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Prévia do material em texto

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um
. N
, Sta
Accepted 29 December 2014
tha
open the possibility of mapping the many parameters determining the rate of a full catalytic reaction
value that corresponds to the highest activity.
This means a lack
ested expe
d to chara
rmediate a
catalyst, or what value of the ‘‘bond strength’’ corresponds
optimum catalyst. For these reasons, the Sabatier principle
be used as a basis for catalyst design rules.
The advent of computational electronic structure methods that
are efficient enough to treat reactions on metal surfaces and accu-
rate enough to have predictive power has significantly changed the
availability of systematic data for adsorption energies and activa-
tion energies for surface chemical reactions. An enormous amount
of effort has gone into establishing methods and data describing
transition-metal surfaces [4–21]; this has enabled a priori
q Paper submitted in recognition of the enormous influence Haldor Topsøe has
had on the advancement of the science of heterogeneous catalysis and his
continued interest and support of the development of a predictive theory of the
phenomenon.
⇑ Corresponding authors at: SLAC National Accelerator Laboratory, 2575 Sand Hill
Road, CA 94025, USA.
E-mail addresses: alevoj@stanford.edu (A. Vojvodic), norskov@stanford.edu
(J.K. Nørskov).
Journal of Catalysis 328 (2015) 36–42
Contents lists availab
Journal of
journal homepage: www.e
how they determine the activity and selectivity of a catalytic mate-
rial. This will allow an understanding of trends from one catalyst to
the next, and it will open the possibility to design catalysts by
searching for materials with descriptors close to the optimum
the major shortcoming that it is not quantitative.
of predictive power, and hence, that it cannot be t
tally. It is not clear which quantity should be use
the ‘‘bond strength’’ between the relevant inte
http://dx.doi.org/10.1016/j.jcat.2014.12.033
0021-9517/� 2015 Published by Elsevier Inc.
rimen-
cterize
nd the
to the
cannot
Understanding how solid surfaces work as catalysts is attracting
renewed interest. Not only is the majority of the chemical industry
relying on catalysis, but the search for renewable energy solutions
and for sustainable production processes also requires completely
new chemical processes and catalysts [1]. The hope is that through
a fundamental understanding of basic concepts in heterogeneous
catalysis, we can develop new catalyst design strategies. The chal-
lenge is to identify descriptors of catalytic activity and discover
optimum catalyst [2,3]. The idea is that the best catalysts should
bind atoms and molecules with an intermediate strength: not too
weakly in order to be able to activate the reactants, and not too
strongly to be able to desorb the products. This leads to a vol-
cano-type relationship between activity and bond strength as illus-
trated in Fig. 1. This picture has been very successful in providing a
general qualitative understanding of why there might be an opti-
mum catalyst. As a theory of heterogeneous catalysis [3], it has
Keywords:
Heterogeneous catalysis
Transition metals
Theory
Computational catalysis
DFT
Sabatier principle
Scaling relation
Descriptor
1. Introduction
onto a few descriptors. The resulting activity map can be viewed as a quantitative implementation of
the classical Sabatier principle, which states that there is an optimum ‘‘bond strength’’ defining the best
catalyst for a given reaction. In the modern version, the scaling relations determine the relevant ‘‘bond
strengths’’ and the fact that these descriptors can be measured or calculated makes it a quantitative the-
ory of catalysis that can be tested experimentally by making specific predictions of new catalysts. The
quantitative aspect of the model therefore provides new possibilities in catalyst design. Finally, the d-
band model provides an understanding of the scaling relations and variations in catalytic activity in terms
of the electronic structure of the transition-metal surface.
� 2015 Published by Elsevier Inc.
