We apply our methodology to Mg migration in 14 TMOs and other typical candidate intercalation compounds for which we have ab initio nudged elastic band (NEB) barriers available as a benchmark. Using a structure matcher implemented in pymatgen, we identify 7 distinct structure groups: layered CoO 2 (1 structure), spinels (4), CaFe 2 O 4 -phase post-spinels (2), α-V 2 O 5 (1), marokite-phase post-spinels (2), β-VOPO 4 (1), δ-V 2 O 5 (1), and ǫ-VOPO 4 (1); more materials information can be found in SI2. The NEB barriers were computed with VASP, and the data can be found in refs. 34-38. Apart from the hopping Mg ion, the host structures did not contain any other guest ion. For electrostatic potential calculations, we use the entirely empty relaxed host structure, and we choose DFT settings that are as similar as possible to the NEB calculations. This entails use of the Perdew-Burke-Ernzerhof (PBE) density functionals without +U -correction. Regarding the choice of the density functional, Medvedev et al. have very recently shown that carefully developed conventional general gradient approximation (GGA) functionals can be more accurate in terms of the electron density (and, thus, electrostatic potential) than novel meta-GGA and hybrid functionals. Further DFT-related details can be found in the Supporting Information (SI1.3). We use the positions of the hopping ion along a given NEB path as an input chain of configurations to our PfEFIS field-living EB relaxation procedure. An example of the procedure and PfEFIS analysis (Mg in δ-V 2 O 5 ) is given in Figure , which underlines the necessity of a low spring constant. The electrostatic jump-diffusion barrier estimate, ∆E el , is then the product of the maximum electrostatic potential difference, ∆ φ, obtained from the EB relaxation and the charge of the ion (here: q = +2):