Nonequivalence of the generalized gradient approximations PBE and PW91

Two of the most popular generalized gradient approximations used in the applications of the density functional theory, PW91 and PBE, are generally regarded as essentially equivalent. They produce similar numerical results for many simple properties, such as lattice constants, bulk moduli, and atomization energies. We examine more complex properties of systems with electronic surface regions, with the specific application of the monovacancy formation energies of Pt and Al. A surprisingly large and consistent discrepancy between PBE and PW91 results is obtained. This shows that despite similarities found between some simple material properties, PBE and PW91 are not equivalent. The differences obtained for the monovacancy formation energies are related to differences in surface intrinsic errors which are substantiated using the idealized, well-controlled, jellium surface model. In view of the differences obtained with the PW91 and PBE functionals we develop separate surface intrinsic error corrections for these and revisit some earlier results.

Figure 1

(Color online) Relative jellium surface energy error of LDA (solid), PBE (dashed), and PW91 (dash-dotted) functionals. The error bars represent the roundoff errors of the integer $\mathrm{RPA}+$ values. While one can be certain that the data is not more accurate than this, actual errors are likely larger. We use the interpolation/extrapolation formula of Ref. 28 for the values of ${\sigma }_{\mathrm{xc}}^{\mathrm{RPA}+}$.

Figure 2

(Color online) Surface energy correction per area $(\mathrm{eV}∕{\mathrm{\AA }}^2)$ for LDA (solid), PBE (dashed), and PW91 (dash-dotted).