This is the peer reviewed version of the following article: Nature Materials 18, 1215-1221(2019),
which has been published in final form at https://www.nature.com/articles/s41563-019-0444-y. This
article may be used for non-commercial purposes in accordance with Macmillan Terms

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https://doi.org/10.1038/s41563-019-0444-y

Dynamic charge and oxidation state of Pt/CeO2
single-atom catalysts
Nathan Daelman , Marçal Capdevila-Cortada

and Núria López *

The catalytic activity of metals supported on oxides depends on their charge and oxidation state. Yet, the determination of the
degree of charge transfer at the interface remains elusive. Here, by combining density functional theory and first-principles
molecular dynamics on Pt single atoms deposited on the CeO2 (100) surface, we show that the common representation of a
static metal charge is oversimplified. Instead, we identify several well-defined charge states that are dynamically interconnected and thus coexist. The origin of this new class of strong metal–support interactions is the relative position of the Ce(4f)
levels with respect to those of the noble metal, allowing electron injection to (or recovery from) the support. This process is
phonon-assisted, as the Ce(4f) levels adjust by surface atom displacement, and appears for other metals (Ni) and supports
(TiO2). Our dynamic model explains the unique reactivity found for activated single Pt atoms on ceria able to perform CO oxidation, meeting the Department of Energy 150 °C challenge for emissions.

H

arnessing the properties of metal/oxide structures lies at the
core of materials science, since such interfaces appear in
many technological applications1. At the interface, diverse
amounts of charge may transfer to and from the metal. The excess
(defect) charge can then be employed by the metal to donate
(accept) charge density to (from) reactants and activate them.
Therefore, the charge transfer at the metal/oxide interface controls
the catalytic activity. Counting the number of electrons transferred
becomes imperative, even though it remains difficult to measure
experimentally2–5.
The most interesting metal/oxide interfaces appear when the
metal-to-metal and metal-to-oxide bonds are of similar bond
strength, preventing phase separation. In particular, strong metal–
support interactions6 occur when the oxides acting as a support
partially cover the metal nanoparticle on reduction7,8. However,
if the bond between the metal and the oxide is stronger than that
of the metal itself, atoms can be dispersed onto the oxide matrix9.
Recently, this category has been redefined as single-atom catalysts
(SACs)10,11. Reducible semiconductor oxides are suitable scaffolds
for SACs, and examples with TiO29, FeOx10, Cu2O12 and CeO2 as supports and Au, Pd or Pt as metals have been reported13–15. For scarce
metals, the atom economy deployed by SACs is the most cost effective while guaranteeing selective processes in hydrogenation, oxidation and other reactions10–12,16–18.
Synthesis procedures can target different nanostructures with
variable ratios of exposed (111), (110) and (100) surfaces19,20. On
these ceria supports, Pt nanoparticles can be deposited and, by oxidizing them over an airflow, the volatile PtO2 units disperse out as
single atoms13,21 with loadings of up to 3 wt.%22. Pt atoms have been
found at grain boundaries23 and (111) steps22,24, and atop very small
(<3 nm) nanoparticles25. All of these environments provide a (100)like, square-planar coordination.
The Pt/CeO2 system has been proposed among the most promising candidates to meet the Department of Energy 150 °C challenge13–15,22 (that is, achieving 90% conversion of all critical pollutants
in exhaust emissions at 150 °C26). The catalytic activity is believed to
be related to well-dispersed single atoms or low-nuclearity clusters.
We have gathered the following observations from the literature on

