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

Abstract

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.