Among the three methods (B3LYP, BP86 and B3LYP*) in density functional theory (DFT), the best tools for predicting the ground state of metal hydride, the B3LYP method for predicting the harmonic frequencies and geometric parameters of the ground state of FeH2 gives result in good accordance with the experimental data; so it is employed to optimize the structure of molecules FeH and FeH2 in possible geometries and multiplicities based on 6-311++g(d,p) level in searching of the structure with the lowest energy. Results show that their electronic states in the ground states are FeH(4Δ) and FeH2(5A1), supposing that the two molecules have three and four unpaired electrons respectively, with spin polarization effect, and they are paramagnetic substances, and the stable structure of molecule FeH2 is of C2v symmetry. The Murrell-Sorbie potential energy function-the sufficient analytical potential function form for biatomic molecules-with 4 parameters in molecule FeH is derived via the least square method. Their spectra data and force constants are deduced according to the results. The analytical potential energy function of FeH2 is also obtained from the many-body expansion theory, which gives the analytical potential function of triatom molecules of the single-value potential surface consisting of three parts with single body terms, two body terms, and three body terms. The deduced analytical functions for FeH2 in this paper predict successfully a global minimum stable structure of quintet FeH2 with a 4.68 eV depth potential trap, and other higher energy stable and saddle structures. This potential function predicts the balanced ground structure and the second derivative force constants of this molecule. According to the potential function of FeH2(C2v), when it is formed from H and FeH, a potential trap with its depth being 4.68 eV is excited and the complex molecule of H–Fe–H is easily formed. The reaction of Fe+H2 → HFeH is exothermic with ΔH=-0.08305 eV.