On the nature of the Schottky anomaly in endohedral water

In this work, we study the heat capacity contribution of a rigid water molecule encapsulated in C₆₀ by performing six-dimensional eigenstate calculations with the inclusion of its quantized rotational and translational degrees of freedom. Two confinement model potentials are considered: in the first, confinement is described using distributed pairwise Lennard-Jones interactions, while in the second, the water molecule is trapped within an eccentric but isotropic 3D harmonic effective confinement potential [Wespiser et al., J. Chem. Phys. 156, 074304 (2022)]. Contributions to the heat capacity from both the ortho and para nuclear spin isomers of water are considered to enable the effects of their interconversion to be assessed. By including a symmetry-breaking quadrupolar potential energy term in the Hamiltonian, we can reproduce the experimentally observed Schottky anomaly at ∼2 K [Suzuki et al., J. Phys. Chem. Lett. 10, 1306 (2019)]. Furthermore, our calculations predict a second Schottky anomaly at ∼0.1 K resulting from the H configuration, a different orientational arrangement of the fullerene cages in crystalline solid C₆₀. Contributions from the H configuration to C_V also explain the second peak observed at ∼7 K in the experimentally measured heat capacity.

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.

Unraveling the Origin of Symmetry Breaking in H2 O@C60 Endofullerene Through Quantum Computations

We explore the origin of the anomalous splitting of the 1₀₁ levels reported experimentally for the H₂O@C₆₀ endofullerene, in order to give some insight about the physical interpretations of the symmetry breaking observed. We performed fully‐coupled quantum computations within the multiconfiguration time‐dependent Hartree approach employing a rigorous procedure to handle such computationally challenging problems. We introduce two competing physical models, and discuss the observed unconventional quantum patterns in terms of anisotropy in the interfullerene interactions, caused by the change in the off‐center position of the encapsulated water molecules inside the cage or the uniaxial C₆₀‐cage distortion, arising from noncovalent bonding upon water's encapsulation, or exohedral fullerene perturbations. Our results show that both scenarios could reproduce the experimentally observed rotational degeneracy pattern, although quantitative agreement with the available experimental rotational levels splitting value has been achieved by the model that considers an uniaxial elongation of the C₆₀‐cage. Such finding supports that the observed symmetry breaking could be mainly caused by the distortion of the fullerene cage. However, as nuclear quantum treatments rely on the underlying interactions, a decisive conclusion hinges on the availability of their improved description, taken into account both endofullerene and exohedral environments, from forthcoming highly demanding electronic structure many‐body interaction studies.

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.

Inelastic Electron Transport and Ortho-Para Fluctuation of Water Molecule in H2O@C60 Single Molecule Transistors

Light molecules such as H₂O are the systems in which we can have access to quantum mechanical information on their constituent atoms. Here, we have investigated electron transport through H₂O@C₆₀ single molecule transistors (SMTs). The H₂O@C₆₀ SMTs exhibit Coulomb stability diagrams that show multiple tunneling-induced excited states below 30 meV. Furthermore, we have performed terahertz (THz) photocurrent spectroscopy on H₂O@C₆₀ SMTs and confirmed the same excitations. From comparison between experiment and theory, the excitations observed below 10 meV are identified to be the quantum rotational excitations of the water molecule. Surprisingly, the quantum rotational excitations of both para- and ortho-water molecule are observed simultaneously even for a single water molecule, indicating that the fluctuation between the ortho- and para-water states takes place in a time scale shorter than our measurement time (∼1 min), probably by the interaction between the encapsulated water molecule and conducting electrons.

