# The role of surface spin polarization on ceria-supported Pt nanoparticles

Byungkyun Kang  Department of Physics and Astronomy, University of Nevada, Las
Vegas, NV 89154, USA  Joshua L.Vincent  School for Engineering of Matter,
Transport, and Energy, Arizona State University, Tempe, AZ 85281, USA  Peter
A. Crozier  School for Engineering of Matter, Transport, and Energy, Arizona
State University, Tempe, AZ 85281, USA  Qiang Zhu  Department of Physics and
Astronomy, University of Nevada, Las Vegas, NV 89154, USA

###### Abstract

In this work, we employ first-principles simulations to investigate the spin
polarization of CeO2-(111) surface and its impact on interactions between a
ceria support and Pt nanoparticles. For the first time, we report that the
CeO2-(111) surface exhibits a robust surface spin polarization due to the
internal charge transfer between atomic Ce and O layers. In turn, it can lower
the surface oxygen vacancy formation energy and enhance the oxide
reducibility. We show that the inclusion of spin polarization can therefore
significantly reduce the major activation barrier in the proposed reaction
pathway of CO oxidation on ceria-supported Pt nanoparticles. For metal-support
interactions, surface spin polarization enhances the bonding between Pt
nanoparticle and ceria surface oxygen, while CO adsorption on Pt nanoparticles
weakens the interfacial interaction regardless of spin polarization.

##  I INTRODUCTION

In heterogeneous catalysis, metal nanoparticles supported on reducible oxide
structures provide unique interfacial interactions which lead to the formation
of active sites at the three-phase boundaries which control activity and
selectivity for oxidation reactions Stair (2011); Yamada  _et al._ (2011).
Many high-performance heterogeneous catalysts have been developed which
exploit the metal/oxide interface properties for reactions such as CO
oxidation at room and low temperature Zhang  _et al._ (2019); Song  _et al._
(2019); Zhu  _et al._ (2015); Fang  _et al._ (2020). The ability of reducible
oxides to donate lattice oxygen during a reaction (the so-called Mars van
Krevellen mechanism) was first described nearly 70 years ago and is now an
accepted kinetic pathway for many reactions Mars and Van Krevelen (1954). The
atomic level details of how such a mechanism operates especially in the
presence of metallic nanoparticles remains poorly understood. Tauster was one
of the first to recognize the unique properties of the metal-support
interaction (MSI) with his observation of metal nanoparticles being
encapsulated with thin overlayers under strong reducing condition Tauster,
Fung, and Garten (1978); Tauster  _et al._ (1981); Tauster (1987). The strong
MSI has been realized in redox transition metal oxides Tauster, Fung, and
Garten (1978); Tauster  _et al._ (1981); Tauster (1987); Tang  _et al._ (2017)
and even a relatively redox-inert alkaline metal oxide MgO Wang  _et al._
(2021). The MSI is also associated with occurrence of charge transfer at the
interface Pacchioni and Freund (2018). Campbell proposed the electronic MSI
mechanism, in which charge transfer at the metal/oxide interface modulates
chemical activity of the supported catalyst Campbell (2012). The electronic
MSI gives rise to a rearrangement of electrons within the interface and
enhances the rate of surface oxygen vacancy creation/annihilation leading to
an enhanced catalytic activity Pacchioni (2013).

To manipulate the role of the interfacial interactions on a catalytic
reaction, the nanoparticle size can be varied to change the contact area
between the metal and support interface Ro, Resasco, and Christopher (2018).
For Au/Co3O4 and Au/Fe2O3, the gold nanoparticles with a diameter smaller than
5 nm show high reaction activity Haruta (1997) and Pt particles of 2-3 nm were
found to be more active for CO oxidation Boubnov  _et al._ (2012). In the
limiting case, the metal nanoparticles may be reduced all the way down to a
single atom, giving rise to the so-called single atom catalysts Liu (2017).
Another approach to manipulate catalytic activity is by tuning the interfacial
interaction directly. This has been realized by varying the support type,
particles shape and size. The aforementioned nanostructuring creates new
metal-support interaction resulting in the metal nanoparticle properties being
substantially different from their bulk counterparts Ro, Resasco, and
Christopher (2018). Doping oxides by heteroatoms can modify the electronic
structure. They enhance surface oxygen reducibility by tuning the interfacial
interaction Ruiz Puigdollers  _et al._ (2017). The increased oxide
reducibility linked to surface oxygen vacancy formation energy is an
indispensable element in oxidation reactions based on the Mars-van Krevelen
mechanism Ruiz Puigdollers  _et al._ (2017); Wang  _et al._ (2013); Liu  _et
al._ (2014); Liu, Wang, and Zhang (2012); Widmann and Behm (2011); Kim, Lee,
and Henkelman (2012). In combination with the smaller nanoparticles, nano-
structured oxide supports further lower the surface oxygen vacancy formation
energy and gives rise to a reverse spillover of the surface oxygen on to the
Pt nanoparticle Vayssilov  _et al._ (2011). These works highlight the
importance of undertaking fundamental studies to elucidate the complex
interfacial interaction underlying catalytic functionality.

