Experimental determination of the interaction potential between a helium atom and the interior surface of a C60 fullerene molecule (original) (raw)
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Journal of the American Chemical Society, 2010
Recent synthesis of the endohedral complexes of C 70 and its open-cage derivative with one and two H 2 molecules has opened the path for experimental and theoretical investigations of the unique dynamic, spectroscopic, and other properties of systems with multiple hydrogen molecules confined inside a nanoscale cavity. Here we report a rigorous theoretical study of the dynamics of the coupled translational and rotational motions of H 2 molecules in C 70 and C 60 , which are highly quantum mechanical. Diffusion Monte Carlo (DMC) calculations were performed for up to three para-H 2 (p-H 2 ) molecules encapsulated in C 70 and for one and two p-H 2 molecules inside C 60 . These calculations provide a quantitative description of the groundstate properties, energetics, and the translation-rotation (T-R) zero-point energies (ZPEs) of the nanoconfined p-H 2 molecules and of the spatial distribution of two p-H 2 molecules in the cavity of C 70 . The energy of the global minimum on the intermolecular potential energy surface (PES) is negative for one and two H 2 molecules in C 70 but has a high positive value when the third H 2 is added, implying that at most two H 2 molecules can be stabilized inside C 70 . By the same criterion, in the case of C 60 , only the endohedral complex with one H 2 molecule is energetically stable. Our results are consistent with the fact that recently both (H 2 ) n @C 70 (n ) 1, 2) and H 2 @C 60 were prepared, but not (H 2 ) 3 @C 70 or (H 2 ) 2 @C 60 . The ZPE of the coupled T-R motions, from the DMC calculations, grows rapidly with the number of caged p-H 2 molecules and is a significant fraction of the well depth of the intermolecular PES, 11% in the case of p-H 2 @C 70 and 52% for (p-H 2 ) 2 @C 70 . Consequently, the T-R ZPE represents a major component of the energetics of the encapsulated H 2 molecules. The inclusion of the ZPE nearly doubles the energy by which (p-H 2 ) 3 @C 70 is destabilized and increases by 66% the energetic destabilization of (p-H 2 ) 2 @C 60 . For these reasons, the T-R ZPE has to be calculated accurately and taken into account for reliable theoretical predictions regarding the stability of the endohedral fullerene complexes with hydrogen molecules and their maximum H 2 content.
Physical Review B, 2012
The quantum dynamics of dihydrogen molecules entrapped inside fullerene cages has been investigated using inelastic neutron scattering (INS). For the endofullerene H 2 @C 60 the low-lying energy levels of the manifold of coupled translational and rotational states have been accurately determined by studying INS spectra recorded in the temperature range 1.5 T 240 K. The majority of transitions observed in the INS spectra interconvert the nuclear spin isomers orthohydrogen and parahydrogen. The cage potential has icosahedral symmetry and splittings observed in the INS spectra reveal the coupling of translational and rotational angular momentum of the H 2 molecules. The effects of nuclear spin symmetry, isotope mass effects, and cage anisotropy have been further investigated by studying HD@C 60 and H 2 inside an open cage endofullerene. The momentum transfer κ arising from the neutron scattering event has also been investigated. The κ-dependence spectra reflect the physical dimensions of the dihydrogen molecule and its confinement in its cage. We show how this may be used as a tool for assigning the INS transitions.
The Journal of Chemical Physics, 2022
We present a methodology that, for the first time, allows rigorous quantum calculation of the inelastic neutron scattering (INS) spectra of a triatomic molecule in a nanoscale cavity, in this case, H2O inside the fullerene C60. Both moieties are taken to be rigid. Our treatment incorporates the quantum six-dimensional translation–rotation (TR) wave functions of the encapsulated H2O, which serve as the spatial parts of the initial and final states of the INS transitions. As a result, the simulated INS spectra reflect the coupled TR dynamics of the nanoconfined guest molecule. They also exhibit the features arising from symmetry breaking observed for solid H2O@C60 at low temperatures. Utilizing this methodology, we compute the INS spectra of H2O@C60 for two incident neutron wavelengths and compare them with the corresponding experimental spectra. Good overall agreement is found, and the calculated spectra provide valuable additional insights.
