A Theoretical Study of Surface Reduction
Mechanisms of CeO
2
ACHTUNGTRENNUNG(111) and (110) by H
2
Hsin-Tsung Chen,
[b]Yong Man Choi,*
[a]Meilin Liu,
[a]and M. C. Lin*
[b, c]1. Introduction
Ceria (CeO2) is an important catalyst in various industrial and environmental applications such as a three-way automotive ex-haust catalyst (TWC),[1] oxygen storage,[2] the oxidation of
hy-drocarbons[3] and CO,[4] and the decomposition of alcohols[5]
and aldehydes.[6]Moreover, rare-earth-doped CeO
2, such as
ga-dolia-doped ceria (GDC), has also been used as an electrolyte for low-temperature solid oxide fuel cells (SOFCs).[7] To
under-stand the catalytic properties of both pure CeO2 and metal/
CeO2 materials, it is imperative to examine the redox surface chemistry. Although many studies regarding the defect chemistry of CeO2 have been conducted,[8] its reduction
pro-cesses have been scarcely examined. In particular, the defect chemistry of CeO2 under H2 atmosphere has been studied by
various experimental techniques, such as temperature-pro-grammed reduction (TPR)[9–11]and NMR.[12]On the basis of
ex-perimental results obtained by using TPR and temperature programmed desorption mass spectrometry (TPD-MS), Bernal and coworkers[13]reported that H
2–CeO2interactions are a
sur-face process rather than the hydroxylation and incorporation of hydrogen into the bulk, as proposed by Bruce and cowork-ers.[10] Although numerous theoretical investigations on bulk
CeO2, its surfaces (including reduced ceria),[14–20]and the
inter-actions of atomic H with CeO2ACHTUNGTRENNUNG(111) and (110)[18]have been
re-ported, to the best of our knowledge, the mechanisms of H2–
CeO2interactions have not been adequately addressed. In this
study, we report the reduction mechanisms of CeO2ACHTUNGTRENNUNG(111) and
(110) surfaces by H2 using periodic density functional theory
(DFT) methods. In particular, to properly characterize the elec-tronic structure of CeO2, the DFT + U method[15, 20–23] was
ap-plied. Detailed potential-energy surfaces for all low-lying reac-tion pathways are reported.
Computational Methods
We performed DFT plane-wave calculations using the Vienna ab initio simulation package (VASP)[24] with the projector-augmented
wave method (PAW).[25] The exchange–correlation function was
treated with the generalized gradient approximation (GGA) of the Perdew–Wang (PW91) functional, which has been shown to work well for bulk and surface properties of CeO2.
[22, 26]
A 400 eV cut-off energy that allows convergence to be 0.01 eV in the total energy was used. The Brillouin zone was sampled with the (6 C 6 C 6) and (6 C 6 C 1) Monkhorst–Pack[27]
mesh k-points for bulk and surface calculations, respectively. To avoid interactions between slabs, all
[a] Dr. Y. M. Choi, Prof. Dr. M. Liu
Center for Innovative Fuel Cell and Battery Technologies School of Materials Science and Engineering
Georgia Institute of Technology, Atlanta, GA 30332 (USA) Fax: (+ 1) 404-894-9140
E-mail: yongman.choi@mse.gatech.edu [b] Dr. H.-T. Chen, Prof. Dr. M. C. Lin
Department of Chemistry, Emory University 1515 Dickey Drive, Atlanta, GA 30322 (USA) Fax: (+ 1) 404-727-6586
E-mail: chemmcl@emory.edu [c] Prof. Dr. M. C. Lin
Center for Interdisciplinary Molecular Science
National Chiao Tung University, Hsinchu, 30010 (Taiwan) Fax: (+ 886) 3-571-2179
Supporting information for this article is available on the WWW under http://www.chemphyschem.org or from the author.