this material: (1) Pt disperses or agglomerates as a function of the
environment14,15,21,27–29; (2) isolated Pt atoms, as prepared, have been
proposed and discarded as potential catalytic centres25,30; (3) shortpulse treatments are needed to render the Pt catalyst active14; and
(4) the nature of the active site remains unknown.
Ceria presents low-energy electron transport mediated by polarons31,32. Therefore, the properties at the metal/ceria interface might
depart from the static interpretations due to electron dynamics.
In the present work, we have performed extensive first-principles
molecular dynamics to unravel the role of charge transfer at the
interface. We identify several metal oxidation and charge states,
reachable at moderate temperatures, and show how they impact the
reactivity and, in particular, how they meet the requirements for
low-temperature (<150 °C) oxidation.
The three lowest-energy surface facets of ceria are (111), (110)
and the polar (100). Platinum adsorption was tested on all of them
using the Perdew–Burke–Ernzerhof functional together with the
Hubbard U correction, PBE+U (Supplementary Table 1). Our results
agree with previous findings21,24,25. The (111) and (110) surfaces cannot stabilize single-atom Pt, thus metal nanoparticles form instead.
Only the (100) surface can stabilize isolated Pt. Therefore, we focus
on these slabs as models for local, nanostructured regions (for example, step or edge sites)24. The low coordination of the surface oxygen
atoms on the oxygen-terminated version increases their mobility33.
As such, (100) restructures into various coexisting patterns at elevated temperatures encountered during pretreatment. Due to this
collection of oxygen distributions, Pt adsorbs on the surface surrounded by a variable number of oxygen ligands (n) in the first coordination sphere, denoted as Pt–nO (n = 2, 3 or 4) (Fig. 1b–d).
When the Pt atom is charged, it transfers one or more electrons
to the surface, which can localize on any cerium atom. All possible
electronic and coordination configurations were sampled via geometry relaxation and we retained only the stable local minima. Their
adsorption energies are shown in Fig. 1a, grouped by coordination
(Pt–nO) and oxidation state (Pt0, Pt+ or Pt2+). To properly assign the
nature of the adsorbed atom, we initially employed Bader charges,
but they are a poor descriptor of oxidation states34. The Pt magnetic
moment (Supplementary Note 1 and Supplementary Fig. 1) and

Institute of Chemical Research of Catalonia, The Barcelona Institute of Science and Technology, Tarragona, Spain. *e-mail: nlopez@iciq.es
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a

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2.0

1.2

1.5

0.7

0.2

1.0

Pt nanoparticle
(2 nm)

∆E (eV)

Eads (eV)

1.7

0.5

Pt b
ulk

–0.3

0
Pt0

b

Pt+
Pt–2O

Pt2+

Pt0

c

Pt+

Pt2+

Pt–3O

Pt0

d

Pt+

Pt2+

Pt–4O

Fig. 1 | Static PBE + U Pt adsorption energies on CeO2 (100). a, Adsorption energy (Eads) of Pt on CeO2 (100), for the different oxidation states (mOSs)
on the surfaces, with distributions stemming from the surface oxygen mobility33. Eads (left y axis) is with respect to the resting 2O surface, while ΔE (right
y axis) is with respect to the most stable Pt–nO configuration. b–d, Three Pt coordination environments (Pt–nO, where n is two (b), three (c) or four
(d) O atoms acting as ligands) appear, where O, Ce and Pt are red, yellow and green, respectively. In a, mOSs are assigned employing Ce magnetization as
a proxy2. Each energy level corresponds to a local minima with a fixed Ce3+ localization (see Supplementary Fig. 3 for examples). Pt–4O only resides in the
Pt2+ state. The horizontal lines present the thermodynamic stability with respect to the Pt bulk and 2-nm-diameter nanoparticle (Supplementary Fig. 4).
Benchmarks with different U values and HSE and RPA functionals are presented in Supplementary Fig. 5 and Supplementary Tables 3–5, and discussed in
the Methods.

X-ray photoelectron spectroscopy (XPS) features (Supplementary
Fig. 2) also depend on the oxidation state. The latter can be mapped
to the experimental XPS spectrum30. The spectral shift from Pt0 to
Pt2+ matches the experimental one35. Note that the peak in between
is assigned there to an intermediate species, which we identify as
Pt+. However, the inhomogeneities and final state effects can make
assignment difficult. Instead, for a most robust fingerprint identification, and considering that single-atom Pt is the sole possible
source of electrons in these models, we can count the number of
Ce3+. This corresponds to the number of electrons lost by the metal
atom. Ce3+ presents a magnetic moment of ~1 μB on the 4f orbitals
(compared with 0 μB of Ce4+), which has already been employed in
the literature2. Therefore, this descriptor is used to trace the metal
oxidation state (mOS) of the Pt atom.
The Pt–4O structure encompasses the lowest energy states of
all geometric and electronic configurations. Its mOS is always confined to Pt2+, with two surface Ce4+ reduced. This behaviour coincides with the coordination rules in coordination chemistry36. The
multiple Ce3+ configurations show a very fine energy distribution,
with spacings of just a few meV (Supplementary Fig. 3). Moreover,
this structure is thermodynamically favourable compared with the
cohesive energy of bulk Pt (horizontal orange line), thus the SAC is
stable against agglomeration37. This explains why Pt–4O species can
be generated from the regular ceria 2O trenches that incorporate
volatile PtO2 species38, making for excellent precursors to the SAC.
Pt–2O is next in energy, with Pt+ being the most stable mOS
within the potential energy manifold associated with this geometry.
Yet, all of these structures are only stable compared with the cohesive
energy of a 2-nm-diameter Pt nanoparticle (Supplementary Fig. 4).
This means that isolated atoms are stable against the initial states of
agglomeration, and even dimerization is unfavoured (Supplementary