Chemistry - A European Journal, 2012
FULL PAPER orientation of the H 2 O molecule inside the fullerene C 60 cage. The observation [27] is in agreement with the report of Shameema et al. [30] who showed, with RHF/6-31G geometry, that the up-shift in the OÀH stretching frequency is a result of an increase in the excitation energy (DE) of the OÀH bond, where DE = E s(OÀH) ÀE s*(OÀH) = 1124 kcal mol À1 at RMP2/6-31G//RHF/6-31G. The above results [27, 30] are further in agreement with a recent MD and ab initio MD (AIMD) oriental relaxation study, which advocates the presence of weak interactions between the entrapped H 2 O molecule and the interior of the C 60 cage. [25] According to Bucher, the H 2 O molecule is capable of interacting with the outside environment as well, [25] although the nuclear spin relaxation study indicates that the endo-H 2 O is sufficiently electrically isolated from the surrounding solvent that its motion is not detectably affected by interaction of the electric dipole moment with a polar medium. [26] The above reports [27, 30] demonstrate a significant decrease in the molecular dipole moment (m) of H 2 O upon encapsulation, and yet the MX06-2X/6-311GA C H T U N G T R E N N U N G (2d,p) calculations of Kurotobi and Murata [18] surprisingly predicted a marginal increase in the value of m (2.02 D for isolated H 2 O and 2.03 D for H 2 O@C 60). This has led them to conclude that the single H 2 O molecule inside the C 60 cage will completely be localized at the center of the C 60 cage. This study revisits to explore the nature of interaction between an encapsulated H 2 O and the interior of the C 60 cage. Towards this aim, we have used density functional theory (DFT) electronic structure calculations to investigate both the qualitative and quantitative aspects of the nature of: 1) the intermolecular potential energy surface, 2) the dipole moment function within the adiabatic approximation, and 3) the charge redistribution both in H 2 O and C 60 upon encapsulation. Particular emphasis has been placed on exploring possible factors that lead to a significant decrease in the value of m upon H 2 O confinement, and the shifts in the vibrational frequency of the OÀH stretching modes as predicted by others. [27, 30] In particular, we address whether encapsulation leads to any significant charge transfer between H 2 O and C 60 , a well-known effect in endohedral fullerene chemistry, in which the C 60 cage effectively accommodates excess charges from an encaged species [12] (rather than having a high hydrophobic interior as previously suggested) [18, 21] regardless of whether the dopant is metallic or non-metallic, charged or neutral. [31-35] We investigate the nature of the electrostatic potential in the radial direction, as this is known to control the bonding in these systems. [32, 33, 36] Particular use is made of several IUPAC recommendations [37, 38] for characterizing noncovalent interactions. Applications of the quantum theory of atoms-in-molecules (QTAIM), [6] a theory that defines atoms and their interactions (bonds) in a molecule in terms of the electron charge density, [5, 6, 38-46] as well as of natural population and bond orbital analyses [2] are used to conclude the bonding interactions in the H 2 O@C 60 system. Computational Methods Computational details are given in the Supporting Information. Briefly, DFT calculations were conducted by using GAUSSIAN 03/09. [47, 48] For reasons of chemical accuracy, [49] and unless and otherwise stated, the present calculation makes use of the one-parameter exchange-correlation functional of Perdew-Burke-Ernzerhof [50] (PBE1PBE, in short PBE0) level together with a triple-x valence quality, 6-311
Physical Review Letters, 2009
We report an inelastic neutron scattering investigation of the quantum dynamics of hydrogen molecules trapped inside anisotropic fullerene cages. Transitions among the manifold of quantized rotational and translational states are directly observed. The spectra recorded as a function of energy and momentum transfer are interpreted in terms of the rotational potential and the cage dimensions. The thermodynamics of orthohydrogen and parahydrogen are investigated through temperature dependence measurements.
