Using the DFT+U method, i.e., first principles density functional theory calculations with the inclusion of on-site Coulomb interaction, the effects of Pd doping on the O vacancy formation energy (E(vac)) in CeO(2) has been studied. We find that E(vac) is lowered from 3.0 eV in undoped ceria to 0.6 eV in the Pd-doped compound. Much of this decrease can be attributed to emerging Pd-induced gap states above the valence band and below the empty Ce 4f states. These localized defect states involve the Pd ion and its nearest neighbors, which are also the main acceptors of the extra electrons left on reduction. The effect of the Pd dopant on the geometric structure is very modest for CeO(2) but considerable for CeO(2-x).

One great challenge for supercapacitor is to achieve high energy capacity and fast charge/discharge rates simultaneously. Porous graphene with large surface area is a promising candidate for electrode materials of supercapacitor. Using first-principles calculations and non-equilibrium Green's function technique, we have explored the formation energies, mechanical properties, diffusion behaviors and electrical conductance of graphene sheets with various hole defects and/or nitrogen doping. Interestingly, graphene sheets with pyridinic-like holes (especially hexagonal holes) can be more easily doped with nitrogen and still retain the excellent mechanical properties of pristine graphene that is beneficial for the long cycle life. Porous graphene electrode with moderate hole diameter of 4.2-10 Å facilitates efficient access of electrolyte and exhibit excellent rate capability. In addition, doping with nitrogen as electron donors or proton attractors leads to charge accumulation and generates higher pseudocapacitance. Transmission coefficients of N-doped graphene sheets with pyridinic-like holes are only moderately reduced with regard to that of pristine graphene and are insensitive to the detailed geometry parameters. Overall, N-doped graphene with pyridinic-like holes exhibits exciting potentials for high performance energy storage in supercapacitor devices.

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The effects of noble metal (NM) dopants (NM = Pt, Rh) on the structural and electronic properties of ceria are studied using a density functional theory (DFT) method, with the inclusion of on-site Coulomb interaction (DFT+U). It is found that these NM dopants give rise to large perturbations of the atomic and electronic structures of ceria and induce metal-induced gap states at the Fermi level suitable for accommodating extra electrons, thereby lowering the reduction energy of ceria and making the NM-doped cerias more reducible than pure ceria. This mechanism for facilitating the reduction of ceria is different from that of Zr-doped ceria where the increased reducibility is largely due to the structural distortions and not to electronic modifications.