There remain a paucity of information about the atomic structure and
structural dynamics of an active metal-support interface performing catalysis.
Recently, there has been an emerging paradigm that has roots in surface
science Somorjai (1991); Imbihl and Ertl (1995); Ertl (2008) and chemistry
Cotton (1975) for understanding catalytically active sites in terms of
dynamic, meta-stable, or so-called fluxional species from both computation
Zhang, Zandkarimi, and Alexandrova (2020); Sun and Sautet (2018); Zhai and
Alexandrova (2017) and experimental work Lawrence  _et al._ (2021); Li  _et
al._ (2021); Vincent and Crozier (2021). This has raised many questions
regarding both the fundamental structure of active sites and the atomic scale
evolution of the interface, metal particle, and adjacent oxide surface during
catalysis. For example, what is the dynamic nature of the metal-support
interface? The adhesion between the metal particle and support may weaken
significantly since bridging oxygen are responsible for anchoring the metal to
the support. How does the metal-support interface change in the presence of
reactant adsorbates and reaction intermediates? How do such structural changes
impact activation of intermediates and facilitate the bond breaking and
formation along the reaction pathways? What happens during the rate limiting
step and where is the likely site for CO2 formation and desorption. In order
to deepen our understanding of the factors affecting catalysis and to develop
strategies for improved catalyst design, it is essential to elucidate and
describe the structural evolution that occurs at the atomic level during
simultaneous catalytic turnover.

In this work, we investigated the interfacial interaction of ceria-supported
Pt nanoparticles by density functional theory (DFT) simulations. We found that
spins are polarized on the CeO2-(111) surface through charge transfer from
surface oxygen to cerium, which can significantly lower the oxygen vacancy
formation energy and alter the interfacial interaction between Pt nanoparticle
and ceria support. In turn, the activated surface plays an essential role in
lowering the major activation barrier in the proposed reaction pathway of CO
oxidation on the ceria-supported Pt nanoparticles. Using the existence of a
robust surface spin polarization, we propose a theoretical description of the
recently observed controversial room temperature magnetism in ceria
nanostructures Ackland and Coey (2018).

##  II Computational Methods

We used the slab model with five O-Ce-O layers to simulate the CeO2-(111)
surface with a 6 $\times$ 6 reconstruction of the primitive unitcell.
Experimental lattice constants ($a$=$b$=5.410 Å) Artini  _et al._ (2015) of
ceria with 15 Å vacuum along the $z$ direction have been used throughout. To
make Pt(111) interface with CeO2-(111), a hexagonal Pt19 single layer (SL) was
built. As initial structure for geometry optimization, we have located the
center of Pt19 SL 2.5 Å above oxygen on the CeO2-(111) surface, while Pt19 SL
[100] and CeO2 [110] are coincided. This model was relaxed at the level of DFT
by using the CP2K package VandeVondele  _et al._ (2005). In CP2K, the
wavefunction was expanded in the double $\zeta$ valence plus polarization and
plane-wave basis sets with an energy cutoff of 400 Ry. We used Geodecker-
Teter-Hutter pseudopotentials Goedecker, Teter, and Hutter (1996) based on the
GGA Perdew, Burke, and Ernzerhof (1996) functional. The van der Waals
interaction was also considered according to the DFT-D3 scheme Grimme  _et
al._ (2010). For all spin polarized calculations, half spin moments on Pt and
Ce atoms were given as the initial guess. To account for the strongly
correlated nature of Ce’s 4$f$ electrons, we employed the DFT+$U$ method with
$U$ = 7 eV, as suggested by the previous studies He  _et al._ (2018); Wang
_et al._ (2015). To check the effect of $U$, we also repeated some
representative calculations using $U$ = 4 eV. The climbing image-nudged
elastic band (CI-NEB) method Henkelman, Uberuaga, and Jónsson (2000) was used
to simulate the activation barriers for the proposed reaction pathway of CO
oxidation on the ceria-supported Pt nanoparticles. To find surface spin
polarization effect on the lattice dynamic reconfiguration, we performed the
ab-initio molecular dynamic (AIMD) simulation at 300 K with 1 fs time step
using Nose-Hover thermostat. To prevent high computational cost, only three
layers of O-Ce-O were considered in the AIMD simulation. In all simulations,
the atoms on the lowest O-Ce-O layer were kept fixed.

From the aforementioned DFT simulations, we obtained the adsorption energy
using the following equation:

$E_{\textrm{ads}}=E_{\textrm{(slab\\_adsorbate)}}-E_{\textrm{slab}}-E_{\textrm{adsorbate}}$
(1)

where $E_{\mathrm{\text{(slab\\_adsorbate)}}}$ is the energy of optimized slab
model with adsorbates, $E_{\mathrm{\text{slab}}}$ is the energy of pure
surface slab, and $E_{\mathrm{\text{adsorbate}}}$ is the energy of adsorbate,
respectively.

