Fig. 1: Anion lone pair rotations accompany cation diffusion.

a Snapshots from a trajectory of AgI at 750 K illustrating the electronic paddle-wheel motion that facilitates Ag⁺ conduction. A single Ag⁺ (orange sphere) and its initial three closest I⁻ (purple spheres) with their lone pairs, represented as maximally localized Wannier function centers (MLWFCs) (small, light purple spheres) are highlighted. All other Ag⁺ and I⁻ are shown as small gray and larger dark gray spheres. The lone pairs rotate concertedly with the motion of Ag⁺ as it moves from one binding site to the next, moving from left to right along the panels shown here. Following one rotation over a 300 fs time interval, the Ag⁺ stays in a binding site until it diffuses with another lone pair rotation, with the waiting time and rotation time totaling approximately 1200 fs. b Radial distribution functions, g(r), between Ag⁺ cations and iodide lone pair MLWFCs. The integration of the first peak (shaded region) is proportional to the coordination number of lone pairs around Ag⁺ ions. c Joint probability distribution of the lone pair-Ag⁺ distance (r) and the I⁻-lone pair-Ag⁺ angle (θ). d Tetrahedral rotor function time correlation functions (TCFs), C₂(t), characterizing I⁻ lone pair rotational dynamics. e Ag⁺ cage TCF, C_R(t), quantifying the diffusion of cations between binding sites.