  We propose an efficient ab initio framework to compute the Gibbs energy of
the transition state in vacancy-mediated diffusion including the relevant
thermal excitations at density-functional-theory level. With the aid of a
bespoke machine-learning interatomic potential, the temperature-dependent
vacancy formation and migration Gibbs energies of the prototype system bcc
tungsten are shown to be strongly affected by anharmonicity. This explains the
physical origin of the experimentally observed non-Arrhenius behavior of W
self-diffusion as a case study. The good agreement of the self-diffusivity with
experiment demonstrates that accurate ab initio diffusion databases are in
reach.
