Interaction potential and infrared absorption of endohedral H2 in C60

A nuclear configuration interaction approach to study nuclear spin effects: an application to ortho- and para-3 He2 @C60

We introduce a non-orthogonal configuration interaction approach to investigate nuclear quantum effects on energies and densities of confined fermionic nuclei. The Hamiltonian employed draws parallels between confined systems and many-electron atoms, where effective non-Coulombic potentials represent the interactions of the trapped particles. One advantage of this method is its generality, as it offers the potential to study the nuclear quantum effects of various confined species affected by effective isotropic or anisotropic potentials. As a first application, we analyze the quantum states of two 3 He atoms encapsulated in C60 . At the Hartree-Fock level, we observe the breaking of spin and spatial symmetries. To ensure wavefunctions with the correct symmetries, we mix the broken-symmetry Hartree-Fock states within the non-orthogonal configuration interaction expansion. Our proposed approach predicts singly and triply degenerate ground states for the singlet (para-3 He2 @C60 ) and triplet (ortho-3 He2 @C60 ) nuclear spin configurations, respectively. The ortho-3 He2 @C60 ground state is 5.69 cm-1 higher in energy than the para-3 He2 @C60 ground state. The nuclear densities obtained for these states exhibit the icosahedral symmetry of the C60 embedding potential. Importantly, our calculated energies for the lowest 85 states are in close agreement with perturbation theory results based on a harmonic oscillator plus rigid rotor model of 3 He2 @C60 .

Electronic Structure Calculations on Endohedral Complexes of Fullerenes: Reminiscences and Prospects

The history of electronic structure calculations on the endohedral complexes of fullerenes is reviewed. First, the long road to the isolation of new allotropes of carbon that commenced with the seminal organic syntheses involving simple inorganic substrates is discussed. Next, the focus is switched to author's involvement with fullerene research that has led to the in silico discovery of endohedral complexes. The predictions of these pioneering theoretical studies are juxtaposed against the data afforded by subsequent experimental developments. The successes and failures of the old and modern quantum-chemical calculations on endohedral complexes are summarized and their remaining deficiencies requiring further attention are identified.

Symmetry Breakings in the interactions of Molecular Hydrogen with Solids

The following conference report considers hydrogen gases with odd and even rotational quantum number as two separate gases, the ortho and para varieties which do not interconvert in absence of a catalyst. The physical catalysis of hydrogen is interpreted in terms of symmetry breakings introduced by the solid to pass round the peculiar selection rules of the molecular hydrogen assigned by the Pauli Principle. The catalytic effect presents the striking effect of reducing drastically the interconversion time, longer than the age of the universe for isolated molecules, to a few seconds or minutes when an hydrogen sample (gaseous or liquid) is brought into contact with an efficient catalyst. In the present report, the variety of new optical and electronic devices, measurements and interpretations that have been reported since the turning of the new century are reviewed. New experiments on non-magnetic catalysts measuring hydrogen conversion on the time scales of one-ten minutes turned upside down the previous theory, established in 1933, of the absolute necessity of a magnetic catalyst to break the Pauli Principle. The o-p catalyzed reaction is discussed for hydrogen molecules adsorbed on electric surfaces, or in confining porous structures or inside nanocages. New concepts and new electromagnetic conversion channels that interpret these experimental renewals are described in terms of how the hydrogen nuclei feel the solid-molecule electron cloud complex. The described channels differentiate one another owing to the catalyst and owing to the electronic path followed in the configuration space by the o-p reaction.

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.

Noncovalently bound molecular complexes beyond diatom–diatom systems: full-dimensional, fully coupled quantum calculations of rovibrational states

The methodological advances made in recent years have significantly extended the range and dimensionality of noncovalently bound molecular complexes for which full-dimensional quantum calculations of their rovibrational states are feasible.

