Interaction potential and infrared absorption of endohedral H2 in C60

We have measured the temperature dependence of the infrared spectra of a hydrogen molecule trapped inside a C(60) cage, H(2)@C(60), in the temperature range from 6 to 300 K and analyzed the excitation spectrum by using a five-dimensional model of a vibrating rotor in a spherical potential. The electric dipole moment is induced by the translational motion of endohedral H(2) and gives rise to an infrared absorption process where one translational quantum is created or annihilated, ΔN = ±1. Some fundamental transitions, ΔN = 0, are observed as well. The rotation of endohedral H(2) is unhindered but coupled to the translational motion. The isotropic and translation-rotation coupling part of the potential are anharmonic and different in the ground and excited vibrational states of H(2). The vibrational frequency and the rotational constant of endohedral H(2) are smaller than those of H(2) in the gas phase. The assignment of lines to ortho- and para-H(2) is confirmed by measuring spectra of a para enriched sample of H(2)@C(60) and is consistent with the earlier interpretation of the low temperature infrared spectra [Mamone et al., J. Chem. Phys. 130, 081103 (2009)].     

Sc2C2@C80 rather than Sc2@C82: templated formation of unexpected C2v(5)-C80 and temperature-dependent dynamic motion of internal Sc2C2 cluster

Unambiguous X-ray crystallographic results of the carbene adduct of Sc(2)C(82) reveal a new carbide cluster metallofullerene with the unexpected C(2v)(5)-C(80) cage, that is, Sc(2)C(2)@C(2v)(5)-C(80). More interestingly, DFT calculations and NMR results disclose that the dynamic motion of the internal Sc(2)C(2) cluster depends strongly on temperature. At 293 K, the cluster is fixed inside the cage with two nonequivalent Sc atoms on the mirror plane, thereby leading to C(s) symmetry of the whole molecule. However, when the temperature increases to 413 K, the (13)C and (45)Sc NMR spectra show that the cluster rotates rapidly inside the C(2v)(5)-C(80) cage, featuring two equivalent Sc atoms and weaker metal-cage interactions.     

Structural elucidation and regioselective functionalization of an unexplored carbide cluster metallofullerene Sc2C2@C(s)(6)-C82

A Sc(2)C(84) isomer, previously assumed to be Sc(2)@C(84), is unambiguously identified as a new carbide cluster metallofullerene Sc(2)C(2)@C(s)(6)-C(82) using both NMR spectroscopy and X-ray crystallography. The (13)C-nuclei signal of the internal C(2)-unit was observed at 244.4 ppm with a 15% (13)C-enriched sample. Temperature-dependent dynamic motion of the internal Sc(2)C(2) cluster is also revealed with NMR spectrometry. Moreover, the chemical property of Sc(2)C(2)@C(s)(6)-C(82) is investigated for the first time using 3-triphenylmethyl-5-oxazolidinone (1) which provides a 1,3-dipolar reagent under heating. Regarding the low cage symmetry of this endohedral which contains 44 types of nonequivalent cage carbons, it is surprising to find that only one monoadduct isomer is formed in the reaction. Single-crystal X-ray results of the isolated pyrrolidino derivative Sc(2)C(2)@C(s)(6)-C(82)N(CH(2))(2)Trt (2) reveal that the addition takes place at a [6,6]-bond junction, which is far from either of the two Sc atoms. Such a highly regioselective addition pattern can be reasonably interpreted by analyzing the frontier molecular orbitals of the endohedral. Electronic and electrochemical investigations reveal that adduct 2 has a larger highest occupied molecular orbital-lowest unoccupied molecular orbital (HOMO-LUMO) gap than pristine Sc(2)C(2)@C(s)(6)-C(82); accordingly, it is more stable.     

13C NMR spectroscopic study of scandium dimetallofullerene, Sc2@C84 vs. Sc2C2@C82

Although Sc2C84 has been widely believed to have the form Sc2@C84, the present 13C NMR study reveals that it is a scandium carbide metallofullerene, Sc2C2@C82, which has a C82(C(3v)) cage.     

