Download Effect of Magnetic States on the Reactivity of an FCC(111) Iron Surface

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Effect of Magnetic States on the Reactivity of an FCC(111) Iron
Surface
Marko Melander,†,‡ Kari Laasonen,*,†,‡ and Hannes Jónsson§,∥
†
COMP Centre of Excellence, ‡Department of Chemistry, and §Department of Applied Physics, Aalto University, FI-00076 Aalto,
Finland
∥
Faculty of Physical Sciences, University of Iceland, 107 Reykjavík, Iceland
ABSTRACT: We have carried out calculations to compare the
catalytic activity of ferromagnetic (FM) and antiferromagnetic
(AFM) states of the (111) surface of an FCC iron film by evaluating
the reaction energy and activation barrier for the dissociation of H2
and CO. The calculations were carried out using density functional
theory and a meta-GGA approximation of the energy functional. The
results show significant sensitivity to the magnetic state of the surface.
We find that charge transfer upon adsorption is more efficient at the
AFM2 surface. For H2, this leads to barrierless dissociative adsorption
on the AFM2 surface, while a molecular adsorbed state is metastable at the FM surface, separated by an activation energy of 0.35
eV from the dissociated state. CO adsorbs more strongly on the AFM2 surface, but the activation energy for dissociation is 0.27
eV lower on the FM surface mainly because the energy of the transition state is lower. The difference in reactivity is analyzed in
terms of integrated density difference and spin-dependent projected density of states. It is concluded that empty, back-bonding
states offer a more favorable overlap at the FM surface leading to a more facile CO dissociation. The results indicate that catalytic
activity can be strongly affected by the application of a magnetic field when it can induce a change in the magnetic state of the
catalyst.
1. INTRODUCTION
Chemical reactions are characterized by reorganization of
electrons and nuclei. From a fundamental point of view, both
charge and spin can affect such transitions and thereby be of
chemical interest. Varying the charge state of a molecule has
well-known and established effects on reactivity, whereas the
effect of spin on reactivity has been explored less. Manipulation
of spin states has been shown to lead to rearrangements of
electrons and hence affect reaction rates, yields, and product
distributions.1−5 For molecules and molecular solids, spincrossover (SCO) between high- and low-spin structures4,5 as
well as magnetic field effects (MFEs) on chemical reactivity1−3
have been observed. However, little is known about the effect
of spin on heterogeneous catalysis at magnetic surfaces. An
especially interesting topic is whether such reactions may be
controlled by an external magnetic field. In principle, spincrossover could be used to affect and even control the reactivity
of catalytic surfaces by an external magnetic field.
The most studied SCO materials are octahedral organometallic compounds where a d4−d7 transition metal ion can
adopt either a high (HS)- or low-spin (LS) electronic
arrangement depending on crystal field splitting. Obviously,
the ligand and oxidation states of the metal are the key factors
in determining the spin state. If the two states have comparable
energy, a transition between HS and LS states may be triggered
by external stimuli, such as light, pressure, magnetic field, or
temperature. The spin-transition can lead to large geometric
and electronic changes enabling spin-state controlled chemistry.
© 2014 American Chemical Society
If several SCO molecules are brought in contact to form either
1D, 2D, or 3D structures, short and long-range interactions
between the monomers can affect the overall response of the
system to external perturbations. These interactions can lead to
the formation of various ferromagnetic, antiferromagnetic, or
noncollinear magnetic structures which can be influenced by
external perturbations. While keeping the temperature and
pressure constant, an external magnetic field provides a natural
way to access different magnetic states.
The MFEs on reactivity have so far mainly focused on
reaction kinetics, while the effect on thermodynamics has been
considered to be negligible.2 The MFE on kinetics takes many
forms, but the basic requirement is that the electronic wave
function in the vicinity of the transition state exhibits some sort
of discontinuity or diabaticity. As the total spin states of both
reactants and products must be the same (in the absence of
spin−orbit coupling), a reaction must follow spin selection
rules. MFEs allow switching between spin-forbidden and spinallowed pathways by altering time-dependent spin evolution.