Experimental determination of the interaction potential between a helium atom and the interior surface of a C60 fullerene molecule

The interactions between atoms and molecules may be described by a potential energy function of the nuclear coordinates. Nonbonded interactions between neutral atoms or molecules are dominated by repulsive forces at a short range and attractive dispersion forces at a medium range. Experimental data on the detailed interaction potentials for nonbonded interatomic and intermolecular forces are scarce. Here, we use terahertz spectroscopy and inelastic neutron scattering to determine the potential energy function for the nonbonded interaction between single He atoms and encapsulating C₆₀ fullerene cages in the helium endofullerenes ³He@C₆₀ and ⁴He@C₆₀, synthesized by molecular surgery techniques. The experimentally derived potential is compared to estimates from quantum chemistry calculations and from sums of empirical two-body potentials.

Temperature-dependent dynamics of endohedral fullerene Sc2@C80(CH2Ph) studied by EPR spectroscopy

Endohedral fullerenes are promising materials for the quantum information and quantum processing due to the unique properties of the electron-nuclear spin system well isolated from the environment inside the fullerene cage. The endofullerene Sc₂@C₈₀(CH₂Ph) features a strong hyperfine interaction between one electron spin 1/2 localized at the Sc₂ dimer and two equivalent ⁴⁵Sc nuclear spins 7/2, which yields 64 well resolved EPR transitions. We report a comprehensive analysis of the temperature dependence of the EPR spectrum of Sc₂@C₈₀(CH₂Ph) dissolved in d-toluene measured in a wide temperature range above and below the melting point. The nature of the electron spin coherence phase memory is investigated. The properties of all resonance lines in a liquid phase were treated within the model of the free rotational diffusion. Both, analytical expressions and numerical examination provide an excellent agreement between the experimental and simulated spectra. A detailed study of the experimental data confirms the assumption of the independent motions of the fullerene cage and the Sc₂ core. The data obtained show three regimes of molecular motion detected at different temperatures: the free rotation of both the fullerene cage and its bi-metal core, the motion of the core in the frozen fullerene cage, and, finally, a state with a fixed structure of both parts of the metallofullerene molecules. The data analysis reveals a significant nuclear quadrupole interaction playing an important role for the mixing of the different nuclear spin multiplets.

Hydrogen Conversion in Nanocages

Hydrogen molecules exist in the form of two distinct isomers that can be interconverted by physical catalysis. These ortho and para forms have different thermodynamical properties. Over the last century, the catalysts developed to convert hydrogen from one form to another, in laboratories and industries, were magnetic and the interpretations relied on magnetic dipolar interactions. The variety concentration of a sample and the conversion rates induced by a catalytic action were mostly measured by thermal methods related to the diffusion of the o-p reaction heat. At the turning of the new century, the nature of the studied catalysts and the type of measures and motivations completely changed. Catalysts investigated now are non-magnetic and new spectroscopic measurements have been developed. After a fast survey of the past studies, the review details the spectroscopic methods, emphasizing their originalities, performances and refinements: how Infra-Red measurements characterize the catalytic sites and follow the conversion in real-time, Ultra-Violet irradiations explore the electronic nature of the reaction and hyper-frequencies driving the nuclear spins. The new catalysts, metallic or insulating, are detailed to display the operating electronic structure. New electromagnetic mechanisms, involving energy and momenta transfers, are discovered providing a classification frame for the newly observed reactions.

Infrared spectroscopy of an endohedral water in fullerene

An infrared absorption spectroscopy study of the endohedral water molecule in a solid mixture of H₂O@C₆₀ and C₆₀ was carried out at liquid helium temperature. From the evolution of the spectra during the ortho-para conversion process, the spectral lines were identified as para-H₂O and ortho-H₂O transitions. Eight vibrational transitions with rotational side peaks were observed in the mid-infrared: ω₁, ω₂, ω₃, 2ω₁, 2ω₂, ω₁ + ω₃, ω₂ + ω₃, and 2ω₂ + ω₃. The vibrational frequencies ω₂ and 2ω₂ are lower by 1.6% and the rest by 2.4%, as compared to those of free H₂O. A model consisting of a rovibrational Hamiltonian with the dipole and quadrupole moments of H₂O interacting with the crystal field was used to fit the infrared absorption spectra. The electric quadrupole interaction with the crystal field lifts the degeneracy of the rotational levels. The finite amplitudes of the pure v₁ and v₂ vibrational transitions are consistent with the interaction of the water molecule dipole moment with a lattice-induced electric field. The permanent dipole moment of encapsulated H₂O is found to be 0.50 ± 0.05 D as determined from the far-infrared rotational line intensities. The translational mode of the quantized center-of-mass motion of H₂O in the molecular cage of C₆₀ was observed at 110 cm^-1 (13.6 meV).