Since the early part of the 20th century, the Sabatier principle
has provided a conceptual framework for our thinking about the
Received 19 November 2014
Revised 22 December 2014
in transition-metal catalysis: scaling relations, activity maps, and the d-band model. Scaling relations are
correlations between surface bond energies of different adsorbed species including transition states; they
From the Sabatier principle to a predictiv
heterogeneous catalysisq
Andrew J. Medford, Aleksandra Vojvodic ⇑, Jens S. H
Felix Studt, Thomas Bligaard, Anders Nilsson, Jens K
SUNCAT Center for Interface Science and Catalysis, Department of Chemical Engineering
SLAC National Accelerator Laboratory, 2575 Sand Hill Road, CA 94025, USA
a r t i c l e i n f o
Article history:
a b s t r a c t
We discuss three concepts
theory of transition-metal
melshøj, Johannes Voss, Frank Abild-Pedersen,
ørskov ⇑
nford University, Stanford, CA 94305, USA
t have made it possible to develop a quantitative understanding of trends
le at ScienceDirect
Catalysis
lsevier .com/locate / jcat
identification of good descriptors for a given catalytic reaction, and
it has made it possible to map out optimum regions of descriptor
space to help discover leads for new catalysts. In the present per-
spective, we briefly highlight some of these new developments.
2. Quantifying the bond strength
One of the first challenges toward a quantified heterogeneous
theory of catalysis is determining a suitable quantity, or ‘‘descrip-
tor’’, to represent the ‘‘bond strength’’ of interest. The early lit-
erature often used bulk properties such as the heat of formation
of the metal oxide [22] or suitable compound [23], or the number
of d-orbital electrons [24]. As noted already by Sabatier, the rele-
vant bond strengths should of course be related to bonds at the
adsorption energies. In this case, there are two descriptors since
Fig. 1. Schematic representation of the qualitative Sabatier principle.
A.J. Medford et al. / Journal of Catalysis 328 (2015) 36–42 37
surface and not in the bulk or in molecules [3]; however, prior to
the recent advances in computational chemistry, bulk formation
energies were the simplest and most reliably determined quanti-
ties to use. An example using the oxide heat of formation to
describe ammonia synthesis activity is shown in Fig. 2a. It can be
seen that while there is some correlation, the ‘‘volcano relation-
ship’’ is far from convincing.
The volcano plot is much improved when the actual nitrogen
adsorption energies on the relevant metal surfaces are used as
the descriptor (see Fig. 2b). Here the same experimental rates are
plotted against the nitrogen adsorption energies as determined
by density functional theory (DFT) calculations [25].
The improved relationship of the volcano plot in Fig. 2b indi-
cates that the adsorption energy of N⁄ at the surface site provides
a much better quantitative description of the ‘‘bond strength’’ con-
cept of the Sabatier principle than the oxide heat of formation. This
is intuitive, since the N⁄ adsorption energy is a surface property,
and the reaction is mediated by the surface. Furthermore, the N⁄
adsorption energy probes the interactions between the transition
metal and nitrogen (rather than oxygen), which is present in all
intermediates of the ammonia synthesis reaction.
3. Dimensional reduction: scaling relations
While nitrogen is undoubtedly a key intermediate for ammonia
synthesis, there are also several other intermediates and transition
states that play a role in the reaction. In order for the bond strength
to be a valid descriptor, it must describe the interaction between
the surface and all relevant intermediates and transition states.
To illustrate why a single descriptor is sufficient,consider the fol-
lowing very simple mechanism for ammonia synthesis:
N2ðgÞ þ 2� ! N—N�þ� ! 2N�
N� þ 3=2H2ðgÞ ! NH3ðgÞþ�
Fig. 2. (a) Volcano plot for the ammonia synthesis reaction over K-promoted transition-m
descriptor (adapted from Ref. [22]). (b) Volcano plot of the same rates with the nitrogen a
the RPBE functional (from Ref. [25]) as a descriptor.
Let us also assume that the first step, N2 dissociation, is rate lim-
iting. Both experiments and theory show that this is the case for
the most active catalysts [26–28]. In this simple model, the rate
is determined by two variables that are in principle independent:
the transition-state energy (activation barrier) for N2 dissociation
(EN–N) (determining the rate of dissociation) and the adsorption
energy of nitrogen (EN) (determining the coverage on the surface).
