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

A simple confined rotor model to describe the ro-translational dynamics of water endofullerenes and to assign the ro-vibrational spectra of solid H2O@C60

A simple Confined Rotor Model (CRM) is used to assign the thirty-nine ro-vibrational transitions observed through the HOH bending and OH stretching ranges of the solid H2O@C60 mid-infrared (MIR) spectra reported in the companion paper [Chartrand et al., J. Chem. Phys. (unpublished) (2024)]. Assuming that the intramolecular vibrations of the water molecules are separable from their rotational and translational motions, the CRM Hamiltonian describes confinement of H2O within C60 as an eccentric, but otherwise isotropic, 3D harmonic oscillator and as an asymmetric rigid rotor. The topology of the effective confinement potential is constrained using seven transitions observed in the HOH bending range of the MIR spectra of solid H2O@C60, yielding an effective force constant, k = (11.86 ± 0.03) J m-2, and an eccentricity, dCI = (7.55 ± 0.07) pm, in good agreement with DF-LMP2/cc-pVDZ results. While twenty-one broad and overlapping spectral features arising from hot band transitions were described and tentatively assigned by Chartrand et al., some of them appear very strongly perturbed compared to the gas phase. Using the CRM, it is shown that the conspicuous shifts displayed by certain very specific pairs of ro-vibrational transitions provide evidence for confinement-induced rotation-translation coupling between the orientational and positional degrees-of-freedom of endohedral water, resulting in a strong mixing between very specific pairs of ro-translational eigenstates of translational and rotational character. The CRM is shown to provide a satisfactory description of all observed ro-vibrational transitions along with a compelling interpretation for the complex confinement-induced quantum nuclear dynamics of endohedral water as revealed by the rotational and ro-vibrational spectra of solid H2O@C60.

Signatures of rotation-translation couplings, symmetry-breaking, and intermolecular interactions in the rovibrational spectra of solid H2O@C60

Some spectral features observed in the rovibrational spectra of solid H2O@C60 are shown to provide spectroscopic signatures of confinement-induced perturbations related to the coupling between the orientational and positional degrees-of-freedom of the water molecules. Their attribution to either para-H2O@C60 or ortho-H2O@C60 is established from their behavior during nuclear spin conversion. The frequency of the rovibrational transitions that emanate from their ground ro-translational (RT) states appears conspicuously redshifted from that of the corresponding transitions in the free water molecule in the gas phase. However, a few of the 21 hot band spectral features, and one ground state transition, observed in the infrared spectrum of solid H2O@C60 and reported here for the first time, cannot be straightforwardly assigned based on the softening of its intramolecular HOH bending and OH stretching vibrational modes due to confinement within C60. The most strongly perturbed transitions provide insights into the complex confinement-induced quantum nuclear dynamics arising from rotation-translation coupling, allowing the topology of the confinement potential to be revealed using a simple confined rotor model [Putaud et al., J. Chem. Phys. 162, 144313 (2025)]. While the line profiles exhibited by most of the transitions are consistent with symmetry-breaking interactions arising from merohedral disorder in solid H2O@C60, evidence for additional perturbations of the 10100 RT state, in the ground and vibrationally excited manifolds, is reported. Moreover, the line profiles displayed by the transitions emanating from the ground RT state of para-H2O@C60 and the observation of nominally forbidden Q-branch transitions, in the intramolecular HOH bending and symmetric OH stretching ranges of solid H2O@C60 samples with a fill ratio of 75%, are shown to provide a spectroscopic signature of intermolecular dipolar interactions between nearest-neighbor H2O@C60 molecules.

Single-Sided Delocalized Polarization of the C60 Cage and Reduced Infrared Intensities and Dipole Moment of H2O@C60

The C60 fullerene cage can encapsulate a small molecule like water and provides room to leave the encapsulated component rather isolated, but the true nature of the intracomplex interactions should be further elucidated for better understanding and utility of this series of complexes. Here, an analysis toward this goal is conducted for H2O@C60 by infrared spectral measurements and theoretical calculations. It is shown that the response of the π electrons of the C60 cage upon encapsulating a water molecule is single-sided and delocalized in that the electron density is partially transferred from the -z side to the +z side of the cage (when the z axis is taken along the water dipole) but almost only inside the cage, explaining the significant reduction of the dipole moment and the infrared intensities. Those infrared intensities have a large temperature dependence in a way that the bands gain intensities upon lowering the temperature down to 10 K, possibly due to coupling with lattice phonons.

The application of THz-TDS in the characterization of Bayan Obo magnetite ore composition

The application of terahertz time-domain spectroscopy (THz-TDS) in the quantitative analysis of major minerals in Bayan Obo magnetite ore was explored. The positive correlation between the optical parameters of the original ore and its iron content is confirmed. The detections of three main iron containing minerals, including magnetite, pyrite, and hematite, were simulated using corresponding reagents. The random forest algorithm is used for quantitative analysis, and FeS2 is detected with precision of R2 = 0.7686 and MAE = 0.6307% in ternary mixtures. The experimental results demonstrate that THz-TDS can distinguish specific iron containing minerals and reveal the potential application value of this testing method in exploration and mineral processing fields.