Thus, the key feature is to alter spin-selective competitive
kinetics, which leads to different product distributions via a
variety of pathways. Experimentally, MFEs have been found to
have important consequences in various areas. Most straightforward is the identification of radical reactions affected by
Received: May 13, 2014
Revised: June 26, 2014
Published: June 30, 2014
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Figure 1. Above: Density of states for FCC iron in ferromagnetic
(FM) and double-layer antiferromagnetic (AFM2) states at the
minimum energy lattice constants (see Figure 2). Below: Comparison
of spin dependent total density of states for high (3.575 Å)- and lowspin (3.55 Å) FCC iron crystals in FM state.
weak magnetic field can cause a change from antiferromagnetic
to ferromagnetic spin ordering and increase ammonia
adsorption by 50%.9,10 In the presence of a weak magnetic
field, CO oxidation on nonmagnetic Pt catalysts supported on
carbon coated magnetic Co particles was found to decrease by
10−14%.11 On lanthanide containing perovskite type structures, conversion of CO oxidation was shown to increase from
5% up to 25%.12 Also, the activation energy for NO reduction
was found to reduce by 6 kJ/mol, leading to a 10% increase in
conversion rate at 453 K in a 0.02 T magnetic field.13
A few computational studies have also demonstrated the
effect of magnetic states on admolecule binding and
dissociation. The adsorption energy of hydrogen on small Rh
clusters was found to vary by 0.5 eV depending on spinmultiplicity.14 N2O dissociation on small Rh clusters was found
to depend on the spin multiplicity of the cluster as charge
transfer is effective only for some of the magnetic states.15
Recently, a computational study showed that during CO
dissociation on a Fe13 nanoparticle, the total magnetic moment
changes from 42 to 40 or 38 μB indicating diabaticity and the
importance of multiple energy surfaces near the transition state.
Furthermore, the dissociation barrier was lowered by 0.2 eV by
optimizing the spin state.16 Thus far, however, theoretical
studies have not addressed the basic mechanism by which
magnetic fields change chemical reactivity in heterogeneous
catalysis nor identified how reaction paths are affected by
changes in the magnetic state of the surface.
In order to study spin state effects in heterogeneous catalysis,
we have performed density functional theoretical calculations of
the reactivity of an FCC(111) iron film in different magnetic
states. It is well established that bulk FCC iron can exist in
various magnetic configurations.17−20 Also, thin films of iron
deposited on, e.g., copper,21−27 can be in either antiferromagnetic or ferromagnetic states. Stability of the different magnetic
states depends strongly on lattice constant, film thickness,
surface orientation, and the presence of adsorbates. Computations using DFT and GGA functionals have been shown to
describe the magnetism of the bulk BCC iron17−20 and also
thin film systems26,27 accurately. As iron is an important catalyst
in the Fischer−Tropsch reaction for the production of
hydrocarbons from a mixture of CO and H2, the surface
chemistry of these reactants has been studied in detail. The
same reactants also form the basis of the water−gas shift
reaction.28 Furthermore, H2 dissociation is well understood and
is sensitive to changes in charge state (electrode potential) of
the catalyst, so it is interesting to see whether changes in spin
states exhibit similar changes in reactivity. CO is not only an
important reactant but also a common probe for surface
chemistry. Our results show that SCO between different
magnetic states in heterogeneous systems can be used to
significantly affect charge transfer and reactivity. Furthermore,
the changes in electronic structure and chemical bonding that
occur when the magnetic state of the iron film changes are
discussed.
A few experimental observations have been reported which
illustrate the possibility of utilizing MFEs in the field of
heterogeneous catalysis. In an early review from 1975, Atkins
and Lambert8 questioned whether an actual proof of MFEs in
heterogeneous catalysis had been realized at that time while
emphasizing its technological importance. Much work has been
done since then. Studies of CuO nanoparticles revealed that a
2. METHODOLOGY
The calculations were carried out within the projector
augmented-wave method as implemented in the GPAW
software.29,30 The total energy calculations, as well as DOS
and PDOS calculations, were carried out using a real-space grid.
PDOS plots were computed using an all-electron wave function
obtained from the PAW calculations. The calculations require a
external magnetic fields, for example, radical enzymatic and
organic reactions. Another important field is photochemistry
where solid state and molecular MFEs have been identified.1−3,6,7
A magnetic field, H, can have a significant thermodynamic
effect on a reaction only if the field strength is high or the
change in magnetization, M, is large. This can be seen from the
change in Helmholtz free energy related to MFE at constant
temperature.2
dFm = μ0 H ·d M
(1)
For a heterogeneous system where a large change in
magnetization occurs, the thermodynamic MFE could be
significant already for a low applied field. An example of such
a transition is an antiferromagnetic-to-ferromagnetic spincrossover controlled by an external magnetic field. The spincrossover leads to changes in the magnetization of the surface
and thereby different orbital populations because of Pauli
repulsion and exchange interaction between the electrons. This
in turn can have a profound effect on charge transfer, donation/
back-donation, Fermi-energy, d-band energy, and atomic
structure, all of which are common reactivity descriptors in
heterogeneous catalysis. As an example, Figure 1 shows how
small alterations in the FCC iron lattice constant and magnetic
state lead to large variations in the spin-dependent density of
states (DOS).
