The lower energy structures of Al2O3H3 molecular clusters are optimized through DFT/B3LYP connected with 6-311g++(d, p) all electrons basis set. It is found that the ground state configuration of Al2O3H3 has 1A' electronic state and Cs symmetry. Based on the research on energy, heat capacity at constant volume, entropy of Al2O3M3 and M2 (M=H, D, T), the hydrogen isotope effects of reactions between Al2O3 and hydrogen (deuterium or tritium) gas are studied by means of the solid electron-vibration approximation. In addition, the changes of enthalpy, entropy and Gibbs free energy, and the relation between equilibrium pressures and temperatures are presented. The investigation suggests that hydrogen can be replaced by deuterium, and deuterium can be replaced by tritium in the reactions between Al2O3 and M2 with the productions of solid Al2O3M3 (M=H, D, T). This replacement sequence is opposite to the metallic isotope effect e. g. for titanium, however these replacement effects are very weak, and they are weaker and weaker as the temperature increases.