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

Squeezing formaldehyde into C60 fullerene

The cavity inside fullerene C60 provides a highly symmetric and inert environment for housing atoms and small molecules. Here we report the encapsulation of formaldehyde inside C60 by molecular surgery, yielding the supermolecular complex CH2O@C60, despite the 4.4 Å van der Waals length of CH2O exceeding the 3.7 Å internal diameter of C60. The presence of CH2O significantly reduces the cage HOMO-LUMO gap. Nuclear spin-spin couplings are observed between the fullerene host and the formaldehyde guest. The rapid spin-lattice relaxation of the formaldehyde 13C nuclei is attributed to a dominant spin-rotation mechanism. Despite being squeezed so tightly, the encapsulated formaldehyde molecules rotate freely about their long axes even at cryogenic temperatures, allowing observation of the ortho-to-para spin isomer conversion by infrared spectroscopy. The particle in a box nature of the system is demonstrated by the observation of two quantised translational modes in the cryogenic THz spectra.

Low-temperature motion of the scandium bimetal in endofullerene Sc2@C80(CH2Ph)

The spin decoherence of the scandium bimetal in Sc2@C80(CH2Ph) is studied at low temperatures (20-120 K) by the electron spin echo technique. The correlation between the magnetic quantum number m of the total spin state of the scandium nuclei j and the decay rates is established. For the total spin j = 5, a decrease of the phase relaxation time by a factor of two is observed by changing the transition from m = -1 to m = +1 and m = -3 at 120 K. The observed results are rationalized in the framework of the rotational diffusion of the endohedral fragment in the fullerene cage. It is found that the characteristic rotation time is of the order of a microsecond at 100 K and increases at lower temperatures.

Quantum Criticality and Universal Behavior in Molecular Dipolar Lattices of Endofullerenes

Fullerene cages allow the confinement of single molecules and the construction of molecular assemblies whose properties strongly differ from those of free species. In this work, we employ the density-matrix renormalization group method to show that chains of fullerenes filled with polar molecules (LiF, HF, and H₂O) can form dipole-ordered quantum phases. In symmetry broken environments, these ordered phases are ferroelectric, a property that makes them promising candidates for quantum devices. We demonstrate that for a given guest molecule, the occurrence of these quantum phases can be enforced or influenced either by changing the effective electric dipole moment or by isotopic substitution. In the ordered phase, all systems under consideration are characterized by universal behavior that depends only on the ratio of the effective electric dipole and of the rotational constant. A phase diagram is derived, and further molecules are proposed as candidates for dipole-ordered endofullerene chains.

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.

Ferroelectric water chains in carbon nanotubes: Creation and manipulation of ordered quantum phases

Systems composed of molecular rotors are promising candidates as quantum devices. In this work, we employ our recently developed density matrix renormalization group approach to study such a rotor system, namely, linear chains of rotating para-water molecules encapsulated in a (6,5)-carbon nanotube. We show that the anisotropic environment provided by the nanotube breaks the inversion symmetry of the chain. This symmetry breaking lifts the degeneracy of the ground state and leads to a splitting between the left- and right-polarized states. In turn, a ferroelectric phase in nanoscopic systems is created, with a polarization that can be switched in a manner analogous to that of a supramolecular qubit. We present results for a few low-lying states and discuss the effect of external electric fields on the energy splitting and the occurrence of a quantum phase transition.

Formation of Para-H2O by Vacuum-UV Photolysis of O2 in Solid Hydrogen: Implication for Astrochemistry

The observation that the ortho to para ratio (OPR) of interstellar H₂O is smaller than 3 is an important yet unresolved subject in astronomy. We irradiated O₂ embedded in solid H₂ at 3 K with vacuum-ultraviolet (VUV) light and observed IR lines associated with para-H₂O (denoted as pH₂O) and nonrotating H₂O-(oH₂)_n (where oH₂ denotes ortho-H₂) but no lines associated with ortho-H₂O (denoted as oH₂O). After maintaining the matrix in darkness for ∼30 h, the amount of pH₂O decreased, accompanied by an increase in H₂O-(oH₂)_n via diffusion of oH₂. After that, the continuous nuclear-spin conversion from oH₂ to para-H₂ (denoted as pH₂) in solid H₂ over time resulted in the conversion of nonrotating H₂O-(oH₂)_n to rotating pH₂O in solid pH₂. The observation of the formation and conversion of pH₂O in our experiment suggests a plausible route in which VUV irradiation of O₂ and H₂ adsorbed on grain surfaces might be responsible for the smaller OPR of interstellar H₂O.

