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Descriptor Analysis in Methanol Conversion on Doped CeO2(111):
Guidelines for Selectivity Tuning
Marçal Capdevila-Cortada* and Núria López*
Institute of Chemical Research of Catalonia (ICIQ), The Barcelona Institute of Science and Technology, Av. Països Catalans, 16,
43007 Tarragona, Spain

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S
* Supporting Information

ABSTRACT: Descriptors are crucial to systematize and optimize the activity,
selectivity, and stability of catalysts. Adsorption energies have usually been
taken as the main representative parameters that can summarize reaction
energies and activation barriers for simple reactions on relatively simple
reaction sites. However, more chemically sound terms, which can be directly
mapped to experiments, would be more desirable. In addition, larger
molecules with more than one potentially active position and complex sites,
such as the acid−base pairs present in oxides, are typically beyond the scope
provided by common linear-scaling methods. In the present work, we have
analyzed the selectivity of the conversion of a polyfunctional molecule on a
complex oxide that presents both acid−base and redox chemistry. The
conversion of methanol to formaldehyde or CO on isovalently doped
ceria(111) has been taken as an example. The selectivity toward CO is
triggered by the competition between formaldehyde desorption and C−H cleavage. Our results show that, by introduction of
dopant cations, the activation energy of the first H stripping of formaldehyde can be decreased so that its conversion becomes
favorable over desorption for Zr- and Hf-doped systems and expanded lattice ceria. More importantly, desorption is controlled by
geometric and acid−base factors, whereas C−H cleavage is exclusively electronically governed through acid−base and redox
factors. Thus, both geometric and electronic structure parameters are needed to optimize the performance of ceria to attain the
desired selectivity. Selectivity is then estimated by a collective descriptor of the surface that incorporates the ensemble size, acid−
base, and redox contributions that can be directly compared to experimental values. In addition, this scaling relationship reduces
the error associated with more traditional energy-based descriptors. We anticipate that the present scheme can be extended to
metal oxides and other polyfunctionalized catalysts.
KEYWORDS: doped ceria, scaling methods, multivariable descriptors, methanol oxidation, formaldehyde oxidation, DFT

1. INTRODUCTION
A detailed understanding of all elementary steps that contribute
to the mechanism of a given catalytic process is essential to
reach a reliable rational catalyst design. From this mechanistic
information it is possible to identify the crucial steps from
which a set of descriptors can be extracted. The ultimate goal of
obtaining these descriptors is to provide a reliable method for
predicting whether a given catalyst is suitable for a specific
process by using a straightforward and costless approach. The
complete set of reactions might be more complex than is
usually assumed, as it should include all the alternative sideproduct formation paths that are detrimental to performance.
The obtained descriptors can then be used in large-scale
predictions to seek the most suitable catalyst for the given
process of interest.1−4 Thermodynamics for adsorption can be
retrieved through linear-scaling relationships by connecting
adsorption energies to those of the central heteroatom of the
adsorbate. This method has been reported for metals,5 oxides,
sulfide, and nitride surfaces,6 as well as for structural defects.7,8
However, the adsorption of large molecules such as
polyalcohols on metal surfaces requires collective variables
© 2015 American Chemical Society

that account for the interactions both with the surface and
within the adsorbate.9 Similar multivariable descriptors were
also required to generalize the adsorption of acids, esters, and
ethers on metals.10,11 Oxygen vacancy formation energy has
been sometimes identified as the crucial step for oxidation
processes on metal oxides,12,13 and thus it has been the focus of
studies on descriptors. Accordingly, an extensive database for
oxygen vacancy formation on oxides and perovskites has been
recently reported. It shows that vacancy formation follows a
collective variable that contains bond strength and electronic
structure data.14,15
Kinetic parameters can also be obtained through the use of
descriptors. The Brønsted−Evans−Polanyi (BEP) relationships
state that, when a group of transition states are similar in
nature, a change in the thermodynamics of the reaction, ΔE, is
proportionally accompanied by a change in the kinetics and
hence the activation energy, Ea, of this reaction.16,17 From this
Received: July 9, 2015
Revised: September 24, 2015
Published: September 28, 2015
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Figure 1. Top view of the (111) facet for undoped CeO2, and Zr-, Hf-, and Th-doped CeO2. Nonequivalent distances are shown in Å. The outmost
oxygen (in red), cerium (in light green), and dopant (Zr in silver gray, Hf in blue, and Th in dark green) layers are highlighted, while the rest of the
atoms are shown dashed.

