temperatures the linear form represents less than 10% of the equilibrium isomeric mixture. Computed IR spectra are also reported. The stability evaluation corresponds to the findings of ion chromatography.     

Computations of Low-Energy Non-Icosahedral Structures of C6− 60

Abstract

Owing to the three-fold degeneracy of the LUMO in C₆₀, its hexa-anion is not subjected to Jahn-Teller distortions. In contrast to the accepted presumptions, however, computations at the MNDO, AMI, PM3, SAM1, HF/STO-3G, HF/3-21G, and HF/4-31G levels show that the completely relaxed, non-icosahedral cage of C^6? ₆₀is lower in energy. The computed energy gain varies between 60 and 150 kJ/mol and thus, it is consistently significant (the most sophisticated approach, HF/4-31G, yields 93 kJ/mol). The longest C-C bond in the relaxed structures is at most computed 0.05 Å longer compared to the 5/6 bond in the icosahedral C^6? ₆₀The symmetry of C^6? ₆₀is relaxed to D₂ A C_2v, isomer is discussed, too.     

B3LYP/6-31G∗//SAM1 Calculations of C36 Fullerene and quasi-Fullerene Cages

Abstract

The recently isolated fullerene C₃₆ is computed by the SAM1 method with energetics refined at the B3LYP/6-31G? level. Twelve low-energy cages are considered in detail, exhibiting both fullerene (pentagons and hexagons) and quasi-fullerene (also squares and heptagons) pattern. In contrast to other fullerene systems, the SAM1 and B3LYP/6-31G? methods do produce somewhat different energetics. Consequently, the equilibrium isomeric composition at high temperatures is different, too. In the best affordable B3LYP/6-31G? approach the fullerene cage with the topological D _6d symmetry represents the most populated species at high temperatures. Hence, an agreement with the solid-state NMR experiment is achieved at the B3LYP/6-31G? theoretical level.     

MOLECULAR AND CRYSTAL STRUCTURE OF THE ADDUCTS OF C60F18 WITH AROMATIC HYDROCARBONS

ABSTRACT

The solubility of C₆₀F₁₈ in aromatic hydrocarbons, benzene, toluene, and xylenes (0.48–1.23?mg/mL), and decomposition enthalpies for the 1?:?1 and 1?:?2 complexes (31–70?kJ/mole) have been determined. The C₆₀F₁₈ molecule has near perfect C_3v symmetry, and the x-ray single-crystal structures of the C₆₀F₁₈?L complexes (L=hexamethylbenzene, o-, m-, p-xylene, and bromobenzene) are compared in terms of 12 types of C?C and four types of C–F bonds. Analysis of the packing modes in the crystals shows an influence of the size and polarity of the aromatic hydrocarbon molecule.     

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.     

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.     

C32: Computations of Low-Energy Cages with Four-Membered Rings

Abstract

C₃₂ cages built from four-, five-, six-, and seven-membered rings are computed. The computations are primarily performed with semiempirical quantum-chemical methods (AM1, PM3, SAM1), and altogether 199 cages are optimized. The energetics is further checked through ab initio HF SCF computations with the standard 3-21G basis set, and also by density functional theory at the B3LYP level in the standard 6-31G? basis set. All five levels of theory suggest a D_4d cage (two four-membered rings, eight pentagons, eight hexagons) as the lowest-energy structure. Temperature effects are treated in the terms of partition functions so that the entropy contributions are considered accordingly. The thermodynamic treatment points out five cages significantly populated at high temperatures. At very high temperatures the structure lowest in energy is not the most abundant isomer. There are just six conventional fullerenes C₃₂, built exclusively from pentagons and hexagons, however, only two of them show significant populations at high temperatures. The remaining three relatively stable cages contain at least one four-membered ring. No structure with a heptagon shows a non-negligible concentration at high temperatures. The study suggests that in the non-IPR region the quasi-fullerene cages with four-membered rings can in some cases be more important than the conventional fullerenes built from pentagons and hexagons only.     

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.     

Temperature Dependence of C60 Solubility in Different Solvents

Abstract

Temperature dependence of C₆₀ solubility in four organic solvents, i.e., hexane, toluene, xylene and cyclohexane, above room temperature is investigated. It is found that the solubilities decrease as temperature rising in hexane, toluene and xylene indicating an exothermic process, while the solubility in cyclohexane increases with the temperature increase denoting an endothermic dissolving process. Least square fit gives the heat of solution of C₆₀ in hexane, toluene, xylene and cyclohexane as ?6.0, ?9.8, ?9.1 and 48.2 kJ/mol respectively. A brief discussion is presented.     

