Improved hybrid algorithm with Gaussian basis sets and plane waves: First-principles calculations of ethylene adsorption onβ−SiC(001)−(3×2)

Abstract

We present an algorithm for DFT calculations employing Gaussian basis sets for the wave function and a Fourier basis for the potential representation. In particular, a numerically very efficient calculation of the local potential matrix elements and the charge density is described. Special emphasis is placed on the consequences of periodicity and explicit $\mathbit{k}$-vector dependence. The algorithm is tested by comparison with more straightforward ones for the case of adsorption of ethylene on the silicon-rich $\mathrm{Si}\mathrm{C}(001)\text{\ensuremath{-}}(3\ifmmode\times\else\texttimes\fi{}2)$ surface clearly revealing its substantial advantages. A complete self-consistency cycle is speeded up by roughly one order of magnitude since the calculation of matrix elements and of the charge density are accelerated by factors of 10 and 80, respectively, as compared to their straightforward calculation. Our results for ${\mathrm{C}}_{2}{\mathrm{H}}_{4}:\mathrm{Si}\mathrm{C}(001)\text{\ensuremath{-}}(3\ifmmode\times\else\texttimes\fi{}2)$ show that ethylene molecules preferentially adsorb in on-top positions above Si dimers on the substrate surface saturating both dimer dangling bonds per unit cell. In addition, a twist of the molecules around a surface-perpendicular axis is slightly favored energetically similar to the case of a complete monolayer of ethylene adsorbed on the $\mathrm{Si}(001)\text{\ensuremath{-}}(2\ifmmode\times\else\texttimes\fi{}1)$ surface.