present work, we have used DFT+U on geometrically modified
CeO2(111) surfaces, either by isovalent doping or by applying
strain. The selectivity toward CO was analyzed through
chemical descriptors that demonstrate the complex balance of
geometric and acid−base contributions in the adsorption of
formaldehyde and redox and acid−base properties in C−H
activation. Our results point out the relevance of chemical
descriptors that can be directly mapped to experimentally
derived properties and, when appropriately combined, provide
a more accurate representation than traditional BEP and TSS
methodologies.

early proposal as a starting point, several alternative
formulations that end up correlating with a single adsorption
energy have been derived.18−23 In particular, the transition state
scaling (TSS) relationships correlate the transition state energy
with the energy of the initial or the final state of the reaction.
Among oxides, CeO2 constitutes a unique catalytic system:24
although it is based on a rare-earth metal, it is relatively
abundant and cheap and can be easily doped. This material
presents a significant charge separation and a surface acid and
basic character. Moreover, cerium cations easily cycle between
the Ce(IV) and Ce(III) oxidation states, rendering a low
vacancy formation energy.25 This feature, together with easy
bulk transport, allows ceria to release or absorb oxygen under
reducing or oxidizing conditions, a phenomenon commonly
known as oxygen storage capacity.26 As a consequence, ceria
has a prominent role in oxidations, either as a catalyst or as a
support in reactions including the water-gas shift (WGS),27,28
SO2 oxidation,29,30 and the Deacon process.31 In addition,
cerium oxide also presents high activity and selectivity in
hydrogenations.32
Several of the ceria catalytic properties can be improved by
using dopants.33 Low-valence dopants induce long-range
effects, whereas tetravalent dopants mostly produce local
effects.34 Among all dopants, tetravalent ions do not imply a
major change in the electronic structure but only a structural
change, the impact of which will depend on the dopant atomic
radius and its concentration. Trivalent cations (e.g., Sm, Gd, La,
and Y) increase the ionic conductivity of ceria,35−38 thus
improving the performance for use in solid oxide fuel cells.39
Ionic conductivity and oxygen vacancy formation on doped
ceria have been extensively analyzed using density functional
theory (DFT).40−49 Another trivalent dopant, Ga, enhances the
activity of alkyne semihydrogenation,50 and Zr, Hf, Pd, or Cu
impurities improve the catalytic activity of the WGS51,52 and
PROX53,54 reactions. On the other hand, isovalent Hf and Zr
dopants enhance the catalytic activity in the Deacon process in
comparison to trivalent dopants, even if it is an oxidation
reaction (HCl).55 Other processes such as NO2 reduction,56
NH3 oxidation,57 and CO2 methanation58−60 have also been
computationally analyzed.
The present study focuses on the catalytic conversion of
methanol on doped ceria(111) to formaldehyde and CO. The
conversion of methanol is considered an ideal test for
characterizing the catalytic behavior of metal oxides, as it
entails acid−base and redox steps61,62 while being one of the
smallest possible surrogates for a large class of biomass-derived
compounds. Methanol decomposition is structure sensitive and
produces formaldehyde on CeO2(111) and CO/H2 on the
(100) facet,63,64 due to the competition between C−H cleavage
in formaldehyde in comparison to its desorption.65 In the

