关键词: Cr$_{2}$, spin polarization, density functional theory, potential function

Abstract: 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 $\times10^{-4}$cm$^{-1}$ respectively.

Key words: Cr$_{2}$, spin polarization, density functional theory, potential function