Spin polarization effect for Ta 2 molecule

Abstract

Density functional theory (DFT) (B3p86) has been used to optimize the structure of the molecule Ta₂. The result shows that the ground state of molecule Ta₂ is a 7-multiple state and its electronic configuration is ⁷Σ_u⁺, which shows the spin polarization effect for molecule Ta₂ 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 Ta₂ is a 7-multiple state indicates a spin polarization effect of molecule Ta₂ 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 Ta₂ is minimized. It can be concluded that the effect of parallel spin of the Ta₂ molecule 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 ⁷Σ_u⁺ and other states of the Ta₂ molecule are derived. The dissociation energy D_e, equilibrium bond length R_e and vibration frequency ω_e for the ground state of Ta₂ molecule are 4.5513eV, 0.2433 nm and 173.06 cm⁻¹, respectively. Its force constants f₂, f₃ and f₄ are 1.5965 × 10²aJ.nm⁻², –6.4722 × 10³aJ.nm⁻³ and 29.4851 × 10⁴aJ.nm⁻⁴, respectively. Other spectroscopic data ω_e χ_e, B_e and α_e for the ground state of Ta₂ are 0.2078 cm⁻¹, 0.0315 cm⁻¹ and 0.7858 × 10⁻⁴ cm⁻¹, respectively.