2. COMPUTATIONAL DETAILS
All calculations were performed at the DFT+U level using the
Vienna ab initio simulation package (VASP, version 5.3.3),66,67
with the Perdew−Becke−Ernzerhof (PBE)68 functional. The
self-interaction error was diminished by the addition of an
effective Hubbard U term, following the approach of Dudarev
et al.69 This Ueff value was set to 4.5 eV, as it was been
previously proven to provide satisfactory results.55,70−72
Projector-augmented wave (PAW) pseudopotentials73 were
used to describe the core electrons with a plane-wave cutoff
energy of 500 eV for the valence electrons (i.e., 5s, 5p, 4f, 6s for
Ce atoms, 2s, 2p for O and C atoms, 4s, 4p, 5s, 4d for Zr atoms,
5s, 5p, 6s, 5d for Hf atoms, and 6s, 6p, 5f, 7s for Th atoms).
Ceria presents a fluorite structure, with a lattice parameter of
aexp = 5.411 Å.74 The lattice parameter was optimized using a
dense Γ-centered 7 × 7 × 7 k-point mesh that leads to a value
of acalc = 5.497 Å, in good agreement with both the
experimental value and previous computational studies.75 The
(111) surface was modeled as p(2 × 2) with periodically
repeated slabs consisting of three O−Ce−O layers separated by
15 Å of vacuum space, which was optimized using a Γ-centered
3 × 3 × 1 k-point mesh. The five outermost single layers and
the adsorbates were allowed to relax, whereas the rest of the
atoms were kept fixed to their bulk positions. Doped (111)
slabs of Ce0.75M0.25O2, where M = Zr, Hf, Th, were obtained by
substituing one cerium atom for one dopant M atom in the
bulk structure’s unit cell. For the description of Th atoms, an
effective U term, Ueff, of 4.5 eV was also used. The doped bulk
structures were then optimized as specified before (the
resulting lattice parameters are acalc,Zr = 5.404 Å, acalc,Hf =
5.394 Å, and acalc,Th = 5.544 Å), and the slabs were built
likewise. Alternatively a lattice strain was applied to the surface
slab on the two periodic dimensions (x and y). Strains of 1%
and 2% expansions and contractions were performed. Density
of states (DOS) calculations were obtained using a denser Γcentered 13 × 13 × 1 k-point mesh.
Transition states were located by means of the climbing
image nudged elastic band (CI-NEB) method.76 In some
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Figure 2. Energy profiles for the conversion of (left) methanol to formaldehyde and (right) formaldehyde to CO upon adsorption on pristine and
doped ceria(111). All relative energies are collected in Table S1 in the Supporting Information. Inset: schematic representation of all intermediates
and transition states involved in each process.

reactions on the undoped facet (Figure 2). The reaction
mechanism for methanol conversion to formaldehyde consists
of the steps

particular cases, the CI-NEB was complemented by the
improved dimer method (IDM).77 The nature of all reaction
minima and transition states was confirmed by performing
numerical frequency analyses (step size ±0.01 Å).

CH3OH + 2* → CH3O* + H*

CH3O* + * → HCHO* + H*

(R2)

