The thermodynamic properties and molecular dynamics of [Li+@C60](PF6-) associated with structural phase transitions

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.

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.

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.

Quantum states of the endohedral fullerene Li+@C60 surrounded by anions: energy decomposition analysis of nuclear wave functions

Lithium is the lightest metal element. To date, little is known about its quantized nuclear motion in nanoscale porous structures. Endohedral fullerene Li+@C60 is an ideal porous system for studying such a quantized motion. Recent studies suggest that the anions surrounding the C60 cage exterior and a slight cage distortion can alter the potential field in the cage interior and thus the nuclear wave function of Li+. It has yet to be clarified how the electronic state, particularly the flexible π electron cloud of the C60 cage, is associated with (de)localization of the Li+ wave function. Focusing on the [Li+@C60]PF6- crystal, we constructed a local structure model considering the PF6- coordination and the cage distortion. We developed model functions that fit the post-Hartree-Fock potential energy surface for the Li+ motion and its decomposed components, four interaction energy surfaces. The decomposition clarified the origins of the shell-like adsorbent potential and the potential wells therein. The Fourier grid Hamiltonian method allowed us to obtain low-energy Li+ wave functions. The ground state is nearly two-fold degenerate, and its wave functions are mostly localized underneath two C6 rings, near the disordered sites of Li+ in the X-ray crystal structure. By extending the energy decomposition analysis within the clamped-nuclei approximation to incorporate the delocalization of nuclear wave functions, we demonstrated that the ground state is stabilized by the polarization, dispersion, and electrostatic interactions. Beyond the common picture of Li+ moving in a classical electrostatic field, our approach will deepen the understanding of the flexible Li+ wave function confined in a polarizable porous structure by various intermolecular interactions.

Cocrystals of Li+ encapsulated fullerenes and Tb(iii) double-decker single molecule magnet in a quasi-kagome lattice

Cocrystallization of a lithium ion encapsulated fullerene Li⁺@C₆₀ with a terbium(iii) phthalocyaninato porphyrinato double-decker single-molecule magnet [Tb(Pc)(OEP)] is reported. The cocrystal, containing PF₆^- as a counter anion, packs in a quasi-kagome lattice, which leads to intermolecular ferromagnetic interactions as well as the modulation of the single-molecule magnet (SMM) properties.