Fig. 3a shows the rate calculated with this mechanism and a mean-
field kinetic model as a function of these two variables. Values of
(EN, EN–N) of stepped transition-metal surfaces are overlaid on
the plot. It can be seen that there is a clear linear scaling relation
between the two variables. This means that a single variable is
enough to define the catalyst in terms of the ammonia synthesis
rates, thus explaining why the experimental data in Fig. 2b and
the model data in Fig. 3b can be ordered very well using the nitro-
gen adsorption energy as the descriptor.
The approach outlined above for a simple reaction can be gen-
eralized to much more complex reaction networks. Consider for
example the hydrogenation of CO to form methane, methanol, or
ethanol. Even a very simple model for this reaction network con-
tains 52 elementary reactions (a subset of which are shown in
Fig. 4, see Ref. 30 for more details) and therefore, in principle,
has approximately 104 independent energy variables (one reaction
energy and one activation energy for each elementary reaction
step) characterizing the reaction. Understanding trends in a space
with more than 3 dimensions is a daunting task, leaving very little
space for intuition or for developing catalyst design principles. A
very considerable reduction in complexity is needed.
The solution to this problem lies in the generality of the scaling
relations. Fig. 4 shows that the intermediates and transition states
of many different classes of elementary steps can be determined
using only a linear combination of the carbon and oxygen
etal catalysts at 523 K and 0.8 bar using oxide heat of formation as a bond strength
dsorption energy at stepped metal surfaces as determined by DFT calculations using
of C
38 A.J. Medford et al. / Journal
the bonding at the surface takes place through both C and O atoms,
and the binding energy of these two atoms is relatively indepen-
dent. The bond energy of H to the surface scales well with that of
C and therefore does not need to be considered an independent
variable. By using the concept of scaling relations, the effective
dimensionality of the problem has therefore been reduced to only
2, leading to a much more manageable problem in terms of both
optimization and understanding.
4. Activity maps: understanding trends in catalytic activity and
selectivity
The scaling relations define the descriptors for a given reaction,
and by combining the scaling relations with a kinetic model we can
Fig. 3. (a) Potential energy diagram for simplified ammonia synthesis reaction, along with
synthesis rate as a function of nitrogen adsorption energy and N2 dissociation barrier w
theoretical limit since the activation barrier (Ea) must always be positive (c) Rate shown a
of EN. The red point marked ‘‘CoMo’’ denotes the expected rate on a mixed site contain
energies [29]. (For interpretation of the references to color in this figure legend, the rea
Fig. 4. Scaling relations for 26 intermediates and 16 transition states in the conversion o
on transition-metal (211) surfaces. Tick marks are 1 eV apart; scaling parameters and m
analysis along with color code are shown (top right) along with the error between scale
references to color in this figure legend, the reader is referred to the web version of thi
atalysis 328 (2015) 36–42
define a mapping of catalytic activity onto descriptor space. This
mapping, which is a generalization of the volcano relations of
Figs. 2 and 3b, we denote activity maps. For CO hydrogenation,
the activity maps for different products as a function of the C
and O adsorption energies are shown in Fig. 5a–c. In such a map,
an active site on a catalyst surface is defined by the values of the
two descriptors, and in the figure, the values for (211) step con-
figurations of a number of relevant transition metals are included.
The maps provide a means to rationalize the known trends about
transition-metal catalysts for these reactions: Cu is the best ele-
mental metal catalyst for methanol synthesis [31], Ru, Co, Ni, and
Rh are the best for methanation [32], and no good elemental metal
catalyst is known for ethanol synthesis (rhodium has been shown
to catalyze the synthesis of ethanol with reasonable selectivity in
active site motif for the (211) surfaces with the step as the active site. (b) Ammonia
ith energetics for FCC/HCP metal step sites and scaling line. Shaded area shows the
s a function of the nitrogen adsorption energy, utilizing that EN–N is a linear function
ing both Co and Mo based on interpolation between the two nitrogen adsorption
der is referred to the web version of this article.)
f CO and H2 to ethanol (left) as a function of carbon and oxygen adsorption energies
ore details can be found in Ref. [30]. Classes of elementary reactions included in the
d and DFT energies for all scaling relations (bottom right). (For interpretation of the
s article.)