HCHO* → HCHO + *

3. RESULTS AND DISCUSSION
3.1. Structural Analysis. The doping of the CeO2(111)
facet has been addressed through two strategies. The bulk
structure was optimized with 25% concentration of dopant,
namely Zr, Hf, and Th, in order to evaluate the effects brought
about by structural variations and the direct impact of dopant−
adsorbate interactions. Additionally, 1% and 2% expansion and
contraction strains were also applied to the undoped bulk
structure to assess the sole effects triggered by structural
variation. Zr- and Hf-doped ceria induce contraction to the unit
cell (1.69 and 1.87%, respectively), whereas Th-doped ceria
expands the cell by 0.86%. Upon doping, surface Ce−O
distances do not increase or decrease evenly, as shown in Figure
1. These distances involving oxygens only surrounded by Ce
atoms slightly decrease (increase) after doping that induces cell
contraction (expansion). The other lattice O atoms are
surrounded by two Ce atoms and the dopant, where the
Ce−O distances greatly increase on Zr and Hf doping, while
they only slightly increase on Th-CeO2. The M−O distances,
where M is the dopant, increase for Th−O in comparison to
Ce−O, whereas they drastically decrease for Zr−O and Hf−O.
It is worth noting that explicit doping with smaller ionic radius
dopants, despite the overall lattice contraction, induces certain
surface motifs with effective expansion.
The electronic structure, analyzed through the band structure
and density of states (DOS), is also altered upon doping. In
particular, the projected DOS (PDOS) of the O(2p) band
corresponding to lattice oxygens is shifted from the Fermi level
reference (Figure S1 in the Supporting Information). The
center of the O(2p) band is shifted toward lower (more stable)
energies for all explicitly doped surfaces: −119, −223, and
−100 meV for Zr-, Hf-, and Th-CeO2. Contraction also shows a
−104 (1%) to −119 meV (2%) O(2p) band shift, while
expanded ceria shifts 51 and 54 meV toward higher energies for
1% and 2% expansions. This fact is directly related to the acid−
base character and therefore activity of the surface.
3.2. Reactivity. The conversion of methanol to formaldehyde and CO was investigated on the (111) facet of ceria
for all aforementioned doping strategies and compared to the

(R1)

(R3)

Methanol adsorbs on ceria dissociatively and leads to a
chemisorbed methoxy group and a surface hydroxyl (R1). This
first step occurs in a dual acid−base site, formed by an
accessible Ce(IV) and a lattice oxygen.61 This is followed by a
C−H cleavage that conducts to chemisorbed formaldehyde and
another surface hydroxyl group (R2). This process entails a
redox step, where the methoxy is oxidized and two surface
Ce(IV) are reduced to Ce(III). The methoxy is partially
reduced in the associated transition state, leading to a radicaloid
species, where one electron is delocalized over the C, H, and
the surface O, and one single Ce(IV) is reduced to Ce(III), as
noted also in ceria and other reducible oxides.65,78−80 In the
final step, formaldehyde desorbs from the surface to the gas
phase (R3). For ceria(111), the barrier for the C−H bond
breaking is 1.03 eV and the reaction is exothermic by 1.78
eV.65,78 The resulting chemisorbed HCHO binds rather
strongly, 1.23 eV, therefore allowing an eventual subsequent
conversion to CO.
The doped facets present two major sites, depending on
whether the adsorbate’s oxygen interacts with the surface
dopant (M···O) or cerium (Ce···O). Since methanol
adsorption is 0.2 eV larger on the M···O site, the reaction
was only considered there. Doped Zr-CeO2 and Hf-CeO2
enhance the dissociative adsorption of methanol. The next
step, C−H cleavage, presents energy barriers of 1.04 and 1.19
eV, respectively, similar to the undoped values. The transition
states exhibit the same nature as on the pristine surface. On the
other hand, the adsorption energies of all intermediates on ThCeO2 are almost identical with those on the pristine surface,
whereas the activation energy for the C−H bond breaking is
0.23 eV higher. The results on the doped surfaces are in
contrast with those obtained after applying strain to the pristine
lattice. Despite the lattice contraction caused by Zr and Hf
doping, an even contraction hinders this particular reaction. In
contrast, lattice expansion favors the reaction, since the energy
barrier for the C−H cleavage is only 0.80 eV for +2% and the
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Therefore, the use of dopants (Zr, Hf) allows modifying the
selectivity of the most stable facet of ceria for the particular
process of methanol conversion. Whereas pristine ceria(111)
converts methanol to formaldehyde, Zr-CeO2 and Hf-CeO2
allow its evolution to CO, which would help to enable the
concomitant production of syngas (CO + H2). Moreover, an
even lattice expansion also allows the conversion of methanol
to CO. This would be the case, for instance, of a rather high
concentration of subsurface doping using dopants larger than
cerium.

