Classical and quantum modeling of Li and Na diffusion in FePO₄

Lithium diffusion in olivine phosphates has been widely studied both experimentally and theoretically. However, nuclear quantum effects (NQEs) of the Li ions have not been accounted for in theoretical studies thus far. In the current work, we compared Li and Na diffusion in Li_0.25FePO₄ and Na_0.25FePO₄ by computing density functional theory based classical diffusion barriers in conjunction with NQEs for the Li and Na ions. The NQEs are computed using a novel three-dimensional wave function method based on a path integral formulation. The calculations of both the potential and free energy diffusion barriers suggest that Li diffusion is faster than Na diffusion, in agreement with recent experiments. The NQEs for lithium ions in Li_0.25FePO₄ are higher than those for sodium ions in Na_0.25FePO₄. Although the contribution of NQEs to the computed Li and Na ion diffusion rates is rather small, the quantum behavior of the Li ions is unusual. Indeed, we observe a reduction in the computed diffusion rate for Li ions due to quantization. We ascribe this effect to the ability of FePO₄ to tightly bind the Li ions in the transient tetrahedral transition state, which reduces the classical diffusion barrier but also enhances quantum confinement.