Depolarization and bonding in quasi-one-dimensional Na structures on Cu(001)

The formation of quasi-one-dimensional (Q1D) $p(n\times2)$-Na/Cu(001) structures is addressed by density-functional theory investigations for adsorbate coverage from low to the saturation one. A general dependence of the dipole moment on the given configuration is deduced by extending that for uniform distributions, and is greatly affecting the energetics of the Na overlayer. Larger stability for Q1D arrangements aligned along $[110]$ and $[1\overline{1}0]$ holds at coverage larger than $0.2$~ML, in agreement with low-temperature He scattering experiments, and can be explained by a reduced dipole-dipole repulsion for the $p(4\times2)$ with respect to hex-like distributions. Interatomic bonding charge displacements along zig-zag rows of Na atoms further support the Q1D structure and contribute significantly to the surface corrugation as seen by the He probe.