reaction energy is 0.3 eV higher than those on the undoped and
the doped facets. The results obtained on the doped facets are
in good agreement with the surface distribution depicted in
Figure 1, where Zr-CeO2 and Hf-CeO2 exhibit motifs of
effective Ce−O expansion.
The conversion of formaldehyde to CO on ceria (111)
comprises the elementary steps
HCHO + * → HCHO*

(R3′)

HCHO* + * → CHO* + H*

(R4)

CHO* + * → CO* + H*

(R5)

CO* → CO + *

(R6)

4. DESCRIPTOR ANALYSIS
The correlation between thermodynamics and kinetics can be
assessed by means of the Brønsted−Evans−Polanyi (BEP) and
the transition state scaling (TSS) relationships, as we stated in
the Introduction. The BEP and TSS relationships for the
selectivity-determining step of this reaction, i.e. the first C−H
cleavage of formaldehyde, are shown in Figure 3. Although the
standard BEP correlating Ea and ΔE provides a reasonable
description of this process, the correlation is improved when
ETS is presented as a function of the initial state energy EIS. This
result is in good agreement with the exothermic nature of the
reaction and the similar geometries of the initial and transition
states.
The individual deviations from some of the points obtained
through the BEP and TSS relationships are, however,
exceedingly large for a sufficiently accurate prediction. For
instance, in the BEP activation energies with an 0.05 eV span
(topmost points) correspond to reaction energies ranging from
−2.12 to −1.84 eV. Similarly, on both TSS Zr- and Hf-CeO2
present ETS values close to the +2% result, whereas their EIS and
EFS values differ by 0.20 and 0.35 eV, respectively. In addition,
for the TSS relationships, strained CeO2 and Th-CeO2 exhibit a
visible linear correlation (red lines), although the trend is not
followed by Zr- and Hf-CeO2 (blue lines). The ultimate
consequence is that the overall fittings are reasonable but the
predictions on different areas of the graphs are affected by
errors that can amount up to 0.21 eV, which limits the
predictive power of the BEP and TSS for the individual points.
It is worth pointing out that BEP and TSS relationships allow
energy-based predictions, which are a useful tool for
computations but are not so straightforward to obtain from
experiments.
Adsorption and reactivity are usually described in terms of
geometric and electronic contributions.81 In the following, we
try to incorporate descriptors that encompass these terms, thus
extending the electronic structure analysis on the metal d-band
center to more complex multifunctional surfaces.82 The
concepts behind our formulation have been qualitatively
described, but to date they lack a complete, physically sound
quantification. Grasselli suggested seven pillars that govern
selectivity in heterogeneous oxidation catalysis: 83 host
structure, metal−oxygen (M−O) bond, lattice oxygen, redox,
multifunctionality of active sites, site isolation, and phase
cooperation. Inspired by these fundamental pillars, we have
developed a set of descriptors that have been employed to
describe the two steps that trigger the selectivity of methanol
conversion to CO: i.e. formaldehyde desorption and HCHO
first C−H stripping. Our set of descriptors include the
following.
(a) Ensemble area, A, which accounts for the host structure
in Grasselli’s nomenclature. In particular, we considered the

