Chemistry Publications
Chemistry
11-2004
Density Functional Study of the Adsorption of
Propene on Silver Clusters, Agqm (m=1–5; q=0,
+1)
Steeve Chrétien
University of California - Santa Barbara
Mark S. Gordon
Iowa State University, [email protected]
Horia Metiu
University of California - Santa Barbara
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Density functional study of the adsorption of propene on silver clusters, Ag m q
(m=1–5; q=0, +1)
Steeve Chrétien, Mark S. Gordon, and Horia Metiu
Citation: The Journal of Chemical Physics 121, 9925 (2004); doi: 10.1063/1.1809600
View online: http://dx.doi.org/10.1063/1.1809600
View Table of Contents: http://scitation.aip.org/content/aip/journal/jcp/121/20?ver=pdfcov
Published by the AIP Publishing
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JOURNAL OF CHEMICAL PHYSICS
VOLUME 121, NUMBER 20
22 NOVEMBER 2004
Density functional study of the adsorption of propene on silver clusters,
q
„ m Ä1 – 5; q Ä0, ¿1…
Agm
Steeve Chrétien
Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106
Mark S. Gordon
Department of Chemistry, Iowa State University, Ames, Iowa 50011
Horia Metiua)
Department of Chemistry and Biochemistry, University of California, Santa Barbara, California 93106
共Received 28 July 2004; accepted 2 September 2004兲
Density functional theory has been used to investigate the binding of propene to small Ag clusters
in the gas phase. The binding mechanism based on frontier orbital theory, which we used previously
to describe the binding between propene and the Au clusters, works for the pure Ag clusters as well.
Among other things, it explains the trends of the desorption energy of propene as a function of the
Ag cluster size. We show that one can predict the binding site of propene by examining the shape
of the lowest unoccupied molecular orbitals 共LUMOs兲 of the bare clusters and correlate the strength
of the bond to the orbital energies of the LUMOs of the bare cluster. © 2004 American Institute
of Physics. 关DOI: 10.1063/1.1809600兴
I. INTRODUCTION
naked cluster where the LUMO1 of the naked cluster protrudes most in the vacuum 共i.e., has the highest overlap with
the ␲ orbital of propene兲.
Rule 2. If a naked Aun cluster of a given shape has
several LUMOs that have low energy, they can all contribute
to propene binding. Various LUMOs account for various
binding sites of propene, hence various isomers of the
关 Aun (C3 H6 ) 兴 q complex 共q is the total charge of the complex兲. The strongest propene–Aun bond is the one whose
binding site is controlled by the overlap with LUMO1, the
next strongest is the one corresponding to sites controlled by
the overlap with LUMO2, etc.
Rule 3. The lower the energy of LUMO1 of the naked
cluster, the higher the desorption energy of propene to the
site where that LUMO1 protrudes in space. In other words,
the variation of the desorption energy of the most stable isomer of 关 Aun (C3 H6 ) 兴 q with n, tracks the dependence of the
energy of LUMO1 on n.
Rule 4. If LUMO1 has protruding lobes at several nonequivalent sites, the propene will make the strongest bond at
the site having the lowest coordination.
We have also noted that since propene tends to donate
electron density to a Au cluster, the bond strength correlates
with the ability of the cluster to accept electrons.18 If these
observations can be extended to pure Ag and to mixed
Au–Ag clusters, we expect the following trends:
共1兲 For a given cluster size, propene should bind most
strongly to a positive ion, less strongly to a neutral one and
even less to a negative one.
共2兲 Propene should bind more strongly to a Au cluster
than to the corresponding Ag one because, for a given cluster
size, the electron affinity of the Ag cluster is smaller than
that of the Au cluster.22,23
共3兲 We anticipate that the desorption energies of propene from mixed Au–Ag clusters are intermediate between
Recent experiments have shown that small Au and Ag
clusters1–16 supported on TiO2 catalyze the epoxidation of
propene with very high selectivity. The present paper is part
of a series that uses density functional theory 共DFT兲 to try to
gain some understanding of the mechanisms of these reactions. We are particularly interested in the possibility of using clusters consisting of a few atoms as catalysts. The catalytic properties of such clusters often change quite
substantially, upon alloying, upon contact with the support,
or upon changing the number of atoms in the cluster.17 In
principle, this makes them more amenable to ‘‘tuning’’ their
properties to optimize the catalytic process.
In a previous paper,18 we have proposed four simple
rules, inspired by the frontier orbital theory,19,20 which can be
used to predict the binding site of propene to Au clusters, and
to estimate the strength of the bond.
There are a lot of papers in the literature where the
‘‘frontier orbital theory’’ was succefully applied. For example, Wells, Delgass, and Thomson used it to predict the
binding site of O2 to small Au clusters using the highest
occupied molecular orbital of the naked cluster.21 Our goal is
not to provide a survey of the literature, but rather to provide
very simple guidance rules that can be used to make useful
predictions related to the Au catalyst.