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.

The nuclear-spin-forbidden rovibrational transitions of water from first principles

The water molecule occurs in two nuclear-spin isomers that differ by the value of the total nuclear spin of the hydrogen atoms, i.e., I = 0 for para-H2O and I = 1 for ortho-H2O. Spectroscopic transitions between rovibrational states of ortho and para water are extremely weak due to the tiny hyperfine nuclear-spin –rotation interaction of only ∼30 kHz and, so far, have not been observed. We report the first comprehensive theoretical investigation of the hyperfine effects and ortho–para transitions in [Formula: see text]O due to nuclear-spin –rotation and spin–spin interactions. We also present the details of our newly developed general variational approach to the simulation of hyperfine effects in polyatomic molecules. Our results for water suggest that the strongest ortho–para transitions with room-temperature intensities on the order of 10−31 cm/molecule are about an order of magnitude larger than previously predicted values and should be detectable in the mid-infrared ν2 and near-infrared 2 ν1 + ν2 and ν1 + ν2 + ν3 bands by current spectroscopy experiments.

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.

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 H2 O@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.

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.

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.

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.

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.

A Solid-State Intramolecular Wittig Reaction Enables Efficient Synthesis of Endofullerenes Including Ne@C60 , 3 He@C60 , and HD@C60

An open-cage fullerene incorporating phosphorous ylid and carbonyl group moieties on the rim of the orifice can be filled with gases (H2 , He, Ne) in the solid state, and the cage opening then contracted in situ by raising the temperature to complete an intramolecular Wittig reaction, trapping the atom or molecule inside. Known transformations complete conversion of the product fullerene to C60 containing the endohedral species. As well as providing an improved synthesis of large quantities of 4 He@C60 , H2 @C60 , and D2 @C60 , the method allows the efficient incorporation of expensive gases such as HD and 3 He, to prepare HD@C60 and 3 He@C60 . The method also enables the first synthesis of Ne@C60 by molecular surgery, and its characterization by crystallography and 13 C NMR spectroscopy.

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).

Formation of unexpected S-S covalent bonds in H2S dimers under confinement

The present work investigates the effect of confinement on the hydrogen bonding interactions in H2S dimers. The interiors of different sized fullerenes (C60, C70, C84, and C120) have been used to model the effect of confinement. It was found that as the degree of confinement increases, the hydrogen bonding between H2S molecules disappears and sulphur-sulphur interactions appear. We obtained clear computational evidence that, inside C60, the H2S dimer is bound by a covalent bond between two sulphur atoms. It was also found that the strength of the S-S bond inside fullerenes is linked to the amount of charge transfer from the H2S dimer to the fullerene.

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.

Hydrogen Dynamics in Supercritical Water Probed by Neutron Scattering and Computer Simulations

In this work, an investigation of supercritical water is presented combining inelastic and deep inelastic neutron scattering experiments and molecular dynamics simulations based on a machine-learned potential of ab initio quality. The local hydrogen dynamics is investigated at 250 bar and in the temperature range of 553-823 K, covering the evolution from subcritical liquid to supercritical gas-like water. The evolution of libration, bending, and stretching motions in the vibrational density of states is studied, analyzing the spectral features by a mode decomposition. Moreover, the hydrogen nuclear momentum distribution is measured, and its anisotropy is probed experimentally. It is shown that hydrogen bonds survive up to the higher temperatures investigated, and we discuss our results in the framework of the coupling between intramolecular modes and intermolecular librations. Results show that the local potential affecting hydrogen becomes less anisotropic within the molecular plane in the supercritical phase, and we attribute this result to the presence of more distorted hydrogen bonds.

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.