Table 2). Comparing all three mOSs on Pt–2O, the (near-)degeneracy
of the electron distributions overlap irrespective of the functional
employed (see Methods, Supplementary Fig. 5 and Supplementary
Tables 3–5). Pt–3O exhibits even larger overlap, but the coordination
as a whole is unstable with respect to agglomeration.
The reason different electronic configurations coexist can be
traced back to the interplay between the ionization potentials of the
isolated gas-phase Pt atoms, surface reduction and distortion, and
changes in electrostatic interactions. This is shown in the Born–
Haber cycle (Supplementary Note 2 and Supplementary Fig. 6),
which starts with an isolated Pt atom and the pristine CeO2 (100)
surface. When Pt adsorbs as Pt0 on the regular 2O surface, the resulting covalent contribution is −1.93 eV, as calculated by the formation
of two Pt–O bonds in Pt(H2O)2. In parallel, the gas-phase ionization
of a Pt atom to Pt+ requires 8.96 eV39. Assuming that the covalent
contribution persists throughout the oxidation steps, the energy
compensation needs to come either from the surface reduction40
and/or the changes in the electrostatic contributions. The Coulomb
interaction41 between the Pt–O and Ce–O pairs stands out with a
value of 9.73 eV. This term is calculated from the charges and the
first neighbour distances of the Pt0–2O and Pt+–2O (Supplementary
Table 6). Adding up these contributions, the step from Pt0 to Pt+ on
Pt–2O is slightly endothermic by 0.3 eV. Indeed, even this simple
thermodynamic cycle highlights that the change in mOS is compensated for by the electrostatic contributions.
To verify whether the charge transfer processes presented above
are kinetically attainable, first-principles Born–Oppenheimer
molecular dynamics (BOMD) were performed on all three Pt–nO
structures, following an approach similar to that described in ref. 42
(Fig. 2, Supplementary Fig. 7 and Supplementary Videos 1–3).
BOMD simulations are computationally very demanding; thus, the
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a
Pt2+

Pt–2O

Pt+

Cetop
A

Pt0

Cetop
B

2Ce3+

Cetop
C

Ce3+

Cetop
D

Ce4+
0

5

10

15

20

25

Time (ps)

b

d

0

Pt-2O frequency (arb. units)

Pt–3O

Cetop
B
Cetop
C
5

10

15

Time (ps)

c
Pt–4O

Lifetime (ps)

1
0

ΣCetop

2

ΣCesub

5
0

5

10
Time (ps)

Pt0 (47.1%)
Pt+ (49.4%)

15
12

Pt2+ (3.5%)

Fig. 2 | BOMD simulations of the Pt–nO systems. a–c, Time evolution at 600 K of the atom-resolved oxidation states of the Pt and surface Ce atoms, for
Pt–2O (a), Pt–3O (b) and Pt–4O (c). The assignment of Ce3+ is discussed in Supplementary Note 3. In c, the oxidation states of Ce are summed together
ÀP top Á
P
Ce
for the top layer
and subsurface layer Cesub , respectively. d, Lifetime distribution of the various mOSs for the Pt–2O structures. The Pt–3O
I
I
trajectory has been included after conversion to Pt–2O (occurring at ~486 K). Trajectories are shown in Supplementary Videos 1–3.