Cover Picture

The cover picture shows a section of the electron charge density of the first metal carbide endohedral metallofullerene (Sc(2)C(2))@C(84) obtained from a synchrotron X-ray powder diffraction study by the maximum entropy method (MEM). The several density maxima, which correspond to scandium and carbon atoms, are clearly seen inside the C(84) carbon cage. The MEM charge density distribution also reveals that the C(84) cage has D(2d) symmetry (no. 23) and that the C(2) axis is parallel to the <100> face-centered cubic (fcc) direction of the unit cell. As a consequence of the site symmetry being 4mm, the C(2) axis of (Sc(2)C(2))@C(84) is oriented to six equivalent <100> directions and shows a merohedral disorder. The resultant Sc small middle dot small middle dot small middle dotSc distances and C-C bond lengths of the Sc(2)C(2) cluster are 0.429(2) and 0.142(6) nm, respectively. The observed C-C bond length is between that of a typical single and a double bond, and is very close to that of the C-C bond (0.143 nm) combining two pentagons in a C(60) molecule. More about this fascinating structure can be found in the contribution by Shinohara and co-workers on p. 397 ff.     

Electronic structure and redox properties of the open-shell metal-carbide endofullerene Sc3C2@C80: a density functional theory investigation

Density functional theory calculations have shown that the open-shell metal-carbide endofullerene Sc3C2@C80 has the valence state (Sc3+)3(C2)(3-)@C80(6-). A lot of low-lying isomers differing in geometries and locations of the endohedral [(Sc3+)3(C2)(3-)] cluster have been located, indicating unusual dual intramolecular dynamic behaviors of this endofullerene at room temperature. The electrochemical redox properties of this endofullerene have been elucidated in terms of electronic structure theory. Its redox states are found to follow the general charge-state formula (Sc3+)3C2(3-q)-@C80(6-) (q is the charge of the whole molecule ranging from +1 to -3), demonstrating the high charge flexibility of the endohedral metal-carbide cluster. The structure of the endohedral [(Sc3+)3C2(3-q)-)] cluster varies with the redox processes, shifting from a planar structure (for q = 0 and -1) to a trifoliate structure (for q = +1, -2, -3).     

Sc2@C70 rather than Sc2C2@C68: density functional theory characterization of metallofullerene Sc2C70

Detailed study on Sc(2)C(70) series has been performed based on fully screening for C(70) tetra- and hexa- anions. With a combined methodology of quantum chemistry and statistical mechanics, our calculation results reveal that the Sc(2)C(70), which was proposed as the first metal-carbide endohedral metallofullerene with a non-isolated pentagon rule (non-IPR) cage (Sc(2)C(2)@C(68):6073_C(2v)), is in fact a C(70) non-IPR metallofullerene structure (Sc(2)@C(70):7854_C(2v)) with three pair of pentagon adjacency thanks to its significant thermodynamic and kinetic stability. According to the natural bond analysis and orbital interaction diagram, each scandium atom should only transfer two 4s electrons to the carbon cages and the valence state of Sc(2)@C(70) is (Sc(2+))(2)@C(70) (4-). In addition, the simulation of UV-Vis-NIR spectrum for Sc(2)@C(70):7854_C(2v) shows good accordance to the experimental spectrum.     

H2, HD, and D2 inside C60: coupled translation-rotation eigenstates of the endohedral molecules from quantum five-dimensional calculations

We have performed rigorous quantum five-dimensional (5D) calculations of the translation-rotation (T-R) energy levels and wave functions of H(2), HD, and D(2) inside C(60). This work is an extension of our earlier investigation of the quantum T-R dynamics of H(2)@C(60) [M. Xu et al., J. Chem. Phys. 128, 011101 (2008)] and uses the same computational methodology. Two 5D intermolecular potential energy surfaces (PESs) were employed, differing considerably in their well depths and the degree of confinement of the hydrogen molecule. Our calculations revealed pronounced sensitivity of the endohedral T-R dynamics to the differences in the interaction potentials, and to the large variations in the masses and the rotational constants of H(2), HD, and D(2). The T-R levels vary significantly in their energies and ordering on the two PESs, as well as from one isotopomer to another. Nevertheless, they all display the same distinctive patterns of degeneracies, which can be qualitatively understood and assigned in terms the model which combines the isotropic three-dimensional harmonic oscillator, the rigid rotor, and the coupling between the orbital and the rotational angular momenta of H(2)/HD/D(2). The quantum number j associated with the rotation of H(2), HD, and D(2) was found to be a good quantum number for H(2) and D(2) on both PESs, while most of the T-R levels of HD exhibit strong mixing of two or more rotational basis functions with different j values.     