Encapsulation of a Water Molecule inside C60 Fullerene: The Impact of Confinement on Quantum Features

We introduce an efficient quantum fully coupled computational scheme within the multiconfiguration time-dependent Hartree (MCTDH) approach to handle the otherwise extremely costly computations of translational–rotational–vibrational states and energies of light-molecule endofullenes. Quantum calculations on energy levels are reported for a water molecule inside C₆₀ fullerene by means of such a systematic approach that includes all nine degrees of freedom of H₂O@C₆₀ and does not consider restrictions above them. The potential energy operator is represented as a sum of natural potentials employing the n-mode expansion, along with the exact kinetic energy operator, by introducing a set of Radau internal coordinates for the H₂O molecule. On the basis of the present rigorous computations, various aspects of the quantized intermolecular dynamics upon confinement of H₂O@C₆₀ are discussed, such as the rotational energy level splitting and the significant frequency shifts of the encapsulated water molecule vibrations. The impact of water encapsulation on quantum features is explored, and insights into the nature of the underlying forces are provided, highlighting the importance of a reliable first-principles description of the guest–host interactions.

Dynamics and magnetic properties of NO molecules encapsulated in open-cage fullerene derivatives evidenced by low temperature heat capacity

Low-temperature heat capacity analyses for an NO-encapsulated fullerene derivative revealed (i) low-energy motion and (ii) strong magnetic anisotropy of the NO molecule due to its orbital angular momentum. The low-energy motion was attributed to reorientational motions of the NO molecules, in which only a small number (n ∼ 0.04) of NO molecules were found to participate. The NO molecules were confirmed to be paramagnetic even at 1 K. Ab-initio calculation indicated that the magnetic properties of the NO unit strongly depended on its surroundings, allowing the conformation of the fullerene cage to be estimated.

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).

Pressure-induced annulative orifice closure of a cage-opened C60 derivative

A cage-opened C60 derivative was found to undergo an unusual annulative orifice-closure reaction under high-pressure conditions, in which the orifice size changed from a 16- to a 13-membered ring. The structure was different from that obtained by the reaction at 1 atm. The theoretical calculations suggested that the formation of the former one is thermodynamically favored.

Rotational coherence of encapsulated ortho and para water in fullerene-C60 revealed by time-domain terahertz spectroscopy

We resolve the real-time coherent rotational motion of isolated water molecules encapsulated in fullerene-C60 cages by time-domain terahertz (THz) spectroscopy. We employ single-cycle THz pulses to excite the low-frequency rotational motion of water and measure the subsequent coherent emission of electromagnetic waves by water molecules. At temperatures below ~ 100 K, C60 lattice vibrational damping is mitigated and the quantum dynamics of confined water are resolved with a markedly long rotational coherence, extended beyond 10 ps. The observed rotational transitions agree well with low-frequency rotational dynamics of single water molecules in the gas phase. However, some additional spectral features with their major contribution at ~2.26 THz are also observed which may indicate interaction between water rotation and the C60 lattice phonons. We also resolve the real-time change of the emission pattern of water after a sudden cooling to 4 K, signifying the conversion of ortho-water to para-water over the course of 10s hours. The observed long coherent rotational dynamics of isolated water molecules confined in C60 makes this system an attractive candidate for future quantum technology.

Rotational and Vibrational Excitations of a Single Water Molecule by Inelastic Electron Tunneling Spectroscopy

Two low-energy excitations of a single water molecule are observed via inelastic electron tunneling spectroscopy, where a significant enhancement is achieved by attaching the molecule to the tip apex in a scanning tunneling microscope. Density functional theory simulations and quantum mechanical calculations of an asymmetric top are carried out to reveal the origin of both excitations. Variations in tunneling junction separation give rise to the quantum confinement effect on the quantum state of a water molecule in the tunneling junction. Our results demonstrate a potential method for measuring the dynamic behavior of a single molecule confined in a tunneling junction, where the molecule-substrate interaction can be purposely tuned.