Reaction mechanisms for the interactions between CeO2ACHTUNGTRENNUNG(111) and
(110) surfaces are investigated using periodic density functional theory (DFT) calculations. Both standard DFT and DFT + U calcu-lations to examine the effect of the localization of Ce 4f states on the redox chemistry of H2–CeO2 interactions are described. For
mechanistic studies, molecular and dissociative local minima are initially located by placing an H2molecule at various active sites
of the CeO2surfaces. The binding energies of physisorbed species
optimized using the DFT and DFT + U methods are very weak. The dissociative adsorption reactions producing hydroxylated sur-faces are all exothermic ; exothermicities at the DFT level range from 4.1 kcal mol1 for the (111) to 26.5 kcal mol1 for the (110) surface, while those at the DFT + U level are between 65.0 kcal
mol1 for the (111) and 81.8 kcal mol1for the (110) surface.
Pre-dicted vibrational frequencies of adsorbed OH and H2O species
on the surfaces are in line with available experimental and theo-retical results. Potential energy profiles are constructed by con-necting molecularly adsorbed and dissociatively adsorbed inter-mediates on each CeO2surface with tight transition states using
the nudged elastic band (NEB) method. It is found that the U cor-rection method plays a significant role in energetics, especially for the intermediates of the exit channels and products that are partially reduced. The surface reduction reaction on CeO2ACHTUNGTRENNUNG(110) is
energetically much more favorable. Accordingly, oxygen vacan-cies are more easily formed on the (110) surface than on the (111) surface.
slabs were separated by a vacuum space greater than 15 G. As de-picted in Figure 1 a, CeO2 has a fluorite structure in which each
cerium cation is surrounded by eight equivalent oxygen ions, while each oxygen ion is surrounded by a tetrahedron of four
equivalent cerium ions.[28]
The CeO2ACHTUNGTRENNUNG(111) and (110) surfaces were
modeled as periodically repeated slabs consisting of twelve and six atomic layers, respectively, which represent pACHTUNGTRENNUNG(p3C1) and pACHTUNGTRENNUNG(1C2) lateral cells, respectively (Figure 1 b). The bottom six and three atomic layers of the CeO2ACHTUNGTRENNUNG(111) and (110) surfaces, respectively,
were unrelaxed and set to the estimated bulk parameters, while the remaining layers were fully relaxed. In this study, the DFT and DFT + U methods[29]
were performed in order to accurately correct the strong on-site Coulomb repulsion of Ce 4f states on reduced ceria surfaces.[15, 20, 22, 23]
For the DFT + U calculations, a series of bulk calculations were carried out by varying the U value from 0.0 to 7.0 eV. As Jiang and coworkers[15]
reported, we found the optimal values of U and J are 7.0 and 0.7 eV, respectively. In this study, we calculated adsorption energies according to Equation (1):
DEads¼ E½slab þ adsorbateðE½slab þ E½adsorbateÞ ð1Þ
where E[slab+adsorbate], EACHTUNGTRENNUNG[slab], and E[adsorbate] are the calcu-lated electronic energies of adsorbed species on a ceria surface, a bare ceria surface, and a gas-phase H2molecule, respectively. The
nudged elastic band (NEB) method[30]
was applied to locate transi-tion states, and potential energy surfaces (PESs) were constructed accordingly. All transition states were identified by the number of imaginary frequencies (NIMG) with NIMG = 1.