Interactions between a water molecule and C60 in the endohedral fullerene H2O@C60

A water molecule encapsulated inside a C60 fullerene cage behaves almost like an asymmetric top rotor, as would be expected of an isolated water molecule. However, inelastic neutron scattering (INS) experiments show evidence of interactions between the water molecule and its environment [Goh et al., Phys. Chem. Chem. Phys., 2014, 16, 21330]. In particular, a resolved splitting of the 101 rotational level into a singlet and a doublet indicates that the water molecule experiences an environment of lower symmetry than the icosahedral symmetry of a C60 cage. Recent calculations have shown that the splitting can be explained in terms of electrostatic quadrupolar interactions between the water molecule and the electron clouds of nearest-neighbour C60 molecules, which results in an effective environment of S6 symmetry [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274 and Bačić et al., Faraday Discussions, 2018, 212, 547-567]. We use symmetry arguments to obtain a simple algebraic expression, expressed in terms of a linear combination of products of translational and rotational basis functions, that describes the effect on a water molecule of any potential of S6 symmetry. We show that we can reproduce the results of the electrostatic interaction model up to ≈12 meV in terms of two unknown parameters only. The resulting potential is in a form that can readily be used in future calculations, without needing to use density functional theory (DFT) for example. Adjusting parameters in our potential would help identify whether other symmetry-lowering interactions are also present if experimental results that resolve splittings in higher-energy rotational levels are obtained in the future. As another application of our model, we show that the results of DFT calculations of the variation in energy as a water molecule moves inside the cage of an isolated C60 molecule, where the water molecule experiences an environment of icosahedral symmetry, can also be reproduced using our model.

Effects of symmetry breaking on the translation-rotation eigenstates of H2, HF, and H2O inside the fullerene C60

Splittings of the translation-rotation (TR) eigenstates of the solid light-molecule endofullerenes M@C60 (M = H2, H2O, HF) attributed to the symmetry breaking have been observed in the infrared (IR) and inelastic neutron scattering spectra of these species in the past couple of years. In a recent paper [Felker et al., Phys. Chem. Chem. Phys., 2017, 19, 31274], we established that the electrostatic, quadrupolar interaction between the guest molecule M and the twelve nearest-neighbor C60 cages of the solid is the main source of the symmetry breaking. The splittings of the three-fold degenerate ground states of the endohedral ortho-H2, ortho-H2O and the j = 1 level of HF calculated using this model were found to be in excellent agreement with the experimental results. Utilizing the same electrostatic model, this theoretical study investigates the effects of the symmetry breaking on the excited TR eigenstates of the three species, and how they manifest in their simulated low-temperature (5-6 K) near-IR (NIR) and far-IR (FIR) spectra. The TR eigenstates are calculated variationally for both the major P and minor H crystal orientations. For the H orientation, the calculated splittings of all of the TR levels of these species are less than 0.1 cm-1. For the dominant P orientation, the splittings vary strongly depending on the character of the excitations involved. In all of the species, the splittings of the higher rotationally excited levels are comparable in magnitude to those for the j = 1 levels. For the levels corresponding to purely translational excitations, the calculated splittings are about an order of magnitude smaller than those of the purely rotational eigenstates. Based on the computed TR eigenstates, the low-temperature NIR (for M = H2) and FIR (for M = HF and H2O) spectra are simulated for both the P and H orientations, and also combined as their weighted sum (0.15H + 0.85P). The weighted sum spectra computed for M = H2 and HF match quantitatively the corresponding measured spectra, while for M = H2O, the weighted sum FIR spectrum predicts features that can potentially be observed experimentally.

