Vacancy formation energies in fcc metals: Influence of exchange-correlation functionals and correction schemes

The performance of various exchange-correlation functionals (LDA, PBE, PW91, and AM05) in predicting vacancy formation energies has been evaluated for 12 fcc metals. A careful analysis of the results shows that differences between the theoretical result and experiment are mainly related to the way the various exchange-correlation functionals describe the internal surface of the vacancy. Based on this insight we propose a modified version of the correction scheme of Mattsson, Wixom, and Armiento [Phys. Rev. B 77, 155211 (2008)]. Applying this approach to our results yields a perfect alignment of vacancy formation energies for all exchange-correlation functionals. These corrected values are also in very good agreement with the vacancy formation energies obtained in experiment.

Figure 1

Charge density in the vicinity of a vacancy in Ag plotted for the (100) plane in Cartesian (left) and relative (right) coordinates. Isosurfaces (for the given fraction of the mean charge density) are indicated by red/light (LDA) and blue/dark (GGA, PBE, and PW91 are indistinguishable) lines.

Figure 2

Deviation of calculated lattice constants and bulk modules from their respective experimental values for different metals and xc functionals.

Figure 3

Calculated (bars from left to right: LDA, PBE, PW91, AM05) and experimental (lines) vacancy formation energies. The darker color bars show the corrected vacancy formation energies. The recommended value based on experimental data (Ref. 28) is shown by filled red squares together with error bars. The scatter in the experimental values from positron annihilation spectroscopy (PAS) (pink) and from others' techniques (yellow) is shown by segments.

Figure 4

Vacancy formation energies with respect to cohesive energies for different metals and xc functionals. Solid lines provide linear regressions for the same element, the dashed black line corresponds to the relation $E_{\mathrm{vac}}=1/3E_{\mathrm{coh}}$ (see text).