2. Results and Discussion
2.1. Bulk and Clean Surfaces of CeO2and Gas-Phase H2, OH,
and H2O Molecules
To ensure the validity of the surface models displayed in Fig-ure 1 b, we first compared our lattice parameters, total density of states, and formation energy of an oxygen vacancy with lit-erature values. As compiled in Table 1, the calculated lattice parameters of bulk CeO2 using the DFT and DFT + U methods
are in very good agreement with the experimental value of 5.411 G.[33] Shown in Figure 2 is the calculated total density of
states for bulk CeO2. While the calculated energy gaps of
O 2p!Ce 4f and O 2p!Ce 5d at the DFT level are 1.8 eV and
5.5 eV, respectively, those by the DFT + U method with the values of U and J of 7.0 and 0.7 eV, respectively, are 2.3 eV and 5.1 eV (see Table S1 in the Supporting Information). It is known that the O 2p!Ce 5d band gapis less important compared to the O 2p!Ce 4f band gap.[15] Similar to previous studies,[19]
the formation energy of an oxygen vacancy within the bulk was also estimated based on the reaction CeO2!CeO2x+
1/2 O2(g). The vacancy energy from the DFT method is
114.1 kcal mol1, whereas that from DFT + U is 92.9 kcal mol1,
providing a better agreement with the experimental value of 94.5 kcal mol1.[34]Shown in Table S2 (see the Supporting
Infor-mation) are the surface energies of CeO2ACHTUNGTRENNUNG(111) and (110)
surfa-ces estimated in units of J m2according to Equation (2):[19]
Esurf¼
1
2SðEslabEbulkÞ ð2Þ
where Esurf, S, Eslab, and Ebulk represent the surface energy, the
surface area, and the calculated electronic energies of the slab and the bulk, respectively. Thus, a lower surface energy corre-sponds to a more stable surface. As summarized in Table S2, our predicted relaxed surface energies for the (111) and (110) surfaces are 0.60 and 0.96 J m2, respectively, which are in line
with other DFT results.[16, 19]In addition, it is consistent with the
experimental data by Lyons et al.,[35]who verified that the (111)
facet of CeO2is the most stable. As Jiang et al.[15]reported, the
surface-energy difference calculated by the DFT and DFT + U methods for perfect CeO2 is negligible. Furthermore, we
esti-mated the adsorption energies of H2O–CeO2ACHTUNGTRENNUNG(111) interactions
with various adsorption configurations similar to those of
Hen-Figure 1. a) The fluorite structure of CeO2. b) Slab models for cubic CeO2ACHTUNGTRENNUNG(111) and (110) surfaces.
Table 1. Experimental and calculated lattice parameters for CeO2. Methods Lattice parameters [G] this work 5.419,[a]5.436[b] GGA-DFT 5.480,[31] 5.470[16] LDA-DFT 5.390,[31] 5.370[16] HF 5.385,[14]5.546[33] Experimental 5.411
[a] Calculated at the DFT level. [b] Calculated at the DFT + U level.
Figure 2. Total density of states of bulk CeO2calculated at the DFT and DFT + U levels. A and B correspond to the calculated energy gaps for O 2p!Ce 4f and O 2p!Ce 5d, respectively.
derson et al.,[38] as shown in Figure 3, since the experimental
data of H2O–CeO2interactions are well-established in the litera-ture.[39] As displayed in Figure 3, our calculated adsorption
en-ergies from DFT vary from 4.4 to 11.9 kcal mol1. Notably,
the ab initio adsorption energies of the stable Ce-end-on and Ce-parallel configurations (11.4 and 11.9 kcal mol1,
respec-tively) are consistent with that of12.2 kcal mol1reported by
Henderson et al.[38]and are slightly different from the values of
13.1–14.1 kcal mol1 measured by Prin et al.[39] In addition,
the adsorption energies of the Ce-end-on and Ce-parallel con-figurations are in line with recent theoretical results of 12.9 and 13.4 kcal mol1, respectively, by Kumar and Schelling.[40]
As summarized in Table 2, predicted geometrical parameters and vibrational frequencies of gas-phase H2, OH, and H2O in a 15 G cubic box are in line with available experimental and the-oretical data.
2.2. Locationof Surface Intermediates
In order to initially locate possible intermediates, an H2
mole-cule was placed on various CeO2 surface sites as shown in
Figure 4, where I and II correspond to the atop site of Ce and O atoms, respectively, while III and IV represent the bridging sites of CeCe and OO bonds, respectively. The atop site on a sublayer oxygen atom is represented by V. For the CeO2ACHTUNGTRENNUNG(110)
surface, IV-S and IV-L correspond to the short and long OO bond-bridging sites, respectively. Furthermore, the H2molecule
was placed both vertically and horizontally (Figure 4 a) on each CeO2 surface site—except the V conformation on CeO2ACHTUNGTRENNUNG(111)—
corresponding to v and h, respectively. Figures S1 and S2 (in the Supporting Information) display various adsorbed H2
spe-cies on CeO2ACHTUNGTRENNUNG(111) and (110). As compiled in Table S3, the ad-sorption energies of these adsorbed H2 species on the (111) and (110) surfaces at the DFT and DFT + U levels are small, and the energy difference between the DFT and DFT + U methods for the stoichiometric surfaces is insignificant (< 0.3 kcal mol1).
