The molecular structures of ground state O2,TiO and TiO2 are calculated on the level of BP86/6-311++g(d, p) using density function theory method in Gaussian09 programs. The results show that the electron states of the ground states of the molecules respectively are O2(X3g),TiO(X3g) and TiO2(X1 A1).The stable structure of TiO2 molecule is of C2v symmetry. Each potential energy curve is obtained via scanning the single point energies of TiO and O2, which match well with those fitted with the four-parameter Murrell-Sorbie Function,according to which spectral data and force constants are deduced. The whole special analytical potential energy function of TiO2 is derived from the many-body expansion theory. And there exists a potential trap of 15.09 eV depth at 0.1652 nm (RTi-O) when the OTiO angle is fixed at 110.5, which suggests that a stable TiO2 molecule could be formed easily.