Perspective: Accurate treatment of the quantum dynamics of light molecules inside fullerene cages: Translation-rotation states, spectroscopy, and symmetry breaking

In this perspective, I review the current status of the theoretical investigations of the quantum translation-rotation (TR) dynamics and spectroscopy of light molecules encapsulated inside fullerenes, mostly C₆₀ and C₇₀. The methodologies developed in the past decade allow accurate quantum calculations of the TR eigenstates of one and two nanoconfined molecules and have led to deep insights into the nature of the underlying dynamics. Combining these bound-state methodologies with the formalism of inelastic neutron scattering (INS) has resulted in the novel and powerful approach for the quantum calculation of the INS spectra of a diatomic molecule in a nanocavity with an arbitrary geometry. These simulations have not only become indispensable for the interpretation and assignment of the experimental spectra but are also behind the surprising discovery of the INS selection rule for diatomics in near-spherical nanocavities. Promising directions for future research are discussed.

Quantum fluctuations of a fullerene cage modulate its internal magnetic environment

To investigate the effect of quantum fluctuations on the magnetic environment inside a C₆₀ fullerene cage, we have calculated the nuclear magnetic shielding constant of protons in H₂@C₆₀ and HD@C₆₀ systems by on-the-fly ab initio path integral simulation, including both thermal and nuclear quantum effects. The most dominant upfield from an isolated hydrogen molecule occurs due to the diamagnetic current of the C₆₀ cage, which is partly cancelled by the paramagnetic current, where the paramagnetic contribution is enlarged by the zero-point vibrational fluctuation of the C₆₀ carbon backbone structure via a widely distributed HOMO-LUMO gap. This quantum modulation mechanism of the nuclear magnetic shielding constant is newly proposed. Because this quantum effect is independent of the difference between H₂ and HD, the H₂/HD isotope shift occurs in spite of the C₆₀ cage. The nuclear magnetic constants computed for H₂@C₆₀ and HD@C₆₀ are 32.047 and 32.081 ppm, respectively, which are in reasonable agreement with the corresponding values of 32.19 and 32.23 ppm estimated from the experimental values of the chemical shifts.

Explaining the symmetry breaking observed in the endofullerenes H2@C60, HF@C60, and H2O@C60

Symmetry breaking has been recently observed in the endofullerenes M@C₆₀ (M = H₂, HF, H₂O), manifesting in the splittings of the three-fold degenerate ground states of the endohedral ortho-H₂, ortho-H₂O and the j = 1 level of HF.

Nuclear conversion theory: molecular hydrogen in non-magnetic insulators

The hydrogen conversion patterns on non-magnetic solids sensitively depend upon the degree of singlet/triplet mixing in the intermediates of the catalytic reaction. Three main 'symmetry-breaking' interactions are brought together. In a typical channel, the electron spin-orbit (SO) couplings introduce some magnetic excitations in the non-magnetic solid ground state. The electron spin is exchanged with a molecular one by the electric molecule-solid electron repulsion, mixing the bonding and antibonding states and affecting the molecule rotation. Finally, the magnetic hyperfine contact transfers the electron spin angular momentum to the nuclei. Two families of channels are considered and a simple criterion based on the SO coupling strength is proposed to select the most efficient one. The denoted 'electronic' conversion path involves an emission of excitons that propagate and disintegrate in the bulk. In the other denoted 'nuclear', the excited electron states are transients of a loop, and the electron system returns to its fundamental ground state. The described model enlarges previous studies by extending the electron basis to charge-transfer states and 'continui' of band states, and focuses on the broadening of the antibonding molecular excited state by the solid conduction band that provides efficient tunnelling paths for the hydrogen conversion. After working out the general conversion algebra, the conversion rates of hydrogen on insulating and semiconductor solids are related to a few molecule-solid parameters (gap width, ionization and affinity potentials) and compared with experimental measures.

