<i>Ab initio</i> calculation of electronic state structure of TiAl

Abstract

The potential energy curves (PECs) of the low-lying electronic states of TiAl are calculated with the complete active space self-consistent field (CASSCF) method combined with the &lt;i&gt;N&lt;/i&gt;-electron valence perturbation theory (NEVPT2) approximation. The complete active space is mainly composed of the (3s&lt;sup&gt;2&lt;/sup&gt;3p&lt;sup&gt;1&lt;/sup&gt;) valence orbital of Al and (3d&lt;sup&gt;2&lt;/sup&gt;4s&lt;sup&gt;2&lt;/sup&gt;) valence orbital of Ti. Moreover, the valence splitting all-electron basis set def2-&lt;i&gt;n&lt;/i&gt;ZVPP (&lt;i&gt;n&lt;/i&gt; = T, Q) proposed by Karlsruhe group is used in the calculation. On the basis of confirming that the ground state of TiAl is a quadruple state, the PECs of the ground state and the lowest two excited states of TiAl are obtained in a range of nuclear distance &lt;i&gt;R&lt;/i&gt; of 0.200–0.500 nm, and the electronic states are identified. It is found that there is a “break” of the electronic structure near &lt;i&gt;R&lt;/i&gt; = 0.255 nm. In the &lt;i&gt;R&lt;/i&gt; &gt; 0.255 nm region, the ground state and the two excited states are X&lt;sup&gt;4&lt;/sup&gt;Δ, A&lt;sup&gt;4&lt;/sup&gt;Π and B&lt;sup&gt;4&lt;/sup&gt;Γ respectively; in the &lt;i&gt;R&lt;/i&gt; &lt; 0.255 nm region, the ground state is still X&lt;sup&gt;4&lt;/sup&gt;Δ, but the two excited states become A'&lt;sup&gt;4&lt;/sup&gt;Φ and B'&lt;sup&gt;4&lt;/sup&gt;Π, and the degeneracy of the excited state tends to be eliminated. Based on the PECs of TiAl obtained by the dynamic correlation correction with NEVPT2, the characteristic parameters of three low-lying quadruple electronic states (such as equilibrium nuclear distance, binding energy, adiabatic excitation energy) and transition dipole moment, are obtained, and these parameters are used to explain the reason why the electronic transition spectrum of TiAl is not observed experimentally. The characteristic of “break” in the electronic state structure also provides a meaningful reference for analyzing and understanding the brittleness of TiAl alloy at room temperature.