The Endofullerene HF@C60: Inelastic Neutron Scattering Spectra from Quantum Simulations and Experiment, Validity of the Selection Rule, and Symmetry Breaking

Accurate quantum simulations of the low-temperature inelastic neutron scattering (INS) spectra of HF@C₆₀ are reported for two incident neutron wavelengths. They are distinguished by the rigorous inclusion of symmetry-breaking effects in the treatment and having the spectra computed with HF as the guest, rather than H₂ or HD, as in the past work. The results demonstrate that the precedent-setting INS selection rule, originally derived for H₂ and HD in near-spherical nanocavities, applies also to HF@C₆₀, despite the large mass asymmetry of HF and the strongly mixed character of its translation-rotation eigenstates. This lends crucial support to the theoretical prediction made earlier that the INS selection rule is valid for any diatomic molecule in near-spherical nanoconfinement. The selection rule remains valid in the presence of symmetry breaking but is modified slightly in an interesting way. Comparison is made with the recently published experimental INS spectrum of HF@C₆₀. The agreement is very good, apart from one peak for which our calculations suggest a reassignment. This reassignment is consistent with the measured INS spectrum presented in this work, which covers an extended energy range.

Rotational Motion and Nuclear Spin Interconversion of H2O Encapsulated in C60 Appearing in the Low-Temperature Heat Capacity

The heat capacity of H₂O encapsulated in fullerene C₆₀ is determined for the first time at temperatures between 0.6 and 200 K. The water molecule in H₂O@C₆₀ undergoes quantum rotation at low temperature, and the ortho-H₂O and para-H₂O isomers are identified by labeling the rotational energy levels with the nuclear spin states. A rounded heat capacity maximum is observed at ∼2 K after rapid cooling due to splitting of the rotational J _KaKc = 1₀₁ ground state of ortho-H₂O. This anomalous feature decreases in magnitude over time, reflecting the conversion of ortho-H₂O to para-H₂O. Time-dependent heat capacity measurements at constant temperature reveal three nuclear spin conversion processes: a thermally activated transition with E_a ≈ 3.2 meV and two temperature-independent tunneling processes with time constants of τ₁ ≈ 1.5 h and τ₂ ≈ 11 h.

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.

Fully Coupled Quantum Treatment of Nanoconfined Systems: A Water Molecule inside a Fullerene C60

We implemented a systematic procedure for treating the quantal rotations by including all translational and vibrational degrees of freedom for any triatomic bent molecule in any embedded or confined environment, within the MCTDH framework. Fully coupled quantum treatments were employed to investigate unconventional properties in nanoconfined molecular systems. In this way, we facilitate a complete theoretical analysis of the underlying dynamics that enables us to compute the energy levels and the nuclear spin isomers of a single water molecule trapped in a C₆₀ fullerene cage. The key point lies in the full 9D description of both nuclear and electronic degrees of freedom, as well as a reliable representation of the guest-host interaction. The presence of occluded impurities or inhomogeneities due to noncovalent interactions in the interfullerene environment could modify aspects of the potential, causing significant coupling between otherwise uncoupled modes. Using specific n-mode model potentials, we obtained splitting patterns that confirm the effects of symmetry breaking observed by experiments in the ground ortho-H₂O state. Further, our investigation reveals that the first rotationally excited states of the encapsulated ortho- and para-H₂O have also raised their 3-fold degeneracy. In view of the complexity of the problem, our results highlight the importance of accurate and computational demanding approaches for building up predictive models for such nanoconfined molecules.

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.

Probing the interaction between the encapsulated water molecule and the fullerene cages in H2O@C60- and H2O@C59N. Chem Sci 2018;9:5666-5671. [PMID: 30062000 PMCID: PMC6050629 DOI: 10.1039/c8sc01031e]

We report a high-resolution photoelectron imaging study of cryogenically-cooled H2O@C60- and H2O@C59N- endohedral fullerene anions. The electron affinity (EA) of H2O@C60 is measured to be 2.6923 ± 0.0008 eV, which is 0.0088 eV higher than the EA of C60, while the EA of H2O@C59N is measured to be 3.0058 eV ± 0.0007 eV, which is 0.0092 eV lower than the EA of C59N. The opposite shifts are found to be due to the different electrostatic interactions between the encapsulated water molecule and the fullerene cages in the two systems. There is a net coulombic attraction between the guest and host in H2O@C60-, but a repulsive interaction in H2O@C59N-. We have also observed low-frequency features in the photoelectron spectra tentatively attributed to the hindered rotational excitations of the encapsulated H2O molecule, providing further insights into the guest-host interactions in H2O@C60- and H2O@C59N-.