Oxygen vacancy formation energy is

$E_{\textrm{Vo}}^{\textrm{F}}=E_{\textrm{(slab\\_Vo)}}-E_{\textrm{slab}}+1/2E_{\textrm{O${}_{2}$}}$
(2)

where $E_{\mathrm{\text{O}_{2}}}$ is the total energy of the ground (triplet)
state of oxygen molecule in the gas phase.

Surface energy of slab is defined by

$E_{\textrm{surf}}=(E_{\textrm{slab}}-nE_{\textrm{bulk}})/(2S)$ (3)

where $n$ is the number of formula unit in the slab, and $S$ is the surface
area.

##  III RESULT AND DISCUSSIONS

Figure 1:  Calculated surface spin polarization and surface oxygen vacancy.
(a) Optimized CeO2-(111) surface. Green (blue) vector denotes calculated
Mulliken up (down) spin population multiplied by scale factor 2.0 for
visualizing the moment (Note that the same scale factor is used for all
figures in this work). For clarity, only the spin population larger than 0.20
$\mu_{\textrm{B}}$ is shown here. The lower inset shows the scale of vectors.
(b) Calculated surface layer projected density of state. The density of state
of upper oxygen and cerium layers marked by grey box in (a) are shown. The
blue (red) arrows denote the relative shifts of Ce-$f$ (O-$p$) states between
SP and NSP simulations. (c) Optimized surface geometry with oxygen vacancy.
(d) Calculated surface layer projected density of state for the oxygen vacancy
configuration. The blue (gray) arrows point to defect states obtained from SP
(NSP) simulation. In (c) and (d), the zero of energy set to chemical potential
of up spin from spin polarized simulation, and relative chemical potentials
are marked by solid (dashed) vertical lines for SP (NSP) simulation.

###  III.1 Surface spin polarization

We first performed the geometry optimization with initial magnetic moment on
all cerium atoms to include surface spin polarization explicitly. Fig. 1a
shows the optimized CeO2-(111) surface where spins are polarized. The average
Mulliken spin moment per atom is 0.60 (-0.35) $\mu_{\textrm{B}}$ on the
uppermost cerium (oxygen) layer. This structure contains spin polarization on
both top and bottom O-Ce-O surface layers. The spin polarization in the bottom
layer (with frozen atoms) is weaker than that in the upper layer (with free
atoms), indicating a Jahn-Teller effect Xiao  _et al._ (2018); Pentcheva  _et
al._ (2005); Kurtulus and Dronskowski (2003); Zywietz, Furthmüller, and
Bechstedt (2000). Fig. 1b shows the projected density of states (DOS) of
surface layers. For a comparison, the DOS without spin polarization is also
shown here. The spin polarized DOS near the Fermi energy is comprised of
appreciable hybridization between Ce-$f$ and O-$p$ orbitals. The occupied
(unoccupied) up spin states derived by bonding (antibonding) of Ce-${f}$ and
O-${p}$ characters form the narrow bands. The exchange splitting is explained
by comprehensive comparison of spin polarized (SP) and non-spin polarized
(NSP) DOS. Compared to the NSP system, the Ce-${f}$ states were split into the
unoccupied down spin states and occupied up spin state (see the blue arrows in
Fig. 1b). In consequence, the net up spin moment is populated on surface
cerium atoms. On the other hand, the original O-${p}$ states (from NSP
calculation) were pushed up into unoccupied state in up spin and pushed down
into lower energy states in down spin (see the red arrows in Fig. 1b),
resulting a population of the net down spin moment on surface oxygen atoms.

Compared to the NSP calculation, the inclusion of spin polarization lowers the
total energy by 7.83 eV. The energy drop is derived by just outermost two
O-Ce-O layers (surface layers) where spins are polarized, since there is no
sizeable spin polarization on other layers. Accordingly, the energy gain
corresponds to 3.92 eV per surface layer or 0.11 eV per O-Ce-O in the surface
layer (there are 36 O-Ce-O units in the surface layer). One can confirm that
this estimation is appropriate based on constant total energy difference
between SP and NSP systems with respect to number of layers, as shown in
Table. 1. This significant energy difference indicates the existence of a
strong spin polarization on CeO2-(111) surface. We did not find any
antiferromagnetic configuration in this system. Therefore, we conclude that
the CeO2-(111) surface is ferromagnetic.