Fig. 5. Rates and selectivities for the formation of methane, methanol, and ethanol as a
o re
rate
whit
of C
the presence of specific promoters or supports, but is often selec-
tive to methane, especially on inert supports [33]).
Knowing the rates of different parallel reaction pathways lead-
ing to different products also allows us to map out the selectivity of
different catalysts as a function of descriptor values. This is illus-
calculated using a microkinetic model, which utilizes the scaling relations of Fig. 4 t
PH2 = 60 bar. (a) The rate of methane formation, (b) rate of methanol formation, (c)
with carbon and oxygen binding energies of A3B transition-metal alloys (indicated as
catalysts. See Ref. [30] for more details.
A.J. Medford et al. / Journal
trated in the selectivity map in Fig. 5d for the production of
methane, methanol, and ethanol over stepped metal surfaces.
Selectivity toward higher alcohols (modeled by ethanol) is only
found in a narrow strip of parameter values, far from elemental
metal values.
5. The electronic structure factor in transition-metal catalysis:
the d-band model
Scaling relations between activation energies and reaction ener-
gies have been known in various subfields of chemistry for decades
as Brønsted relations [34], Evans–Polanyi relations [35,36], or the
Hammett equation [37]. The adsorption energy scaling relations
represent a significant extension of this concept since they cover
not only activation energies but also energies of intermediates,
and since they relate these energies to any suitable adsorption
energy rather than just the reaction energy [38]. Establishing the
scaling relations relies on access to adsorption energies and transi-
tion-state energies for many adsorbates on a statistically large
enough number of surfaces. Systematic data did not become avail-
able until theoretical methods for calculating such quantities
became accurate and fast enough to treat the complex systems of
interest in heterogeneous catalysis [38]. Benchmarking the compu-
tational methods against measurements is a very important part of
establishing such a procedure, and it has been shownthat modern
theoretical methods provide reasonably accurate adsorption ener-
gies [39,40]. Most recently, it was shown that the scaling relations
and the position of the maximum in activity maps are quite insen-
sitive to errors in underlying electronic structure treatment for
exchange and correlation effects, a result that helps understand
the success of the approach outlined above [41].
One important question is to understand the physical basis for
these relationships and why they are so general. Electronic struc-
ture calculations and spectroscopic measurements have been used
to provide detailed answers to this question. Fig. 6a shows the cal-
culated variations in the adsorption energy of nitrogen, EN, and in
function of carbon and oxygen adsorption energies. The rates and selectivities are
duce the complexity. The reaction conditions are as follows: T = 593 K, PCO = 30 bar,
of ethanol formation, and (d) selectivity map for the three different products along
e x’s). The inset of (d) shows several alloys that were identified as promising ethanol
atalysis 328 (2015) 36–42 39
the energy of the transition-state energy, EN–N, as a function of a
parameter describing the electronic structure of the metal surfaces.
The parameter chosen is the upper band edge of the metal d band
projected onto the surface atom(s) to which the adsorbates bond
[42,43]. In the d-band model, this parameter (or the d-band center,
in cases where the coupling matrix elements are roughly constant
[44]) correlates with the hybridization energy. The reason is that
the interaction strength is related to the filling of the anti-bonding
states formed between themetal d states and the adsorbate valence
states. The higher the d states are in energy relative to the highest
occupied states at the Fermi energy, the higher in energy the anti-
bonding states are, the more empty they are, and the stronger the
interaction becomes. This picture has been confirmed by direct
spectroscopic measurements, as illustrated in Fig. 6.