Determining the Humidity-Dependent Ortho-to- Para Ratio of Water Vapor at Room Temperature Using Terahertz Spectroscopy

The origin of the water spin isomers observed under various physico-chemical conditions is of great interest, including that of H₂O molecules in the gas phase. Here, terahertz time-domain spectroscopy (THz-TDS) was used to study the humidity-dependent ortho-to- para (O/P) ratio of water vapor at room temperature. The relative contents of para and ortho molecules were obtained by fitting the absorption lines of water vapor showing the relationship between the spin isomer contents and humidity. Larger O/P ratios with values of ∼3.2 were observed at lower humidity (<20%) due to the stronger attractive forces of para molecules. The concentration of the ortho isomers then began to decrease at higher humidity (>20%) due to the preferential formation of dimers and clusters at increasing concentrations. Thus, the ratio gradually decreased with increasing humidity.

Spin-Isomer Conversion of Water at Room Temperature and Quantum-Rotor-Induced Nuclear Polarization in the Water-Endofullerene H_{2}O@C_{60}

Water exists in two forms, para and ortho, that have nuclear spin states with different symmetries. Here we report the conversion of fullerene-encapsulated para water to ortho water. The enrichment of para water at low temperatures is monitored via changes in the electrical polarizability of the material. Upon rapid dissolution of the material in toluene the excess para water converts to ortho water. In H_{2}^{16}O@C_{60} the conversion leads to a slow increase in the NMR signal. In H_{2}^{17}O@C_{60} the conversion gives rise to weak signal enhancements attributed to quantum-rotor-induced nuclear spin polarization. The time constants for the para-to-ortho conversion of fullerene-encapsulated water in ambient temperature solution are estimated as 30±4  s for the ^{16}O isotopolog of water, and 16±3  s for the ^{17}O isotopolog.

Fast Rotational Diffusion of Water Molecules in a 2D Hydrogen Bond Network at Cryogenic Temperatures

Individual water molecules or small clusters of water molecules contained within microporous minerals present an extreme case of confinement where the local structure of hydrogen bond networks are dramatically altered from bulk water. In the zinc silicate hemimorphite, the water molecules form a two-dimensional hydrogen bond network with hydroxyl groups in the crystal framework. Here, we present a combined experimental and theoretical study of the structure and dynamics of water molecules within this network. The water molecules undergo a continuous phase transition in their orientational configuration analogous to a two-dimensional Ising model. The incoherent dynamic structure factor reveals two thermally activated relaxation processes, one on a subpicosecond timescale and another on a 10-100 ps timescale, between 70 and 130 K. The slow process is an in-plane reorientation of the water molecule involving the breaking of hydrogen bonds with a framework that, despite the low temperatures involved, is analogous to rotational diffusion of water molecules in the bulk liquid. The fast process is a localized motion of the water molecule with no apparent analogs among known bulk or confined phases of water.

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.

Alignment of 17O-enriched water-endofullerene H2O@C60 in a liquid crystal matrix

We present a 17O and 1H NMR study of molecular endofullerene H2O@C60 dissolved in the nematic liquid crystal N-(4-methoxybenzylidene)-4-butylaniline (MBBA). The 17O NMR peak is split into five components by the 17O residual quadrupolar coupling, each of which is split into a triplet by the 1H-17O residual dipolar coupling and scalar coupling. The splittings are analysed in terms of the partial alignment of the encapsulated water molecules. Order parameters describing the alignment are estimated. It is found that the preferential orientation of the endohedral water molecule has the molecular plane perpendicular to the liquid crystal director.