Pt–nO structures were simulated in (2 × 2) supercells. Before that, it
was assessed that the patterns in Fig. 1 are still properly represented
in the smaller cell (Supplementary Fig. 8). Vice versa, a short heating
simulation of Pt–2O in the (3 × 3) slabs also confirmed the polaroninduced charge transfer for larger supercells (Supplementary Video 4).
Figure 2a shows the oxidation state per atom, gathered for the
Pt–2O system over a 27-ps time period after heating up to 600 K.
The simulation exhibits an alternating number of Ce3+ centres,
confirming the dynamic nature of the mOS directly. A visualization of the trajectory is shown in Supplementary Video 1, where
the smooth nature of the electron transfer events can be observed.
An individual transfer is captured in Supplementary Fig. 7, with the
top
top
electron in CeC moving to CeA by temporarily crossing over Pt.
I
I
In the case of Pt–3O (Fig. 2b), the coordination shell starts opening at ~300 K during the heating process. On opening, the oxygen
atoms adopt the regular row pattern of the Pt–2O configuration.
This corroborates that Pt–3O is a metastable state, as found in
Fig. 1a. Remarkably, Pt–3O does not reconstruct to the global minimum, namely Pt–4O. Finally, the Pt–4O system (Fig. 2c) remains
stable with respect to its coordination, and maintains the mOS in
accordance with Fig. 1a. Since the extra surface electrons for Pt–4O
reside in the slab throughout the full simulation, they have the
opportunity to exchange with the subsurface centres reducing the
Ce3+–Ce3+repulsion.
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Considering that Pt–3O transforms into the Pt–2O coordination, their data can be analysed together to illustrate the persistence
of different oxidation and charge states. The frequency histogram
in Fig. 2d presents their lifetimes (that is, the time interval that Pt
resides uninterruptedly in a single mOS (Supplementary Note 3)).
Even though Pt0 and Pt+ take up almost equal portions of time (47
and 49%, respectively), Pt0 can vastly outlive Pt+, with outliers of up
to 5 and 12 ps. Therefore Pt+—the most stable state at 0 K—is no
longer the longest-living species at 600 K.
To understand the origin of the Pt mOS dynamics on the CeO2
(100) surface, the density of states (DOS) of the full Pt–2O system
is decomposed into the metal and oxide units at the geometries of
the different lowest-energy mOSs (Fig. 3). The DOS diagram features the filled O(2p) valence band (red) and the empty Ce(4f) levels
(orange) placed in the band gap. Figure 3a shows the 2O-terminated
CeO2 (100), while Fig. 3f corresponds to the isolated, gas-phase Pt
atom in a d9s1 electronic configuration in a structure where Pt is far
away from the surface. All systems are aligned according to the 2s
band centre of the central oxygen atoms in the slab. As in the Born–
Haber cycle, the isolated Pt atom is first allowed to interact with
two water molecules, forming Pt–(H2O)2 in Fig. 3e. The Pt levels
shift higher up to the Fermi level (green line) due to the covalent
(antibonding) interaction. In the simulations for the Pt–2O system,
we identified that the presence of Pt distorts the CeO2 surface to

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a

b

c

d

e

f

0

0

–1

–1

–2

E (eV)

1

–2

–3

–3

g

E (eV)

1

(Pt0)

CeO2

(Pt+)

(Pt2+)

Pt0–(H2O)2

2.01 Å

1.93 Å

1.89 Å

2.01 Å

2.01 Å

1.95 Å

1.89 Å

Pt

2.01 Å

3.88 Å

Osurf Obulk

Cesurf

Cebulk

Pt

Ptplaceholder

H

Fig. 3 | DOS decomposition for the Pt–2O systems with different oxidation states. a, DOS of the pristine CeO2 surface, showing the filled valence band
(red) and empty Ce(4f) bands (orange). b–d, DOSs of 2O systems with oxide geometries of Pt0–2O (b), Pt+–2O (c) and Pt2+–2O (d). The lowering of
the Ce(4f) levels allows electron injection from the higher Pt-filled states, as indicated by the Fermi level in e (green line). e,f, Gas-phase Pt levels when
covalently interacting with water (e) or when isolated (f). The gas-phase systems are separated by more than 7 Å from any side of the slabs.
All systems are aligned according to the 2s band centre of the central oxygen layer in the slab. g, Local coordination of the unrelaxed oxygen ligands
around the Pt vacancy. Each coordination is aligned with its respective DOS panels. Tests with different functionals show no significant changes (see
Supplementary Fig. 9).