An Internuclear J-Coupling of 3He Induced by Molecular Confinement

The solution-state ¹³C NMR spectrum of the endofullerene ³He@C₆₀ displays a doublet structure due to a J-coupling of magnitude 77.5 ± 0.2 mHz at 340 K between the ³He nucleus and a ¹³C nucleus of the enclosing carbon surface. The J-coupling increases in magnitude with increasing temperature. Quantum chemistry calculations successfully predict the approximate magnitude of the coupling. This observation shows that the mutual proximity of molecular or atomic species is sufficient to induce a finite scalar nuclear spin-spin coupling, providing that translational motion is restricted by confinement. The phenomenon may have applications to the study of surface interactions and to mechanically bound species.

Bond Dissociation and Reactivity of HF and H2O in a Nano Test Tube

Molecular motion and bond dissociation are two of the most fundamental phenomena underpinning the properties of molecular materials. We entrapped HF and H₂O molecules within the fullerene C₆₀ cage, encapsulated within a single-walled carbon nanotube (X@C₆₀)@SWNT, where X = HF or H₂O. (X@C₆₀)@SWNT represents a class of molecular nanomaterial composed of a guest within a molecular host within a nanoscale host, enabling investigations of the interactions of isolated single di- or triatomic molecules with the electron beam. The use of the electron beam simultaneously as a stimulus of chemical reactions in molecules and as a sub-angstrom resolution imaging probe allows investigations of the molecular dynamics and reactivity in real time and at the atomic scale, which are probed directly by chromatic and spherical aberration-corrected high-resolution transmission electron microscopy imaging, or indirectly by vibrational electron energy loss spectroscopy in situ during scanning transmission electron microscopy experiments. Experimental measurements indicate that the electron beam triggers homolytic dissociation of the H-F or H-O bonds, respectively, causing the expulsion of the hydrogen atoms from the fullerene cage, leaving fluorine or oxygen behind. Because of a difference in the mechanisms of penetration through the carbon lattice available for F or O atoms, atomic fluorine inside the fullerene cage appears to be more stable than the atomic oxygen under the same conditions. The use of (X@C₆₀)@SWNT, where each molecule X is "packaged" separately from each other, in combination with the electron microscopy methods and density functional theory modeling in this work, enable bond dynamics and reactivity of individual atoms to be probed directly at the single-molecule level.

Dielectric ordering of water molecules arranged in a dipolar lattice

Intermolecular hydrogen bonds impede long-range (anti-)ferroelectric order of water. We confine H₂O molecules in nanosized cages formed by ions of a dielectric crystal. Arranging them in channels at a distance of ~5 Å with an interchannel separation of ~10 Å prevents the formation of hydrogen networks while electric dipole-dipole interactions remain effective. Here, we present measurements of the temperature-dependent dielectric permittivity, pyrocurrent, electric polarization and specific heat that indicate an order-disorder ferroelectric phase transition at T₀ ≈ 3 K in the water dipolar lattice. Ab initio molecular dynamics and classical Monte Carlo simulations reveal that at low temperatures the water molecules form ferroelectric domains in the ab-plane that order antiferroelectrically along the channel direction. This way we achieve the long-standing goal of arranging water molecules in polar order. This is not only of high relevance in various natural systems but might open an avenue towards future applications in biocompatible nanoelectronics.

Despite the apparent simplicity of a H2O molecule, the mutual ferroelectric ordering of the molecules is unresolved. Here, the authors realize a macroscopic ferroelectric phase transition in a network of dipole-dipole coupled water molecules located in nanopores of gemstone.

Solid wetting-layers in inorganic nano-reactors: the water in imogolite nanotube case

By combined use of wide-angle X-ray scattering, thermo-gravimetric analysis, inelastic neutron scattering, density functional theory and density functional theory molecular dynamics simulations, we investigate the structure, dynamics and stability of the water wetting-layer in single-walled aluminogermanate imogolite nanotubes (SW Ge-INTs): an archetypal system for synthetically controllable and monodisperse nano-reactors. We demonstrate that the water wetting-layer is strongly bound and solid-like up to 300 K under atmospheric pressure, with dynamics markedly different from that of bulk water. Atomic-scale characterisation of the wetting-layer reveals organisation of the H₂O molecules in a curved triangular sublattice stabilised by the formation of three H-bonds to the nanotube's inner surface, with covalent interactions sufficiently strong to promote energetically favourable decoupling of the H₂O molecules in the adlayer. The evidenced changes in the local composition, structure, electrostatics and dynamics of the Ge-INT's inner surface upon the formation of the solid wetting-layer demonstrate solvent-mediated functionalisation of the nanotube's cavity at room temperature and pressure, suggesting new strategies for the design of nano-rectors towards potential control of chemical reactivity in nano-confined volumes.

