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Density functional theory (DFT) (B3P86) of Ganssian 03 has been used to optimize the structure of the Cr2 molecule, a transition metal element molecule. The result shows that the ground state for the Cr2 molecule is a 13-multiple state, indicating that there exists a spin polarization effect in the Cr2 molecule. Meanwhile, we have not found any spin pollution because the wave function of the ground state does not mingle with wave functions of higher-energy states. So the ground state for Cr2 molecule being a 13-multiple state is indicative of spin polarization effect of the Cr2 molecule among transition metal elements, that is, there are 12 parallel spin electrons in the Cr2 molecule. The number of non-conjugated electrons is greatest. These electrons occupy different spatial orbitals so that the energy of the Cr2 molecule is minimized. It can be concluded that the effect of parallel spin in the Cr2 molecule is larger than the effect of the conjugated molecule, which is obviously related to the effect of electron d delocalization. In addition,the Murrell-Sorbie potential functions with the parameters for the ground state and other states of the Cr2 molecule are derived. The dissociation energy De for the ground state of the Cr2 molecule is 0.1034eV, equilibrium bond length Re is 0.3396nm, and vibration frequency ωe is 73.81cm-1. Its force constants f2, f3 and f4 are 0.0835, -0.2831 and 0.3535 aJ·nm-4 respectively. The other spectroscopic data for the ground state of the Cr2 molecule ωeχe, Be and αe are 1.2105, 0.0562 and 7.2938 × 10-4cm-1 respectively.