Since both EN–N and EN depend linearly on a parameter describ-
ing the surface electronic structure, they also depend linearly on
each other. The explanation of the scaling relations is therefore
that both transition-state and adsorption energies of different
intermediates depend on the surface electronic structure in similar
ways. Different adsorbate states hybridize with the surface d elec-
trons to form bonding and anti-bonding states. The strength of the
interaction depends critically on the degree of filling of the anti-
bonding states, which in turn depends on the position of the d
states relative to the Fermi level. This picture has been confirmed
in detailed X-ray spectroscopy experiments probing the filled and
empty states in adsorbate systems, see inset in Fig. 6 [43,45].
6. Catalyst design strategies
Perhaps the most important consequence of a quantitative
model of catalytic activity and selectivity is the possibility of using
2 1 0 1 2 3 4 5
εTd [eV]
4
2
0
2
4
6
8
N
itr
og
en
ad
so
rp
tio
ne
ne
rg
y 
[e
V
]
Fe
CoNi
Cu
RuRh
Pd
Ag
Re
Pt
(a)
2 1 0 1 2 3 4 5
εTd [eV]
4
2
0
2
4
6
8
N
2
di
ss
oc
ia
tio
nb
ar
ri
er
 [
eV
]
FeCo
Ni
Cu
RuRh
Pd
Ag
Re
Pt
(b)
XES
XAS
XES
XASN/Cu
N/Ni
Fig. 6. Nitrogen adsorption energy (a) and N2 transition-state potential energy (b) as a function of the upper band edge of the d projected density of states of the metal surface
atoms. The insets in (a) show experimental X-ray absorption and emission spectra for N adsorbed on the (111) surface of Cu and Ni measuring the filled (indicated by shaded
N-2p
40 A.J. Medford et al. / Journal of Catalysis 328 (2015) 36–42
activity and selectivity maps to aid the search for new catalysts,
either for known reactions or for new reactions and process
conditions.
The reduction in the number of parameters characterizing a cat-
alyst system for a given reaction offered by the scaling relations
allows for identification of a few descriptors and enables one to
identify the optimum values. This accrued knowledge opens the
possibility for a more rigorous route to catalyst design. An early
example of such an approach was the suggestion based on a vol-
cano relation similar to Fig. 2b that a mixed Co–Mo catalyst should
be close to optimum as a catalyst for ammonia synthesis [29]. The
idea is quite intuitive from Fig. 2b or 3b: having N adsorption ener-
gies somewhere between Co, which binds N too weakly, and Mo,
which binds N too strongly, should give a close to optimum cata-
lyst. The intermediate bond energy is borne out by detailed calcu-
lations of different model systems of the Co–Mo active site. These
Co–Mo mixed metal catalysts were shown experimentally to give
activities comparable to Ru [29]. Such an intuition could not have
been obtained from Fig. 2a.
More generally, calculation (or measurement) of descriptor val-
ues for a range of possible catalysts can be used to screen for new
catalysts. Fig. 5d includes a screening of clean (211) stepped metal
sites for higher alcohol synthesis (the effect of additives is not
included here). The calculations point to a series of potentially
areas) and empty N-induced states, respectively. The emptying of the anti-bonding
considerably stronger [43,45].
interesting catalyst candidates. The prediction that unpromoted
Pt–Co and, in particular, Cu–Co should be good candidates with a
high selectivity has been verified experimentally [46,47].
Fig. 7. (a) Ammonia synthesis rate as a function of nitrogen adsorption energy and N2 dis
packed (111) surfaces (red), (211) steps (black), and (211) K-promoted steps (blue). (b
other conditions are the same as in Fig. 3. (For interpretation of the references to color
The scaling relations, here presented for the stepped (211) met-
al surfaces, provide some very stringent restrictions on the possi-
bilities of finding good catalysts. Take the example of ammonia
synthesis to illustrate this. It would be desirable to find an ammo-
nia synthesis catalyst that has a lower barrier for N2 dissociation
and does not bind N atoms stronger at the same time. Fig. 3a shows
how the scaling relation effectively makes that impossible for the
elemental (211) stepped transition-metal surfaces. Given the scal-
ing relations, finding a good catalyst becomes a question of identi-
fying the best compromise between different competing factors
(e.g., N2 dissociation and NH3 desorption).
