We have performed density-functional theory calculations, including the spin-orbit correction, to investigate atomic gold chains on Ge͑001͒. A set of 26 possible configurations of the Au/Ge͑001͒ system with c͑4 ϫ 2͒ and c͑8 ϫ 2͒ symmetries is studied. Our data show that the c͑4 ϫ 2͒ order results in the lowest energy, which is not in direct agreement with recent experiments. Using total-energy calculations, we are able to explain these differences. We address the electronic band structure and

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... ply the Tersoff-Hamann approach to correlate our data to scanning-tunneling microscopy ͑STM͒. We obtain two highly competitive structures of the atomic Au chains for which we report simulated STM images in order to clarify the composition of the experimental Au/Ge͑001͒ surface.