Abstract The density functional theory (DFT)(b3p86) of Gaussian 03 has been used to optimize the structure of the Co$_{2}$ molecule, a transition metal element molecule. The result shows that the ground state for the Co$_{2}$ molecule is a 7-multiple state, indicating a spin polarization effect in the Co$_{2}$ molecule. Meanwhile, we have not found any spin pollution because the wavefunction of the ground state is not mingled with wavefunctions of higher-energy states. So for the ground state of Co$_{2}$ molecule to be a 7-multiple state is the indicative of spin polarization effect of the Co$_{2}$ molecule, that is, there exist 6 parallel spin electrons in a Co$_{2}$ molecule. The number of non-conjugated electrons is the greatest. These electrons occupy different spacial orbitals so that the energy of the Co$_{2}$ molecule is minimized. It can be concluded that the effect of parallel spin in the Co$_{2}$ 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 the other states of the Co$_{2}$ molecule are derived. The dissociation energy $De$ for the ground state of Co$_{2}$ molecule is 4.0489eV, equilibrium bond length $R_{\rm e}$ is 0.2061 nm, and vibration frequency $\omega _{\rm e} $ is 378.13 cm$^{ - 1}$. Its diatomic molecule force constants $f_2$, $f_3$, and $f_4$ are 2.4824 aJ$\cdot$nm$^{ - 2}$, -7.3451 aJ$\cdot$nm$^{ - 3}$, nd 11.2222 aJ$\cdot$nm$^{ - 4 }$respectively(1 aJ=$10^{-18}$ J). The other spectroscopic data for the ground state of Co$_{2}$ molecule $\omega_{\rm e}\chi _{\rm e}$, $B_{\rm e}$, and $\alpha_{\rm e}$ are 0.7202 cm$^{-1}$, 0.1347 cm$^{-1 }$, and 2.9120$\times $ 10$^{-1}$ cm$^{-1}$ respectively. And $\omega_{\rm e}\chi _{\rm e}$ is the non-syntonic part of frequency, $B_{\rm e}$ is the rotational constant, $\alpha_{\rm e}$ is revised constant of rotational constant for non-rigid part of Co$_2$ molecule.
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