An alternative strategy is to find ways in which to circumvent
the scaling relations, that is, find ways to stabilize the adsorbed
state of one of the intermediates or transition state without stabi-
lizing others. Fig. 3a indicates that there is ample room for finding
a better ammonia synthesis catalyst if we could find effective ways
of circumventing the scaling relations, or find active site motifs
that have a lower-lying scaling relation than the (211) stepped
metal surfaces [42]. For example, if the close-packed surface is con-
sidered as the active site, the scaling relation will change, as shown
in Fig. 7a; however, this shift leads to a significant increase in the
transition-state energy, and thus a decrease of many orders of
magnitude in the rate as seen in Fig. 7b. Another possible strategy
is to add alkali metals as promoters. As seen in Fig. 7, a potassium
/metal-3d states on going from Cu to Ni is clearly seen, explaining why Ni binds N
promoter stabilizes the transition state for N2 dissociation without
affecting the N adsorption energy significantly [48], leading to a
different scaling relation and an order of magnitude increase in
sociation barrier, similar to Fig. 3b. Scaling relation lines correspond to metal close-
) Volcano plots corresponding to each scaling relation line. The kinetic model and
in this figurelegend, the reader is referred to the web version of this article.)
of C
rate. Designing active site motifs with a three-dimensional charac-
ter that can distinguish between various intermediates and transi-
tion-state structures is a very important path toward engineering
catalyst structures that can further escape the scaling relations;
biological catalysts exploit this strategy extensively. Two recent
studies show possibilities of escaping the scaling relations by
exploiting the strategy of metal doping [49] and the importance
of 3D confinement in oxides [50].
The quantitative theory outlined above for thermal heteroge-
neous catalysis has been extended to a predictive theory of hetero-
geneous electrochemical systems by taking the electrochemical
potential and pH effects into account when modeling the thermo-
dynamics of electrocatalytic reactions on surfaces [51,52]. This the-
ory has formed the basis for computational searches for new
electrode materials [16,53,54].
We have briefly outlined elements of a consistent quantitative
theory of transition-metal surface catalysis. There are many chal-
lenges ahead before we have a complete theory of heterogeneous
catalysis. Outstanding issues include an understanding of finite
size effects, the role of supports, and a proper description of the
surface chemistry of transition-metal compounds. All of this
requires new theoretical methods, increased accuracy, better
kinetic models including the ability to treat complex systems and
reaction networks, and better methods for storage, retrieval, shar-
ing, and mining of data and information [55,56]. Given the devel-
opments in the last decade this is not outside our reach.
Author contributions
The manuscript was written through contributions of all
authors. All authors have given approval to the final version of
the manuscript.
Funding sources
U.S. Department of Energy Office of Basic Energy Science.
U.S. Department of Defense National Defense Science and
Engineering Graduate Fellowship (A.J.M).
Acknowledgments
Support from the U.S. Department of Energy Office of Basic
Energy Science to the SUNCAT Center for Interface Science and Cat-
alysis is gratefully acknowledged. A.J.M. is grateful for support by
the U.S. Department of Defense through the National Defense
Science and Engineering Graduate Fellowship Program.
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42 A.J. Medford et al. / Journal of Catalysis 328 (2015) 36–42
	From the Sabatier principle to a predictive theory of transition-metal heterogeneous catalysis
	1 Introduction
	2 Quantifying the bond strength
	3 Dimensional reduction: scaling relations
	4 Activity maps: understanding trends in catalytic activity and selectivity
	5 The electronic structure factor in transition-metal catalysis: the d-band model
	6 Catalyst design strategies
	Author contributions
	Funding sources
	Acknowledgments
	References