While the room temperature magnetism in CeO2 has been studied extensively, its
origin remains unclear Ackland and Coey (2018). Here, we propose a new
theoretical description of the room temperature ferromagnetism in undoped
ceria nanostructure Anwar  _et al._ (2011); Li  _et al._ (2009a); Paunović
_et al._ (2012); Phokha, Swatsitang, and Maensiri (2015); Sundaresan and Rao
(2009); Liu  _et al._ (2008); Li  _et al._ (2010) and thin films Fernandes
_et al._ (2010a, b, 2009); Li  _et al._ (2008); Figueiredo-Prestes  _et al._
(2016). It was suggested that the ferromagnetism is confined to the ceria
nanostructure surface where oxygen vacancy may play an important role
Sundaresan and Rao (2009); Phokha, Swatsitang, and Maensiri (2015); Fernandes
_et al._ (2010a). On the contrary, Li et al. Li  _et al._ (2009a) and Liu et
al. Liu  _et al._ (2008) proposed that the ferromagnetism does not relate to
the surface oxygen vacancy but to the surface Ce3+/Ce4+ pairs. A number of DFT
studies have attributed the ferromagnetism to native defects such as oxygen
vacancy. The defect formation causes spin polarization of ${f}$ electrons for
Ce ions near the vacancy, resulting in a nonzero net magnetic moment on the
ceria surface Fernandes  _et al._ (2009); Ge  _et al._ (2008); El Hachimi  _et
al._ (2014); Keating  _et al._ (2012); Ribeiro and Ferreira (2017); Han  _et
al._ (2016); Han, Lee, and Yoo (2009). Nevertheless, based on our results, the
ferromagnetism may emerge in a bare surface without any defect or impurity. In
general, it was perceived that ions on the surface with lower coordination
numbers can cause an unusual spin population Ribeiro  _et al._ (2018); Hashim
_et al._ (2018); Munoz, Gallego, and Sanchez (2011). In our case, vacuum acts
as a virtual doping on the surface: hole doping for oxygen layer lowering the
chemical potential of surface oxygen and electron doping for cerium layer.
Upon significant spin exchange interaction on the surface, the virtual doping
leads to a charge transfer from oxygen layer to cerium layer, resulting in
Ce${}^{4+}\rightarrow$ Ce3+ transition and partially filled O-${p}$ on the
surface layer (see Figure 1a-b). In consequence, the spin on ions couples
ferromagnetically, which gains significant energy comparing to the NSP system.
In addition, we emphasize that the charge transfer is fully triggered by the
surface effect. As shown in Table 1, increasing the number of layers reduces
the surface/bulk ratio, resulting in an increased chemical potential which
approaches to that of the bulk, while other quantities show no sizeable
variation.

Table 1: The slab size effect on surface spin polarization. The O1 (O2)
denotes oxygen atoms on the top (bottom) layer within the surface O-Ce-O
layer. The calculated quantities by surface spin polarized (SP) and non-spin
polarized (NSP) simulations are presented. $E_{\textrm{surf}}$ is the
calculated surface energy. $E_{\textrm{F}}^{\textrm{bulk}}$ and
$E_{\textrm{F}}^{\textrm{slab}}$ are the Fermi energies for ceria bulk and
slab, respectively. $E_{\textrm{SP}}$ and $E_{\textrm{NSP}}$ are total
energies of SP and NSP systems, respectively. {O-Ce-O}${}_{\textrm{surf}}$
denotes O-Ce-O in the surface layer.

|  Number of O-Ce-O layers
---|---
| 3 | 5 | 7 | 9 | 11
Spin population in surface layer ($\mu_{\textrm{B}}$/atom) | Ce | 0.55 | 0.60 | 0.58 | 0.56 | 0.56
O1 | -0.32 | -0.35 | -0.34 | -0.33 | -0.33
O2 | -0.19 | -0.20 | -0.20 | -0.20 | -0.20
$E_{\textrm{surf}}$ (J/$\textrm{m}^{2}$)111a | SP | 0.94 | 0.94 | 0.95 | 0.95 | 0.96
NSP | 1.07 | 1.08 | 1.08 | 1.08 | 1.08
$E_{\textrm{F}}^{\textrm{bulk}}$ \- $E_{\textrm{F}}^{\textrm{slab}}$ (eV) | SP | 8.34 | 6.86 | 5.59 | 4.70 | 4.04
NSP | 8.44 | 6.93 | 5.64 | 4.77 | 4.12
$E_{\textrm{SP}}$-$E_{\textrm{NSP}}$ (eV/{O-Ce-O}${}_{\textrm{surf}}$ ) | -0.11 | -0.11 | -0.10 | -0.10 | -0.10

  * a

Experimental surface energy is 1.2 $\pm$ 0.2 J/$\textrm{m}^{2}$ Hayun,
Ushakov, and Navrotsky (2011).

Figure 2:  Low-energy oxygen vacancy structures. In the sub-figures, the left
panel shows the calculated Mulliken up (down) spin population
($\mu_{\textrm{B}}$) denoted by Green (blue) vector. The right panel shows
wavefunction isosurface ($0.05e/\textrm{\AA}^{3}$) of the localized defect
states. The yellow/cyan (green/blue) correspond to positive/negative
wavefunction of spin up (down) defect state. (a) the most stable
configuration, one spin up excess electron at three nearest neighbor Ce atoms
and the other spin down excess electron at next nearest neighbor Ce atom, (b)
one spin down excess electron at nearest neighbor two Ce atoms and the other
spin up excess electron at nearest neighbor Ce atom, (c) one spin down excess
electron at the nearest neighbor Ce atom and the other spin up excess electron
at next nearest neighbor Ce atom, (d) one spin up excess electron at the
nearest neighbor Ce atom and the other spin down excess electron at next
nearest neighbor Ce atom, (e) two excess electrons at nearest neighbor Ce
atoms, (f) two excess electrons at next nearest neighbor Ce atoms, and (g) one
spin up excess electron at three nearest neighbor Ce atoms and the other spin
down excess electron at Ce atom in the middle layer.

