Spin polarization effect for Cr₂ molecule

Density functional theory (DFT) (B3P86) of Gaussian 03 has been used to optimize the structure of the Cr_2 molecule, a transition metal element molecule. The result shows that the ground state for the Cr_2 molecule is a 13-multiple state, indicating that there exists a spin polarization effect in the Cr_2 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 Cr_2 molecule being a 13-multiple state is indicative of spin polarization effect of the Cr_2 molecule among transition metal elements, that is, there are 12 parallel spin electrons in the Cr_2 molecule. The number of non-conjugated electrons is greatest. These electrons occupy different spatial orbitals so that the energy of the Cr_2 molecule is minimized. It can be concluded that the effect of parallel spin in the Cr_2 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 Cr_2 molecule are derived. The dissociation energy De for the ground state of the Cr_2 molecule is 0.1034 eV, equilibrium bond length Re is 0.3396 nm, and vibration frequency \omega_\rm e is 73.81 cm^-1. Its force constants f_2, f_3 and f_4 are 0.0835, -0.2831 and 0.3535 aJ \cdot nm^- 4 respectively. The other spectroscopic data for the ground state of the Cr_2 molecule \omega_\rm e\chi _\rm e, B_\rm e and \alpha_\rm e are 1.2105, 0.0562 and 7.2938 \times10^-4cm^-1 respectively.