Quantum translator-rotator: inelastic neutron scattering of dihydrogen molecules trapped inside anisotropic fullerene cages

Reversible Diels–Alder Addition to Fullerenes: A Study of Dimethylanthracene with H2@C60

The study of isolated atoms or molecules inside a fullerene cavity provides a unique environment. It is likely to control the outer carbon cage and study the isolated species when molecules or atoms are trapped inside a fullerene. We report the Diels–Alder addition reaction of 9,10-dimethyl anthracene (DMA) to H2@C60 while 1H NMR spectroscopy is utilized to characterize the Diels–Alder reaction of the DMA with the fullerene. Through 1H NMR spectroscopy, a series of isomeric adducts are identified. The obtained peaks are sharp, precise, and straightforward. Moreover, in this paper, H2@C60 and its isomers are described for the first time.

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.

H2O inside the fullerene C60: Inelastic neutron scattering spectrum from rigorous quantum calculations

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.

Dynamics & Spectroscopy with Neutrons-Recent Developments & Emerging Opportunities

This work provides an up-to-date overview of recent developments in neutron spectroscopic techniques and associated computational tools to interrogate the structural properties and dynamical behavior of complex and disordered materials, with a focus on those of a soft and polymeric nature. These have and continue to pave the way for new scientific opportunities simply thought unthinkable not so long ago, and have particularly benefited from advances in high-resolution, broadband techniques spanning energy transfers from the meV to the eV. Topical areas include the identification and robust assignment of low-energy modes underpinning functionality in soft solids and supramolecular frameworks, or the quantification in the laboratory of hitherto unexplored nuclear quantum effects dictating thermodynamic properties. In addition to novel classes of materials, we also discuss recent discoveries around water and its phase diagram, which continue to surprise us. All throughout, emphasis is placed on linking these ongoing and exciting experimental and computational developments to specific scientific questions in the context of the discovery of new materials for sustainable technologies.

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.

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 Dynamics of H_{2} Trapped within Organic Clathrate Cages

The rotational and translational dynamics of molecular hydrogen trapped within β-hydroquinone clathrate (H_{2}@β-HQ)-a practical example of a quantum particle trapped within an anisotropic confining potential-were investigated using inelastic neutron scattering and Raman spectroscopy. High-resolution vibrational spectra, including those collected from the VISION spectrometer at Oak Ridge National Laboratory, indicate relatively strong attractive interaction between guest and host with a strikingly large splitting of rotational energy levels compared with similar guest-host systems. Unlike related molecular systems in which confined H_{2} exhibits nearly free rotation, the behavior of H_{2}@β-HQ is explained using a two-dimensional (2D) hindered rotor model with barrier height more than 2 times the rotational constant (-16.2  meV).

Synthesis and Properties of Open Fullerenes Encapsulating Ammonia and Methane

We describe the synthesis and characterisation of open fullerene (1) and its reduced form (2) in which CH₄ and NH₃ are encapsulated, respectively. The ¹H NMR resonance of endohedral NH₃ is broadened by scalar coupling to the quadrupolar ¹⁴n nucleus, which relaxes rapidly. This broadening is absent for small satellite peaks, which are attributed to natural abundance ¹⁵N. The influence of the scalar relaxation mechanism on the linewidth of the ¹H ammonia resonance is probed by variable temperature NMR. A rotational correlation time of τ_c=1.5 ps. is determined for endohedral NH₃, and of τ_c=57±5 ps. for the open fullerene, indicating free rotation of the encapsulated molecule. IR spectroscopy of NH₃@2 at 5 K identifies three vibrations of NH₃ (ν₁, ν₃ and ν₄) redshifted in comparison with free NH₃, and temperature dependence of the IR peak intensity indicates the presence of a large number of excited translational/ rotational states. Variable temperature ¹H NMR spectra indicate that endohedral CH₄ is also able to rotate freely at 223 K, on the NMR timescale. Inelastic neutron scattering (INS) spectra of CH₄@1 show both rotational and translational modes of CH₄. Energy of the first excited rotational state (J=1) of CH₄@1 is significantly lower than that of free CH₄.

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).

Dynamics of H2 adsorbed in porous materials as revealed by computational analysis of inelastic neutron scattering spectra

This perspective article reviews the different types of quantum and classical mechanical methods that have been implemented to interpret the INS spectra for H₂ adsorbed in porous materials.