On account of the robust surface spin coupling, we investigated the impact of
surface spin polarization on surface oxygen vacancy formation. Figure 1c-d
show the optimized structure, spin population and DOS of surface layer with
oxygen vacancy. In the SP simulation, the two excess electrons produced by the
oxygen vacancy are populated on neighboring cerium atoms forming localized
polaronic states. One electron was captured by three nearest neighboring Ce
atoms, with the spin moments of 0.82, 0.68 and 0.70 $\mu_{\textrm{B}}$,
respectively. The other electron was localized on the next nearest neighboring
Ce atom with 0.98 $\mu_{\textrm{B}}$ down spin moment having antiferromagnetic
coupling with the surrounding Ce atoms (see Fig. 2a). The latter is associated
with the increased local spin moment by Hund’s rule within our singlet
simulation. The oxygen vacancy defect states in the SP system are shallow,
whereas the same defect states are below conduction band minimum in the NSP
system. With this configuration, we found the lowest surface oxygen vacancy
formation energy is 0.38 eV in the surface spin polarized system. In contrast,
the NSP simulations show higher oxygen vacancy formation energy values: 4.06
eV ($U$ = 7 eV) and 3.04 eV ($U$ = 4 eV), as compared to several previous
reports ranged from 2.13 to 3.20 eV Song  _et al._ (2013); Li  _et al._
(2009b, 2010); Ganduglia-Pirovano, Da Silva, and Sauer (2009). Note that two
electrons are almost equally populated on two nearest neighbor Ce atoms and
one next nearest neighbor Ce in our NSP simulation. In the SP system, the less
ionized oxygen ions bond weakly with cerium ions, resulting in lower cost of
vacancy formation in comparison to NSP system which does not involve charge
transfer process. Therefore, our results indicate that surface spin
polarization can lower the oxygen vacancy formation energy, and enhance the
oxide reduciblility of the CeO2-(111) surface.

Figure 3:  Optimized Pt single layer on ceria. (a) Pt19 single layer on a non-
spin polarized CeO2-(111) surface. (b) Pt19[CO]12 on a non-spin polarized
CeO2-(111) surface. (c) Pt19 single layer on a spin polarized CeO2-(111)
surface. (d) Pt19[CO]12 on a spin polarized CeO2-(111) surface. The side view
of the structures are shown in the top panel. The calculated bond lengths (Å)
between Pt and surface oxygen are shown in the middle panel.

In addition to the most stable oxygen vacancy defect state, we found several
other low-energy spin configurations. In Fig. 2c, local spin moments on two Ce
atoms are exchanged in comparison to the most stable configuration in Fig. 2a.
This vacancy configuration gives rise to down spin flipping on another nearest
neighbor Ce atom and cause an increase in formation energy of 0.2 eV from the
most stable oxygen vacancy. In the configuration of Fig. 2b, one electron was
equally distributed on two nearest neighbor Ce atoms which have down spin
moment of 0.75 $\mu_{\textrm{B}}$ opposite to the majority up surface spin.
This configuration leads to increased formation energy of 0.18 eV in
comparison to the most stable oxygen vacancy. These indicate that surface
spins favor ferromagnetic coupling with excess electrons. In Figure 2d-f, we
found very localized defect states with a Mulliken population close to 1.0
$\mu_{\textrm{B}}$ on two Ce atoms. However, that localization does not only
weaken ferromagnetic coupling by producing opposite spin moments on the
surface, but also increases the repulse Coulomb interaction between excess
electrons, resulting in a higher formation energy. In particular, the
configuration of Fig. 2f, where two excess electrons are localized on next
nearest neighbor Ce atoms, was reported as the most stable oxygen vacancy
state by other DFT studies Song  _et al._ (2013); Li  _et al._ (2009b); Han
_et al._ (2018). However, the configuration is no longer the ground state by
considering the spin effect. As shown in Fig. 2g, we also found outstanding
oxygen vacancy configuration to be energetically degenerated with the most
stable oxygen vacancy configuration. One defect state located on three nearest
neighbor Ce atoms increasing spin moment 0.75 $\mu_{\textrm{B}}$ around oxygen
vacancy in the ferromagnetic coupling, whereas the other excess electron is
moved to the farthest site from surface, which has no spin coupling. In
comparison to total spin population on oxygen layer of the most stable
configuration, this configuration further increased total spin moment of 0.58
(0.39) $\mu_{\textrm{B}}$ on the uppermost (middle) two oxygen layers. This
ascertains additional charge transfer to localize the excess electrons. These
configurations suggest that even in the presence of oxygen vacancies, there is
still surface spin polarization, and it can even be enhanced for some vacancy
configurations as shown in Fig. 2.