Structures, stabilities, electronic, and optical properties of C64 fullerene isomers, anions (C64(2-) and C64(4-)), metallofullerene Sc2@C64, and Sc2C2@C64

The 3465 classical isomers of C(64) fullerene have been investigated by quantum chemical methods PM3, and the most stable isomers have been refined with HCTH/3-21G//SVWN/STO-3G, B3LYP/6-31G(d)//HCTH/3-21G, and B3LYP/6-311G(d)//B3LYP/6-31G(d) level. C(64)(D(2):0003) with the lowest e(55) (e(55) = 2), the number of pentagon-pentagon fusions, is predicted to be the most stable isomer and it is followed by the C(64)(C(s):0077) and C(64)(C(2):0103) isomers within relative energy of 20.0 kcal/mol. C(64)(D(2):0003) prevails in a wide temperature range according to energy analysis with entropy contribution at B3LYP/6-31G(d) level. The simulated IR spectra and electronic spectra help to identify different fullerene isomers. All the hexagons in the isomers with e(55) = 2 display local aromaticity. The relative stabilities of C(64) isomers change with charging in ionic states. Doping also affects the relative stabilities of fullerene isomers as demonstrated by Sc(2)@C(64)(D(2):0003) and Sc(2)@C(64)(C(s):0077). The bonding of Sc atoms with C(64) elongates the C-C bond of two adjacent pentagons and enhances the local aromaticity of the fullerene cages. Charging, doping, and derativization can be utilized to isolate C(64) isomers through differentiating the electronic and steric effects.     

X-ray structures of Sc2C2@C2n (n = 40-42): in-depth understanding of the core-shell interplay in carbide cluster metallofullerenes

X-ray analyses of the cocrystals of a series of carbide cluster metallofullerenes Sc(2)C(2)@C(2n) (n = 40-42) with cobalt(II) octaethylporphyrin present new insights into the molecular structures and cluster-cage interactions of these less-explored species. Along with the unambiguous identification of the cage structures for the three isomers of Sc(2)C(2)@C(2v)(5)-C(80), Sc(2)C(2)@C(3v)(8)-C(82), and Sc(2)C(2)@D(2d)(23)-C(84), a clear correlation between the cluster strain and cage size is observed in this series: Sc-Sc distances and dihedral angles of the bent cluster increase along with cage expansion, indicating that the bending strain within the cluster makes it pursue a planar structure to the greatest degree possible. However, the C-C distances within Sc(2)C(2) remain unchanged when the cage expands, perhaps because of the unusual bent structure of the cluster, preventing contact between the cage and the C(2) unit. Moreover, analyses revealed that larger cages provide more space for the cluster to rotate. The preferential formation of cluster endohedral metallofullerenes for scandium might be associated with its small ionic radius and the strong coordination ability as well.     

Multipole induced splitting of metal-cage vibrations in crystalline endohedral D2d-M2@C84 dimetallofullerenes

Metal-carbon cage vibrations of crystalline endohedral D2d-M2@C84 (M=Sc,Y,Dy) dimetallofullerenes were analyzed by temperature dependent Raman scattering and a dynamical force field model. Three groups of metal-carbon cage modes were found at energies of 35-200 cm(-1) and assigned to metal-cage stretching and deformation vibrations. They exhibit a textbook example for the splitting of molecular vibrations in a crystal field. Induced dipole-dipole and quadrupole-quadrupole interactions account quantitatively for the observed mode splitting. Based on the metal-cage vibrational structure it is demonstrated that D2d-Y2@C84 dimetallofullerene retains a monoclinic crystal structure up to 550 K and undergoes a transition from a disordered to an ordered orientational state at a temperature of approximately 150 K.     

