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.
Received: 04 November 2007
Revised: 25 January 2008
Accepted manuscript online:
Altmetric calculates a score based on the online attention an article receives. Each coloured thread in the circle represents a different type of online attention. The number in the centre is the Altmetric score. Social media and mainstream news media are the main sources that calculate the score. Reference managers such as Mendeley are also tracked but do not contribute to the score. Older articles often score higher because they have had more time to get noticed. To account for this, Altmetric has included the context data for other articles of a similar age.