Abstract The structure and stability of the compounds MRg+ and MRgF (Rg= Ar, Kr and Xe; M= Co, Rh and Ir ) were investigated using the B3LYP, MP2, MP4(SDQ) and CCSD(T) methods. We reported the geometry, vibrational frequencies and thermodynamics properties of these compounds. A series of theoretical methods on the basis of wavefunction analysis, including NBO, AIM, ELF and energy decomposition analysis, were performed to explore bonding nature of the M-Rg and Rg-F bonds. These bonds are mainly noncovalent, the metal weakly interacts with Rg in MRg+, but their interaction is much stronger in MRgF. The neutral molecule MRgF can be well described by the Lewis structure [MRg]+F-.