different extents depending on the mOS. Therefore, the electronic
structure of the oxide in the geometry corresponding to the lowest
energy configuration of each Pt-2O mOS occupies the panels shown
in Fig. 3b–d. Surface distortions push the ligand O(2p) levels up
to higher energies. Concomitantly, the cation cavity increases, the
repulsion with their O neighbours decreases, and the Ce(4f) states
drop below the Fermi level of Pt–(H2O)2. This establishes the driving force for electron transfer from Pt to the oxide. Our results are
robust compared with other functionals (Supplementary Fig. 9 and
Supplementary Note 4). Therefore, electron transfer at the Pt–nO
interface can be understood as a phonon-assisted metal-support
interaction that can appear when: (1) the metal levels lie either in
the band gap or closely above the Fermi level of the reducible semiconductor; (2) the surface is flexible enough to allow surface distortions; and (3) empty cation states appear in the band gap within an
energy range accessible as a consequence of the geometric distortion. To assess the scope of phonon-assisted metal-support interaction, we performed a scan (similar to Fig. 1) for Ni on the same
CeO2 surface or for the same metal on a different oxide rutile TiO2
(110). Supplementary Fig. 10 suggests the coexistence of multiple
oxidation states for these systems as well.
The variable coordination and oxidation states affect the reactivity (Fig. 4). Pt2+–4O is the most robust state, in agreement with
the ionic nature identified in experiments21,28, and breaking this

coordination by removing an oxygen is very endothermic
(~1.84 eV). Thus, Pt2+–4O is the resting state of the material under
most conditions (in particular, under the oxidative preparation
route from the metal nanoparticles that results in PtO2 volatilization and deposition). Under mild, reducing conditions and
medium to high temperatures, like the pulses employed in catalytic
activation, both H2 and CO can open up Pt–4O (Fig. 4a (cycle 1)
and Supplementary Table 7). In Fig. 4a, molecular hydrogen has
to overcome a relatively large activation barrier35 (1.35 eV) to split
over Pt and O (−0.67 eV below reactants). Next, the hydrogen and
hydroxyl group recombine to form a water molecule, which readily
leaves the surface. H2 dissociates over the regular O-termination
pristine CeO2 via a transition state at 0.82 eV, with the final state
lying −3.00 eV below gas-phase reactants (see ref. 41). Alternatively,
if Pt–4O is reduced by CO, the molecule adsorbs onto a lattice oxygen of this unit and evolves towards CO2. The highest activation
barrier in this path is ~1 eV and the final state is −1.23 eV below
reactants. Therefore, the relative inertness of Pt SACs against H2,
and the low CO uptake in the temperature programmed desorption experiments, are related to the low pressures employed in
ultra-high vacuum experiments21,30. The activation process, as
described here, is reversible in an oxidizing environment. A deactivation switch is what sets this system apart from other catalysts,
such as nanoclusters, which can be prepared using oxidizing
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O

a

C

‡

OC

CO

O
–1.61

CO

CO2

+0.97

+0.29

CO

‡

O2
lI

I
CO

–1.14

+0.10

CO2

1

8/9 Osurf

+1.35

H2

–0.75
‡

H2

H

H

O
2

9/9 Osurf

H2O

‡

IV

H H

CO

O

TSa
O

10/9 Osurf

–2.02

llIa

CO

‡

+0.76
CO2

b
0
2

0

Pt
+
Pt
2+
Pt

100

–2
–3

47

mOS total
lifetime (%)

∆E (eV)

