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The ab-initio molecular orbital method and different approximations with the First-principle method have been used for quantum mechanical calculations in present investigation. It calculates the structural geometries and the total energies for reactants, products and intermediate states (transition states) in various processes presented above. In this paper, we propose a generalized transition state location scheme where both oxygen atoms diffusion and periodic models can be treated within the same framework. Our first derivative was based on approach closely follows and builds upon the ideas of the traditional Linear Synchronous Transit (LST) [14] and Quadratic Synchronous Transit (QST) method in conjunction with conjugate minimization ideas of Bell and Crighton[15]. Density functional theory calculations were performed with the program package DMol3 [16-18] on personal computers. In the DMol3 method, the physical wave functions were expanded in terms of accurate numerical basis sets. We used the Double Numeric plus D-functions (DND), A Fermi smearing for 0.005Ha (1Ha=27.2114eV) and a global orbital cutoff for 4.5Å were used to improve computational performance. The exchange and correlation terms were described with the generalied gradient approximation (LDA[19]) in the scheme of Vosko-Wilk-Nusair (VWN)[20-21] . A K-Points grid is 3×3×2. Other parameters pick out to medium. Here, all calculation work was completed in the Key Laboratory of Advanced Materials of Yunnan Province, Kunming University of Science and Technology.

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