Extended Data Fig. 8: NEB barriers categorized by their mechanism at the start (x ≈0) and end (x ≈ 2) of the discharge in Li_3+xV₂O₅.

Panels a–c refer to Li interstitial migration barriers in Li₁₉V₁₃O₃₂ (equivalent to Li₃V₂O₅) and panels d and e refer to Li vacancy migration in Li₃₂V₁₃O₃₂ (equivalent to Li₅V₂O₅). a, Concerted Li migration barriers in Li₃V₂O₅ based on four representative configurations. Five paths from four orderings contribute to super-low NEB barriers ranging from 166 meV to 290 meV. The hopping type is opposing T1-O-T1, which refers to cooperative hops between two T1 (0-TM) tetrahedral sites through an octahedral site. The relative positions between the initial and final tetrahedral sites are opposing versus the central octahedral site. b, Concerted Li migration barriers in Li₃V₂O₅ based on four representative configurations. Seven paths from four orderings contribute to relatively low NEB barriers ranging from 204 meV to 435 meV. The hopping type is corner-sharing T1-O-T1, which refers to cooperative hops between two T1 (0-TM) tetrahedral sites through an octahedral site. The relative positions between the initial and final tetrahedral sites are corner-shared with each other. c, Direct Li migration barriers in Li₃V₂O₅ based on four representative configurations. Four paths from four orderings contribute to high NEB barriers ranging from 634 meV to 1,049 meV. The hopping type is edge-sharing T1-T1, which refers to the direct hops between two nearest edge-sharing T1 (0-TM) tetrahedral sites. d, Vacancy migration barriers in the lowest-energy configuration of Li₅V₂O₅. Direct tetrahedron-to-tetrahedron (t-t) hops with super-low NEB barriers ranging from 181 meV to 310 meV. e, Hops by the t-o-t mechanism refer to the migration from one tetrahedron to the other through an empty face-shared octahedron. The barriers from 703 meV to 1,109 meV are much higher than for the direct t-t mechanism, which makes this mechanism unfavourable.