–1

63

49

36
4

1

–4
I

IIIa

II

TSa

c

IV
O(g) Pt

Ce O(s)

l

+CO

ll

+O2

llla

C

lV
TSa

–CO2

Fig. 4 | CO oxidation on Pt–nO structures. a, Reaction energy cycles (in eV) for surface reduction (cycle 1; black by CO; blue by H2) and CO oxidation
(cycle 2), with red spheres denoting the Pt coordination. The dagger represents the transition states. Oxygen exchange/diffusion processes are marked
in red, and the boxes below the Pt–3O structures denote the ratio of surface oxygen atoms in the (3 × 3) supercell. The numerals in cycle 2 refer to the
reaction path of CO oxidation on Pt–2O in b and c. b, Reaction profile of cycle 2 for each oxidation state of Pt. The mOS lifetimes are presented in the inset,
as retrieved from BOMD 10.5-ps trajectories of the reaction intermediates. In step II, Pt+ and Pt2+ collapse to the same energy level. The inset supports this
by showing that both mOSs coexist and are dynamically connected. c, Side (top) and top (bottom) views of the reaction steps. Dark red denotes oxygen
from the bulk phase (s) and bright red denotes oxygen from the gas phase (g).

airflow43. After the CO or H2 treatment, the Pt–4O coordination is
reduced to Pt–3O.
The Pt–3O system is labile with respect to oxygen diffusion, as
shown by the molecular dynamics simulations, where it converts
into Pt–2O in <0.5 ps at 300 K. Therefore, our results show that
reducing atmospheres convert the resting Pt–4O state into Pt–2O
species. This explains why recent experiments need short, reducing
pulses at 250 °C to generate the active platinum species14 that we can
now identify as Pt–2O. The barriers of ~1 eV explain why temperatures of at least 250 °C are required during activation, while higher
exposure times to reducing atmospheres induce Pt agglomeration.
However, the transient nature of Pt–2O makes it difficult to characterize it experimentally, even under operando conditions. Note
that even single atoms have only recently been clearly identified in
microscopy10.
The system then enters cycle 2 of Fig. 4a,b. Complementary data
for the elementary steps, alternative routes and structures can be
found in Supplementary Fig. 11 and Supplementary Table 8. On
Pt–2O state I in Fig. 4b, the three mOSs coexist and have been
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investigated separately for CO reduction. Overall, CO adsorption
is relatively weak, but the gas-phase CO pressures are large under
low-temperature (<150 °C) conditions and ionic Pt has the largest
adsorption energies. Indeed, charge dependence for CO adsorption
on SACs was also reported for Pt1/TiO2 anatase44. The CO vibrational shift for this state is around 60 cm−1, similar to the experimental value reported (75 cm−1)21 (see Supplementary Table 9).
The BOMD for this intermediate shows larger lifetimes for the ionic
Pt configurations (with a 1:2 ratio between Pt+ and Pt2+). Then, O2
can adsorb, forming a percarbonate species with an O–O bond distance of 1.452 Å. In the BOMD, this state of the SAC corresponds to
no electron transfer to the Ce4+ centres. However, in this particular
coordination, the formal oxidation state of the metal is Pt2+, regardless of its previous state. Hence, the O2 adsorption energy depends
on the electronic state of configuration (II), and can be as large as
−1.20 eV. From this configuration on, CO2 formation easily pushes
the system to the low-lying Pt0 state. The barrier for this step is
about 0.56 eV. To evolve to Pt+, the energy required is much larger
(namely, 1.11 eV). Therefore, during the CO oxidation cycle in the