Formaldehyde chemisorbs on ceria (R3′). This is the reverse
process of the last step of the previous reaction (R3). Upon
adsorption, formaldehyde suffers a C−H bond breaking that
leads to chemisorbed CHO and a surface hydroxyl through an
overall redox step (R4), where again two surface cerium cations
are reduced to Ce(III). The transition state also involves the
reduction of one Ce(IV) to Ce(III), where the other electron is
delocalized over the C, H, and the surface oxygen.65 This is
followed by a second C−H cleavage that results in physisorbed
CO and a second surface hydroxyl group (R5). Finally, CO
desorbs from the partially hydroxylated surface to the gas phase
(R6). On the undoped facet, the energy barrier for formaldehyde C−H cleavage is 1.19 eV. This process is 0.32 eV
more demanding than formaldehyde desorption, and this fact is
ultimately responsible for the experimentally observed formaldehyde selectivity.65 Then, the energy required for the second
C−H stripping is 1.60 eV, through an endothermic reaction of
0.98 eV. The final CO desorption only demands 0.13 eV.
The adsorption of formaldehyde on Zr-CeO2(111) and HfCeO2(111) is 0.5 eV stronger than that on the undoped facet.
It presents binding energies of −1.33 and −1.36 eV,
respectively (Figure 2). For HCHO conversion, the M···O
site was also considered, since it is the starting point after
methanol conversion and this site is 0.4 eV more stable than
the Ce···O site. The energy barrier to C−H bond breaking is
1.22 eV on both doped facets, similar to the case for the
undoped surface. However, given the high binding energy of
formaldehyde in these doped surfaces, C−H cleavage requires
0.11 (Zr) and 0.15 eV (Hf) less energy than HCHO desorption
and therefore both processes will compete. Th-CeO2 exhibits
values similar to those of the undoped surface for the
adsorption and the first C−H stripping. The reaction then
proceeds with similar adsorption energies for I2 and CO on the
three doped and the undoped facets. The energy barrier of the
second C−H cleavage increases for the three doped surfaces in
comparison to the undoped surface, increasing up to 2.0 eV for
Zr- and Th-CeO2 and to 2.2 eV for Hf-CeO2. Similar to what
was observed for the methanol conversion to formaldehyde,
lattice contraction exhibits lower binding energies of all
intermediates and higher energy barriers and thus impedes
the decomposition of formaldehyde to CO. All intermediates,
in contrast, bind more tightly on the expanded lattice. The first
C−H cleavage requires 0.4 eV less energy on +2% than on
pristine CeO2, whereas the second H stripping demands 0.2 eV
more energy. On this expanded surface, formaldehyde
desorption is 1.13 eV and the energy barrier for its first C−H
bond breaking is 0.98 eV, hence enabling the conversion of
formaldehyde to CO.
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(d) Basicity of lattice oxygens, O(2p), equivalent to
Grasselli’s lattice oxygen. This term is obtained as the center
weighted average in the PDOS of the O(2p) band.
(e) Redox character, red, which refers to Grasselli’s redox. It
is estimated to be the energy difference between the surface and
the reduced surface upon the addition of one electron, with the
concomitant reduction of one Ce(IV) to Ce(III), after
relaxation.84
Grasselli’s site isolation would be required to analyze possible
condensation routes in methanol conversion,85 but it does not
apply to the present analysis. Similarly, phase cooperation does
not contribute either, due to the stability of the CeO2 phase in
comparison to other methanol conversion catalysts such as
MoOx.86,87
In summary, we consider three geometric (i.e., ensemble
area, M−O distance, and lattice parameter) and two electronic
(i.e., basicity and redox) descriptors. The values for all of these
parameters for all the surfaces in the study are collected in
Table S2 in the Supporting Information. Geometric descriptors
have provided important insights in describing the adsorption
and dissociation of CO on metal surfaces.88,89 Acid−base
properties have been shown to control adsorption and reactions
on metal oxides90 and metals,91 whereas the redox character
controls the conversion of methanol to formaldehyde on
vanadia supported on ceria.12,79 It is worth noting that these
properties are easily accessible. Geometric parameters can be
obtained by performing a simple calculation on the optimized
cell and can be derived experimentally from the XRD data or
more accurately from adsorption measurements (BET). The
acid−base character can be experimentally measured by the
adsorption of probe molecules (CO or NH3), monitored
through FTIR spectroscopy,92 whereas the redox properties can
be investigated experimentally by temperature-programmed
reduction (TPR) or oxygen isotopic exchange.93
The performance of these five descriptors has been evaluated
for the two competing steps: formaldehyde desorption energies,
Edes, and the C−H activation barriers, Ea (see Figures S3 and S4
in the Supporting Information). Among all the individual
descriptors, Edes only correlates well with the ensemble area.
The rationale behind this is that a larger ensemble area permits
a better accommodation of chemisorbed formaldehyde, thus
increasing its desorption energy. The same magnitude,
however, does not describe the activation energy for the next
step. For C−H stripping, three of the descriptors, redox
character, lattice parameter, and the M−O distance, provide a
relevant correlation. This is due to the fact that the transition
state TS2 encompasses the reduction of a surface Ce(IV) to
Ce(III), and since the Ce(III) cation is larger than Ce(IV), it is
stabilized in larger cells. The other descriptors considered are
unable to correlate either the formaldehyde desorption energy
or the activation energy of its first C−H cleavage. Although
these descriptors are based on fairly accessible properties of the
catalyst, they do not actually improve the previous results
provided by the BEP and TSS relationships.
As some of the steps seem to have a mixed component, twovariable descriptors were then investigated. Formaldehyde
chemisorbs on a lattice oxygen, forming an O−C bond, and
the first C−H stripping forms a surface hydroxyl, suggesting
that oxygen basicity may be relevant on both steps. Thus, our
collective descriptors embrace the main descriptor previously
identified together with the corresponding oxygen basicity. As
can be seen, this approach provides a notable improvement on
both correlations (see Figure 4). Hence, the basicity of lattice