In particular, because the calculated energies are within the average bond-energy errors of the GGA method (2.0 kcal mol1)[45]and to ensure the existence of initial
inter-mediates for mechanistic studies on CeO2ACHTUNGTRENNUNG(111) and (110), we carried out additional minimum-energy path (MEP) calculations at the DFT + U level using II-v-(111) and IV-S-v-(110) configura-tions with the lowest adsorption energy among intermediate states optimized on the (111) and (110) surfaces, respectively. Shown in Figure S3 are shallow wells with adsorption energies of approximately0.5 and 1.4 kcal mol1, indicating that the
II-v-(111) and IV-S-v-(110) configurations are van der Waals in-termediates. It should be noted that the DFT method used in this study may not be suitable to describe long-range disper-sion interactions (van der Waals interactions),[46] and to the
best of our knowledge, van der Waals complexes for H2–CeO2 interactions have not been experimentally reported. However, we assume that these complexes are physisorbed intermedi-ates,[47] which are adsorbed by molecular adsorption and
con-nectable to chemisorbed local minima. These minima are relat-ed to dissociative adsorption processes, giving rise to LM2 and LM3 and LM5 and LM6 in Figures 5 and 6, to be discussed in the following section. Furthermore, to test the coverage effects of H2–surface interactions, we compared 0.5- and
1.0-monolay-er cov1.0-monolay-erage using the II-v-(111) (LM1) configuration; the ad-sorption energy difference is negligible ( 0.1 kcal mol1).
2.3. ReactionMechanisms
The decomposition of H2on CeO2may occur via a stepwise
re-action mechanism, in which H2 first adsorbs at a favorable
active Ce4 + or O2site. Then, the adsorbed H
2species directly
dissociates, followed by the formation of OH species. Surface OH species can further diffuse on the reduced CeO2 surface
and interact with each other to produce H2O, which is
accom-Figure 3. Optimized geometries and adsorption energies for H2O adsorption on the CeO2ACHTUNGTRENNUNG(111) surface at the DFT level.
Table 2. Geometrical parameters and vibrational frequencies of gas-phase H2, OH, and H2O calculated by the DFT method.
H2 OH H2O Symmetry D1V C1V C2V Calcd Exptl[41] Calcd Exptl[42] Calcd Exptl[43, 44] r(OH or HH) [G] 0.743 0.740 0.986 0.970 0.957 0.972 qACHTUNGTRENNUNG(HOH) [8] – – – – 104.5 104.7 vasym[cm 1] – – 3642 3738 3856 3738 vsym[cm1] 4435 4400 – – 3741 3436 vbend[cm1] – – – – 1585 1392
Figure 4. a) Schematics of vertical and horizontal configurations of H2on CeO2surfaces. b) Topviews of active sites on the CeO2ACHTUNGTRENNUNG(111) and (110) surfa-ces (see text for details).
panied by the reduction of Ce4 + to Ce3 +and the formation of
an oxygen vacancy when H2O desorbs.
We performed both the standard DFT and DFT + U calcula-tions to mapout the potential energy surfaces (PESs). Figure 5 and Figure S4 illustrate the geometries of optimized intermedi-ates and products and transition stintermedi-ates for the H2reactions on the CeO2ACHTUNGTRENNUNG(111) and (110) surfaces, respectively, using the DFT and DFT + U methods. Compiled in Table 3 are the predicted relative energies at the DFT and DFT + U levels. These results
show that our calculated energetics, except for the initial inter-mediates LM1 and LM4, are significantly influenced by the in-clusion of U–J, leading to different structural relaxations during H2–surface interactions. In particular, to examine the energy difference between DFT and DFT + U, LDOS (local density of states) calculations for adsorbed hydrogen species and Ce and O ions on the toplayer of the LM2 intermediate were p er-formed. As illustrated in Figure S5, Ce 5d and Ce 4f states above the Fermi level may be a main factor for the large energy difference between DFT and DFT + U methods for the H2–CeO2 interactions. In the following, we will discuss
mecha-nistic details based on the DFT + U results.