Thermodynamic Properties and Decomposition of Lithium Hexafluoroarsenate, LiAsF6

The heat capacity of lithium hexafluoroarsenate is determined in the temperature range 50–750 K by adiabatic and differential scanning calorimetry techniques. The thermodynamic properties of LiAsF₆ under standard conditions are evaluated: C _p ⁰(298.15 K) = 162.5 ± 0.3 J/(K mol), S ⁰(298.15 K) = 173.4 ± 0.4 J/(K mol), ⁰(298.15 K) = 81.69 ± 0.20 J/(K mol), and H ⁰(298.15 K) – H ⁰(0) = 27340 ± 60 J/mol. The C _p(T) curve is found to contain a lambda-type anomaly with a peak at 535.0 ± 0.5 K, which is due to the structural transformation from the low-temperature, rhombohedral phase to the high-temperature, cubic phase. The enthalpy and entropy of this transformation are 5.29 ± 0.27 kJ/mol and 10.30 ± 0.53 J/(K mol), respectively. The thermal decomposition of LiAsF₆ is studied. It is found that LiAsF₆ decomposes in the range 715–820 K. The heat of decomposition, determined in the range 765–820 K using a sealed crucible and equal to the internal energy change U _r(T), is 31.64 ± 0.08 kJ/mol.     

Anharmonicity in the V<Subscript>2</Subscript>O<Subscript>3</Subscript> molecule and thermodynamic properties of V<Subscript>2</Subscript>O<Subscript>3</Subscript> in the gas phase

A quantum-mechanical calculation of the relative stability, structural parameters, and vibrational frequencies of V₂O₃ molecule isomers for different spin states was carried out using the BPW91/6-311+G(d, p) method. It was shown that the isomer with the C _s structure (nonplanar VOVO rectangle with an O atom attached to it) in the X ⁵ A″ electronic state possesses the maximum stability. The energy of the C _2v symmetry structure was higher than the lowest energy by just 23 cm⁻¹. It definitely indicated the impossibility of usage of the harmonic model in order to calculate the thermodynamic functions of V2O3 (g). A model is proposed based on which the energy levels and vibrational sums of states for this type of motion were calculated for the C _s → C _2v → C _s transition coordinate. These data, as well as results obtained from quantum-mechanical calculations, were used to calculate the thermodynamic functions of V₂O₃ (g) in the temperature range of T = 100–6000 K. The calculations were performed with the five excited electronic states with energies from 1000 to 9000 cm⁻¹ taken into account. A comparison with the data calculated in the “rigid rotator-harmonic oscillator” approximation was performed.     

CO-DEPOSITION OF FULLERENES AND SULFUR FROM DILUTED SOLUTION

ABSTRACT

A new method to synthesize fullerene and sulfur compounds has been developed. Using this method, C₆₀S₁₆ and C₇₀S₁₆ compounds were grown from dilute fullerene and sulfur toluene solution. Their atomic structures were analyzed by x-ray diffraction with the single crystal. The C₆₀S₁₆ crystal is C-centered monoclinic structure of a=2.0874?nm, b=2.1139?nm, c=1.05690?nm and β=111.93°, and the C₇₀S₁₆ has a primitive monoclinic, P2₁/c, with lattice parameters of a=1.5271?nm, b=1.49971?nm, c=2.18024?nm and β=109.791°. In this compound, the structure of fullerenes is maintained and sulfur atoms form S₈ rings placed around the fullerenes.     

Effect of Substituents on the Redox Potentials of C60 Derivatives

Abstract

The electrochemical properties of four C₆₀ derivatives (compounds 1～4) were investigated with cyclic voltammetry (CV), and compared with that of C₆₀. The reduction potentials of compound 1～3 shifted to more negative positions than C₆₀, and their oxidation peaks appeared at the lower potentials. Significantly, the reduction potentials of compound 4 shifted to more positive positions than C₆₀, which is advantageous to form charge-transfer complexes with more donors. So the reduction properties in different solvents and in situ NIR absorption spectra of compound 4 were studied in more details. In addition, the AM1 molecular orbital calculation was performed on C₆₀ and compound 1～4 for the explanation of the potential shifts. The reduction potentials of these compounds exhibited good linear relationships with the calculation LUMO or LUMO+1 energy levels.     

