Molecular self-assembly is the spontaneous organization of molecules under thermodynamic equilibrium conditions into well-defined arrangements via cooperative effects between chemical bonds and weak noncovalent interactions. Molecules undergo self-association without external instruction to form hierarchical structures. Molecular self-assembly is ubiquitous in nature and has recently emerged as a new strategy in chemical biosynthesis, polymer science and engineering. NO monomer is apt to be absorbed on the surfaces of some metals such as Ir(111), Ni(111), Pd(111), Pt(111), Rh(111) and Au(111), and the interactions of NO monomer with the metal surfaces have been extensively studied. When NO monomer is weakly adsorbed on the noble-metal surface, it cannot be reduced completely but forms a stable structure, which is named NO dimer. The first-principle technique is employed to determine the structures of NO dimer ((NO)2) molecular chains and monolayers on virtual Rh(111), as well as (NO)2 monolayer and multilayer on Rh(111). First, (NO)2 monomers are assembled into two stable molecular chains on the virtual Rh(111) surface, whose bind energies are 0.309 and 0.266 eV, respectively. The molecular chains are self-assembly systems, in which (NO)2 monomers are parallel and ordered, and the O atoms and N atoms are shown to be of (100) and (111) structures, respectively. Then, the two molecular chains are assembled into two stable monolayers (denoted as M1 and M2) on the virtual Rh(111)-(13), and the coverage is 1.00 ML. In the M1 monolayer, the angle between the NN bond of (NO)2 monomer and the substrate is in a range of 70-90, and in the M2 monolayer, the NN bond is parallel to the substrate.In the adsorption system of M2/Rh(111), (NO)2 molecules can be adsorbed on the top as well as the hcp and fcc hollow sites. When (NO)2 molecules are adsorbed on the top site, the adsorption system is best described by the electron structure Rh+0.14N0=O-0.14, and when (NO)2 molecules are absorbed on the two hollow sites, the adsorption system is described by the electron structure Rh+0.34N-0.18=O-0.16. Therefore, (NO)2 molecules are more apt to be adsorbed on the two hollow sites than on the top site. In the adsorption systems of M1+M2/Rh(111) and M1+(M1+M2)/Rh(111), (NO)2 molecules are adsorbed vertically on the two hollow sites, the NN bond is parallel to the substrate in the first monolayer, and the angle between the NN bond and the substrate is in a range of 70-90 in the second and third monolayers. The interaction between the neighbor monolayers is about 0.01 eV, and the thickness of the vacuum layer is 0.31 nm0.02 nm.