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Figure 2. Left: Schematic illustrations of collinear antiferromagnetic (AFM1), bilayer-antiferromagnetic (AFM2), and ferromagnetic (FM) spin
structures of FCC iron crystal where the c/a ratio is 21/2. Right: Relative energy and atomic magnetic moments of various spin structures as a
function of the lattice constant.
reliable performance for adsorption energy without structural
compromises.36−38 Also, a particularly important aspect for the
present study, the magnetic moments and relative energy of
magnetic structures in BCC Fe and FCC Ni, is well produced
by revTPSS.39
The iron film was modeled with a slab of FCC atomic
structure with a 3 × 3 × 5 unit cell periodically replicated in the
x- and y-directions with an 8 Å vacuum in the z-direction. The
two bottom layers were held fixed during geometry and spin
optimization. Periodicity of the wave function was modeled
using a 5 × 5 × 1 k-point sampling. Bulk properties were
calculated using a 2 × 2 × 8 unit cell with 8 × 8 × 4 k-point
sampling. Structure optimizations were carried out using the
BFGS (Quasi-Newton) algorithm until forces dropped below
0.05 eV/Å. Dissociation pathways were calculated using the
climbing image nudged elastic band method (CI-NEB).40,41
The concept of varying spring constants, as described in ref 41,
was also applied. All the NEB paths were optimized using the
FIRE algorithm,42 which is more stable than, e.g., BFGS. The
convergence criterion for atomic forces was 0.2 eV/Å. Spinpolarization was included in all the calculations with an
optimization of the magnetic moments.
The adsorption energy is defined as Eads = Esurf+mol − Esurf −
Emol, so a more negative value means stronger binding. CO
adsorption on ferro- and antiferromagnetic surfaces was also
studied by computing the density difference defined as
rather dense grid-spacing of 0.14 Å to converge. The SCF
convergence threshold for the wave functions was 10−6.
The choice of the exchange-correlation functional must be
made with care as the magnetism and chemical properties of
FCC iron are highly sensitive to even small changes in
electronic and atomic structure. Thus, to study adsorption on
Fe-FCC(111) surfaces, the magnetic, structural, and energetic
properties must be reliably obtained. This presents a serious
challenge for the commonly used GGA functionals that depend
on the electron density and its gradient. For example, pure
PBE31is often used for studying heterogeneous catalysis. It gives
rather accurate results on structure and total energy for a wide
range of systems. By changing the exchange enhancement
factor, other functionals such as revPBE,32 RPBE,33 and
PBEsol34 have been constructed to improve the results for
specific categories of systems. Both revPBE and RPBE give
improved estimates of adsorption energy32,33 but make a
compromise in structural factors and yield, e.g., too large lattice
constants.35,36 PBEsol, however, gives improved estimates of
structural properties but yields poor adsorption energy.37 This
example illustrates a common feature of GGA functionals: not
all properties can be accurately computed. A more flexible
functional form includes also the Laplacian of the electron
density, the so-called meta-GGAs. Since the meta-GGA
functional form provides more flexibility, the compromises
made by GGAs may be partly alleviated. We have used the
revTPSS meta-GGA functional.38 It was designed as an allpurpose functional for both solid and molecular systems with
Δρ(x , y , z) = ρFeCO − ρFe − ρCO
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how different spin states can affect heterogeneous catalysis and
high quantitative accuracy for each structure is not needed.
To study the effect spin states can have on the reactivity of
iron, we chose to study the close-packed Fe-FCC(111) surface
slab with a lattice constant of 3.575 Å. This lattice constant
corresponds to the AFM2 bulk structure, but the FM state is
only 0.07 eV/atom higher in energy. This lattice constant was
chosen as most of the experimental examples on MFEs in
heterogeneous reactions (see Introduction) were made on
antiferromagnetic nanoparticles. Thorough computational26,27
studies have shown that the double-layered antiferromagnetic
structure is the most stable spin-structure of 4 to 10 ML thick
Fe films on copper. Also, the transition from AFM2 to FM can
be achieved by applying an external magnetic field, whereas
changing from ferromagnetic to antiferromagnetic structure is
experimentally more difficult. At this value of the lattice
constant, the changes in magnetization are large when going
from AFM2 to FM so that thermodynamic changes given by eq
1 can also be significant. The larger the changes in
magnetization are, the more pronounced is the thermodynamic
effect.