Figure 3. (top) Brønsted−Evans−Polanyi (BEP) and (bottom)
transition state scaling (TSS) relationships for the first C−H cleavage
of formaldehyde. The fittings were done in two different ways:
including all the points (blue) and excluding Zr and Hf (red). MAEs
are given in eV.

area comprised in the triangle formed by three lattice oxygens
(Figure S2 in the Supporting Information).
(b) Lattice parameter, a, which would be equivalent to the
host structure in Grasselli’s formulation. It is a direct
consequence of the expansion or contraction introduced by
doping.
(c) M−O distance, rM−O, accounting for the M−O bond in
Grasselli’s formulation. This is obtained as the mean value of
the three M−O distances of the oxygen of interest, where M is
either Ce or the dopant.
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Hence, the energy of the transition state for the C−H
stripping is the value that ultimately determines selectivity:
positive ETS translates to Ea > Edes (i.e., MeOH reacts toward
HCHO), whereas a negative value implies Ea < Edes (i.e.,
MeOH converts into CO). Substitution of eqs 1 and 2 into eq
3 results in a general description of ETS based on our previous
findings:
E TS = δ[red] − αA + (γ − β)[O(2p)] + (λ − ζ )

(4)

The values previously obtained fitting the two-variable
descriptors on eqs 1 and 2 can be introduced in eq 4 (Figure
5). Our results manifest a clear improvement in comparison to

Figure 5. ETS as a function of a three-variable descriptor, embracing
redox, site area, and oxygen basicity, based on eq 4 and the previous
fitted relations.

Figure 4. (top) Edes and (bottom) Ea as a function of a two-variable
descriptor, embracing the site area and oxygen basicity for formaldehyde desorption and the redox character and oxygen basicity for
the first C−H cleavage.

the TSS relationships, which also provided a prediction for ETS.
This is seen in the individual errors and the MAE. The ultimate
consequence is that the present results reduce the errors by
more than 0.1 eV, thus improving the predictive power of the
scaling relationships. For instance, this error reduction would
lead to the improvement of predicted rates by 1 order of
magnitude (for a reaction at 500 K).