To explain these rules we use the following nomenclature: we call SOMO, an orbital that is occupied by one electron 共singly occupied MO兲 and reserve the names LUMO1,
LUMO2,... for the lowest lying empty orbitals. Among these,
LUMO1 has the lowest energy, the energy of LUMO2 is the
next lowest, etc.
Rule 1. Propene binds preferentially to the site on the
a兲
Electronic mail: [email protected]
0021-9606/2004/121(20)/9925/6/$22.00
9925
© 2004 American Institute of Physics
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9926
J. Chem. Phys., Vol. 121, No. 20, 22 November 2004
the ones of the pure Ag and pure Au clusters because, according to our calculations, the electronic affinities of the
mixed clusters are in between the ones of the pure Ag and Au
clusters.
共4兲 We expect propene to bind more strongly to a Ag
atom in a mixed cluster than on the same atom in a the pure
Ag cluster of the same size and shape; since Au is more
electronegative than Ag, an electron transfer from Ag to Au
atoms should occur in the mixed clusters.24,25 This creates an
electron deficiency on the Ag atoms in the mixed clusters
and activates these atoms towards the adsorption of propene.
In the present work we use DFT to calculate the desorption energy of propene to neutral and positively charged Ag
clusters and to test whether the rules proposed for propene
adsorption on Au clusters work for Ag. The adsorption of
propene on the neutral mixed Au–Ag clusters is discussed in
an accompanying paper.
It is possible in principle to ‘‘derive’’ these rules from
quantum mechanics, but such an approach would be complex
and not necessarily more enlightening than these ‘‘empirical’’ observations based on the results of DFT calculations.
The rules are useful in systematizing and ‘‘explaining’’
trends in desorption energy. They also allow us to cut down
substantially the number of calculations, since we can use
the properties of the naked clusters 共the shape and the energy
of their LUMOs兲 to guess reliably which propene-cluster isomers are likely to have the largest desorption energy.
II. COMPUTATIONAL DETAILS
A detailed presentation of the method of computation is
available in Ref. 18. Briefly, density functional calculations
have been performed with the VASP program 共version
4.4.5兲.26 –29 The potential energy surfaces for all the systems
discussed in this paper were initially explored using the combination of the exchange and correlation functionals of
Perdew and Wang 1991 共PW91兲.30–33 Ultrasoft pseudopotentials with one 共hydrogen兲, four 共carbon兲, and eleven electrons
共silver and gold兲 optimized for the PW91 functional were
used.34 Relativistic effects were partially taken into account
through the use of relativistic scalar pseudopotentials for all
atoms. The Brillouin zone was sample at only one k point.
The energy cutoff for the plane-wave expansion was 180.7
and 349.4 eV for the bare clusters and the complexes, respectively. The convergence criterion was 10⫺4 for the selfconsistent electronic minimization and for the change of the
total free energy between two consecutive ionic steps.
All the low-energy structures obtained with the PW91
functional were reoptimized again using the revised Perdew–
Burke–Ernzerhof 共r-PBE兲 functional35 and the projector
augmented-wave pseudopotentials36 optimized for the PBE
functional.37 It has been demonstrated, recently, that this
functional gives better desorption energies35 than the PW91
functional. The latter seems to systematically overestimate
the value of the desorption energies of propene and CO from
Au clusters.18,38 The desorption energies of propene adsorbed
q
(m⫽1 – 5; q⫽0, ⫹1兲, computed with
on Ag clusters, Agm
r-PBE are smaller, by about 0.27 eV, than those calculated
with PW91. This decrease of the desorption energies with the
Chrétien, Gordon, and Metiu
r-PBE functional correlates with an upward shift of 0.1–0.2
eV of the LUMO energy of the bare Ag clusters.
The desorption energy of propene in the 关 Ag共C3 H6 )] ⫹
complex has been measured recently by Manard, Kemper,
and Bowers39 to be 1.65⫾0.04 eV; the r-PBE calculation
gives 1.72 eV, PW91 gives 2.02 eV, and B3LYP gives 1.52
eV.39 This latter value include a zero-point energy correction
of 0.04 eV while the other two do not contain such a correction.
The geometries of the bare clusters and the propenecluster complexes have been optimized 共by using a conjugated gradient algorithm40兲 starting from many different
structures, without symmetry constraints. We used the methodology proposed in Ref. 18 to reduce the number of initial
structures to be optimized for the adsorption of propene on
the Ag clusters. As we showed previously,18 we need to consider only the adsorption of propene on the clusters at the
positions where a low-lying LUMO protrudes into the
vacuum. Some tests have been performed to ensure that this
applies to Ag clusters as well. We have not considered the
dissociative adsorption of propene. All of the starting structures were optimized in a 15 Å cubic supercell. Optimized
structures were not characterized by vibrational analysis because this procedure is not available in the version of VASP
we used. Consequently, we cannot exclude the possibility
that some of the low-lying isomers presented in this paper
correspond to transition states. The number of unpaired electrons was kept fix during the geometry optimization. We
have considered only the singlet state for the molecules containing an even number of electrons and the doublet state for
odd numbers of electrons. Our calculations on the adsorption
of propene on small Au clusters showed that the equilibrium
structures with higher number of unpaired electrons are less
stable by at least 2.0 eV. We have made some tests to ensure
that this is true as well for the adsorption of propene on Ag
clusters.