Electron elastic scattering off endohedral fullerenes A @C 60 : the initial insight
Journal of Physics B: Atomic, Molecular and Optical Physics, 2014
The initial insight into electron elastic scattering off endohedral fullerenes A@C 60 is gained in the framework of a theoretical approach where the C 60 cage is modelled by a rectangular (in the radial coordinate) potential well, as in many other A@C 60 studies. The effect of a noticeably weaker electron elastic scattering off A@C 60 compared to that off empty C 60 or even the isolated atom A itself, as well as a strong sensitivity of e + A@C 60 scattering to the spin of the captured atom A are unraveled, for certain kinds of atoms. Obtained results lay out the initial qualitative basis for identifying interesting measurements and/or more rigorous calculations of e + A@C 60 elastic scattering to perform.
Building Carbon Bridges on and between Fullerenes in Helium Nanodroplets
Journal of Physical Chemistry Letters, 2016
We report the observation of sequential encounters of fullerenes with C atoms in an extremely cold environment. Experiments were performed with helium droplets at 0.37 K doped with C 60 molecules and C atoms derived from a novel, pure source of C atoms. Very high-resolution mass spectra revealed the formation of carbenes of the type C 60 (C:) n with n up to 6. Bridge-type bonding of the C adatoms to form the known dumbbell C 60 CC 60 also was observed. Density functional theory calculations were performed that elucidated the carbene character of the C 60 (C:) n species and their structures. Mass spectra taken in the presence of water impurities and in separate experiments with added H 2 also revealed the formation of the adducts C 60 C n (H 2 O) n and C 60 C n (H 2) n probably by H−OH and H−H bond insertion, respectively, and nonreactivity for the dumbell. So C adatoms that form carbenes C 60 (C:) n can endow pristine C 60 with a higher chemical reactivity.
Electronic interactions in fullerene molecules
1993
We study the Coulomb interactions in fullerene molecules within a continuum formalism. The model gives rise to a renormalizable field theory, which has many similarities to standard quantum electrodynamics. The effective electric charge at low energies is reduced by screening processes. The associated renormalization of the one electron Green's function leads to the vanishing of the quasiparticle pole. It implies the dissappearance of coherent one particle excitations, in close analogy to the one dimensional Luttinger liquid. The relevance of these results for C 60 and related molecules is discussed. 75.10.Jm, 75.10.Lp, 75.30.Ds.
Journal of Physics B: Atomic, Molecular and Optical Physics, 2010
Within the framework of a model representing the potential of a C 60 cage as a spherical electro-neutral layer U(r) formed by smeared carbon atoms, the effect of the details of the potential on spectral characteristics of atoms localized inside the fullerene shell has been studied. Using examples of encapsulated H and He atoms, it is shown that for potential shell thickness not exceeding 1.3-1.5 au, confinement resonance oscillations in the photoionization cross section weakly depend on the shape of the function U(r). With increasing width of the potential well, the confinement resonances in the energy dependence of the photoionization cross section disappear. In addition, it is demonstrated that displacing the doped atom from the centre of the cavity also diminishes the amplitude of the confinement resonance.
Electronic interactions in fullerene spheres
Physical Review B, 1993
The electron-phonon and Coulomb interactions inC 60 , and larger fullerene spheres are analyzed. The coupling between electrons and intramolecular vibrations give corrections ∼ 1 − 10 meV to the electronic energies for C 60 , and scales as R −4 in larger molecules. The energies associated with electrostatic interactions are of order ∼ 1 − 4 eV, in C 60 and scale as R −1 . Charged fullerenes show enhanced electronphonon coupling, ∼ 10 meV, which scales as R −2 . Finally, it is argued that non only C − 60 , but also C −− 60 are highly polarizable molecules. The polarizabilities scale as R 3 and R 4 , respectively. The role of this large polarizability in mediating intermolecular interactions is also discussed. 75.10.Jm, 75.10.Lp, 75.30.Ds.