Spin polarization effect for molecule Ta₂

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 10^2aJ\cdotnm^-2, --6.4722\times 10^3aJ\cdotnm^-3 and 29.4851\times 10^4aJ\cdotnm^-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.