Revised Huang-Carter nonlocal kinetic energy functional for semiconductors and their surfaces

Abstract

Nonlocal kinetic energy functionals with a density-dependent kernel are the most accurate functionals available for carrying out orbital-free density functional theory simulations. Among them, the Huang and Carter (HC) functional [Huang and Carter, Phys. Rev. B 81, 045206 (2010)] is the most accurate for bulk semiconductors. A major hurdle in applying HC to nonbulk systems (such as clusters and surfaces which have at least one nonperiodic dimension where the density decays to zero) lies in its numerical instability for large values of the reduced density gradient, $s(\mathbf{r})\ensuremath{\propto}\frac{|\mathbf{\ensuremath{\nabla}}\mathbf{n}(\mathbf{r})|}{{\mathbf{n}}^{\mathbf{4}/\mathbf{3}}(\mathbf{r})}$, where $n$ is the electron density. We propose a revision to the HC functional, revHC, that allows it to achieve dramatically improved numerical stability, efficiency (in terms of timing to solution), and applicability. Not only does revHC reproduce all previously presented results for HC, but it extends them to a crucially important class of materials: surfaces. We show that surface energy trends of clean-cut and reconstructed surfaces of group IV and III-V semiconductors are recovered and, where available semiquantitatively, reproduce the experimental results.