关键词: Ta$_2 $, spin polarization, density functional theory, potential function

Abstract: Density functional theory (DFT) (B3p86) has been used to optimize the structure of the molecule Ta$_2 $. The result shows that the ground state of molecule Ta$_2 $ is a 7-multiple state and its electronic configuration is $^{7}\Sigma _{u}^{ + }$, which shows the spin polarization effect for molecule Ta$_2 $ of transition metal elements for the first time. Meanwhile, spin pollution has not been found because the wavefunction of the ground state does not mix with those of higher states. So, the fact that the ground state of molecule Ta$_2 $ is a 7-multiple state indicates a spin polarization effect of molecule Ta$_2 $ of the transition metal elements, i.e. there exist 6 parallel spin electrons and the non-conjugated electrons are greatest in number. These electrons occupy different space orbitals so that the energy of molecule Ta$_2 $ is minimized. It can be concluded that the effect of parallel spin of the molecule Ta$_2$ is larger than the effect of the conjugated molecule, which is obviously related to the effect of d-electron delocalization. In addition, the Murrell--Sorbie potential functions with parameters for the ground state $^{7}\Sigma _{u}^{ + }$ and other states of the molecule Ta$_2$ are derived. The dissociation energy $D_{\rm e}$, equilibrium bond length $R_{\rm e}$ and vibration frequency $\omega_{\rm e}$ for the ground state of molecule Ta$_2$ are 4.5513eV, 0.2433 nm and 173.06\,cm$^{-1}$, respectively. Its force constants $f_2$, $f_3$ and $f_4$ are 1.5965$\times $10$^{2}$aJ$\cdot$nm$^{-2}$, --6.4722$\times $10$^{3}$aJ$\cdot$nm$^{-3}$ and 29.4851$\times $10$^{4}$aJ$\cdot$nm$^{-4}$, respectively. Other spectroscopic data $\omega_{\rm e}$ $\chi_{\rm e}$, $B_{\rm e}$ and $\alpha_{\rm e}$ for the ground state of Ta$_2 $ are 0.2078 cm$^{-1}$, 0.0315 cm$^{-1}$ and 0.7858$\times $ 10$^{-4}$ cm$^{-1}$, respectively.

Key words: Ta$_2 $, spin polarization, density functional theory, potential function