Isotopic Effects on Covalent Bond Confined in a Penetrable Sphere

A model of confinement of the covalent bond by a finite potential beyond the Born-Oppenheimer approximation is presented. A two-electron molecule is located at the center of a penetrable spherical cavity. The Schrödinger equation has been solved by using the diffusion Monte Carlo method. Total energies, internuclear distances, and vibrational frequencies of the confined molecular system have been obtained. Even for confining potentials of a few electronvolts, a noticeable increase in the bond energy and the nuclear vibrational frequency is observed, and the internuclear distance is lowered. The gap between the zero point energy of different molecular isotopes increases with confinement. The confinement of the electron pair might play a role in chemical reactivity, providing an alternative explanation for the tunnel effect, when large values of primary kinetic isotopic effect are observed. The Swain-Schaad relation is still verified when confinement changes the zero point energy. A semiquantitative illustration is proposed using the data relative to an hydrogen transfer involving a C-H cleavage catalyzed by the bovine serum amine oxidase. Changes on the confining conditions, corresponding to a confinement/deconfinement process, result in a significant decrease in the activation energy of the chemical transformation. It is proposed that confinement/deconfinement of the electron-pair bonding by external electrostatic forces inside the active pocket of an enzyme could be one of the basic mechanisms of the enzyme catalysis.

General Selection Rule in the Inelastic Neutron Scattering Spectroscopy of a Diatomic Molecule Confined Inside a Near-Spherical Nanocavity

Knowledge of the relevant selection rules is crucial for the accurate interpretation of experimental spectra in general. There has been a consensus for a long time that the incoherent inelastic neutron scattering (INS) spectroscopy of the vibrations of discrete molecular compunds is free from any selection rules. We contradict this widely held view by presenting an analytical derivation of the general selection rule for the INS spectroscopy of a hydrogen molecule inside a near-spherical nanocavity. It defines all forbidden transitions, originating in a range of initial translation-rotation (TR) states, ground and excited, of the caged para- and ortho-H2, as well as HD, that are unobservable in the INS spectra. These predictions are amenable to experimental verification. In addition, we demonstrate that the general selection rule applies to the INS spectroscopy of any diatomic molecule in a nanocavity with near-spherical symmetry, which exhibits strong TR coupling. Its existence strongly suggests that similar selection rules apply to the INS spectra of other molecular and supramolecular systems, and need to be identified.

Confirming a predicted selection rule in inelastic neutron scattering spectroscopy: the quantum translator-rotator H2 entrapped inside C60

We report an inelastic neutron scattering (INS) study of a H2 molecule encapsulated inside the fullerene C60 which confirms the recently predicted selection rule, the first to be established for the INS spectroscopy of aperiodic, discrete molecular compounds. Several transitions from the ground state of para-H2 to certain excited translation-rotation states, forbidden according to the selection rule, are systematically absent from the INS spectra, thus validating the selection rule with a high degree of confidence. Its confirmation sets a precedent, as it runs counter to the widely held view that the INS spectroscopy of molecular compounds is not subject to any selection rules.

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.

An optimised scalable synthesis of H2O@C60 and a new synthesis of H2@C60

New efficient and practical routes to H₂O@C₆₀, D₂O@C₆₀ and H₂@C₆₀ are described.

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.

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.

Quantum confinement of the covalent bond beyond the Born-Oppenheimer approximation

Dirichlet boundary conditions with different symmetries, spherical and cylindrical impenetrable surfaces, are imposed on the covalent electron pair of a molecular bond. Accurate results for different observable like energy and interparticle distances are calculated using quantum Monte Carlo methods beyond the Born-Oppenheimer approximation. The spherical confinement induces a raise in the bond energy and shortens the internuclear distances even for a relatively soft confinement. When cylindrical symmetry is considered, similar qualitative behavior is observed though only the electrons are confined. A compression followed by a relaxation process of the confined bond is shown to induce a vibrationally excited state. Finally, a brief qualitative discussion based on a simplified picture of the role of compression/relaxation cycles in enzyme catalysis is given.

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.

Theoretical studies of CH4 inside an open-cage fullerene: translation-rotation coupling and thermodynamic effects

Molecules trapped inside fullerenes exhibit interesting quantum behavior, including quantization of their translational degrees of freedom. In this study, a theoretical framework for predicting quantum properties of nonlinear small molecules in nonsymmetric open-cage fullerenes (OCFs) has been described along the lines of similar theories which treat small molecules inside C(60) and clathrate cages. As an example, the coupled translational-rotational energy structure has been calculated for the case of CH(4) inside a known OCF. The calculated energy levels have been used to calculate the equilibrium fraction of incorporated CH(4) as well as the translational heat capacity for the encapsulated molecule. The heat capacity shows an anomalous maximum at 239 K for CH(4) and 215 K for CD(4) which are not present in free methane.

