The structure and stability of thin H-passivated $<$112$>$ silicon nanowires

Recent experiments on the synthesis on monocrystalline nanowires reveal that their axis can only have a limited number of crystalline orientations. Among these orientations, $<$112$>$ is the highest Miller-index wire axis and generates a rectangular cross-sectional shape. Using a combination between genetic algorithm search and density functional theory calculations, we determine the precise shape of the wire cross-section that corresponds to the lowest formation energy per silicon atom. We analyze the deviations of the cross-sectional shape from the Wulff shape, and show how the shape of the nanowires evolves as a function of cross-sectional area and the chemical potential of hydrogen.