Fullerenes containing water molecules: a study of reactive molecular dynamics simulations

A different technique was used to investigate fullerenes encapsulating a polar guest species. By reactive molecular dynamics simulations, three types of fullerenes were investigated on a gold surface: an empty C60, a single H2O molecule inside C60 (H2O@C60), and two water molecules inside C60 ((H2O)2@C60). Our findings revealed that despite the free movement of all fullerenes on gold surfaces, confined H2O molecules within the fullerenes result in a distinct pattern of motion in these systems. The (H2O)2@C60 complex had the highest displacement and average velocity, while C60 had the lowest displacement and average velocity. The symmetry of molecules and the polarity of water seem to be crucial in these cases. ReaxFF simulations showed that water molecules in an H2O molecule, H2O@C60, and (H2O)2@C60 have dipole moments of 1.76, 0.42, and 0.47 D, respectively. A combination of the non-polar C60 and polar water demonstrated a significant reduction in the dipole moment of H2O molecules due to encapsulation. The dipole moments of water molecules agreed with those in other studies, which can be useful in the development of biocompatible and high-efficiency nanocars.

Optical rectification and electro-optic sampling in quartz

We report the electro-optic sampling (EOS) response and the terahertz (THz) optical rectification (OR) of the z-cut α-quartz. Due to its small effective second-order nonlinearity, large transparency window and hardness, freestanding thin quartz plates can faithfully measure the waveform of intense THz pulses with MV/cm electric-field strength. We show that both its OR and EOS responses are broad with extension up to ∼8 THz. Strikingly, the latter responses are independent of the crystal thickness, a plausible indication of dominant surface contribution to the total second-order nonlinear susceptibility of quartz at THz frequencies. Our study introduces the crystalline quartz as a reliable THz electro-optic medium for high field THz detection, and characterize its emission as a common substrate.

OH Stretching and Libration Bands of Solitary Water in Ionic Liquids and Dipolar Solvents Share a Single Dependence on Solvent Polarity

Ionic liquids are an emerging class of materials which are finding application in a variety of technologically important areas. Because of their hydrophilic character, at least a small concentration of water is often present when ionic liquids are used in practical applications. This study employs infrared spectroscopy in the OH stretching and libration regions together with DFT calculations to better characterize the state of dilute water in ionic liquids. Water mole fractions (x_w ∼ 0.1) are chosen such that nearly all water occurs in monomeric form and spectra probe the solvation structure and dynamics of solitary water molecules. New data are reported for a series of 1-ethyl-3-methylimidazolium liquids [Im₂₁][X] with X^- = (C₂F₅)₃F₃P^-, (CF₃SO₂)₂N^-, BF₄^-, B(CN)₄^-, CF₃SO₃^-, C₂H₅SO₄^-, NO₃^-, SCN^-, and CH₃CO₂^-, as well as for the two 1-hexyl-3-methylimidazolium liquids [Im₆₁][Cl] and [Im₆₁][I]. For comparison, spectra are also recorded in a variety of dipolar solvents, and much of the available literature data are summarized, providing a comprehensive perspective on monomeric water in homogeneous solution. Most prior studies of dilute water in ionic liquids interpreted OH stretching spectra only in terms of water being specifically bonded to two anions in A^-···H-O-H···A^- type solvates. The more detailed analysis presented here indicates the additional presence of asymmetrically solvated water, which in some cases includes both singly solvated (A^-···H-O-H) and more subtle forms of asymmetric solvation. The same pattern of solvation also pertains to dipolar solvents capable of accepting hydrogen bonds from water. No clear distinction is found between OH spectra in high-polarity conventional solvents and ionic liquids. In all solvents, OH frequencies are strongly correlated to measures of solvent basicity or hydrogen bond accepting ability. Far-infrared spectra of the water libration band also show common trends in ionic and dipolar solvents. Despite the different character of the libration and OH modes, the frequencies of these vibrations show virtually the same solvent dependence (apart from sign) except in weakly polar or nonpolar solvents.

Vibronic Coupling in Spherically Encapsulated, Diatomic Molecules: Prediction of a Renner-Teller-like Effect for Endofullerenes

In the year 1933, Herzberg and Teller realized that the potential energy surface of a triatomic, linear molecule splits into two as soon as the molecule is bent. The phenomenon, later dubbed the Renner–Teller effect due to the detailed follow-up work of Renner on the subject, describes the coupling of a symmetry-reducing molecular vibration with degenerate electronic states. In this article, we show that a very similar type of nonadiabatic coupling can occur for certain translational degrees of freedom of diatomic, electronically degenerate molecules when trapped in a nearly spherical or cylindrical quantum confinement, e.g., realized through electromagnetic fields or molecular encapsulation. We illustrate this on the example of fullerene-encapsulated nitric oxide, and provide a prediction of its interesting, perturbed vibronic spectrum.

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.

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.

Chemical shielding of H2O and HF encapsulated inside a C60 cage

Molecular surgery provides the opportunity to study relatively large molecules encapsulated within a fullerene cage. Here we determine the location of an H₂O molecule isolated within an adsorbed buckminsterfullerene cage, and compare this to the intrafullerene position of HF. Using normal incidence X-ray standing wave (NIXSW) analysis, coupled with density functional theory and molecular dynamics simulations, we show that both H₂O and HF are located at an off-centre position within the fullerene cage, caused by substantial intra-cage electrostatic fields generated by surface adsorption of the fullerene. The atomistic and electronic structure simulations also reveal significant internal rotational motion consistent with the NIXSW data. Despite this substantial intra-cage interaction, we find that neither HF or H₂O contribute to the endofullerene frontier orbitals, confirming the chemical isolation of the encapsulated molecules. We also show that our experimental NIXSW measurements and theoretical data are best described by a mixed adsorption site model.

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).