Equilibrium yield for helium incorporation into buckminsterfullerene: Quantum-chemical evaluation

Terahertz spectroscopy of the helium endofullerene He@C60

We studied the quantized translational motion of single He atoms encapsulated in molecular cages by terahertz absorption. The temperature dependence of the THz absorption spectra of ³He@C₆₀ and ⁴He@C₆₀ crystal powder samples was measured between 5 and 220 K. At 5 K there is an absorption line at 96.8 cm^-1 (2.90 THz) in ³He@C₆₀ and at 81.4 cm (2.44 THz) in ⁴He@C₆₀, while additional absorption lines appear at higher temperature. An anharmonic spherical oscillator model with a displacement-induced dipole moment was used to model the absorption spectra. Potential energy terms with powers of two, four and six and induced dipole moment terms with powers one and three in the helium atom displacement from the fullerene cage center were sufficient to describe the experimental results. Excellent agreement is found between potential energy functions derived from measurements on the ³He and ⁴He isotopes. One absorption line corresponds to a three-quantum transition in ⁴He@C₆₀, allowed by the anharmonicity of the potential function and by the non-linearity of the dipole moment in He atom displacement. The potential energy function of icosahedral symmetry does not explain the fine structure observed in the low temperature spectra.

Noble gas endohedral fullerenes

This review focuses on the available experimental and theoretical investigations on noble gas (Ng) endohedral fullerenes, addressing essential questions related to the mutual effects that confinement of one or more Ng atoms induces on the electronic structure, bonding, and different properties of fullerenes. It also summarizes the different contributions to the mechanisms of formation and decomplexation, the reactivity towards Diels-Alder cycloaddition reactions, the chemical bonding situation of Ng endohedral fullerenes, and the interactions that dominate within these systems.

Quantum mechanical calculation of nanomaterial-ligand interaction energies by molecular fractionation with conjugated caps method

Molecular fractionation with conjugate caps (MFCC) method is introduced for the efficient estimation of quantum mechanical (QM) interaction energies between nanomaterial (carbon nanotube, fullerene, and graphene surface) and ligand (charged and neutral). In the calculations, nanomaterials are partitioned into small fragments and conjugated caps that are properly capped, and the interaction energies can be obtained through the summation of QM calculations of the fragments from which the contribution of the conjugated caps is removed. All the calculations were performed by density functional theory (DFT) and dispersion contributions for the attractive interactions were investigated by dispersion corrected DFT method. The predicted interaction energies by MFCC at each computational level are found to give excellent agreement with full system (FS) calculations with the mean energy deviation just a fractional kcal/mol. The accurate determination of nanomaterial-ligand interaction energies by MFCC suggests that it is an effective method for performing QM calculations on nanomaterial-ligand systems.

Formation of dimers of light noble atoms under encapsulation within fullerene's voids

Van der Waals (vdW) He2 diatomic trapped inside buckminsterfullerene's void and preserving its diatomic bonding is itself a controversial phenomenon due to the smallness of the void diameter comparing to the He-He equilibrium distance. We propound a computational approach, including smaller fullerenes, C20 and C28, to demonstrate that encapsulation of He2 inside the studied fullerenes exhibits an interesting quantum behavior resulting in a binding at shorter, non-vdW internuclear distances, and we develop a computational model to interpret these He-He bonding patterns in terms of Bader's atom-in-molecule theory. We also conjecture a computational existence of He2@C60 on a solid basis of its theoretical UV absorption spectrum and a comparison with that of C60.

THEORETICAL STUDY ON ENDOHEDRAL COMPLEXES C2H2–C60, C2H4–C60, AND C2H6–C60

Three endohedral fullerenes C 2 H 2– C 60, C 2 H 4– C 60, and C 2 H 6– C 60 are investigated theoretically using density functional theory. Their electronic and structural properties are studied. The calculations suggest that the formations of these complexes are endothermic; the dopant and C 60 cage affect each other rarely except for the slight distortion of C 60 cage and compression of the hydrocarbon molecules. A small quantity of electron transfer from C 60 to the hydrocarbon molecule was also observed. Accordingly, C 60 could theoretically be a good container for some small hydrocarbon molecules.

Rational synthesis, enrichment, and (13)C NMR spectra of endohedral C(60) and C(70) encapsulating a helium atom

Endohedral fullerenes encapsulating a helium atom, i.e., He@C(60) and He@C(70), at occupation levels of 30% were prepared by rational chemical synthesis. The existence of weak interactions between the inner helium and the outer fullerene cages was demonstrated by experimental and computational investigations.

A tight-binding potential for helium in carbon systems

The presence of helium in carbon systems, such as diamonds and fullerenes is of interest for planetary sciences, geophysics, astrophysics, and evolution biology. Such systems typically involve a large number of atoms and require a fast method for assessing the interaction potential and forces. We developed a tight-binding approach, based on density functional calculations, which includes a many-body potential term. This latter term is essential for consolidating the density functional results of helium in bulky diamond and Helium passing through a benzene ring which is important for helium-fullerene applications. The method is simple to apply and exhibits good transferability properties.

