atoms. If the electronic correlation is stronger than the crystal fields, the orbital moment is large, otherwise small. The absorbed Ti,V,Co atoms have visible orbital moments 0.086$\mu_{_{B}}$, 0.082$\mu_{_{B}}$ and 0.092$\mu_{_{B}}$ on the Au(110)-(1$\times$2) surface, and 0.006$\mu_{_{B}}$, 0.071$\mu_{_{B}}$ and 0.247$\mu_{_{B}}$ on the Au(111) surface respectively. Cabria, et.al obtained larger orbital moment (about 0.5$\mu_{_{B}}$) of Fe and Co atoms absorbed on Au(001) surface using the spin polarization relativistic KKR methods including the orbital polarization term [@Cabria1; @Nonas1]. The usual exchange-correlation potentials (LDA or GGA) underestimate the electronic correlations such as the Coulomb correlation and the orbital polarization, thus the obtained orbital moments in this work are generally small compared with experimental values [@Brooks1; @Solovyev1; @Eriksson1; @Nonas1] although our work includes the spin-orbit coupling interaction. The small values of orbital moments of the absorbed Cr atoms in our calculations are not related to the crystal field but to its electronic structure. In the individual Cr atom, five 3d-electrons half-fill the 3d states, the total orbital moment is very small.

The coordination number of surface atoms is generally smaller than those in bulk. So the magnetism of surface is generally stronger than that in bulk. The supported atoms on the surface are in the 