354
W. Piskorz and F. Zasada
surface undergoes negligible relaxation [120], while the reconstruction of the other
low-index surfaces, (110) [121] and (100) [122], is significant. These surfaces differ
in their reactivity in oxidation (the most active: (110) and (100) [123]) and hydrogenation processes (the most active: (111)). Thus, the understanding of the morphology
of the nanograins is crucial in the prediction of the catalytic properties.
It was also shown by Fronzi et al. [124] that, when moving from the oxygen-rich
to oxygen-lean environment, the most stable surface is in the following sequence:
the stoichiometric CeO 2 (111), the CeO 2 (111) surface with subsurface O vacancies,
and, eventually, the CeO 2 (111): Ce-terminated surface.
Morphology
The ceria lattice parameters have been successfully calculated using either pure GGA
(PBE), GGA+U, or hybrid functionals (HSE06) with discrepancies, comparing to
experimental values [125, 126], in the range of ca. +1.1%, +1.5%, or −0.4%,
respectively [27]. The computational values of bulk properties of CeO 2 and Ce 2 O 3
are also summarised in the article by Fronzi et al. [124]. According to them, the
calculated cerium sesquioxide Ce 2 O 3 lattice constant a for LDA and GGA functionals
is 3.86 Å and 3.77 Å, respectively, what is close to the results of Da Silva et al. [27]
(3.83 Å and 3.77 Å respectively), who also report that the hybrid DFT and LDA+U
give comparable lattice constants to those obtained by pure DFT, while application
of GGA+U worsens the lattice parameters (too large a and c values).
The issue of the equilibrium morphology of ceria nanograins was studied computationally by many researchers, e.g. ref. [123, 124, 127, 128], to mention a few.
Although theoretical investigations on stoichiometric bulk ceria and gas–surface
reactions are readily available, there are very scarce computational analyses about the
similar systematic studies of moderately cerium oxide particles of catalytic relevance.
Chen et al. employed simulated annealing method to find the structures of (CeO 2 ) n
(n = 1, . . . , 5) with global minimum potential energy, and refined obtained structures
with DFT simulation showing that the coordination numbers of Ce and O atoms are
very different from those in bulk CeO 2 material [129]. By combination of DFTbased modelling and spectroscopic studies, Burrow et al. revealed that the cerium
oxide gas-phase clusters show structural motifs reminiscent of the bulk ceria, in
contrast to TMI oxide clusters [130]. Theoretical study of Wu et al. indicates that
the Ce n O
−
2n+1 clusters contain oxygen-centred radicals (O
−• ) and the nature of the
spin density distributions within the clusters controls the experimentally observed
size-dependent reactivity. The reactivity of the oxygen-deficient cerium oxide cluster
ions, Ce n O
+
m (n = 2, . . . , 10, m 2n), was investigated using DFT method, and it
was shown that CeO 2 NPs are able to extract oxygen atoms from CO, CO 2 , NO, N 2 O,
and O 2 in the gas phase [131]. It was also revealed that oxygen transfer reactions may
be explained in terms of the energy balance between the bond dissociation energy
of the oxygen-containing molecule and the oxygen affinity of the oxygen-deficient
cerium oxide cluster.
W. Piskorz and F. Zasada
surface undergoes negligible relaxation [120], while the reconstruction of the other
low-index surfaces, (110) [121] and (100) [122], is significant. These surfaces differ
in their reactivity in oxidation (the most active: (110) and (100) [123]) and hydrogenation processes (the most active: (111)). Thus, the understanding of the morphology
of the nanograins is crucial in the prediction of the catalytic properties.
It was also shown by Fronzi et al. [124] that, when moving from the oxygen-rich
to oxygen-lean environment, the most stable surface is in the following sequence:
the stoichiometric CeO 2 (111), the CeO 2 (111) surface with subsurface O vacancies,
and, eventually, the CeO 2 (111): Ce-terminated surface.
Morphology
The ceria lattice parameters have been successfully calculated using either pure GGA
(PBE), GGA+U, or hybrid functionals (HSE06) with discrepancies, comparing to
experimental values [125, 126], in the range of ca. +1.1%, +1.5%, or −0.4%,
respectively [27]. The computational values of bulk properties of CeO 2 and Ce 2 O 3
are also summarised in the article by Fronzi et al. [124]. According to them, the
calculated cerium sesquioxide Ce 2 O 3 lattice constant a for LDA and GGA functionals
is 3.86 Å and 3.77 Å, respectively, what is close to the results of Da Silva et al. [27]
(3.83 Å and 3.77 Å respectively), who also report that the hybrid DFT and LDA+U
give comparable lattice constants to those obtained by pure DFT, while application
of GGA+U worsens the lattice parameters (too large a and c values).
The issue of the equilibrium morphology of ceria nanograins was studied computationally by many researchers, e.g. ref. [123, 124, 127, 128], to mention a few.
Although theoretical investigations on stoichiometric bulk ceria and gas–surface
reactions are readily available, there are very scarce computational analyses about the
similar systematic studies of moderately cerium oxide particles of catalytic relevance.
Chen et al. employed simulated annealing method to find the structures of (CeO 2 ) n
(n = 1, . . . , 5) with global minimum potential energy, and refined obtained structures
with DFT simulation showing that the coordination numbers of Ce and O atoms are
very different from those in bulk CeO 2 material [129]. By combination of DFTbased modelling and spectroscopic studies, Burrow et al. revealed that the cerium
oxide gas-phase clusters show structural motifs reminiscent of the bulk ceria, in
contrast to TMI oxide clusters [130]. Theoretical study of Wu et al. indicates that
the Ce n O
−
2n+1 clusters contain oxygen-centred radicals (O
−• ) and the nature of the
spin density distributions within the clusters controls the experimentally observed
size-dependent reactivity. The reactivity of the oxygen-deficient cerium oxide cluster
ions, Ce n O
+
m (n = 2, . . . , 10, m 2n), was investigated using DFT method, and it
was shown that CeO 2 NPs are able to extract oxygen atoms from CO, CO 2 , NO, N 2 O,
and O 2 in the gas phase [131]. It was also revealed that oxygen transfer reactions may
be explained in terms of the energy balance between the bond dissociation energy
of the oxygen-containing molecule and the oxygen affinity of the oxygen-deficient
cerium oxide cluster.