Density functional method (B3p86) was used to optimize the structure of the molecule Fe2. The result showed that the ground electronic state for the molecule Fe2 is nonet state instead of septet state, which indicates that there is a spin polarization effect in the molecule Fe2, i.e., in which there are 8 parallel spin electrons.In this case, the number of the unpaired d-orbit electrons is the largest, and these electrons occupy different spatial orbitals so that the energy of the molecule Fe2 is minimized. Meanwhile, the spin pollution was not found because the wave functions of the ground state do not mix with those of the higher energy states. In addition, the Murrell-Sorbie potential functions with the parameters for the ground electronic state and other exited electronic states of the molecule Fe2 were derived. The dissociation energy, equilibrium bond length and the vibration frequency for the ground electronic state of the molecule Fe2 are 3.5522 eV, 0.2137 nm and 292.914 cm-1, respectively. Its force constants f2, f3 and f4 are 1.4115×102 a J/nm2, -37.1751×103aJ/nm3 and 98.7596× 104 a J/nm4, respectively. The other spectroscopic parameters ωexe, Be and αe for the ground electronic state of Fe2 are 0.3522, 0.0345 and 0.4963× 10-4 cm-1, respectively.