Supporting Information

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1 Supporting Information Density Functional Theory plus Hubbard U Study of the Segregation of Pt to the CeO 2-x Grain Boundary Guoli Zhou 1, Pan Li 1, Qingmin Ma 2, Zhixue Tian 1 *, and Ying Liu 1,3 1 Department of Physics and Hebei Advanced Thin Film Laboratory, Hebei Normal University, Shijiazhuang, Hebei , China 2 Department of Chemistry, Hebei Normal University, Shijiazhuang , China 3 State Key Lab of Nonferrous Metals & Processes, General Research Institute for Nonferrous Metal, Beijing , China The comparisons on the results based on the PBE and PBE-sol functionals. We have calculated the segregation energies of Pt at the GB (with and without oxygen vacancies) and the three surfaces ((111), (110), and (112))that are the edge facets of the model for the CeO 2 3 (111) GB using the PBE-sol 1 functional with the cutoff energy of 500 ev. To evaluate the accuracy of our results, we compared the results based on the PBE and PBE-sol functionals, and shown them in TABLE S1. These two functionals yields the similar segregation energies of Pt. The differences in the solution energies of Pt are very small using the two functionals. It was found that Pt had a strong tendency to segregate to the GB and surfaces whatever the value of U eff. The (112) surfaces was the most favorable site for Pt, followed by the 3[110] /(111) GB. The impact of the Coulomb repulsion of the Pt 5d orbital on the segregation energy of Pt looks very similar in the different functional calculations.

2 TABLE S1. The calculated relative solution energies of Pt as a function of its position using U eff (Pt) = 0 and 7.5 ev with U eff (Ce) = 6 ev in the PBE-sol and PBE calculations. E (Pt) means the difference in the segregation energy of Pt at the GB and the (111) surface, defined as: GB E(Pt) E E sol surf. sol Relative energy(ev) U (Pt) 0 eff U eff (Pt) 7.5 PBE PBE-sol PBE PBE-sol Bulk GB GB Surf. (111) Surf. (110) Surf. (112) E (Pt) The contributions 2, 3 to Pt segregation calculated by the PBE-sol functional were presented in Figure S2. The solution energies of Pt are mainly due to the chemical part. Due to the similar magnitude of the chemical contributions for all five systems, the segregation energy relative to Pt inside the grain, depends mainly on the mechanical contribution. However, the strong tendency of Pt to segregate to the (112) surface is due to the chemical contribution which is much smaller than others. The similar results were also found in the PBE calculations. Obviously, the two methods predict the similar properties for the segregation of Pt.

3 Figure S1. The calculated solution energy along with the mechanical and chemical contributions for Pt in the bulk, at the 3 (111) GB and the surfaces, using PBE-sol. We compared the stability of an oxygen vacancy in the bulk and at the 3 (111) GB of CeO 2, using PBE and PBE-sol. They both predicted that the 3 (111) GB is much more favorable than the bulk for an oxygen vacancy with the energy difference being about 2.37 and 2.06 ev, respectively. To understand the interaction between Pt and oxygen vacancies, we have to compare the segregation energy of Pt at the GB with and without a vacancy. The segregation energies of Pt in the vacancy-containing GBs were calculated using PBE and PBE-sol. As shown in Figure S2, the obvious divergences in relative energies appear in the vacancy-containing GBs, especially for the Pt@GB-V O-1 system. Based on the PBE calculations, GB-V O-1 is the most favorable site for Pt segregation, followed by GB-V O-4. The vacancy at the GB enhances the tendency of Pt to the GB with the energy change being about 1.20 ev, indicating the binding energy between Pt and oxygen vacancy is about 1.20 ev. In the PBE-sol calculations, GB-V O-4 is more

4 favorable than others for Pt segregating, followed by GB-V O-2/3. The change of the segregation energy of Pt associated with the oxygen vacancy formed at the V O-4 site is about 1.0 ev. As a result, although the favorable sites for vacancies are different in the Pt@GB, the two functionals predict the same interaction between Pt and oxygen vacancies. Figure S2. The calculated relative solution energies of Pt in the GB with and without vacancies as a function of its position using PBE-sol. The solution energies of Pt inside the bulk are considered as the reference state, i.e. the zero point. In the PBE-sol calculations, when the neutral oxygen vacancies forms at V O-1/2/3 site adjacent to Pt, Pt has four nearest O atoms (Fig. S3 (b)). The charge density difference and the results from Bader-charge analysis are similar to the case of the neutral vacancy formed at V O-2/3 based on the PBE calculations. We obtained almost the same results on the properties of the charge density difference of Pt in the GB-V O-4 from the PBE and PBE-sol calculations. As shown Fig. S3 (c)), there are six nearest O atom surrounded Pt. The charge density difference looks similar to that in the original Pt@GB (Fig. S3 (a)), except for the changes in the bond lengths and bond

5 angles. The Pt-O bonds lengths which are in the GB region decrease by 1.68%, and the other three bonds away from the GB region are increased by 3.0%. Thus, the interactions between Pt and the three O atoms farther away from the GB are weakened. Bader-charge analysis provided the same conclusions. Therefore, the stability of the vacancy-containing Pt@GB is related to the coordination environment of the Pt atom. Figure S3. Charge density differences are shown in two side views for several configurations at the GB. Part (a) is for the Pt@GB, while parts (b) and (c) are for the neutral oxygen vacancy formed at the V O-1 and V O-4 sites, respectively. The charge accumulation and depletion are indicated by the yellow and blue regions, respectively. The isosurface value is e/a.u. 3. Therefore, our results indicate that PBE yields comparable results with PBE-sol for the segregation of Pt and the Pt-oxygen vacancy interaction at the CeO 2 3 (111) GB. 1. Perdew, J. P.; Ruzsinszky, A.; Csonka, G. I.; Vydrov, O. A.; Scuseria, G. E.; Constantin, L. A.; Zhou, X.; Burke, K. Phys. Rev. lett. 2008, 100, (13), Wu, R.; Freeman, A. J.; Olson, G. B. Science 1994, 265, (5170), Geng, W. T.; Freeman, A. J.; Olson, G. B. Phys. Rev. B 2001, 63, (16).