The multilayer relaxations of the (311), (511), (711), and (911) Cu surfaces are investigated using the all-electron full-potential linearized augmented plane-wave (FLAPW) method. We found relaxation sequences like -+-(...), --+-(...), ---+-(...), and ----+-(...) for (311), (511), (711), and (911), respectively, where the - and + signs indicate contraction and expansion, respectively, of the interlayer spacing. Furthermore, we found that the first-neighbor distances between the Cu atoms in the step edges do not depend on the surface termination, i.e., d(SC-CC) is the same for all studied surfaces. Our FLAPW relaxation sequences are in full agreement with quantitative low-energy electron diffraction (LEED) results, as well as with the multilayer relaxation-coordination trend proposed recently. However, large discrepancies are found for the magnitude of the interlayer relaxations, particularly for those involving atoms at the step edges. From our calculations, we suggest that these discrepancies are due to the fact that the atomic displacements parallel to the surface were not take into account in the quantitative analysis of the LEED intensities, which we found to play an important role for a quantitative description of the stepped Cu (2n-1, 11) surfaces.
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