Figure 4:  (a) The calculated energy profiles for proposed reaction pathway
for CO oxidation on Pt19[CO]11 with the ceria support. The black solid (blue
dotted) lines show the calculated energy profiles by using $U$ = 7.0 (4.0) eV
from the spin polarized simulations. The black dashed lines show the
calculated energy profiles by using $U$ = 7.0 eV from the non-spin polarized
simulations. TS1 and TS2 denote two transition states. CO is absorbed on green
colored Pt atom. C (O) atoms involved in the reaction were colored by black
(yellow). (b) Calculated surface oxygen vacancy formation energies within SP
simulations. Filled circles represent the formation energies at corresponding
sites. The surface oxygen which react with CO was marked by the red box. The
surface oxygen with exceptional low vacancy formation energy was marked by the
green circle. The energy level of oxygen vacancy formation for the most stable
configuration on bare ceria surface is marked by red line on the energy color
bar.

###  III.2 Pt on the ceria support with CO

To date, surface spin polarization has not been taken into account for nano-
structured heterogeneous catalysts. Hence we investigated the influence of
surface spin polarization on the interaction between Pt nanoparitcle and
ceria. As shown in Fig. 3a, the optimized Pt19 SL on CeO2-(111) consisted of
platinum and surface oxygen (O${}_{\textrm{surf}}$) bonds mostly on perimeter
of the SL in NSP simulation. On the other hand, the SP simulation (see Fig.
3c) generates a configuration with more Pt-O${}_{\textrm{surf}}$ bonds. In
addition, the averaged bond length is also shorter than that of the NSP
configuration. This indicates that the interaction between ceria surface and
Pt19 SL is significantly enhanced by the surface spin polarization. We
attribute the strong Pt-O${}_{\textrm{surf}}$ bonds to electron depletion
oxygen layer by the charge transfer on the spin polarized surface, where Pt
atoms are more prone to oxidation. The enhanced interfacial interaction
induces spin moments on Pt and Ce atoms and coupling between them. The surface
oxygens were pulled out from ceria surface by this interaction. As a result,
the donation of Pt valance electrons to surface oxygens increases the unpaired
spin density around the Pt site. The pronounced on-site spin populations on Pt
atoms are denoted in Fig. 3c. The interfacial interaction also affects the
electronic configuration of Ce atoms on the surface layer. The less oxidized
Ce atoms has a large unpaired spin population which couples with the polarized
Pt spins through surface oxygen. The majority of magnetic coupling is
antiferromagnetic, resulting in a zero net spin moment on the intermediate
surface oxygen.

Our simulation shows that adsorption energy of CO on the spin polarized
CeO2-(111) surface is -0.31 eV (see Fig. S1). The result agrees with previous
observations that CO on CeO2-(111) surface is either unstable or has weak
interaction with the surface Chen  _et al._ (2012); Huang and Fabris (2008);
Nolan and Watson (2006) (see Section B in the SI). In terms of CO’s adsorption
energy on the ceria-supported Pt nanoparticle, our calculation reveals a wide
distribution from -3.14 to -1.02 eV, depending on the choice of adsorption
sites (see Fig. S2). These results indicate that CO molecules are strongly
adsorbed on Pt nanoparicles Lu  _et al._ (2020). In this work, we constructed
ceria-supported Pt19 SL with 12 CO molecules which were initially located at
the bridging sites of the perimeter of Pt19. Optimized geometries of
Pt19[CO]12 with/without surface spin polarization are shown in Fig. 3b and d.
We again observed that surface spin polarization enhances the interaction
between Pt19[CO]12 and ceria, i.e., more bonds and shorter bond lengths.

Fig. 3 shows that the CO adsorption on Pt19 breaks a few
Pt-O${}_{\textrm{surf}}$ bonds on the perimeter of Pt19 in both NSP and SP
calculations. Thus, the adsorption weakens the interfacial interaction. The
weakening can be understood from Mulliken spin population analysis in the SP
system. The strong CO adsorption on Pt19, due to the $\pi$-back bonding
between Pt and CO Das  _et al._ (2015), can reduce the donation of Pt’s
valence electron to surface oxygen. As a result, the pairing electrons on Pt
atoms decreases the net spin moment on the Pt19 (see Figure 3c-d).

###  III.3 Reaction pathway in CO oxidation

Table 2: The list of activation barriers in energy profiles for proposed reaction pathway. The major activation barriers are hilighted in bold. Calculation Type | Parameter | Reaction Barrier (eV)
---|---|---
|  $U$ (eV) |  TS1 |  -CO2 |  TS2
Spin Polarization | 7.0 | 0 | 1.05 | 0.29
Spin Polarization | 4.0 | 0 | 0.47 | 0.11
Non-spin Polarization | 7.0 | 0.82 | 2.19 | 0.65

