“This document is the Accepted Manuscript version of a Published Work that appeared in final form in
ACS Catalysis, copyright © American Chemical Society after peer review and technical editing by the
publisher. To access the final edited and published work see
http://pubs.acs.org/doi/abs/10.1021/acscatal.5b01427“

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), Barcelona Institute of Science and Technology (BIST),
Av. Països Catalans, 16, 43007 Tarragona, Spain

Keywords: doped ceria; scaling methods; multivariable descriptors; methanol
oxidation; formaldehyde oxidation; DFT.
ABSTRACT: Descriptors are crucial to systematize and optimize activity, selectivity,
and stability of catalysts. Adsorption energies have usually been taken as the main
representative parameter 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.
Besides, larger molecules with more than one potentially active position and complex
sites, like 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 towards CO is triggered by the competition between formaldehyde
desorption and C-H cleavage. Our results show that, by introducing 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, 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
to more traditional energy-based descriptors. We can anticipate that the present
scheme can be extended to metal oxides and other polyfunctionalized catalysts.

	
  

1

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 (or more generally a
material) is suitable for a specific process by using a straightforward and costless
approach. The complete set of reactions might be more complex than it is usually
assumed, as it shall include all the alternative side-product 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 like
polyalcohols on metal surfaces requires collective variables that account for the
interactions both with the surface and within the adsorbate.9 Similar multivariable
descriptors were also required to generalize 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, ∆E, is
proportionally accompanied by a change in the kinetics, hence the activation energy,
Ea, of this reaction.16,17 Starting from this early proposal, 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 albeit based on a rareearth metal, it is relatively abundant, 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 the easy bulk

	
  

2

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
support in reactions including the water-gas shift (WGS),27,28 SO2 oxidation,29,30 or 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 Lowvalence dopants induce long-range effects, whereas tetravalent dopants majorly
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, or Y) increase the ionic conductivity of ceria,35–38 thus improving the
performance when used 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 semi-hydrogenation,50 and Zr, Hf, Pd, or Cu impurities improve the catalytic
activity of the WGS51,52 or the PROX53,54 reactions. On the other hand, isovalent Hf or
Zr dopants enhance the catalytic activity in the Deacon process more than trivalent
dopants, even if it is an oxidation reaction (HCl).55 Other processes like NO2
reduction,56 NH3 oxidation,57 or 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 entitles acid-base and
redox steps61,62 whilst 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 compared to its desorption.65 In
the present work, we have used DFT+U on geometrically modified CeO2(111) surfaces,
either by isovalent doping or by applying strain. The selectivity towards 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.

	
  

3

2. COMPUTATIONAL DETAILS
All the 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 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 7x7x7 k-point mesh that
leads to a value of acalc = 5.497 Å, in good agreement both with the experimental value
and previous computational studies.75 The (111) surface was modeled as p(2x2) 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 3x3x1 k-point mesh. The five
outermost single layers and the adsorbates were allowed to relax whereas the rest of
atoms were kept fixed to their bulk positions. Doped (111) slabs of Ce0.75M0.25O2, where
M = Zr, Hf, or 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;
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 Γ-centered 13x13x1 k-point mesh.
Transition states were located by means of the climbing image nudged elastic band
(CI-NEB) method.76 In some particular cases, the CI-NEB was complemented with 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).
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

	
  

4

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 are surrounded by
two Ce and the dopant, where the Ce-O distances majorly increase on Zr and Hf
doping, while they slightly do on Th-CeO2. The M-O distances, where M is the dopant,
rise for Th-O compared 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 are shifted from the Fermi level reference
(Figure S1). The center of the O(2p) band is shifted towards 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%) -119 (2%) meV O(2p) band shift, while
expanded ceria shift 51 and 54 meV towards higher energies for 1 and 2% expansions.
This fact is directly related to the acid-base character and therefore activity of the
surface.

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 grey, Hf in blue, and Th in dark green) layers are highlighted, while the rest
of atoms are shown dashed.

3.2. Reactivity. The conversion of methanol to formaldehyde and CO were
investigated on the (111) facet of ceria for all aforementioned doping strategies, and
compared to the reactions on the undoped facet (Figure 2). The reaction mechanism
for methanol conversion to formaldehyde consists of the following steps:

	
  

5

CH3OH + 2* → CH3O* + H*

(R1)

CH3O* + * → HCHO* + H*

(R2)

HCHO* → HCHO + *

(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 to 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. On the contrary, lattice expansion favors it, since the energy barrier
for the C-H cleavage is only 0.80 eV for +2% and the reaction energy is 0.3 eV higher
than 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 ZrCeO2 and Hf-CeO2 exhibit motifs of effective Ce-O expansion.