The structural and magnetic properties of Fe-FCC(111)
slabs in AFM2 and FM magnetic states at a lattice constant of
3.575 Å are given in Table 1. It can be seen that the FM state
When CO is aligned along the z-axis, integration of the density
difference over the x and y axes gives the charge displacement
along the CO axis
Δq(z) =
∞
∞
∫−∞ dz′ ∫−∞ ∫−∞ dxdyΔρ(x , y , z′)
z
(3)
For charge-neutral systems, Δq(∞) should be zero. This
function can be used to interpret and study the charge-transfer
upon adsorption. According to the Blyholder model,43,44 CO
adsorption is governed by bonding 5σCO → Fe(dz2) and
backbonding effects from d Fe(xz/yz/d x 2 − y 2 /d xy ) → 2π* CO
interactions. As these effects are controlled by the orbital
overlap, filling, and energies, each contribution can be affected
by changing the spin state of the iron surface. As bonding
contributions are characterized by positive and back-bonding by
negative Δq(z) values,45 charge displacement analysis given by
eq 3 can be used to analyze bonding/back-bonding effects.
Furthermore, spin-polarized charge-transfer can be obtained
when Δq(z) is evaluated from either α or β spin-density
difference instead of the total electron density difference.
Charge-transfer was also studied by estimating atomic charges
using the Bader scheme46 implemented with the grid
approach.47
3. RESULTS
3.1. Magnetic Structure of FCC Iron and the FCC(111)
Surface. Iron crystals have many stable magnetic states with
different spin structure and atomic magnetic moments. The
relative stability of different spin structures and the magnitude
of the magnetic moments are highly sensitive to the lattice
constant and to the crystal structure. BCC is the most stable
structure and is always ferromagnetic, whereas the FCC iron is
higher in energy and exhibits various collinear and noncollinear
spin structures depending on the lattice constant.17−20 The
FCC iron becomes more stable than BCC at high temperature
(∼1200 K20) or can be grown as a thin film on FCC crystal
surfaces (see Introduction and Discussion). This opens the
possibility of tuning the magnetism of FCC iron films by
choosing the substrate and thereby the lattice constant. Here,
we focus on the three most stable collinear structures of FCC
iron depicted in Figure 2 and their reactivity. Also, the energy
and atomic magnetic moments are shown.
Figure 2 shows the large changes in stability of various
magnetic states of an iron crystal with FCC structure as a
function of the lattice constant. For a small lattice constant, the
various collinear spin structures are almost equally stable and
have small magnetic moments. Earlier studies have shown that
a noncollinear magnetic state is lowest in energy when the
lattice constant is below 3.5 Å.17−20 We thus focus on lattice
constants beyond this value. Our results show that between 3.5
and 3.6 Å, AFM2 is the lowest energy state of the collinear
FCC iron. At about 3.6 Å, the FM structure becomes the most
stable. The increased stability of the ferromagnetic state is
associated with an abrupt change from a low-spin to a high-spin
state. As a general feature, the magnetic moments of all of the
structures studied increase as the lattice constant is increased.
As shown in Figure 1, the electronic density of states (DOS) of
FCC iron also changes significantly as the lattice constant is
changed. These results are in good qualitative agreement with
earlier studies on the magnetism of FCC iron, but denser kpoint sampling is required to achieve closer, quantitative
agreement. Here, the main objective is to qualitatively study
Table 1. Magnetic Moments (μB) and Surface Relaxation
(%) of Clean AFM2 and FM Slabs with a Lattice Constant of
3.575 Å in the Surface Plane
layer
1
mag. mom.
relaxation
2.69
−0.39
mag. mom.
relaxation
2.78
1.45
2
AFM2
2.13
−4.02
FM
2.69
3.59
3
4
5
−1.98
−0.05
−2.00
0
2.52
0
2.66
2.95
2.67
0
2.78
0
has larger atomic magnetic moments and that surface relaxation
depends strongly on the spin structure. The FM surface is
slightly relaxed outward, whereas AFM2 is relaxed inward. On
both surfaces, the magnetic moments are larger than the
corresponding bulk moments as has previously been observed
for iron surfaces and nanoparticles (see, e.g., ref 48). The
magnetic moments correspond to high-spin states as has been
found previously both by experiments25 and computations.26,27
The projected DOS (PDOS) on the d-orbitals, which is
shown in Figure 3, can give valuable information about
reactivity. The well-known d-band model describes how the
center and width of the d-band energy obtained from the
PDOSs can be used to understand trends in catalytic
activity.49−51 According to this model, a higher d-band center
and decreasing width are indications of stronger bonding of
admolecules. Both the total PDOS and contributions from each
d-type orbital change when switching between FM and AFM2
states. Also, the d-band energy center and width of both upand down-spin components differ between the AFM2 and FM
structures. The d-bands of AFM2 are slightly narrower for both
spin channels, whereas the d-band centers of FM lie closer to
the Fermi-energy. However, AFM2 has a significant “shoulder”
in the PDOS around 1.5 eV. The PDOS is the first indication
that a change in the spin state (by an external magnetic field)
may be used to control orbital occupation and energy, the key
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the top-site and dissociates spontaneously. The dissociation
energy is −2.28 eV compared to that of H2 in gas phase and
that of the clean AFM2 surface. However, on the FM surface
H2 is molecularly adsorbed, and a stable Kubas complex53,54 is
formed. In the Kubas complex, the H−H bond is elongated to
0.85 Å from 0.74 Å in the gas phase. The molecular adsorption
and atomic adsorption energies are −0.51 eV and −1.04 eV
compared to those of the gas-phase H2 and clean FM surface,
respectively. The energy barrier for H2 dissociation going from
the molecularly adsorbed state to the H-adatom state on FM is
0.35 eV, which shows that the Kubas complex is quite stable on
the FM surface and may have a significant effect on hydrogen
desorption from the FM iron surface53 (see also the Discussion
section). Furthermore, these results show that H2 dissociation
is much more facile on the AFM2 than on the FM surface.