We found that surface spin polarization may play an important role in the
catalytic activity. On a spin polarized surface, the electrophilic oxygens in
the electron deficient condition are more reactive with other species in
comparison to the NSP system. In addition, new species formed by the reaction
are easily removable owing to the high reducibility on the spin polarized
surface. The impact of spin polarization on surface catalytic activity is
illustrated in Fig. 4a. We started with a CO desorpted Pt19[CO]11 with ceria
support in CO rich conditions. The Pt19[CO]11 can adsorb one more CO molecule
to form Pt19[CO]12, with a shallow adsorption energy of -0.08 eV. The adsorbed
CO reacts with O${}_{\textrm{surf}}$ to form CO2, gaining an energy of 2.60
eV. While there is no activation barrier for the reaction in the SP system,
calculated activation barrier is 0.82 eV in the NSP system. Taking off the CO2
molecule from the reaction site leaves a surface oxygen vacancy, costing an
penalty energy of 1.05 eV for $U$ = 7 eV (0.47 eV for $U$ = 4 eV). This is the
main barrier in the proposed reaction pathway. The Pt SL can subsequently
adsorb another incoming CO, while the ceria surface can attract O2 at the
oxygen vacancy site. The molecular O2 and CO further react to form a new CO2.
The calculated activation barrier for the reaction are 0.29 ($U$ = 7 in the SP
system), 0.11 ($U$ = 4 in SP system), and 0.65 ($U$ = 7 in the NSP system) eV,
respectively. Thereafter, the catalytic cycle is completed by desorption of
the CO2, which is an exothermic process releasing energy of 1.74 eV to recover
to Pt19[CO]11. This proposed reaction pathway is manifested by MvK mechanism
Mars and Van Krevelen (1954). The simulated reaction pathway using $U$ = 4 eV
has the same trend with $U$ = 7 eV, as shown in Fig. 4a. However, the NSP
system shows different reaction energy profiles from the SP system. Table. 2
summarizes the activation barriers for each system. The major activation
barriers (0.47-1.05 eV) of the SP system are apparently close to the measured
activation energies ranging from 0.37 to 0.77 eV Lu  _et al._ (2020); Ke  _et
al._ (2015); Cargnello  _et al._ (2013); Kopelent  _et al._ (2015); Vincent
and Crozier (2021), while the NSP system has a much higher barrier (2.19 eV).
The elevated barrier in the NSP system is caused by high formation energy of
oxygen vacancy, that hampers the release of CO2 from the surface.

Figure 5:  (a) The snap shot of NSP AIMD simulation of the ceria-supported
Pt19 single layer with 12 CO molecules at 0, 9 and 14 ps. (b) The snap shot of
SP AIMD simulation of the ceria-supported Pt19 single layer with 12 CO
molecules at 0, 2 and 3.4 ps. The red box shows that the CO and surface O bind
to form CO2. (c) Left panel: calculated distance between the average z
coordinates of surface Ce atoms and the average z coordinates of Pt atoms,
right panel: standard deviation of z coordinates of Pt atoms. (d) Schematic
diagram of lattice dynamic in SP and NSP systems. (e) Atomic resolution
transmission electron microscope images of fluxional Pt nanoparticle on
CeO2-(100) surface in a CO atmosphere (7 x 10-4 Torr) at room temperature. Pt
columns are visible as white dots whereas (100) Miller planes in CeO2 appear
as white horizonal lines. The two images are from the same nanoparticle with
right-hand image recorded 0.5s after the left-hand image. The Pt nanoparticles
undergoes 7.5° clockwise rotation resulting in Pt (111) becoming approximately
parallel to (100) CeO2 plane (see red dotted guide to eye on right-hand
panel). The Pt atomic plane near the CeO2 is not straight and curves up on
left-hand side and also the atomic columns on the right are slightly blurred
suggesting a high degree of instability in their position. Other changes in
the Pt surface structure are apparent due to the strong interaction with CO.

In addition to lowering the activation barrier, the surface spin polarization
enables the adsorbed CO on Pt SL to react with O${}_{\textrm{surf}}$ to form
CO2. While this reaction is endothermic in the NSP system, the energy released
by the reaction is large in the SP system, owing to high surface oxygen
reactivity. Compared to the most stable oxygen vacancy on a bare ceria
surface, the surface oxygen (at the reaction site marked by red box in Fig.
4b) vacancy formation energy with Pt19[CO]12 is lowered by 0.15 eV, thus
significantly boosting the reaction with surface oxygen. In Fig. 4b, we show
the calculated vacancy formation energies for all surface oxygen sites. The
interaction between Pt19[CO]12 and CeO2 generally lowers the vacancy formation
energies for surface oxygen at exterior sites of the contact zone. However,
within the contact zone, the majority of surface oxygens strongly bond with Pt
ions (see Fig. 3d). The vacancy formation energies are relatively high for
these oxygen, except the oxygen which bonds with Pt-CO (marked by green circle
in Fig. 5b). The O${}_{\textrm{surf}}$-Pt-CO at the exceptional site may
migrate by forming dynamic low-coordinated atoms, which has been proposed as
the prime cause of dynamic structure of ceria supported gold nanoparticles
upon exposing to CO and oxygen gases He  _et al._ (2018). The impact of
surface spin polarization on structural dynamics will be discussed in the
following section.