A master equation for spin systems far from equilibrium

The quantum dynamics of spin systems is often treated by a differential equation known as the master equation, which describes the trajectories of spin observables such as magnetization components, spin state populations, and coherences between spin states. The master equation describes how a perturbed spin system returns to a state of thermal equilibrium with a finite-temperature environment. The conventional master equation, which has the form of an inhomogeneous differential equation, applies to cases where the spin system remains close to thermal equilibrium, which is well satisfied for a wide variety of magnetic resonance experiments conducted on thermally polarized spin systems at ordinary temperatures. However, the conventional inhomogeneous master equation may fail in the case of hyperpolarized spin systems, when the spin state populations deviate strongly from thermal equilibrium, and in general where there is a high degree of nuclear spin order. We highlight a simple case in which the inhomogeneous master equation clearly fails, and propose an alternative master equation based on Lindblad superoperators which avoids most of the deficiencies of previous proposals. We discuss the strengths and limitations of the various formulations of the master equation, in the context of spin systems which are far from thermal equilibrium. The method is applied to several problems in nuclear magnetic resonance and to spin-isomer conversion.

Switching of the reaction enthalpy from exothermic to endothermic for decomposition of H2CO3 under confinement

Various size fullerenes (C₆₀, C₇₀ and C₈₄) have been used as a means of confinement to study the decomposition reaction of carbonic acid alone as well as in the presence of a single water molecule in a confined environment. Quantum chemical calculations reveal that as the effect of confinement increases by reducing the size of the fullerene cage, the bare reaction switches from exothermic to endothermic gradually. As a result, the equilibrium of the reaction shifts toward the reactant side, which suggests that the decomposition of carbonic acid becomes thermodynamically disfavored under confinement. In the presence of a single water molecule inside the C₈₄ fullerene cage, the barrier height of unimolecular decomposition is found to be decreased by ∼2.1 kcal mol^-1 as compared to the gas phase reaction. Besides the effect of confinement, we have also studied the pressure dependency of and the effect of an external electric field on the title reaction. By parameterizing the behavior of the system inside the fullerene in terms of pressure, we have shown that the fullerene cage can act as a high pressure container for this reaction. Our investigations also reveal that, similar to confinement, an external electric field could also switch the reaction from exothermic to endothermic in nature.

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.

Tuneable single-molecule electronic conductance of C60 by encapsulation

It has been demonstrated that the single-molecule transport properties of fullerene C₆₀ can be modulated by encapsulating endohedral species, i.e. Li⁺ and H₂O, which exhibit different degrees of van der Waals interactions with the C₆₀ cage. Single-molecule junctions were prepared between the gaps of Au electrodes using a break junction technique. Encapsulation of H₂O inside the cage caused a slight decrease in the electronic conductivity relative to that of pristine C₆₀. This is in sharp contrast to Li⁺ encapsulation, which results in a twofold-to-fourfold increase in the conductivity. The electronic couplings between the C₆₀ cage and the Au electrodes were weakly dependent on the endohedral species in the cage, though the molecular orbital energy levels were remarkably modulated upon encapsulation.

First Synthesis and Characterization of CH4 @C60

The endohedral fullerene CH4 @C60 , in which each C60 fullerene cage encapsulates a single methane molecule, has been synthesized for the first time. Methane is the first organic molecule, as well as the largest, to have been encapsulated in C60 to date. The key orifice contraction step, a photochemical desulfinylation of an open fullerene, was completed, even though it is inhibited by the endohedral molecule. The crystal structure of the nickel(II) octaethylporphyrin/ benzene solvate shows no significant distortion of the carbon cage, relative to the C60 analogue, and shows the methane hydrogens as a shell of electron density around the central carbon, indicative of the quantum nature of the methane. The 1 H spin-lattice relaxation times (T1 ) for endohedral methane are similar to those observed in the gas phase, indicating that methane is freely rotating inside the C60 cage. The synthesis of CH4 @C60 opens a route to endofullerenes incorporating large guest molecules and atoms.

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.