Structural determination of metallofullerene Sc3C82 revisited: a surprising finding

We report here the structural determination of the Sc3C82 molecule by 13C NMR spectroscopy and X-ray single-crystal structure analysis. From the present study, it is obvious that the structure of Sc3C82 is not Sc3@C82 but Sc3C2@C80.     

Rotational-vibrational rainbows in impulsive electron-diatomic molecule collisions

Rotational and vibrational rainbow effects in electron-diatomic molecule scattering at intermediate impact energies (≈10² eV) are discussed in a simple quantum mechanical spectator model within the rigid rotor/harmonic oscillator approximation. The total vibrational (summed over all final rotational quantum numbers) and rotational (vibrationally summed) transition probabilities show vibrational or rotational rainbow patterns, characteristic steps, and rainbow singularities, which are analyzed and interpreted in terms of classical cross sections.     

Infrared spectroscopy of endohedral HD and D2 in C60

We report on the dynamics of two hydrogen isotopomers, D(2) and HD, trapped in the molecular cages of a fullerene C(60) molecule. We measured the infrared spectra and analyzed them using a spherical potential for a vibrating rotor. The potential, vibration-rotation Hamiltonian, and dipole moment parameters are compared with previously studied H(2)@C(60) parameters [M. Ge, U. Nagel, D. Hüvonen, T. R??m, S. Mamone, M. H. Levitt, M. Carravetta, Y. Murata, K. Komatsu, J. Y.-C. Chen, and N. J. Turro, J. Chem. Phys. 134, 054507 (2011)]. The isotropic part of the potential is similar for all three isotopomers. In HD@C(60), we observe mixing of the rotational states and an interference effect of the dipole moment terms due to the displacement of the HD rotation center from the fullerene cage center.     

The shape of the Sc2(μ2-S) unit trapped in C82: crystallographic, computational, and electrochemical studies of the isomers, Sc2(μ2-S)@C(s)(6)-C82 and Sc2(μ2-S)@C(3v)(8)-C82

Single-crystal X-ray diffraction studies of Sc(2)(μ(2)-S)@C(s)(6)-C(82)·Ni(II)(OEP)·2C(6)H(6) and Sc(2)(μ(2)-S)@C(3v)(8)-C(82)·Ni(II)(OEP)·2C(6)H(6) reveal that both contain fully ordered fullerene cages. The crystallographic data for Sc(2)(μ(2)-S)@C(s)(6)-C(82)·Ni(II)(OEP)·2C(6)H(6) show two remarkable features: the presence of two slightly different cage sites and a fully ordered molecule Sc(2)(μ(2)-S)@C(s)(6)-C(82) in one of these sites. The Sc-S-Sc angles in Sc(2)(μ(2)-S)@C(s)(6)-C(82) (113.84(3)°) and Sc(2)(μ(2)-S)@C(3v)(8)-C(82) differ (97.34(13)°). This is the first case where the nature and structure of the fullerene cage isomer exerts a demonstrable effect on the geometry of the cluster contained within. Computational studies have shown that, among the nine isomers that follow the isolated pentagon rule for C(82), the cage stability changes markedly between 0 and 250 K, but the C(s)(6)-C(82) cage is preferred at temperatures ≥250 °C when using the energies obtained with the free encapsulated model (FEM). However, the C(3v)(8)-C(82) cage is preferred at temperatures ≥250 °C using the energies obtained by rigid rotor-harmonic oscillator (RRHO) approximation. These results corroborate the fact that both cages are observed and likely to trap the Sc(2)(μ(2)-S) cluster, whereas earlier FEM and RRHO calculations predicted only the C(s)(6)-C(82) cage is likely to trap the Sc(2)(μ(2)-O) cluster. We also compare the recently published electrochemistry of the sulfide-containing Sc(2)(μ(2)-S)@C(s)(6)-C(82) to that of corresponding oxide-containing Sc(2)(μ(2)-O)@C(s)(6)-C(82).     

