Functional designed to include surface effects in self-consistent density functional theory

We design a density-functional-theory (DFT) exchange-correlation functional that enables an accurate treatment of systems with electronic surfaces. Surface-specific approximations for both exchange and correlation energies are developed. A subsystem functional approach is then used: an interpolation index combines the surface functional with a functional for interior regions. When the local density approximation is used in the interior, the result is a straightforward functional for use in self-consistent DFT. The functional is validated for two metals (Al, Pt) and one semiconductor (Si) by calculations of (i) established bulk properties (lattice constants and bulk moduli) and (ii) a property where surface effects exist (the vacancy formation energy). Good and coherent results indicate that this functional may serve well as a universal first choice for solid-state systems and that yet improved functionals can be constructed by this approach.

Figure 1

Parametrizations of Airy exchange ${\widehat{ϵ}}_x^{\text{Airy}}$ vs scaled spatial coordinate $\zeta$. The solid black line is the true Airy exchange from Eq. (3). The inset shows the difference between the parametrizations and the true exchange. Far outside the edge, the LAA is more accurate than the LAG due to the former’s proper limiting behavior.

Figure 2

Local surface XC energy for the $r_s=2.66$ jellium surface. The main figure shows the quantity that integrates to the surface energy ${\sigma }_{xc}$ in $\mathrm{ergs}∕{\mathrm{cm}}^2$. The upper inset shows the difference between the functionals and LDA. The lower inset shows the interpolation indices $X$. Integration gives in $\mathrm{ergs}∕{\mathrm{cm}}^2$ for LDA 1188, for LAG 1121, and for LDA-LAG(LAA) the “exact” $\mathrm{RPA}+$ value of 1214.