Multilayer relaxation of Cu(331)

Both quantitative low-energy electron diffraction (LEED) analysis and theoretical predictions based on the embedded-atom method suggested that Cu(331) has a sequence of interlayer spacing contractions and expansions dissimilar to that expected for a terrace with three atomic layers. To understand the anomalous behavior of Cu(331), we have performed a comparative study of Cu(331) and Cu(211) by using the first-principles full-potential linearized augmented plane-wave method within the generalized gradient approximation. For both surfaces, our calculations reproduce the multilayer relaxation sequences given by LEED measurements. The electronic structure analysis indicates that the seemingly anomalous multilayer relaxation in Cu(331) can also be understood in the charge smoothing picture. However. the trend of charge smoothing in such transition metal surfaces depends not only on how many atomic layers a terrace has, but also on the bond-length-bond-order interplays.