Tunable charge-transport properties of I(h)-C80 endohedral metallofullerenes: investigation of La2@C80, Sc3N@C80, and Sc3C2@C80

Fullerene crystals or films have drawn much interest because they are good candidates for use in the construction of electronic devices. The results of theoretical calculations revealed that the conductivity properties of I(h)-C(80) endohedral metallofullerenes (EMFs) vary depending on the encapsulated metal species. We experimentally investigated the solid-state structures and charge-carrier mobilities of I(h)-C(80) EMFs La(2)@C(80), Sc(3)N@C(80), and Sc(3)C(2)@C(80). The thin film of Sc(3)C(2)@C(80) exhibits a high electron mobility μ = 0.13 cm(2) V(-1) s(-1) under normal temperature and atmospheric pressure, as determined using flash-photolysis time-resolved microwave conductivity measurements. This electron mobility is 2 orders of magnitude higher than the mobility of La(2)@C(80) or Sc(3)N@C(80).     

Chemical reactivity of sc3n @ c80 and la2 @ c80

Sc3N@C80 has a lower thermal reactivity than La2@C80, although Sc3N@C80 has the same carbon cage (Ih) and oxidation state (C806-) as La2@C80. This result is attributed to the difference in the energy level and distribution of LUMO between Sc3N@C80 and La2@C80.     

Quantum sum formulae for the collision-induced spectroscopies: Molecular systems as H2-H2

Quantum expressions for the second moment of collision-induced spectra are developed in the low-density limit. Previous work by Moraldi is extended to account for the rotational structure of colliding linear molecules; isotropic interaction is assumed. Computations of the lowest three moments are presented for the case of infrared absorption and Raman scattering of molecular hydrogen pairs at temperatures from 77 to 300 K. The radial distribution functions of pairs, mean energy and angular momentum, which are required for that purpose, are obtained for the case of H₂ molecules interacting with H₂, and compared with their classical counterparts. The simple classical approximations with lowest-order Wigner-Kirkwood quantum corrections serve as an accurate representation of the quantum expressions at large separations and may be sufficient for massive systems at high temperatures.     

Gd2@C79N: isolation, characterization, and monoadduct formation of a very stable heterofullerene with a magnetic spin state of S = 15/2

The dimetallic endohedral heterofullerene (EHF), Gd(2)@C(79)N, was prepared and isolated in a relatively high yield when compared with the earlier reported heterofullerene, Y(2)@C(79)N. Computational (DFT), chemical reactivity, Raman, and electrochemical studies all suggest that the purified Gd(2)@C(79)N, with the heterofullerene cage, (C(79)N)(5-) has comparable stability with other better known isoelectronic metallofullerene (C(80))(6-) cage species (e.g., Gd(3)N@C(80)). These results describe an exceptionally stable paramagnetic molecule with low chemical reactivity with the unpaired electron spin density localized on the internal diatomic gadolinium cluster and not on the heterofullerene cage. EPR studies confirm that the spin state of Gd(2)@C(79)N is characterized by a half-integer spin quantum number of S = 15/2. The spin (S = ?) on the N atom of the fullerene cage and two octet spins (S = 7/2) of two encapsulated gadoliniums are coupled with each other in a ferromagnetic manner with a small zero-field splitting parameter D. Because the central line of Gd(2)@C(79)N is due to the Kramer's doublet with a half-integer spin quantum number of S = 15/2, this relatively sharp line is prominent and the anisotropic nature of the line is weak. Interestingly, in contrast with most Gd(3+) ion environments, the central EPR line (g = 1.978) is observable even at room temperature in a toluene solution. Finally, we report the first EHF derivative, a diethyl bromomalonate monoadduct of Gd(2)@C(79)N, which was prepared and isolated via a modified Bingel-Hirsch reaction.     

Ambiguities in the semiclassical assignment of the asymmetric rotor rotational quantum numbers

The semiclassical quantization of the rigid asymmetric rotor is revisited in the context of classical inelastic collisions. It is shown that the standard bin histogram method, widely used in quasiclassical trajectory calculations involving linear target molecules, cannot be generalized to the case of asymmetric top molecules owing to ambiguities in the assignment of the final classical action to a particular rotational quantum state. These ambiguities result from pairs of states which are indistinguishable within the bin histogram approach at all the common levels of semiclassical theory. A single value of the classical action can thus correspond to two different quantum states, preventing the distinction between these states in the calculation of rotational cross sections. Our results are illustrated for the rotational states J=1-4 of the water molecule at its equilibrium geometry.