Comparative NMR properties of H2 and HD in toluene-d8 and in H2/HD@C60

Spin-lattice relaxation times, T(1), have been measured from 200-340 K for the protons in H(2) and HD molecules dissolved in toluene-d(8) and incarcerated in C(60). It is found that HD relaxes more slowly than H(2) in both environments and at all temperatures, as expected from the smaller values of the spin-rotation and dipole-dipole coupling in HD compared to H(2). More detailed analysis using models developed to describe relaxation in both condensed media and the gas phase indicates that transitions among the rotational states of H(2) occur at a rate similar to those of HD in both toluene-d(8) solution and in C(60), in contrast to the situation in gas phase collisions between hydrogen and He or Ar, where the lifetimes of rotational states of HD are markedly shorter than those for H(2). Measurements of the relative (1)H chemical shifts of H(2) and HD, the coupling constant J(HD), and the widths of the HD peaks at various temperatures revealed only small effects with insufficient accuracy to warrant more detailed interpretation.

The spin chemistry and magnetic resonance of H2@C60. From the Pauli principle to trapping a long lived nuclear excited spin state inside a buckyball

One of the early triumphs of quantum mechanics was Heisenberg's prediction, based on the Pauli principle and wave function symmetry arguments, that the simplest molecule, H(2), should exist as two distinct species-allotropes of elemental hydrogen. One allotrope, termed para-H(2) (pH(2)), was predicted to be a lower energy species that could be visualized as rotating like a sphere and possessing antiparallel ( upward arrow downward arrow) nuclear spins; the other allotrope, termed ortho-H(2) (oH(2)), was predicted to be a higher energy state that could be visualized as rotating like a cartwheel and possessing parallel ( upward arrow upward arrow) nuclear spins. This remarkable prediction was confirmed by the early 1930s, and pH(2) and oH(2) were not only separated and characterized but were also found to be stable almost indefinitely in the absence of paramagnetic "spin catalysts", such as molecular oxygen, or traces of paramagnetic impurities, such as metal ions. The two allotropes of elemental hydrogen, pH(2) and oH(2), may be quantitatively incarcerated in C(60) to form endofullerene guest@host complexes, symbolized as pH(2)@C(60) and oH(2)@C(60), respectively. How does the subtle difference in nuclear spin manifest itself when hydrogen allotropes are incarcerated in a buckyball? Can the incarcerated "guests" communicate with the outside world and vice versa? Can a paramagnetic spin catalyst in the outside world cause the interconversion of the allotropes and thereby effect a chemical transformation inside a buckyball? How close are the measurable properties of H(2)@C(60) to those computed for the "quantum particle in a spherical box"? Are there any potential practical applications of this fascinating marriage of the simplest molecule, H(2), with one of the most beautiful of all molecules, C(60)? How can one address such questions theoretically and experimentally? A goal of our studies is to produce an understanding of how the H(2) guest molecules incarcerated in the host C(60) can "communicate" with the chemical world surrounding it. This world includes both the "walls" of the incarcerating host (the carbon atom "bricks" that compose the wall) and the "outside" world beyond the atoms of the host walls, namely, the solvent molecules and selected paramagnetic molecules added to the solvent that will have special spin interactions with the H(2) inside the complex. In this Account, we describe the temperature dependence of the equilibrium of the interconversion of oH(2)@C(60) and pH(2)@C(60) and show how elemental dioxygen, O(2), a ground-state triplet, is an excellent paramagnetic spin catalyst for this interconversion. We then describe an exploration of the spin spectroscopy and spin chemistry of H(2)@C(60). We find that H(2)@C(60) and its isotopic analogs, HD@C(60) and D(2)@C(60), provide a rich and fascinating platform on which to investigate spin spectroscopy and spin chemistry. Finally, we consider the potential extension of spin chemistry to another molecule with spin isomers, H(2)O, and the potential applications of the use of pH(2)@C(60) as a source of latent massive nuclear polarization.

Rotational sublevels of an ortho-hydrogen molecule encapsulated in an isotropic C60 cage

From specific heat measurements in high quality H2@C60 samples performed over a broad temperature range, we obtain the smallest yet observed splitting of rotational energy sublevels of encapsulated single H2 molecules, 0.1-0.2 meV, in the nearly spherical potential well provided by highly isotropic C60 cages. Additionally, we find evidence of the quantized oscillation state of isolated H2 in the C60 cage. The minuscule splitting indicates that H2@C60 provides unprecedented opportunities to study free-molecule quantum dynamic properties.