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Pt–2O structure, the electronic structure of the material needs to
be dynamic to allow both the adsorption of CO (occurring at ionic
states) and oxidation (occurring at the neutral state) elementary
steps in the mechanism. Separate BOMD runs were also performed
on the reaction intermediates, showing that some of them exhibit
dynamic electron transfer (see insets in Fig. 4b and Supplementary
Fig. 11b). We have added the weights (percentage of lifetimes)
of the different mOSs in the band below each structure, indicating
that for some intermediates (CO) dynamic electron transfer occurs,
while with others (percarbonate) a single electronic configuration
is more likely.
Regarding the stability of Pt–2O (and Pt–4O), Pt diffusion
is impeded by 2.9 eV. Dimerization on the trenches is also endothermic, regardless of mOS (see Supplementary Note 5 and
Supplementary Table 2). This reinforces the role of isolated Pt atoms
in CO oxidation. If CO is adsorbed, the barriers slightly lower, but
dimerization remains difficult in most cases. Volatilization of Pt as
molecular PtO2 is also endothermic (by ~1 eV); thus, volatilization
is negligible at the reaction temperatures employed in low-temperature CO oxidation, and only taking place in oxidizing conditions
that lock Pt in the Pt–4O coordination.
Therefore, the Pt/CeO2 behaviour can be summarized as follows:
Pt0–2O is the longest-lasting state in the molecular dynamics simulations, but its ability to trap CO is low. In turn, the short lifetime
of the Pt+ species will impact the reactivity of the SAC. Addressing
the microkinetics of the Pt/CeO2 system thus requires the use of
accessible ensemble concepts45. The overall CO oxidation reaction
barrier is ~0.56 eV; this energy is compatible with the high activity
observed at temperatures lower than the 150 °C requirement of the
exhaust emission challenge.
In summary, the common assignment of a fixed oxidation state in
single-atom catalysts is exceedingly simple. Depending on the metal/
oxide combination, a dynamic charge transfer between the metal and
the oxide appears instead. The electron transfer is assisted by phonons and stems from the level alignment between the metal and the
defect states in the oxide. As a result, several oxidation and charge
states might coexist, enriching the chemistry of single atoms on oxide
surfaces. We demonstrated how the reactivity is closely related to
the dynamic behaviour. Our results explain the latest experimental
observations that indicate the need for short pulses to redisperse Pt
nanoparticles in order to be activated as single atoms to perform lowtemperature oxidations (in the 150 °C challenge). We identify how the
metal/oxide dynamic charge transfer is crucial to understanding the
nature of the active site and the mechanism in these SACs. This newly
gained degree of freedom, introduced by the presence of the reducible
support, might break linear scaling relationships and thus open the
path to more active and selective catalysts.

Online content

Any methods, additional references, Nature Research reporting
summaries, source data, statements of code and data availability and
associated accession codes are available at https://doi.org/10.1038/
s41563-019-0444-y.
Received: 22 July 2018; Accepted: 24 June 2019;
Published: xx xx xxxx

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Acknowledgements

This research has been supported by the Ministerio de Economía y Competitividad
(CTQ2015-68770-R). The authors acknowledge BSC-RES and BIFI for providing
generous computational resources. We also thank A. Bruix for critically reading the
manuscript, and T. Schäfer for help with the random phase approximation (RPA)
methodology.

Author contributions

N.D. performed the calculations. N.D., M.C.-C. and N.L. analysed the data and prepared
the manuscript.

Competing interests

The authors declare no competing interests.

Additional information

Supplementary information is available for this paper at https://doi.org/10.1038/
s41563-019-0444-y.
Reprints and permissions information is available at www.nature.com/reprints.
Correspondence and requests for materials should be addressed to N.L.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in
published maps and institutional affiliations.
© The Author(s), under exclusive licence to Springer Nature Limited 2019