	
  

6

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. Inset: schematic representation of all intermediates and transition states
involved in each process.

The conversion of formaldehyde to CO on ceria (111) comprises the following
elementary steps:
HCHO + * → HCHO*

(R3’)

HCHO* + * → CHO* + H*

(R4)

CHO* + * → CO* + H*

(R5)

CO* → CO + *

(R6)

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 the ultimate 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.

	
  

7

The adsorption of formaldehyde on Zr-CeO2(111) and Hf-CeO2(111) is 0.5 eV
stronger than 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 undoped surface. However, given the high binding
energy of formaldehyde in these doped surfaces, C-H cleavage requires 0.11 (Zr-) and
0.15 (Hf-) eV less than HCHO desorption and therefore both processes will compete.
Th-CeO2 exhibits similar values to 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 compared to the undoped one, raising
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, on the contrary,
bind tighter on the expanded lattice. The first C-H cleavage requires 0.4 eV less on
+2% than on pristine CeO2, whereas the second H stripping demands 0.2 eV more. 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.
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 syn-gas
(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 bigger than cerium.
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 ∆E 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
	
  

8

with the exothermic nature of the reaction and the similar geometry of the initial and
transition states.

Figure 3. Brønsted-Evans-Polanyi, BEP, relationship (top) and transition state scaling, TSS,
relationships (bottom) 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.

	
  

9

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 close ETS to the +2% result, whereas their EIS and EFS 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 no 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 up to date it lacks a complete physically sounding
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:
§

Ensemble area, A, which accounts for the host structure in Grasselli’s
nomenclature. In particular, we considered the area comprised in the triangle
formed by three lattice oxygens (Figure S2).

§

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.

§

M-O distance, rM-O, accounting for 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.

§

Basicity of lattice oxygens, O(2p), equivalent to Grasselli’s lattice oxygen. This
term is obtained as the center, weighed average, in the PDOS of the O(2p) band.

	
  

10

§

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 compared
to other methanol conversion catalysts like 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 these parameters for all the surfaces in the study are collected in the Supporting
Information, Table S2. Geometric descriptors have provided important insights on
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
Supporting Information, Figures S3-S4. 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 Ce(III) cation is bigger 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.

	
  

11

Figure 4. Edes (top) and Ea (bottom) 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.

As some of the steps seem to have a mixed component, two-variable 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 it can be seen, this approach provides a notable improvement on both correlations,
see Figure 4. Hence, the basicity of lattice oxygens plays a prominent role on 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 those with the
	
  

12

lattice parameter or the M-O bond, although they also improved the correlation yielded
by the single-variable descriptor (Figure S5). It is finally worth noting that these twovariable 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 = α A + β O(2p) + ζ

(1)

Ea = δ red + γ O(2p) + λ

(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 = ETS – EIS = ETS + Edes

(3)

Hence, the energy of the transition state for the C-H stripping is the value that
ultimately determines selectivity: positive ETS translates in Ea > Edes (i.e. MeOH reacts
towards HCHO), whereas a negative value implies Ea < Edes (i.e. MeOH converts into
CO). Substitution of Eq. (1) and (2) on Eq. (3) results in a general description of ETS
based on our previous findings.
ETS = δ red – α A + (γ – β) O(2p) + (λ – ζ)

(4)

The values previously obtained fitting the two-variable descriptors on Eq. (1) and (2)
can be introduced in Eq. (4), Figure 5. Our results manifest a clear improvement
compared to 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 one order of magnitude (for a reaction at 500 K).

	
  

13

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.

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 like
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 compared
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 lack 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
correlations but the associated individual errors can exceed 0.1 eV; besides, there is a
notable underperformance for doped Zr- and Hf-CeO2 compared to the rest of
surfaces. Instead, with the chemical descriptors, formaldehyde desorption energy is
described by a 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. Based on the obtained
equations, ETS is expressed as a function of the aforementioned terms (ensemble,

	
  

14

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 one 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
Supporting Information
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. Values
for all descriptors considered in this work.
AUTHOR INFORMATION
Corresponding Authors
*E-mail: mcapdevila@iciq.es
*E-mail: nlopez@iciq.es
Notes
The authors declare no competing financial interest.
TABLE OF CONTENTS

	
  

15

ACKNOWLEDGEMENTS
This research has been supported by the ERC Starting Grant (ERC-2010-StG258406), the Ministerio de Economía y Competitividad – MINECO (CTQ2012-33826),
and the Generalitat de Catalunya – AGAUR (SGR-2014-SGR-145). We acknowledge
BSC-RES for providing generous computational resources.
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