Experimental, theoretical and computational investigation of the inelastic neutron scattering spectrum of a homonuclear diatomic molecule in a nearly spherical trap: H2@C60

In this paper we report a methodology for calculating the inelastic neutron scattering spectrum of homonuclear diatomic molecules confined within nano-cavities of spherical symmetry.

Symmetry-breaking in the H2@C60 endofullerene revealed by inelastic neutron scattering at low temperature

The fine structure of the rotational ground state of molecular ortho-hydrogen confined inside the fullerene cage C₆₀ is investigated by inelastic neutron scattering (INS).

Chiral recognition by fullerenes: CHFClBr enantiomers in the C82cage

Theoretical studies of complexes of the enantiomers of CHFClBr with C₈₂-3 show that the too large guests are stabilized in the C₈₂cage by electrostatic interactions. The sign of v(CH) stretching vibration of S-CHFClBr@C₈₂-3 in the VCD spectrum is reversed as compared to that of the free guest. Spectra of the complexes exhibit differences.

Symmetry-breaking in the endofullerene H2O@C60 revealed in the quantum dynamics of ortho and para-water: a neutron scattering investigation

The splitting of the ortho-H₂O ground state is clearly revealed by inelastic neutron scattering.

Magic-angle spinning NMR of cold samples

Magic-angle-spinning solid-state NMR provides site-resolved structural and chemical information about molecules that complements many other physical techniques. Recent technical advances have made it possible to perform magic-angle-spinning NMR experiments at low temperatures, allowing researchers to trap reaction intermediates and to perform site-resolved studies of low-temperature physical phenomena such as quantum rotations, quantum tunneling, ortho-para conversion between spin isomers, and superconductivity. In examining biological molecules, the improved sensitivity provided by cryogenic NMR facilitates the study of protein assembly or membrane proteins. The combination of low-temperatures with dynamic nuclear polarization has the potential to boost sensitivity even further. Many research groups, including ours, have addressed the technical challenges and developed hardware for magic-angle-spinning of samples cooled down to a few tens of degrees Kelvin. In this Account, we briefly describe these hardware developments and review several recent activities of our group which involve low-temperature magic-angle-spinning NMR. Low-temperature operation allows us to trap intermediates that cannot be studied under ambient conditions by NMR because of their short lifetime. We have used low-temperature NMR to study the electronic structure of bathorhodopsin, the primary photoproduct of the light-sensitive membrane protein, rhodopsin. This project used a custom-built NMR probe that allows low-temperature NMR in the presence of illumination (the image shows the illuminated spinner module). We have also used this technique to study the behavior of molecules within a restricted environment. Small-molecule endofullerenes are interesting molecular systems in which molecular rotors are confined to a well-insulated, well-defined, and highly symmetric environment. We discuss how cryogenic solid state NMR can give information on the dynamics of ortho-water confined in a fullerene cage. Molecular motions are often connected with fundamental chemical properties; therefore, an understanding of molecular dynamics can be important in fields ranging from material science to biochemistry. We present the case of ibuprofen sodium salt which exhibits different degrees of conformational freedom in different parts of the same molecule, leading to a range of line broadening and line narrowing phenomena as a function of temperature.

Nuclear magnetic resonance of hydrogen molecules trapped inside C70 fullerene cages

We present a solid-state NMR study of H2 molecules confined inside the cavity of C70 fullerene cages over a wide range of temperatures (300 K to 4 K). The proton NMR spectra are consistent with a model in which the dipole-dipole coupling between the ortho-H2 protons is averaged over the rotational/translational states of the confined quantum rotor, with an additional chemical shift anisotropy δ(H)(CSA)=10.1 ppm induced by the carbon cage. The magnitude of the chemical shift anisotropy is consistent with DFT estimates of the chemical shielding tensor field within the cage. The experimental NMR data indicate that the ground state of endohedral ortho-H2 in C70 is doubly degenerate and polarized transverse to the principal axis of the cage. The NMR spectra indicate significant magnetic alignment of the C70 long axes along the magnetic field, at temperatures below ~10 K.