ARTICLES
Methods

Slab preparation. Bulk CeO2 has a fluorite crystal structure with an experimental
lattice parameter of 5.497 Å. When optimized at the PBE + U level, the bulk yields
a theoretical lattice parameter of 5.410 Å. Slabs were cleaved at the (111), (110) and
(100) Miller indices. For the (100) surface, half of the topmost oxygens were moved
from the surface top layer to the bottom layer in order to reduce the polarity and
render the system stoichiometric. Starting from this trench-like structure, two
other low-energy reconstructions were investigated33. Each of these reconstructions
allows for a different coordination shell around single-atom Pt. To support these
reconstructions, the slabs have to span at the least a (2 × 2) supercell. In this work,
they were extended to (3 × 3) supercells ((2 × 3) in the case of (110)) to sample
lower Pt loadings. Along the vertical axis, the slabs are nine atom layers thick, with
the five top layers allowed to relax, and a 15 Å vacuum.
Density functional theory computational methods. All calculations were
performed at density functional theory + U level, as implemented by the Vienna
Ab initio Simulation Package (VASP; version 5.4.4)46–48. The PBE functional49 was
used together with a Hubbard U term to enforce charge localization at the atom
centres following the approach of Dudarev et al.50. For the cerium 4f orbitals,
U = 4.5 eV was used, based on the work in ref. 51. Projector-augmented waves were
employed to describe the core electrons, while the valence electrons were expanded
in a plane-wave basis set with a cut-off energy of 500 eV. Unless stated otherwise,
a gamma-centred k-mesh of (3 × 3 × 1) was used for (2 × 2) and (3 × 3) supercells
alike. All of the systems considered are neutral. Spin polarization was accounted
for where necessary. We assessed the influence of surface reduction on the mOS
by either adsorbing a hydrogen atom as a surface hydroxyl group (one additional
electron stored in the oxide) or generating a surface oxygen vacancy (two) (see
Supplementary Note 6 and Supplementary Fig. 12). The latter would be akin to the
surface state directly after the activation step. In all cases, different oxidation states
for Pt exist and their variability depends on the nature of the surface modification.
The electronic entropy contributions of the newly created Ce3+ centres never
exceed 1 meV K−1 at 600 K when using Fig. 1 in ref. 52. To account for the role of
dispersion in the binding energy of CO, the van der Waals contributions were
modelled using the D3 model. When applied to the adsorption of CO, it was
found to contribute less than 0.1 eV and was hence disregarded in the remainder
of this work (Supplementary Table 9). The 2-nm nanoparticle was built as a
cuboctahedron with a final stoichiometry of Pt935 and was calculated in a cubic box
with 35-Å edges (Supplementary Fig. 4).
Benchmarking. We verified the robustness of our model with respect to different
functionals, examining three routes: (1) different Hubbard parameters (U = 3.5,
4.5 and 5.5 eV; Supplementary Fig. 5); (2) two hybrid functionals (namely, Heyd–
Scuseria–Ernzerhof (HSE-06) and HSE03-13; Supplementary Tables 3 and 4); and
(3) the random phase approximation for Pt–2O, starting from PBE + U (U = 4.5 eV)
at the gamma point for the (3 × 3 × 1) supercell (Supplementary Table 5). Overall,
multiple coexisting mOSs are recovered using different functionals, although the
relative order of the Ce3+ distributions can change between functionals. In contrast
with HSE, random phase approximation (RPA) favours a strongly ionic character
(in this case, Pt2+; ref. 53), although the other mOSs would still be accessible at
elevated temperatures. The hybrid DOSs are presented in Supplementary Fig. 9.
Modelling XPS data. The core-level binding energies were computed for the
Pt(4f) states, using the Janak–Slater approach with excitation to the vacuum level
(ICORELEVEL = 2 and CLZ = 0.5). To prevent spurious electron transfer, the

NATURE MATERIALS
excited electron was removed from the system. Those core-level binding
energies represent the spectral peaks of each electronic configuration, and
were averaged over the coordination and oxidation states to obtain the peaks in
Supplementary Fig. 2.
Ab initio molecular dynamics simulations. Molecular dynamics simulations
were performed within the canonical NVT ensemble (that is, constant number of
particles, the system’s volume and the temperature) in a smaller (2 × 2) supercell
with a k-mesh of (3 × 3 × 1). The trajectories can be found in Supplementary
Videos 1–3. The slabs were set up by first heating them from 0–300 K in 0.5 ps, then
equilibrating for 1.5 ps, and subsequently further heating from 300–600 K in 0.5 ps.
The time step remained 1 fs throughout the set-up. Finally, the data were collected
at 600 K with a 3-fs time step. In the case of the (3 × 3) slab in Supplementary
Video 4, the system was heated up from 0–600 K in one session of 0.5 ps. The k-mesh
was reduced to a gamma point. In all cases, the electronic structures were well
converged to 10−7 eV. The temperature in the stable regions was regulated by the
Nosé–Hoover thermostat54. During the runs, the magnetizations were found to
change gradually and continuously, ensuring that the transitions were not the result
of any artefacts or poor convergence (Supplementary Figs. 7 and 13). The BOMD
runs for the intermediates in CO oxidation were shortened to 10.5 ps, but still
managed to show that the dynamics depends on the particular intermediate. The
lifetime histogram parameters and the magnetization cut-off were calibrated with a
sensitivity test in Supplementary Note 3 and Supplementary Fig. 14.

Data availability

The datasets generated during the current study are available in the ioChem-BD
database55 (https://doi.org/10.19061/iochem-bd-1-78).

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