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

Abstract

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.