Vacancy formation enthalpy of filled d-band noble metals by hybrid functionals

First-principles determination of the vacancy formation enthalpies has been long-term believed to be highly successful for metals. However, a widely known fact is that the various conventional density functional theory (DFT) calculations with the typical semilocal approximations show apparent failures to yield accurate enthalpies of Ag and Au. Recently, the previously commonly assumed linear Arrhenius extrapolation to determine the vacancy formation enthalpies at T = 0 K from the high-temperature measured concentration of thermally created vacancies has been demonstrated to have to be replaced by the non-Arrhenius local Gruneisen theory (LGT) [A. Glensk, B. Grabowski, T. Hickel, and J. Neugebauer, Phys. Rev. X 4, 011018 (2014)]. The large discrepancies between the conventional DFT-PBE data and the unrevised experimental vacancy formation enthalpies disappear for Cu and Al. Even by following the same LGT revisions for Ag, the large discrepancies still remain substantial at T = 0 K. Here, we show that the hybrid functional (HSE), by including nonlocal exchange interactions to extend the conventional DFT method, can further correct these substantial failures. Upon a comparison of the experimental valence-band spectra for Cu, Ag, and Au, we have determined the HSE exchange-correlated mixing parameters a of 0.1, 0.25, and 0.4, and further derived the HSE enthalpies of vacancy formation of 1.09, 0.94, and 0.72 eV, respectively; in nice agreement with available LGT-revised experimental data. Our HSE results shed light on how to improve the theoretical predictions to accurately determine the defect formation energies and related thermodynamical properties.