To understand the difference between FM and AFM2 toward
H2 dissociation, atomic charges and density difference integrals
of eq 3 were computed for the dissociated states. On both
surfaces, each hydrogen adatom is positively charged by +0.4 e.
It is concluded that the total charge transfer between the
dissociated hydrogen and the two surfaces remains unchanged
when the spin structure is changed. The density difference
integrals presented in Figure 6 show how the density is
reorganized upon bond formation between the surface and
dissociated H2. From this figure, it is readily visible that on the
AFM2 surface the accumulation of charge between Fe and H
(peak at ∼17 Å) is greater than that on the FM surface.
Furthermore, both spin channels donate electrons when the
bond is formed on AFM2. On the FM surface, however,
electrons are donated only from the β channel, whereas α
electrons do not participate in charge transfer from the surface
to hydrogen adatoms. As a result, less charge is accumulated
between the surface and hydrogen adatoms leading to weaker
bonding. In the dissociated state, the magnetic moment of the
Fe atom, which is in between the hydrogen adatoms, decreases
from 2.69 to 2.43 μB on AFM2 and from 2.78 to 2.56 μB on
FM. The larger decrease in magnetic moments on AFM2 is
attributed to stronger charge donation to hydrogen from both
spin channels.
3.3. Magnetic State Effects on the Stability and
Reactivity of CO Admolecules. Adsorption and dissociation
of CO are common probe reactions in surface chemistry and
are important in, e.g., Fischer−Tropsch and water−gas shift
chemistry on iron.28,55 On BCC iron surfaces, CO is
molecularly adsorbed in an upright fashion with carbon closer
to the surface. Depending on the surface structure, nanoparticle
size, and lattice-constant, either top- or hollow sites are the
favorable adsorption sites.56 Below, we analyze how the spin
structure of FM and AFM2 affects CO adsorption and
dissociation on the FCC(111) iron surface.
CO adsorption on all relevant sites was studied for both FM
and AFM2 slabs. The adsorption energy values are given in
Table 2 where it can be seen that top-sites are the most
favorable adsorption sites on both surfaces. Adsorption on
AFM2 is slightly stronger than that on FM. During adsorption
on top- and hcp/fcc sites, the C−O bond is elongated from the
gas-phase value of 1.14 Å to 1.17 or 1.19 Å, respectively, on
both surfaces. Also, the atomic charges of carbon and oxygen in
the adsorption complex are effectively the same on both
surfaces, and the total charge transfer is similar. However,
density differences integrated using eq 3 show that on the
AFM2 surface, both donation and back-donation are larger than
those on the FM surface, as can be seen in Figure 7. It is also
Figure 3. PDOS of FM and AFM2 magnetic states of the FCC(111)
slab of iron. ed is the d-band energy center and Wd its width.
aspects of modifying reactivity. However, the d-band characteristics do not provide clear predictions of which surface should
be more reactive. Below, we present results of studies of H2 and
CO adsorption to learn about the reactivity.
3.2. Magnetic State Effects on Fe−H2 Adsorption. An
understanding of the chemistry of H2 on metallic surfaces is
vital for both practical and fundamental reasons since hydrogen
is involved in so many important reactions, and so much work
has been done to obtain a comprehensive understanding of
both adsorption and reaction of hydrogen at metal surfaces. H2
is adsorbed dissociatively on most neutral transition metal
surfaces,52 but, for example, on Pt surfaces, the adsorption/
desorption processes depend strongly on the charge state
(electric potential) and the surface structure. Thus, it is of
interest to study the interaction of hydrogen with FM and
AFM2 iron surfaces.
