The ground states of TiH2,TiD2 and TiT2 are determined as 3A2 based on atomic and molecular statics and ground theory. The energy E, heat capacity Cv and entropy S of hydrogen isotopic molecules and its titanium compounds have been calculated using density functional theory (DFT) with basis set 6-311G**. The electronic and vibrational energy and entropy of single molecules TiH2,TiD2 and TiT2 are used as the energy and entropy in their solid states approximately, which is called the electron-vibration motion approximation theory(EVMAT). The calculated results of hydrogenation (and of its isotopes) thermodymical functions ΔH0, ΔS0, ΔG0 and equilibrium pressure of metallic titanium changing with temperature are in good agreement with experimental data, which confirms EVMAT theory further.