Impression creep behavior of different zones in friction stir welded Mg–Zn–Mn wrought alloy

The friction stir welded joint of wrought ZM21 alloy was divided into five parts, and their localized creep behavior was studied via the impression method. The tests were carried out in the stress range of 300–450 MPa (σ_imp/G ≈ 0.02–0.03) and in the temperature range of 448–523 K. Optical and SEM micrographs and EDS taken before and after the impression tests were used to study the microstructure of various zones of the FS welded joint. Power law was found to satisfactorily relate the stress and strain rates. The steady-state impression velocity was found to vary significantly between the advancing and retreating sides of TMAZ and HAZ. For TMAZ, the creep exponent on the AS was 4.8, and on the RS, it was 7.8. The activation energy on the AS was ~?133 kJ/mol, and on the RS, it was ~?101 kJ/mol. Similarly, for HAZ, the creep exponent on the AS was found to be 5.5 and on the RS, it was 4.9. The activation energy on the AS was ~?86 kJ/mol and on the RS, it was ~?232 kJ/mol. The cross-over of steady-state impression velocity of different zones indicates that the weak zone was temperature and stress dependent. Within the stresses and temperatures studied, the weld zone's creep resistance (i.e., lower minimum impression velocity) was found to be better than the base material. As it is with most magnesium alloys, dislocation climb was found to be the operative mechanism in the FS weldments of ZM21 alloy. The rate-controlling mechanism remains to be identified because the wide variation in n and Q values suggests that different creep mechanisms are in operation in different zones.

Graphical abstract

     

Electronic structure of boron-doped diamond with B–H complex and B pair

Abstract

The electronic structure of boron–hydrogen complex and boron pair in diamond are studied by first-principles density-functional calculations with supercell models. The electronic structure calculated for the B–H complexes with C_2v or C_3v symmetry and the nearest-neighbor B pair is used to interpret recent experimental results such as B 1s x-ray photoemission spectroscopy, ¹¹B nuclear quadruple resonance and B K-edge x-ray absorption spectroscopy, which cannot be explained solely by the isolated substitutional boron.     

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.     

Temperature Dependence of C60 Solubility in Different Solvents

Abstract

Temperature dependence of C₆₀ solubility in four organic solvents, i.e., hexane, toluene, xylene and cyclohexane, above room temperature is investigated. It is found that the solubilities decrease as temperature rising in hexane, toluene and xylene indicating an exothermic process, while the solubility in cyclohexane increases with the temperature increase denoting an endothermic dissolving process. Least square fit gives the heat of solution of C₆₀ in hexane, toluene, xylene and cyclohexane as -6.0, -9.8, -9.1 and 48.2 kJ/mol respectively. A brief discussion is presented.     

Thermodynamic properties of NaZr2(PO4)3

The heat capacity of crystalline NaZr₂(PO₄)₃ was measured between 7 and 340 K by adiabatic calorimetry. The results were used to calculate the thermodynamic functionsC _p ⁰ ,H ⁰(T) -H ⁰(0),S ⁰(T), andG ⁰(T) -H ⁰(0) in the range 0-340 K. The absolute entropy was found to be S⁰NaZr₂(PO₄)₃, cr, 298.15 K) = 327.1 ±1.0 J/(mol K), and the standard entropy of formation Δ_fS⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -1101±1 J/(mol K). Solution calorimetry was used to determine the standard enthalpy of formation, Δ_f H ⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -5236 ±5 kJ/mol. By combining the data obtained by the two techniques, the standard Gibbs energy of formation was determined to be Δ_fG⁰(NaZr₂(PO₄)₃, cr, 298.15 K) = -4908 ±5 kJ/mol.     

Molecular Complex of [60]Fullerene with 2-(4-thione-l,3-dithiolan-5-yliden)-4,5-dimethyl-1,3-diselenol [C60·2(DTDS)]: Synthesis,Crystal Structure and Properties

Abstract

New molecular complexes of [60]fullerene with 2-(4-thione-l,3-dithiolan-5-yliden)-4,5-dimethyl-l,3-diselenol [C₆₀·2(DTDS)] have been synthesized, crystal structure, IR spectral and electrochemical properties have been studied. Partial charge transfer has been found. An unusual shortening of the endocyclic S-C(sp²) bond in the DTDS molecule has been found to be stipulated by conformational vibrations of the >CH₂ group. A comparative analysis of the X-ray data for the [C₆₀·2(DTDS)] crystals and the quantum chemical calculations (SCF MO, 6-31G? basis) for the DTDS molecules and its radical ions showed charge transfer not to be the cause for the shortening of the exocyclic C=S bonds.