On both surfaces, molecular H2 adsorption was considered at
both bridge and top-sites depicted in Figure 4. The bridge sites
were unstable on both surfaces, and H2 moved spontaneously
to top-sites during energy minimization. Pathways for H2
adsorption at top-sites on both FM and AFM2 surfaces are
presented in Figure 5. On AFM2, the molecule is unstable at
Figure 4. Adsorption sites on an FCC(111) surface. Symbols 1, 2, 3,
and 4 refer to top, bridge, HCP, and FCC sites, respectively.
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Figure 5. Energy along optimal paths for H2 adsorption on FM and AFM2 surfaces. The local minimum for the H2 admolecule on the FM surface
was found from minimum energy path calculation and corresponds to a Kubas complex (H−H bond length 0.85 Å). At the transition state for
dissociation, the H−H bond length is 0.95 Å. On the AFM2 surface, dissociation is barrierless, and an admole is not formed. (Note: The clean AFM2
slab is 0.033 eV/atom higher in energy than the FM slab. For the crystal, AFM2 is 0.03 eV/atom lower in energy than FM.)
Figure 6. Density difference integrals for H-adatoms on FM and AFM2 (111) surfaces of the FCC iron. The horizontal axis is the distance along the
surface z-direction, and the vertical axis is the integral of the charge difference.
interesting to note the two donation mechanisms are highly
dependent on spin polarization: back-donation is due to the
changes in spin-up density, whereas donation is reflected in
spin-down density differences. For top-site adsorption, the
magnetic moment of the underlying iron atom decreased from
2.69 to 1.21 μB on AFM2 and from 2.78 to 1.60 μB on FM. This
observation is in line with the larger charge transfer on AFM2
Table 2. CO Adsorption Energy on the FCC(111) Surface of
Fe in FM and AFM2 States (in eV)
FM
AFM2
top
HCP
FCC
−2.15
−2.31
−1.72
−1.90
−1.73
−1.61
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Figure 7. Charge density difference integrals (eq 3) for CO adsorption on top sites of FM and AFM2 surfaces. The horizontal axis gives the distance
along the surface’s z-direction, and the vertical axis gives the integral of charge difference.
For this interaction, both up-spin channels (Figure 8A and C)
and the down-spin channels (Figure 8B and D) have similar
peak positions and heights below the Fermi-level. However, the
largest difference between the two magnetic states is the larger
amount of empty 2π* states above the Fermi-level (at 0 eV) for
FM. As these states remain empty during CO adsorption, they
are unimportant for adsorption of the energy, but as shown in a
previous article,56 they can play a key role in the dissociation
process. On FM, the empty 2π* states have more overlap with
the metal and can accept electrons from the surface allowing
electron flow to the antibonding 2π*-orbital during dissociation. This may be classified as a back-donation effect, but note
that these states are empty in the adsorption complex. Thus,
they do not contribute to charge transfer or back-bonding
during adsorption but become important in the transition state
for CO dissociation.
To study the difference in reactivity, minimum energy paths
for CO dissociation starting from top-sites were computed.
During the reaction, the carbon atom moves to a 4-fold
coordinated HCP-type site, while the oxygen atom moves to an
adjacent HCP site. On the FM and AFM2 surfaces, the barrier
for CO dissociation is calculated to be 1.40 and 1.67 eV,
respectively. The calculated reaction energy is −0.17 eV and
−0.16 eV, respectively. Viewing this in light of adsorption
energy and charge transfer, it is interesting to notice that
stronger charge transfer on AFM2 increases the stability of the
adsorption complex and makes it more difficult to dissociate
the molecule. However, the energy at the saddle point is −0.75
and −0.64 eV on FM and AFM2 surfaces, respectively, with
respect to gas phase CO. This means that the transition state
for CO dissociation is lower in energy on the FM surface even
though the reaction energy is independent of the magnetic state
of the surface. This may be explained by the amount of
available empty 2π* states above the Fermi-level, as discussed
above.
surface. Thus, the spin structure may be used to affect the
degree of charge transfer in the case of CO adsorption.
