First-principles local density approximation (generalized gradient approximation) +U study of catalytic CenOm clusters: U value differs from bulk

Abstract

Ceria possesses strong catalytic properties for C O ∕ N O x removal and H 2 production. Clusters often show more intriguing functionalities than their bulk counterparts. Here, the geometric and electronic structures of Ce n O m ( n = 1 – 4 , m = 2 n − 1 , 2 n ) clusters are studied for the first time using the projected augmented wave method in density functional theory with detailed assessment of the exchange-correlation functional and the Hubbard parameter U . We note that the U value strongly affects the electronic structures of the oxygen-deficient Ce n O 2 n − 1 clusters, though less so on the stoichiometric Ce n O 2 n . Furthermore, the local density approximation ( LDA ) + U method is more accurate than the generalized gradient approximation + U in describing the localization of the 4 f electrons of the Ce n O m clusters. The calculated vibration frequency of the CeO molecule with the LDA + U ( U = 4 eV ) is 818.4 cm − 1 , in close agreement with experimental values of 820 – 825 cm − 1 for the low lying states. Different optimal U values were noted for the ceria cluster ( 4 eV ) and its bulk ( 6 eV ) , due to quantum-size and geometric effects. The largely reduced formation energy of an oxygen vacancy indicates that the catalytic effect of the Ce n O m clusters are far greater than bulk Ce O 2 .