中国物理B ›› 2008, Vol. 17 ›› Issue (8): 2925-2931.doi: 10.1088/1674-1056/17/8/028
阎世英
Yan Shi-Ying(阎世英)†
摘要: 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 {\it D}e for the ground state of the Cr$_{2}$ molecule is 0.1034\,eV, equilibrium bond length {\it R}e 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.
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