The orbital interactions between CO and the two FeFCC(111) surfaces may be investigated further by projecting
the Kohn−Sham states (KS) on frontier orbitals of CO in a top
adsorption site and the nearest iron atom. The former yields
three molecular orbital density of states (molDOS), whereas
the latter gives PDOS broken down into specific atomic orbital
symmetries. The equations are as follows:
molDOS:
PDOS:
ρi (ε) =
a
ρl (ε) =
∑ ⟨ψn|φiCO⟩⟨φiCO|ψn⟩δ(ε − εn)
n
∑ ⟨ψn|ϕia⟩⟨ϕla|ψn⟩δ(ε − εn)
n
(4)
where |ψn⟩ are the KS states of the adsorption complex, |φCO
i ⟩ is
one of the frontier orbitals in CO, and |ϕal ⟩ is the l atomic
orbital of atom a. The DOSs represent hybridized orbitals in
the adsorption complex. As can be seen from eq 4, both the
molDOS and PDOS have peaks at the same values of the
orbital energy, εn, and the height of these peaks corresponds to
the overlap of the integrals. Thus, the peaks with the same
energy correspond to the same hybrid orbital. From the DOSs
in Figure 8, one can infer to which d-orbital a frontier orbital is
coupled.
From Figure 8, it can be seen that the HOMO of CO, the 5σ,
is mainly coupled to the dz2−r2 orbital in all cases, which is in
line with the Blyholder model. Both bonding (around −9.8 eV)
and antibonding (−8 to −6 eV) parts of 5σ lie almost
completely below the Fermi-level in the down-spin channel
(Figure 8B and D), whereas the up-spin channels (Figure 8A
and C) have also some empty states. Also the 5σ-molDOSs are
rather similar for both spin states, and it may be concluded that
the 5σ−dz2−r2 interaction cannot explain reactivity differences
between the FM and AFM2 states.
Interactions between the surface and the two LUMO orbitals
of CO can mainly be attributed to 2π* − dxz+yz contributions.
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Figure 8. Molecular DOS (above) and d-orbital projected DOS (below) for both spin channels of the FM (A and B) and AFM2 (C and D) surfaces.
4. DISCUSSION
state of the iron catalyst. Thus, the effect of the spin-state on
reactivity could be useful for modifying rates and thermodynamics of a reaction with the possibility of controlling yield and
selectivity.
As an example, we have considered the chemistry of CO and
H2, which are reactants in iron catalyzed Fischer−Tropsch
synthesis (FTS) and the water−gas shift (WGS) reaction.28 As
several reaction pathways for these reactions are feasible,
selective stabilization of certain surface complexes of carbon,
hydrogen, and iron could help in controlling yield and the
selectivity of these industrially important reactions. Controlling
surface reactivity by switching between different magnetic
As presented in the Results section, changing the magnetic state
of the FCC iron provides a way to modify band structure,
orbital population, and d-band characteristics. These findings
alone suggest that the reactivity of iron is sensitive to its spinstructure and that magnetism is an important aspect for
understanding the reactivity of iron surfaces. From Figures 6
and 7, it becomes evident that charge transfer between the
surface and admolecules can be affected by changes in spin
state. Depending on the reaction, the increased charge transfer
may lead to either stabilization or destabilization of the
reactants. Also, activation energy is sensitive to the magnetic
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Figure 9. Simulated TPD curves for H2 desorption from an Fe-FCC(111) film in AFM2 and FM states. The upper panel gives the surface coverage
as a function of temperature, while the lower one shows the desorption rate as a function of temperature.
changes in the magnetic structure change electronic structure in
both materials enabling magnetic control of reactivity.
The above discussion gives an indication of the various
magnetic properties that are present in iron containing systems.
As changes in magnetic structure are intimately coupled to
electronic and even geometric properties, access to different
magnetic states allows modifications in the chemical reactivity
of surfaces of iron-based catalysts. The various spin-states can
be accessed in several ways, but applied external magnetic fields
provide a natural way of controlling the spin-structure of a
magnetic system, and MFEs on reactivity should be visible in
several iron-based catalysts. If changes in magnetization are
large, both thermodynamic and kinetic MFEs are possible.
However, experimental realization of these effects requires
careful consideration in the choice of reaction and system.
From the results described above, one can think of various
experiments for realizing the effect of a magnetic field on the
adsorption or desorption of hydrogen from the surface of a FeFCC(111) thin film. Since the binding energy of the adatoms is
quite different depending on the magnetic state, a temperatureprogrammed desorption (TPD) experiment66 should give
different results depending on the magnetic state of the slab.
Figure 9 shows simulated spectra using the calculated H2
desorption energy and the Redhead equation as follows:67
structures could be realized, e.g., by application of an external
magnetic field.
Even though FCC iron is seldom found and used in catalysis,
several iron containing systems with interesting magnetic
properties can be realized. First, iron thin films may be grown
on various substrates with different lattice constants and crystal
structure. 57,58 These films can have various magnetic
states21−27,59 similar to the ones considered in this article. In
addition to collinear (anti)ferromagnetic states, noncollinear17−20,24 states may have unexpected effect on reactivity.
