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

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.

Localization of nuclear wave functions of lithium in [Li+@C60]PF6-: molecular insights into two-site disorder-order transition

Lithium endohedral fullerene, Li⁺@C₆₀, is a porous system ideal for studying the quantized translational motion of the Li⁺ nucleus under subnanoscale confinement. The quantized nuclear motion strongly depends on the anharmonic and polarizable adsorbent potential within the C₆₀ cage, which can be perturbed by cage distortion and/or exterior ions. In our recent paper, H. Ando and Y. Nakao, Phys. Chem. Chem. Phys., 2021, 23, 9785-9803, we focused on a [Li⁺@C₆₀]PF₆^- salt and theoretically investigated how the Li⁺ ion in each C₆₀ cage is simultaneously localized at two equivalent disordered sites in 24 K < T ≪ 100 K. At 24 K, the salt exhibits a disorder-order transition, whereby every Li⁺ ion becomes mostly localized at one of the two disordered sites below that temperature. Herein we discuss the origin of this transition with special attention to the local structural distortion and intermolecular interactions. Using the Fourier grid Hamiltonian method and a model function that fits a post-Hartree-Fock potential energy surface, we obtained hundreds of low-energy nuclear wave functions of Li⁺ confined within the cage. The weak distortions of the C₆₀ cage and the PF₆^- coordination sphere below 24 K and concurrent inversion-symmetry breaking affect intermolecular interactions, thus making the wave functions of the nuclear ground state and several low-energy excited states localized around the experimental high-occupancy disordered site. This demonstrates that the distortions correlate closely with the two-site disorder-order transition. Finally, we reveal that two absorption peaks in the terahertz frequency range show substantial blueshifts upon cooling below 24 K, which serve as fingerprints of the transition.

Smolyak Algorithm Adapted to a System-Bath Separation: Application to an Encapsulated Molecule with Large-Amplitude Motions

A Smolyak algorithm adapted to system-bath separation is proposed for rigorous quantum simulations. This technique combines a sparse grid method with the system-bath concept in a specific configuration without limitations on the form of the Hamiltonian, thus achieving a highly efficient convergence of the excitation transitions for the "system" part. Our approach provides a general way to overcome the perennial convergence problem for the standard Smolyak algorithm and enables the simulation of floppy molecules with more than a hundred degrees of freedom. The efficiency of the present method is illustrated on the simulation of H₂ caged in an sII clathrate hydrate including two kinds of cage modes. The transition energies are converged by increasing the number of normal modes of water molecules. Our results confirm the triplet splittings of both translational and rotational (j = 1) transitions of the H₂ molecule. Furthermore, they show a slight increase of the translational transitions with respect to the ones in a rigid cage.

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.

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.

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.