2.3.1. CeO2ACHTUNGTRENNUNG(111) Reduction by H2
The reduction of the CeO2ACHTUNGTRENNUNG(111) surface by H2 may occur
ac-cording to the reaction pathway shown in Figure 6 a. The initial interaction of the hydrogen molecule approaching the metal oxide surface is a van der Waals attraction, leading to LM1, II-v-(111), with a physorsorption energy of 0.5 kcal mol1. In the
optimized LM1 structure, the HH distance is 0.754 G, and the HOsurfacedistance is 2.489 G. In the following stepof the
reac-tion, the LM1 complex has to overcome a 5.7 kcal mol1
activa-tion barrier for the dissociaactiva-tion process via TS1, producing the OH-containing LM2 intermediate with the equivalent OH bonds of 0.972 G. At TS1, the breaking HH bond is 1.156 G. The interaction of the two OH species in LM2 via TS2 with a
Figure 5. Optimized geometries with selected bond lengths [G] and angles [8] of intermediates, transition states and products for the H2–CeO2 interac-tions. The values in parentheses are calculated by the DFT method; other-wise the values are from the DFT + U level.
Figure 6. Reaction pathways for the reduction of a) CeO2ACHTUNGTRENNUNG(111) and b) CeO2ACHTUNGTRENNUNG(110) by H2along with corresponding schematic energy profiles for the H2–CeO2interactions at the DFT + U level. The values in parentheses are those calculated by the DFT method.
Table 3. Relative energies [kcal mol1] of the intermediates, transition states, and products of CeO2+H2interactions calculated at the DFT and DFT + U levels. Species or reaction DFT DFT + U CeO2ACHTUNGTRENNUNG(111)+O2 0.0 0.0 LM1 0.7 0.5 LM2 4.1 65.0 LM3 27.0 15.0 TS1 9.3 5.2 TS2 29.1 8.1 TS3 31.1 24.8 P111 + H2O 36.9 3.6 CeO2ACHTUNGTRENNUNG(110)+O2 0.0 0.0 LM4 1.6 1.4 LM5 26.5 81.8 LM6 8.4 65.1 LM7 22.4 28.3 TS4 13.4 10.9 TS5 3.2 53.2 TS6 16.1 15.2 TS7 23.7 27.3 P110 + H2O 28.7 22.9
high reaction barrier of 57 kcal mol1
leads to the formation of a chemisorbed H2O molecule in LM3, with an overall endo-thermicty of 50.0 kcal mol1. The breaking OH bond and form-ing HO bond in TS2 are 2.908 G and 1.288 G, respectively. As mentioned above, Ce4 +cations can be reduced by the
forma-tion of H2O species, and subsequently generating an oxygen vacancy (V, see Figure 5). The LM3 intermediate can also be formed by abstracting a surface oxygen via TS3 with a high re-action barrier of 25.3 kcal mol1, bringing about concurrent O
H bond-forming and HH bond-breaking processes with their corresponding bond lengths of 0.981 and 1.815 G. This path-way is less favorable than the process via TS1 due to its higher reaction barrier. Eventually, the LM3 intermediate can barrier-lessly dissociate to produce P111 (Figure 5), and a gas-phase H2O molecule with a 11.4 kcal mol1endothermicity, leading to
nonstoichometric CeO2 and an oxygen vacancy. The overall exothermicity of this process is 3.6 kcal mol1 at the DFT + U
level.
2.3.2. CeO2ACHTUNGTRENNUNG(110) Reduction by H2
Similar to LM1 on the CeO2ACHTUNGTRENNUNG(111) surface, the H2–CeO2ACHTUNGTRENNUNG(110) complex, IV-S-v-(110), (LM4) can be formed with a binding energy of 1.4 kcal mol1(Figure 6 b). In the LM4 complex, the
HH distance is 0.752 G, and the two HO bonds are 2.817 and 2.864 G. As summarized in the reaction pathway in Fig-ure 6 b, there are two possible pathways to produce P110 (Figure 5) and H2O.