Vibration-rotation spectroscopy of molecules trapped inside C60

A simple model is developed to treat the energy levels and spectroscopy of diatomic molecules inside C 60. The C 60 cage is treated as spherically symmetric, and the coupling to the C 60 vibrations is ignored. The remaining six degrees of freedom correspond to the vibrations and rotations of the diatomic molecule and the rattling vibration of the molecule inside the cage. By using conservation of angular momentum, we can remove two of these motions and simplify the calculations. The resulting energy levels are simple and can be labeled by a set of quantum numbers. The IR and Raman spectra look like those of gas-phase diatomic molecules at low temperatures. At higher temperatures, hot bands due to the low-frequency rattling mode appear, and the spectrum becomes congested, looking like a solution spectrum.

Density Functional Calculations of 3He Chemical Shift in Endohedral Helium Fullerenes: Neutral, Anionic, and Di-Helium Species

We report density functional calculations of 3He nuclear magnetic resonance chemical shifts in a series of experimentally known endohedral helium fullerenes, He(n)@Cm(q) (n = 1, 2; m = 60, 70, 76, 78; q = 0, 6-), including for the first time anionic and di-helium species. Despite the lack of dispersion in the density functional model, the results are in promising agreement with experiment. Density functional theory performs better than Hartree-Fock for the anionic systems. In the di-helium species confined in the small C60 cage, besides the atomic displacements from the center position, the direct He-He interactions contribute to the 3He shift.

Unimolecular dissociations of C70+ and its noble gas endohedral cations Ne@C70+ and Ar@C70+: cage-binding energies for C2 loss

The energetics and dynamics of unimolecular decompositions of C70+ and its noble gas endohedral cations, Ne@C70+ and Ar@C70+, have been studied using tandem mass spectrometry techniques. The high-resolution mass-analyzed ion kinetic energy (HR-MIKE) spectra for the unimolecular reactions of C70+, Ne@CC70+, and Ar@C70+ were recorded by scanning the electrostatic analyzer and using single-ion counting that was achieved by combination of an electron multiplier, amplifier/discriminator, and multichannel analyzer. These cations dissociate unimolecularly via loss of a C2 unit, and no endohedral atom is observed as fragment. The activation energies for C2 evaporation from Ne@C70+ and Ar@C70+ are lower than those for elimination of the endohedral noble gas atoms. The kinetic energy release distributions (KERDs) for the C2 evaporation have been measured and, by use of the finite heat bath theory (FHBT), the binding energies for the C2 emission have been deduced from the KERDs. The C2 evaporation energies increase in the order DeltaEvap(C70+) < DeltaEvap(Ne@C70+) < DeltaEvap(Ar@C70+), but no big difference in the cage binding was observed for C70+, Ne@C70+, and Ar@C70+, indicating incorporations of the Ne and Ar atoms into C70 contribute a little to the stability of C70 toward C2 loss, which is in good agreement with theoretical calculations but contrasts with the findings in their C60 analogues and in metallofullerenes that the decay energies of the filled fullerenes are much higher than those of the corresponding empty cages.

Open-Cage Fullerene Derivatives Suitable for the Encapsulation of a Hydrogen Molecule

The encapsulation of molecular hydrogen into an open-cage fullerene having a 16-membered ring orifice has been investigated. It is achieved by the pressurization of H2 at 0.6-13.5 MPa to afford endohedral hydrogen complexes of open-cage fullerenes in up to 83% yield. The efficiency of encapsulation is dominantly dependent on both H2 pressure and temperature. Hydrogen molecules inside the C60 cage are observed in the range of -7.3 to -7.5 ppm in 1H NMR spectra, and the formations of hydrogen complexes are further confirmed by mass spectrometry. The trapped hydrogen is released by heating. The activation energy barriers for this process are determined to be 22-24 kcal/mol. The DSC measurement of the endohedral H2 complex reveals that the escape of H2 from the C60 cage corresponds to an exothermic process, indicating that encapsulated H2 destabilizes the fullerene.

Helium Entry and Escape through a Chemically Opened Window in a Fullerene

(3)He has been inserted into the cavity of an open-cage fullerene derivative close to room temperature, reaching an incorporation fraction of 0.1%. The rate of escape of (3)He from this fullerene was monitored by (3)He NMR to yield the activation barrier and to compare the size of the orifice to those of other open-cage fullerenes. The equilibrium constant was also measured.

Using cyanide to put noble gases inside C60

After fullerenes are heated in the presence of a noble gas or an unreactive molecule at 650 degrees C and 3000 atm pressure, a small fraction of the fullerene molecules contain the atom or molecule. The incorporation fraction is greatly enhanced by adding potassium cyanide to the reaction mixture. The details of the preparation are described here.

Thermodynamic stability of hydrogen clathrates

The stability of the recently characterized type II hydrogen clathrate [Mao, W. L., Mao, H.-K., Goncharov, A. F., Struzhkin, V. V., Guo, Q., et al. (2002) Science 297, 2247-2249] with respect to hydrogen occupancy is examined with a statistical mechanical model in conjunction with first-principles quantum chemistry calculations. It is found that the stability of the clathrate is mainly caused by dispersive interactions between H2 molecules and the water forming the cage walls. Theoretical analysis shows that both individual hydrogen molecules and nH2 guest clusters undergo essentially free rotations inside the clathrate cages. Calculations at the experimental conditions--2,000 bar (1 bar = 100 kPa) and 250 K confirm multiple occupancy of the clathrate cages with average occupations of 2.00 and 3.96 H2 molecules per D-5(12) (small) and H-5(12)6(4) (large) cage, respectively. The H2-H2O interactions also are responsible for the experimentally observed softening of the H[bond]H stretching modes. The clathrate is found to be thermodynamically stable at 25 bar and 150 K.