Electron-vibration approximate method for hydrogen isotope compounds Al₂O₃X₂ (X = H, D, T)

The geometric configurations, vibration frequencies and thermodynamics properties of Al₂O₃X₂ (X = H, D, T) molecular clusters with lower energy are optimized using the B3LYP/6-311++g (d, p) method. The changes of entropy, enthalpy and Gibbs free energy of the reactions between Al₂O₃ and hydrogen (deuterium or tritium) gas are calculated by the solid electron-vibration approximate method and thermodynamic formulae at temperatures of 298, 398, 498, 598, 698, 798, 898, 998 and 1098 K, and then the relationships between the equilibrium pressure of hydrogen (deuterium or tritium) gas and temperature in these reactions are obtained. The results show that the ground state of the gaseous Al₂O₃H₂is Al₂O₃X₂ (X = H, D, T) (¹A') C_s. Hydrogen can be displaced by deuterium; deuterium can be displaced by tritium in the reactions between Al₂O₃ and X₂ with the productions of solid Al₂O₃X₂ which relates to ground gaseous Al₂O₃X₂ with C_s symmetry. This displacement sequence is opposite to that in the reactions between titanium and X₂. These displacement effects are very weak, and they are weaker and weaker as the temperature increases.