###  III.4 Structural dynamics

The dynamic lattice reconfiguration of nanoparticles upon exposing to
oxidizing and reducing gases (e.g. CO and O2) has been intensively studied by
Transmission Electron Microscopy (TEM) in the recent years Hansen  _et al._
(2002); Nagai  _et al._ (2008); Vendelbo  _et al._ (2014); Gänzler  _et al._
(2015, 2017); He  _et al._ (2018); Lawrence and Crozier (2018); Lawrence  _et
al._ (2021); Li  _et al._ (2021); Miller and Crozier (2021); Tao and Crozier
(2016); Vincent and Crozier (2020, 2021). These studies imply that the surface
and perimeter of nanoparticle strongly interact with CO and O2 gases. To
explore the potential influence of surface spin polarization on the dynamic
lattice reconfiguration, we performed two independent AIMD simulations of
ceria-supported Pt nanoparticles for 20 ps with and without the inclusion of
spin polarization. Due to the limitation of computational resources, we used
only three layers of O-Ce-O. Therefore, the CeO2 support is highly reducible,
resulting in a unrealistically fast CO oxidation even at 300 K in our AIMD
simulation.

Despite the artefact due to the choice of a thin CeO2 slab, our simulations
still reveal distinct physical pictures due to the inclusion of spin
polarization. In the NSP AIMD simulation (Fig. 5a), the whole system does not
show any obvious structural change for 20 ps. On the other hand, we observed
rapid CO2 formation at around 3 ps (Fig. 5b) when the spin polarization is
turned on. Fig. 5c plots the calculated distance between the averaged $z$
coordinates of surface Ce/Pt atoms, as well as the standard deviation to
evaluate dispersion of $z$ coordinates of Pt atoms during the simulation.
Clearly, the Pt atoms in the SP system are more distant from surface Ce atoms
with a larger fluctuation, in comparison to the NSP system. Accordingly, we
identify four different features of the SP system (in schematic Fig. 5d).
First, strong bonds between Pt and surface oxygen atoms are found in the SP
system. This is shown by more bonds and shorter bond lengths because oxygen
has moved towards the Pt layer as seen in Fig. 3. Second, the large distances
between surface Ce and Pt atoms are present consistently in the SP AIMD
simulations. Highly reducible surface oxygen in the SP surface bond strongly
with Pt atoms, resulting in an elevation of surface oxygen and Pt atoms from
CeO2 surface. This shifting is also manifested in the optimized structures in
Fig. 3. Third, substantial fluctuations of Pt atoms are displayed in the SP
AIMD simulations, indicating that the elevated Pt nanoparticle from CeO2
surface are flexible. Fourth, asymmetric CO oxidation was raised by irregular
structure of Pt and nonuniform surface O vacancy formation energies as shown
in Fig. 4b.

Recently, experimental evidence has been published that shows significant
lattice reconfiguration on Pt nanoparticles supported on CeO2 on exposure to
CO and other gases Li  _et al._ (2021); Vincent and Crozier (2020, 2021) While
the timescales for the computation and experimental datasets are very
different, precluding a detailed quantitative structural comparison, there is
qualitative agreement in the trends in structural dynamics from both theory
and experiment. Fig. 5e is in situ electron microscopy data showing dynamic
structural change taking place in a CO atmosphere (for experimental details
see reference Vincent and Crozier (2020)). The Pt nanoparticles undergoes
complex lattice changes such as clockwise rotation, uneven Pt atomic plane
near the CeO2, instability its atomic position, and apparent change on the Pt
surface. There are also continuing changes in the interface structure due to
the constant creation and annihilation of oxygen vacancies at perimeter sites.
This occurs due to the weakening of the interfacial bonds in the presence of
CO and the experimental observation can be understood in terms of the
schematic diagram of Fig. 5d. There are many other fluxional observations such
as dynamic changes in cation positions due to breaking and formation of
chemical bonds at the perimeter sites which are described in greater detail in
the author’s paper Vincent and Crozier (2021) . These complex dynamics may be
described by concerted effect from aforementioned four features, which are
pronounced in our SP AIMD simulation. Thus, we suggest that surface spin
polarization may play a deterministic role in promoting the dynamic lattice
reconfiguration of ceria-supported Pt nanoparticles.

##  IV Conclusions

In summary, we report the robust surface spin polarization on the CeO2-(111)
surface due to charge transfer from surface oxygen to cerium. The surface spin
polarization appears to be essential to describe the existing important
observations such as ferromagnetism in undoped CeO2 nanostructures and thin
films, high reducibility of ceria support, and low CO oxidation reaction
barrier. In addition, the surface spin polarization enhances the bonding
between platinum and surface oxygen. However, the CO adsorption on the
perimeter of platinum single layer is inclined to weaken the interfacial
interaction. We expect the presence of vigorous surface spin polarization at
ambient temperature will be useful to understand the interfacial interaction
and guide the design high-performance heterogeneous catalyst.

## Acknowledgments

The computing resources are provided by XSEDE (TG-DMR180040). The authors
gratefully acknowledge financial support from the National Science Foundation
(NSF). BK and QZ are supported by NSF-OAC award 1940272. NSF-CBET Award
1604971 and NSF-OAC Award 1940263 supported JLV and PAC, who acquired and
processed the experimental data and participated in extensive discussion of
the calculations. The authors thank Arizona State University’s John M. Cowley
Center for High Resolution Electron Microscopy for microscope access and use.

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