Ceria (CeO₂) offers unique properties as a heterogeneous catalyst or catalyst support for a number of applications, such as three-way automotive catalysts, preferential CO oxidation, and catalytic oxidation of hydrocarbons. For each of these applications, the use of ceria is motivated by its ability to store and release oxygen, or more generally to readily transition between oxidation states. The addition of low levels of rare-earth or noble metals alters the redox properties and hydrocarbon oxidation activity of ceria-based materials. We use density functional theory, with the inclusion of an on-site Coulombic interaction (DFT+U), to examine the energetics of oxygen vacancy formation and methane oxidation over ceria surfaces with the addition of Zr or Pd. We address the thermodynamic preference for Zr or Pd to substitute into the CeO₂ lattice, with specific emphasis on the relative stability of different phases as a function of temperature and oxidizing conditions. The thermodynamic preference for Zr or Pd to incorporate into the ceria lattice is evaluated by considering the relative energy of different phase combinations including segregated CeO₂ and bulk Zr or Pd phases, segregated CeO₂ and ZrO₂ or PdO phases, Zr or Pd incorporated into a M_xCe_1-xO₂ phase. The relative energy of each configuration is calculated as a function of partial pressure of oxygen (P_O2) and temperature. The incorporation of Zr or Pd into the CeO₂ lattice becomes thermodynamically favorable over segregated configurations at certain temperatures and oxygen partial pressures of relevance for hydrocarbon oxidation. The sensitivity of results to the value of the Hubbard U-term is discussed to rationalize the U value used herein, and to explore the use of DFT+U to accurately represent the electronic structure of ceria-based oxides.

The partial reduction of ceria may occur through the formation of oxygen vacancies, during which cerium atoms are formally reduced from Ce⁴⁺ to Ce³⁺. The inclusion of the Hubbard U-term within the DFT approach corrects for the fact that DFT representations overestimate the preference for Ce 4f electrons to delocalize upon Ce reduction. This reduction results in partial occupation of 4f states, which is realized through the appearance of a “gap state” between the valence band and Ce 4f band in CeO₂. The value of U dictates the position of the gap state, and we calculate the energy gap between this state and the valence band for a series of U values. Oxygen vacancy formation in pure ceria and Zr-substituted ceria results in the reduction of cerium atoms, and we find a linear correlation between vacancy formation energy and U value. However, oxygen vacancy formation in Pd-substituted ceria reduces Pd rather than Ce, and thus the vacancy formation energy is weakly dependent on U value. The adsorption energy of methane, which also leads to reduction of the oxide surface, is more exothermic over Zr-substituted ceria surfaces than over pure ceria, and even more exothermic over Pd-substituted surfaces. These results provide insight into the mechanism by which metal addition alters the redox properties and catalytic activity of ceria. The energetics of reductive process on ceria can be influenced by the value of the Hubbard U-term, which allows for reasonable representations of the electronic structure. These results aid in both interpreting experimental behavior and guiding design of improved ceria-based catalysts.