algorithm [@Kresse1] with the (6$\times$6$\times$1) Monkhorst-Pack grids sampling the first Brillouin zone. If the changes of the total energies are smaller than 0.0001eV between two electronic self-consistent (SC) steps the SC-loops break. We set the Methfessel-Paxton smearing width equal to 0.20eV to accelerate the speed of convergence. The energy-cutoffs of plane-wave for different atoms are summarized in table (\[table1\]). The magnetic moments for a single atom are calculated by considering the electrons in a Wigner-Seitz sphere centered at the position of the atom. The Wigner Seitz Radii for 3d transition metal atoms are also summarized in table (\[table1\]). We choose the C-\[110\] direction as the quantization axis. We emphasize the influence of surface deformation on the orbital moments of the absorbed atoms. The orbital polarization interaction omits in this work but includes the spin-orbit coupling interaction. We obtain smaller orbital moments compared with pervious density functional calculation including the orbital polarization interaction [@Nonas1].

\[mag\_3d\_relax\] The influence of structural relaxations on the magnetism of a single absorbed 3d transition atom
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It’s seem that collinear DFT calculation is enough to the study of magnetism of a single transition metal absorbed on the gold surface. However, if we want to know the 