The surface H2species in LM4 can dissociate to generate the more stable OH-containing LM5 intermediate by overcoming an activation barrier of 12.3 kcal mol1at TS4. The breaking H
H bond length in TS4 is 0.853 G and the two OH bonds in LM5 are essentially the same length (0.993 G and 0.991 G). One of the H atoms in LM5 can migrate to a neighboring O atom via TS5 with a 28.6 kcal mol1 barrier, thus producing LM6,
which has a new OH bond of 0.991 G. The OH bond lengths of LM6 (0.972 and 0.991 G) are slightly different. The energetic difference between these two OH-containing intermediates, LM5 and LM6, stems from hydrogen bonding in these struc-tures; there are two possibilities for hydrogen bonding with neighboring O atoms in LM5 but only one such possibility in LM6 (see Figure 5). In addition to the aforementioned reaction pathway, LM6 can also be formed directly via TS6 with a reac-tion barrier of 16.6 kcal mol1. At TS6, the cleaving H
H bond is 0.812 G, which is 0.06 G longer than in LM4, indicating that TS6 is an early transition state. The two OH groups in LM6 can interact to form LM7 through TS7, in which the H atom of the OH grouplying parallel to the surface migrates to the OH group bonded perpendicular to the surface, generating a chemisorbed H2O molecule and an oxygen vacancy with a
re-action barrier of 38 kcal mol1. Finally, the weakly bound H 2O
species in LM7 can desorb from the surface with an endother-micity of 5.4 kcal mol1. This process takes place with an overall
exothermicity of 22.9 kcal mol1 [about 19 kcal mol1 lower
than that of CeO2ACHTUNGTRENNUNG(111)], producing P110 and H2O.
MEP calculations clearly show that the reduction mechanism of CeO2 by H2 occurs via a stepwise reaction, as discussed
above. The molecular-level interpretation using quantum chemical calculations supports the reaction mechanism pro-posed on the basis of experimental results.[9]For the reduction
of CeO2ACHTUNGTRENNUNG(111) by H2, the predicted highest barrier, 25 kcal mol1,
is in good agreement with the 27.5 kcal mol1 activation
energy reported by Al-Madfa et al.[48] A detailed rate-constant
prediction based on the potential-energy profiles and experi-mental data will be carried out in the future.
2.4. Analysis of Vibrational Frequencies of Adsorbed OH and H2O Species
Compiled in Table 4 is a summary of predicted vibrational fre-quencies of adsorbed OH (LM2, LM5, and LM6) and H2O (LM3
and LM7) species at the DFT + U level. A variety of OH and H2O
species were observed using Fourier transform infrared (FTIR) spectroscopy.[49]It was reported that the bands at 3710, 3660,
and 3600 cm1 are attributed to one-, two- and
three-coordi-nated configurations, respectively, of adsorbed OH species on CeO2surfaces, while those in the range of 3400–3450 cm1are
related to H-bonded OH species.[49] The bands at 3686, 3140,
and 1640 cm1and 3686, 3620, and 1595 cm1are assigned to
a H-bonded and non-H-bonded H2O species, respectively.[50]
The calculated OH frequencies of LM2 (3641 and 3650 cm1)
are consistent with the experimental value of 3600 cm1 for
the three-coordinated configuration of an adsorbed OH spe-cies and a theoretical result of 3627 cm1 by Vicario and
et al.[18] The calculated OH frequencies of LM5 (3258, and
3234 cm1) are slightly different from the theoretical value of
3100 cm1,[18] assigned to an H-bonded OH species using
ex-perimental data[49]of 3400–3450 cm1. The predicted
vibration-al frequencies of the OH stretching of LM6 (3636 and 3266 cm1) are close to those of H-bonded H
2O-like species
(3686 and 3140 cm1).[50]Calculated vibrational frequencies
cor-responding to asymmetric, symmetric, and bending modes of the H2O-like species of LM3 (3657, 3605, 1535 cm1,
respective-ly) are in line with experimental values (3686, 3620, 1595 cm1,
respectively),[50] while the frequencies found for LM7 (3814,
3694, and 1591 cm1) are close to those of a gas-phase H 2O
molecule (Table 2), implying that LM7 has more product char-acter than LM3.