oxygens plays a prominent role in both steps, despite not being
able to correlate any of these magnitudes as a single descriptor.
The two-variable description improves the previous scaling
methods, halving the mean absolute errors (MAE). Furthermore, this approach naturally includes Zr- and Hf-CeO2, which
were outliers in the BEP and TSS relationships. The collective
descriptor including the redox character provided a better result
than that with the lattice parameter or the M−O bond,
although they also improved the correlation yielded by the
single-variable descriptor (Figure S5 in the Supporting
Information). It is finally worth noting that these two-variable
descriptors accurately represent Grasselli’s multifunctionality of
the active sites.
To summarize, formaldehyde desorption energy is described
as a sum of ensemble area and basicity contributions and its
first C−H cleavage activation energy as a sum of redox and
basicity contributions:
Edes = αA + β[O(2p)] + ζ

(1)

Ea = δ[red] + γ[O(2p)] + λ

5. CONCLUSIONS
In the present work, a thorough analysis of potential descriptors
for the chemistry on oxides has been carried out focusing on
the selective dehydrogenation of methanol on doped
ceria(111), by means of density functional theory. This
methodology can help to assign these effects in a structured
manner and to upgrade wide concepts such as acidity, basicity,
ensemble, and redox to descriptors that can be mapped to
calculated quantities and/or experiments with probe molecules.
To prove the principle, we took methanol decomposition on
the pristine surface, where methanol selectively converts to
formaldehyde due to the high activation energy for its first C−
H cleavage in comparison to its desorption. In contrast, we
showed that, when properly doped, the final product can be
CO. For this mechanism we compared the traditional BEP and
TSS linear relationships to the performance of newly defined
descriptors that summarize three geometric and two electronic
parameters that can be directly mapped to experiments. Our
work evidences the difficulties of adaptability of BEP and TSS
relationships and single descriptors to explain the complexity of
multifunctionalized intermediates and mixed sites on the
surfaces. BEP and TSS are still able to provide rather acceptable

(2)

As mentioned before, the competition between these two
steps triggers the selectivity in methanol conversion. Given the
definition of Ea, these two variables are related by the transition
state energy ETS:
Ea = E TS − E IS = E TS + Edes

(3)
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correlations, but the associated individual errors can exceed 0.1
eV; in addition, there is a notable underperformance for doped
Zr- and Hf-CeO2 in comparison to the rest of the surfaces.
Instead, with the chemical descriptors, formaldehyde desorption energy is described by geometric and acid−base
contributions, whereas its first C−H stripping is driven by
redox and acid−base contributions. With these rules, the
unique magnitude that ultimately controls selectivity, ETS, can
be retrieved. On the basis of the obtained equations, ETS is
expressed as a function of the aforementioned terms (ensemble,
redox, acid−base), providing a correlation that improves the
previous value obtained by means of the BEP-derived TSS
relationships. The collective descriptor improves the correlation
and diminishes the associated errors below 0.1 eV. This means
that for a typical reaction at 500 K the error in the predicted
rates is diminished by 1 order of magnitude.
The present results open a new concept for the use of linear
scaling relationships to complex surfaces as oxides and
polyfunctionalized molecules.

■

ASSOCIATED CONTENT

S
* Supporting Information

The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acscatal.5b01427.
Projected DOS (PDOS) of the O(2p) band corresponding to lattice oxygens of pristine and doped CeO2(111),
ensemble area descriptor, formaldehyde desorption
energy (Edes) and activation energy (Ea) for the first
C−H cleavage as a function of the five descriptors, Ea as a
function of the two-variable descriptor that includes
lattice parameter or M−O bond and oxygen basicity, all
relative energies of Figure 2, and values for all descriptors
considered in this work (PDF)

■

AUTHOR INFORMATION

Corresponding Authors

*E-mail for M.C.-C.: mcapdevila@iciq.es.
*E-mail for N.L.: nlopez@iciq.es.
Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS
This research has been supported by an ERC Starting Grant
(ERC-2010-StG-258406), the Ministerio de Economı ́a y
Competitividad-MINECO (CTQ2012-33826), and the Generalitat de Catalunya-AGAUR (SGR-2014-SGR-145). We
acknowledge the BSC-RES for providing generous computational resources.

■

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