Spectroscopy of light-molecule endofullerenes

Molecular endofullerenes are supramolecular systems consisting of fullerene cages encapsulating small molecules. Although most early examples consist of encapsulated metal clusters, recently developed synthetic routes have provided endofullerenes with non-metallic guest molecules in high purity and macroscopic quantities. The encapsulated light molecule behaves as a confined quantum rotor, displaying rotational quantization as well as translational quantization, and a rich coupling between the translational and rotational degrees of freedom. Furthermore, many encapsulated molecules display spin isomerism. Spectroscopies such as inelastic neutron scattering, nuclear magnetic resonance and infrared spectroscopy may be used to obtain information on the quantized energy level structure and spin isomerism of the guest molecules. It is also possible to study the influence of the guest molecules on the cages, and to explore the communication between the guest molecules and the molecular environment outside the cage.

Nuclear spin isomers of guest molecules in H₂@C₆₀, H₂O@C₆₀ and other endofullerenes

Spectroscopic studies of recently synthesized endofullerenes, in which H₂, H₂O and other atoms and small molecules are trapped in cages of carbon atoms, have shown that although the trapped molecules interact relatively weakly with the internal environment they are nevertheless susceptible to appropriately applied external perturbations. These properties have been exploited to isolate and study samples of H₂ in C₆₀ and other fullerenes that are highly enriched in the para spin isomer. Several strategies for spin-isomer enrichment, potential extensions to other endofullerenes and possible applications of these materials are discussed.

Anisotropic nuclear spin interactions in H₂O@C₆₀ determined by solid-state NMR

We report a solid-state NMR study of the anisotropic nuclear spin interactions in H₂O@C₆₀ at room temperature. We find evidence of significant dipole-dipole interactions between the water protons, and also a proton chemical shift anisotropy (CSA) interaction. The principal axes of these interaction tensors are found to be perpendicular. The magnitude of the CSA is too large to be explained by a model in which the water molecules are partially aligned with respect to an external axis. The evidence indicates that the observed CSA is caused by a distortion of the geometry or electronic structure of the fullerene cages, in response to the presence of the endohedral water.

Infrared spectroscopy of small-molecule endofullerenes

Hydrogen is one of the few molecules that has been incarcerated in the molecular cage of C₆₀ to form the endohedral supramolecular complex H₂@C₆₀. In this confinement, hydrogen acquires new properties. Its translation motion, within the C₆₀ cavity, becomes quantized, is correlated with its rotation and breaks inversion symmetry that induces infrared (IR) activity of H₂. We apply IR spectroscopy to study the dynamics of hydrogen isotopologues H₂, D₂ and HD incarcerated in C₆₀. The translation and rotation modes appear as side bands to the hydrogen vibration mode in the mid-IR part of the absorption spectrum. Because of the large mass difference of hydrogen and C₆₀ and the high symmetry of C₆₀ the problem is almost identical to a vibrating rotor moving in a three-dimensional spherical potential. We derive potential, rotation, vibration and dipole moment parameters from the analysis of the IR absorption spectra. Our results were used to derive the parameters of a pairwise additive five-dimensional potential energy surface for H₂@C₆₀. The same parameters were used to predict H₂ energies inside C₇₀. We compare the predicted energies and the low-temperature IR absorption spectra of H₂@C₇₀.

HD in C₆₀: theoretical prediction of the inelastic neutron scattering spectrum and its temperature dependence

We report rigorous quantum calculations of the inelastic neutron scattering (INS) spectra of HD@C₆₀, over a range of temperatures from 0 to 240 K and for two incident neutron wavelengths used in recent experimental investigations. The computations were performed using our newly developed methodology, which incorporates the coupled five-dimensional translation-rotation (T-R) eigenstates of the guest molecule as the initial and final states of the INS transitions, and yields highly detailed spectra. Depending on the incident neutron wavelength, the number of computed INS transitions varies from almost 500 to over 2000. The low-temperature INS spectra display the fingerprints of the coupling between the translational and rotational motions of the entrapped HD molecule, which is responsible for the characteristic splitting patterns of the T-R energy levels. INS transitions from the ground T-R state of HD to certain sublevels of excited T-R multiplets have zero intensity and are absent from the spectra. This surprising finding is explained by the new INS selection rule introduced here. The calculated spectra exhibit strong temperature dependence. As the temperature increases, numerous new peaks appear, arising from the transitions originating in excited T-R states which become populated. Our calculations show that the higher temperature features typically comprise two or more transitions close in energy and with similar intensities, interspersed with numerous other transitions whose intensities are negligible. This implies that accurately calculated energies and intensities of INS transitions which our methodology provides will be indispensable for reliable interpretation and assignment of the experimental spectra of HD@C₆₀ and related systems at higher temperatures.

