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.

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.

An off-center endohedrally confined hydrogen molecule

In this study, we address the problem of a C₆₀ endohedrally confined hydrogen molecule through a configuration-interaction approach to electronic dynamics. Modeling the confinement by means of a combination of two Woods-Saxon potentials, we analyze the stability of the system as a function of the nuclei position through the behavior of the electronic spectrum. After studying the convergence of two different partial wave expansions, one related to the molecular Coulomb centers and the other related to the off-centering of the C₆₀ well, we found that the second approach provides a more accurate description of the system. Furthermore, we observed that the inter-atomic distance changes based on the position of the atoms inside the cavity. Thus, to obtain the most favourable energetic configuration for the molecule, it should be positioned inside the cavity next to the structure, where its size decreases.

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.

Li@C60 thin films: characterization and nonlinear optical properties

Organic materials have attracted considerable attention in nonlinear optical (NLO) applications as they have several advantages over inorganic materials, including high NLO response, and fast response time as well as low-cost and easy fabrication. Lithium-containing C₆₀ (Li@C₆₀) is promising for NLO over other organic materials because of its strong NLO response proven by theoretical and experimental studies. However, the low purity of Li@C₆₀ has been a bottleneck for applications in the fields of solar cells, electronics and optics. In 2010, highly purified Li@C₆₀ was finally obtained, encouraging further studies. In this study, we demonstrate a facile method to fabricate thin films of Li@C₆₀ and their strong NLO potential for high harmonic generation by showing its comparatively strong emission of degenerate-six-wave mixing, a fifth-order NLO effect.

A facile way is shown to obtain thin films of Li@C₆₀ as well as their characterization and nonlinear optical properties. Our results suggest Li@C₆₀ to be a suitable candidate for high-harmonic generation.

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.

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.

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).

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.

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.

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.

Spin density transfer from guest to host in endohedral heterofullerene dimers

The endohedral heterofullerenes (B@C₅₉B)₂, (B@C₅₉N)₂, (N@C₅₉B)₂ and (B@C₅₉N–N@C₅₉B) are investigated using dispersion corrected density functional theory.

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-.

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.