NMR of molecular endofullerenes dissolved in a nematic liquid crystal

We report the NMR of the molecular endofullerenes H₂@C₆₀, H₂O@C₆₀ and HF@C₆₀ dissolved in the nematic liquid crystal N-(4-methoxybenzylidene)-4-butylaniline (MBBA).

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.

Temperature Dependence of HeBr2 Isomers' Stability through Rovibrational Multiconfiguration Time-Dependent Hartree Calculations

The multiconfiguration time-dependent Hartree (MCTDH) method using a six-dimensional Hamiltonian that includes all rotational and vibrational degrees of freedom and an ab initio potential energy surface was employed to calculate the rovibronic states of the HeBr₂ van der Waals complex. All rotational states of energies within 7 cm ^-1 with respect to the energy of the linear ground state were calculated without restriction of the total angular momentum. In total, we obtained 500 and 320 rotationally excited states of the ground vibrational T-shaped and linear isomers of the HeBr₂, respectively, and compared them with those predicted by the rigid rotor model. A thermodynamic model was then introduced to determine the relative stability of the two conformers as a function of the temperature. On the basis of the present results, the linear conformers were found to be energetically more stable than the T-shaped ones by 1.14 cm^-1 at T = 0 K, whereas conversion from linear to T-shaped complexes was observed at temperatures above 2.87 K.

Rotational dynamics of Li+ ions encapsulated in C60 cages at low temperatures

Li⁺ ions encapsulated in fullerene C₆₀ cages (Li⁺@C₆₀) are expected to be suitable as molecular switches that respond to local electric fields. In this study, the rotational dynamics of Li⁺ ions in C₆₀ cages at low temperatures are experimentally revealed for the first time using terahertz absorption spectroscopy. In crystalline [Li⁺@C₆₀](PF₆^-), the Li⁺ ion rotates in the carbon cage even at 150 K. The rotational mode gradually changes into a librational mode below 120 K, which is associated with the localization of Li⁺ ions due to the electrostatic interactions with its screening image charge on the C₆₀ cage as well as with the neighboring Li⁺@C₆₀ and PF₆^- ions. A simple rotational/librational energy scheme for the Li⁺ ions successfully explains the spectroscopic results, and the potential of Li⁺@C₆₀ as a molecular switch is discussed based on the energy scheme.

Quantum Tunneling of Water in Beryl: A New State of the Water Molecule

Using neutron scattering and ab initio simulations, we document the discovery of a new "quantum tunneling state" of the water molecule confined in 5 Å channels in the mineral beryl, characterized by extended proton and electron delocalization. We observed a number of peaks in the inelastic neutron scattering spectra that were uniquely assigned to water quantum tunneling. In addition, the water proton momentum distribution was measured with deep inelastic neutron scattering, which directly revealed coherent delocalization of the protons in the ground state.

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).

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.

Electrical detection of ortho-para conversion in fullerene-encapsulated water

Water exists in two spin isomers, ortho and para, that have different nuclear spin states. In bulk water, rapid proton exchange and hindered molecular rotation obscure the direct observation of two spin isomers. The supramolecular endofullerene H2O@C60 provides freely rotating, isolated water molecules even at cryogenic temperatures. Here we show that the bulk dielectric constant of this substance depends on the ortho/para ratio, and changes slowly in time after a sudden temperature jump, due to nuclear spin conversion. The attribution of the effect to ortho-para conversion is validated by comparison with nuclear magnetic resonance and quantum theory. The change in dielectric constant is consistent with an electric dipole moment of 0.51±0.05 Debye for an encapsulated water molecule, indicating the partial shielding of the water dipole by the encapsulating cage. The dependence of bulk dielectric constant on nuclear spin isomer composition appears to be a previously unreported physical phenomenon.