Theoretical study of the energies and activation barriers of elementary reactions of hydrogenation of the Ti-doped closo-aluminide cluster Al@TiAl₁₁ and its anion Al@TiAl ⁻₁₁

Abstract

The potential energy surfaces, energies E, and activation barriers h of elementary reactions of addition of an H₂ molecule to the Ti-doped closo-aluminide cluster Al@TiAl₁₁ and its anion Al@Ti ⁻₁₁ with an icosahedral and marquee structure in the states with different multiplicity were calculated within the B3LYP approximation of the density functional theory using the 6–31G* and 6–311+G* basis sets. The results were compared with the data calculated at the same level of theory for the related reactions of hydrogenation of bare closo-aluminides Al₁₃ and Al ⁻₁₃ and their B-, C-, Si-, and Ge-doped derivatives. The computations demonstrated that, depending on the structure, charge, and multiplicity of the Al@TiAl₁₁ cluster, the hydrogenation energy varies in the range 15–23 kcal/mol. At the first stage of addition (chemisorption) of H₂, a μ-H₂ complex at the Ti atom (intermediate) forms with the distance R(Ti-H₂) ∼ 1.9–2.0 Å, which is accompanied by an energy decrease of ∼4–10 kcal/mol. The H-H bond in the μ-H₂ complex is ∼0.1 Å longer and the stretching vibration frequency V_val(HH) is ∼700–1500 cm⁻¹ (or more) lower than the corresponding characteristics of the isolated H₂ molecule. In the transition state with an imaginary frequency of ∼600i–1100i, the H₂ molecule is coordinated to the attacked edge Ti-Al_r, and its length increases to ∼0.9–1.1 Å. The activation barrier height h varies from a few kcal/mol to ∼8–10 kcal/mol when measured from the μ-H₂ complex and is within 18–22 kcal/mol when measured from the product (dihydride Al@TiAl₁₁H₂). The latter barrier (to the reverse reaction of dehydrogenation) is considerably higher than the barriers to migration of hydrogen atoms around the metal cage in the Al@TiAl₁₁H₂ dehydrides. There is a correlation between the energies E and barriers h of hydrogenation reactions and the structure, external charge, and multiplicity of the Al@TiAl₁₁ cluster. In all cases, the hydrogenation should occur significantly more readily than dehydrogenation. It was shown that these reactions can be both irreversible (for example, for an icosahedron in the singlet state) and reversible (for a marquee in the triplet state and others). The conclusion was drawn that the elementary reactions of hydrogenation and dehydrogenation for Ti-doped aluminides should occur considerably faster and under milder conditions than for bare aluminides or their analogues doped with main-group atoms.