  Developing an accurate simulation method for the electrochemical stability of
solids, as well as understanding the physics related with its accuracy, is
critically important for improving the performance of compounds and predicting
the stability of new materials in aqueous environments. Herein we propose a
workflow for the accurate calculation of first-principles electrochemical phase
(Pourbaix) diagrams. With this scheme, we study the electrochemical stabilities
of Ti and Ti oxides using density-functional theory. First, we find the
accuracy of an exchange-correlation functional in predicting formation energies
and electrochemical stabilities is closely related with the electronic exchange
interaction therein. Second, the metaGGA and hybrid functionals with a more
precise description of the electronic exchange interaction lead to a systematic
improvement in the accuracy of the Pourbaix diagrams. Furthermore, we show that
accurate Ti Pourbaix diagrams also require that thermal effects are included
through vibrational contributions to the free energy. We then use these
diagrams to explain various experimental electrochemical phenomena for the
Ti--O system, and show that if experimental formation energies for Ti oxides,
which contain contributions from defects owing to their generation at high
(combustion) temperatures, are directly used to predict room temperature
Pourbaix diagrams then significant inaccuracies result. In contrast, the
formation energies from accurate first-principles calculations, e.g., using
metaGGA and hybrid functionals, are found to be more reliable. Finally to
facilitate the future application of our accurate electrochemical phase
equilibria diagrams, the variation of the Ti Pourbaix diagrams with aqueous ion
concentration is also provided.