Also, the low Curie temperature of thin films (around 220−300
K for Fe on FCC copper,23 for example) can result in the
formation of a paramagnetic state at rather low temperature.
These disordered states are expected to have average
adsorption/reactivity properties of the different, ordered spin
structures.
Second, depending on size, geometry, and the synthesis
method, both pure and bimetallic nanoparticles with various
magnetic properties can be synthesized.60 Small, gas-phase iron
nanoparticles are icosahedral and have antiferromagnetic spinstructure,56 and icosahedral iron particles up to 13 nm have
been synthesized,61 while bulk and nanoparticles of BCC iron
are ferromagnetic.62 Alloying of iron nanoparticles with other
metals can also be used to tune magnetic properties. Iron−
platinum nanoparticles, especially, have varying magnetic
properties; antiferromagnetic FePt particles are characterized
by large coercivity63 or superparamagnetism,64 whereas FCCstructured FePt3 is antiferromagnetic with high Curie temperature.65
Oxides are a third class of iron compounds whose catalytic
activity could be manipulated by a magnetic field. Several iron
oxides present in FTS and WGS are antiferrimagnetic or have
Fe(II) in octahedral coordination28,55 both of which have
plausible structures for magnetically controlled reactivity.4
Here, magnetism rises from metal ions with atomically localized
unpaired electrons rather than the band magnetism in metals.
Despite the different origin of magnetism in metals and oxides,
rd = −
⎡ E ⎤
k
d θ (T )
= 0 θ n(T )exp⎢ − d ⎥
dT
βH
⎣ kbT ⎦
(5)
where k0 = 1013 s−1 is the temperature-independent frequency
factor, βH = 0.6 K/s is the heating rate, kb is the Boltzmann
factor, and Ed is the desorption energy from the dissociated
state (2.28 eV for AFM2 and 1.04 eV for FM). n = 2 is the
reaction order for the H2 desorption reaction, 2H* → H2(g) +
2* . The prediction is that H2 is desorbed around 380 K from
the FM surface and around 790 K from the AFM2 surface, a
clear difference.
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Another possibility is to use a thick enough film that the
AFM2 state is lower in energy but prepare the iron film initially
in the FM state by using an external magnetic field. If the
temperature is not too high, the H2 molecules will then adsorb
in a Kubas complex and will not climb the 0.35 eV barrier to
the dissociated state. Then, as the magnetic field is turned off
and the system switches to the AFM2 state, spontaneous
dissociation of the H2 molecules should occur (unless coercivity
is too large). A third option is to keep the temperature fixed
and adsorb H2 on the surface of a film in the AFM2 magnetic
state, which binds hydrogen atoms more strongly. Then, use a
magnetic field to switch to the FM state and observe hydrogen
desorption.
5. CONCLUSIONS
This article presents a computational study of the effect
magnetic states can have on the reactivity of an iron surface.
More specifically, the reactivity of antiferromagnetic (AFM2)
and ferromagnetic (FM) FCC(111) iron slabs have been
compared using DFT calculations at the meta-GGA level. The
results show that spin-structure can strongly affect orbital
occupation of the surface and especially charge-transfer
between the catalyst surface and the adsorbate. It is shown
that H2 and CO adsorption and dissociation are modified by
changes in spin-structure. In both cases, charge transfer on
AFM2 is greater than that on FM. Interestingly, H2 dissociation
occurs more readily on AFM2, whereas CO dissociation is
more facile on the FM surface, which is explained by the
presence of empty 2π* states. The calculations show that the
reactivity of the surface can be affected significantly by changing
the magnetic state. These findings suggest that several
important reactions utilizing H2 and CO as reactants, including
Fischer−Tropsch synthesis and the water−gas shift reaction on
magnetic iron catalysts, may be sensitive to the spin-state of the
catalyst. As the magnetic state can be changed by applying
external perturbations, such as a magnetic field, these
considerations point to ways of modifying the thermodynamics
and kinetics of heterogeneously catalyzed reactions.
■
AUTHOR INFORMATION
Corresponding Author
*Tel: +358 405 570 044. E-mail: kari.laasonen@aalto.fi.
Notes
The authors declare no competing financial interest.
■
ACKNOWLEDGMENTS
CSC IT Center of Science is acknowledged and thanked for
providing ample computing resources through their Grand
Challenge project gc6260. H.J. thanks Björgvin Hjörvarsson for
stimulating discussions. Funding from the Academy of Finland
through Project No. 140115, Centre of Excellence Program
(Project No. 251748), and FiDiPro program (Grant No.
263294) is acknowledged.
■
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