Quantum rotation and translation of hydrogen molecules encapsulated inside C₆₀: temperature dependence of inelastic neutron scattering spectra

The quantum dynamics of a hydrogen molecule encapsulated inside the cage of a C60 fullerene molecule is investigated using inelastic neutron scattering (INS). The emphasis is on the temperature dependence of the INS spectra which were recorded using time-of-flight spectrometers. The hydrogen endofullerene system is highly quantum mechanical, exhibiting both translational and rotational quantization. The profound influence of the Pauli exclusion principle is revealed through nuclear spin isomerism. INS is shown to be exceptionally able to drive transitions between ortho-hydrogen and para-hydrogen which are spin-forbidden to photon spectroscopies. Spectra in the temperature range 1.6≤T≤280 K are presented, and examples are given which demonstrate how the temperature dependence of the INS peak amplitudes can provide an effective tool for assigning the transitions. It is also shown in a preliminary investigation how the temperature dependence may conceivably be used to probe crystal field effects and inter-fullerene interactions.

Nuclear-orbital/configuration-interaction study of coupled translation-rotation states in (H2)2@C70

The quantal translation-rotation states of two endohedral H(2) moieties in C(70) are computed by means of a nuclear-orbital/configuration-interaction method. H(2) "nuclear orbitals" are calculated as the translation-rotation eigenfunctions of one H(2) molecule interacting with C(70) and the mean field of the second H(2) molecule. Configurations are constructed as symmetrized bilinear products of these orbitals. These configurations are employed as the basis in which the matrix of the translation-rotation Hamiltonian of the cluster is computed and diagonalized. We show that this scheme allows for an efficient means to calculate the Hamiltonian matrix elements. We show that the configuration basis states represent excellent first approximations to the eigenstates of the species. Finally, we present results pertaining to the (H(2))(2)@C(70) low-energy translation-rotation level structure that can be understood in terms of a small number of H(2) excitation types.

Molecular structure, electronic property and vibrational spectroscopy of C24-glycine and Gd@C24-glycine complexes

Structure, electronic property and vibrational spectroscopy of C(24)-glycine and Gd@C(24)-glycine were systematically explored using the hybrid DFT-B3LYP functional. The interaction between empty C(24) cage and the smallest amino acid (glycine) was also investigated. It was found that the glycine molecule is energetically favorable to interact with the Mid-site on the C(24) cage through the amino nitrogen active site, rather than Top-site. The endohedral Gd atom increases the volume of the cage by around 6.7-9.8%. Analysis of frontier molecular orbitals reveals that the Gd@C(24)-glycine has the low-kinetic stability, being consistent with its thermodynamic property reflected by dissociation energy. We also see that the VIE and VEA of empty C(24) cage are slightly affected by absorbed glycine and endohedral Gd atom. Additionally, the assignments of simulated IR spectra are explored. The work may provide a theoretical reference for further application related structurally to potential antitumour activity.

Quantum rotation of ortho and para-water encapsulated in a fullerene cage

Inelastic neutron scattering, far-infrared spectroscopy, and cryogenic nuclear magnetic resonance are used to investigate the quantized rotation and ortho-para conversion of single water molecules trapped inside closed fullerene cages. The existence of metastable ortho-water molecules is demonstrated, and the interconversion of ortho-and para-water spin isomers is tracked in real time. Our investigation reveals that the ground state of encapsulated ortho water has a lifted degeneracy, associated with symmetry-breaking of the water environment.

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. Rõõm, 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.