Both quantitative low-energy electron diffraction (LEED) analysis and theor
etical predictions based on the embedded-atom method suggested that Cu(331)
has a sequence of interlayer spacing contractions and expansions dissimila
r to that expected for a terrace with three atomic layers. To understand th
e anomalous behavior of Cu(331), we have performed a comparative study of C
u(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 seq
uences given by LEED measurements. The electronic structure analysis indica
tes 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 a
tomic layers a terrace has, but also on the bond-length-bond-order interpla
ys.