Table 4. Predicted vibrational frequencies of OH or H2O species on CeO2.[a]
Surface Intermediate Adsorbed species This work [cm1] Literature[18] [cm1] ACHTUNGTRENNUNG(111) LM2 OH 3641, 3650 3627 ACHTUNGTRENNUNG(111) LM3 H2O 3657, 3605, 1535 – ACHTUNGTRENNUNG(110) LM5 OH 3258, 3234 3100 ACHTUNGTRENNUNG(110) LM6 OH 3636, 3266 – ACHTUNGTRENNUNG(110) LM7 H2O 3814, 3694, 1591 –
3. Conclusions
The reduction mechanisms of the CeO2ACHTUNGTRENNUNG(111) and (110) surfaces
by H2 have been elucidated using periodic DFT and DFT + U calculations. The validity of the surface models was verified by estimating various properties, such as the lattice parameters, total density of states of bulk CeO2, the formation energy of an oxygen vacancy, adsorption energies of H2O on CeO2ACHTUNGTRENNUNG(111), and the surface stability of CeO2ACHTUNGTRENNUNG(111) and (110), in line with avail-able literature data. For the mechanistic studies, molecular and dissociative local minima were initially located by placing an H2 molecule at various active sites on each CeO2 surface. The adsorption energies of the DFT and DFT + U methods of these molecular adsorption intermediates are small, whereas the dis-sociative adsorption processes producing hydroxylated surfa-ces are energetically favored, with exothermicity increasing from 65.0 kcal mol1on the (111) surface to 81.8 kcal mol1on
the (110) surface. The DFT + U methodology produced more accurate energetics, especially on the reduced ceria surfaces. The potential-energy profiles for these surface reactions have been constructed by mapping out their MEPs using the NEB method. The intermediates of the molecular and dissociative adsorption on each CeO2 surface were connected by the NEB method with well-defined transition states. It was found that the reduction of the CeO2 surface takes place via a stepwise mechanism: adsorption/dissociation of H2 with the formation of OH species and desorption of H2O along with the reduction of Ce4 +and the formation of an oxygen vacancy. According to
the MEP calculations, the less stable (110) surface is energeti-cally more favorable. Our estimated vibrational frequencies of adsorbed OH and H2O species agree well with available experi-mental and theoretical results.
Acknowledgements
We acknowledge the use of CPU’s from National Center for High-Performance Computing, Taiwan, supported by INER under con-tract No. NL 940251. M.C.L. also wants to acknowledge the sup-port from the MOE ATP program, Taiwan Semiconductor Manu-facturing Co. for the TSMC Distinguished Professorship and Taiwan National Science Council for the Distinguished Visiting Professorship at the Center for Interdisciplinary Molecular Science, National Chiao Tung University, Hsinchu, Taiwan. We greatly ap-preciate the reviewer’s valuable comments and suggestions.
Keywords: density functional calculations · reaction mechanisms · reduction · surface chemistry · vibrational spectroscopy
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Received: September 21, 2006 Revised: February 15, 2007 Published online on March 21, 2007
![Table 3. Relative energies [kcal mol 1 ] of the intermediates, transition states, and products of CeO 2 + H 2 interactions calculated at the DFT and DFT + U levels](https://thumb-ap.123doks.com/thumbv2/9libinfo/7955794.157973/4.892.77.429.524.988/table-relative-energies-intermediates-transition-products-interactions-calculated.webp)
![Table 4. Predicted vibrational frequencies of OH or H 2 O species on CeO 2 . [a]](https://thumb-ap.123doks.com/thumbv2/9libinfo/7955794.157973/5.892.457.824.442.589/table-predicted-vibrational-frequencies-oh-h-species-ceo.webp)
