Fig. 1

Structures and DFT computations of vanadium oxides with high electronic conductivity and ionic accessibility. a Atomic schematic illustration for the isomeric vanadium oxides produced by in situ corundum-to-rutile-phase transformation, which consist of corundum-type V2O3 and rutile r-VO2−x core/shell structure. Yellow dashed lines denote the electron transport pathways along short V–V bonds. Purple and blue balls represent vanadium atoms in corundum-type V2O3 and rutile-type VO2−x, red and white ones denote oxygen atoms and ordered oxygen vacancies. b Representative atomic structure of the r-VO2−x layer with ordered 1D quasi-hexagonal tunnels along z-axis. c, d Comparison of intercalation energy (Eint) (c) and energy barrier (Eb) (d) for Na+ in the tunnels of the r-VO2 and r-VO2−x with x = 0.25 and 0.167. e–g Electron density distributions of the projected orbitals for the quasi-hexagonal tunnel (e) and the V-O walls of quasi-hexagonal tunnel (f) and rutile slab (g)