III. RESULTS AND DISCUSSION
q
A. The properties of the naked Agm
clusters
We do not report our results for the naked neutral and
charged Ag clusters since they are close to the ones presented
in Refs. 41 and 42.
B. The geometries of the †Agm „C3 H6 …‡ q
„ m Ä1 – 5; q Ä0, ¿1… complexes
The lowest-energy structures of the Agm (C3 H6 ) and
关 Agm (C3 H6 ) 兴 ⫹ (m⫽1 – 5) complexes are shown in Figs. 1
q
clusters in the
and 2, respectively. The shapes of the Agm
q
complexes 关 Agm (C3 H6 ) 兴 (m⫽1 – 5; q⫽0, ⫹1兲 are close to
q
clusters; the adsorption of propene
those of the bare Agm
slightly changes the geometry of the cluster but not its shape.
There are many similarities between the geometries of
the complexes propene makes with the Ag and the Au clusters: 共1兲 The lowest energy structures of the 关 M n (C3 H6 ) 兴 q
complexes are similar, whether M is Ag or Au 共see Figs. 1
and 2 of the present paper and Figs. 1 and 5 of Ref. 18兲; 共2兲
when bonded to a single Ag atom located at the periphery of
a Ag cluster, the propene molecule rotates almost freely
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J. Chem. Phys., Vol. 121, No. 20, 22 November 2004
Adsorption of propene on metal clusters
FIG. 1. Lowest energy isomers of the Agm (C3 H6 ) complexes (m⫽1 – 5)
calculated with the r-PBE functional. ⌬E is the excess energy of an isomer
as compared to the energy of the most stable isomer. D e is the desorption
energy of the propene from the cluster 共see text for the definition of the
desorption energy兲. The orbital energies ␧ of the LUMO involved in the
binding of propene is indicated also. All energies are in eV.
around that Ag atom, just as it does for Au clusters; 共3兲 the
structure of the propene molecule in complexes with Au or
Ag is very close to its gas phase structure; 共4兲 propene does
not bind to a flat facet of a Ag or Au cluster.
C. The desorption energy of propene from the
†Agm „C3 H6 …‡ q „ m Ä1 – 5; q Ä0, ¿1… complexes
The desorption energy of propene from a cluster is calculated with the formula
q
D e ⫽E 关 Agm
兴 ⫹E 关 C3 H6 兴 ⫺E 关 Agm 共 C3 H6 兲 q 兴 .
共1兲
q
q
cluster obHere E 关 Agm
兴 is the energy of the naked Agm
tained by energy minimization starting with the geometry of
the Ag cluster having the same shape as in the
关 Agm (C3 H6 ) 兴 q complex. For example, if the Ag atoms in
关 Ag3 (C3 H6 ) 兴 q form a triangle, then E 关 Agq3 兴 is the lowest
energy triangular Agq3 cluster. No zero-point energy correction is made since the difference between the zero-point energies of the ‘‘products’’ and that of the ‘‘reactants,’’ is small
compared to D e . For example, this correction is 0.04 eV for
the 关 Ag共C3 H6 )] ⫹ complex.39
All attempts to optimize an Ag⫹
5 cluster with a trapezoidal shape failed with the r-PBE functional. The energy dif-
9927
FIG. 2. Lowest energy isomers of the Agm 关 (C3 H6 ) 兴 ⫹ complexes (m
⫽1 – 5) calculated with the r-PBE functional. ⌬E is the excess energy of an
isomer as compared to the energy of the most stable isomer. D e is the
desorption energy of the propene from the cluster 共see text for the definition
of the desorption energy兲. The orbital energies ␧ of the LUMO involved in
the binding of propene is indicated also. All energies are in eV.
ference between this conformation and the one in structure
2I 共without propene兲 is less than 0.1 eV with the PW91
functional. Consequently, we have used the energy of the
later structure to calculate the desorption energy of propene
from Ag⫹
5 in structures 2J, 2K, 2L, and 2M 共see Fig. 2兲.
The desorption energies of propene from 关 Agm (C3 H6 ) 兴 q
(m⫽1 – 5; q⫽0, ⫹1兲, are given in Figs. 1 and 2 and a comparison between propene desorption energies to Au and Ag
clusters 共neutral and positively charged兲 is made in Table I.
Since propene binds to a Au or a Ag cluster by donating
electrons to them, we expect the bond strength to correlate
with the tendency of the cluster to accept electrons. Since the
electron affinities of the Ag clusters are less than those of the
Au clusters 共of the same size and similar shape兲, we expect
TABLE I. Comparison of the desorption energies D e 共in eV兲 of propene
from the Ag and the Au clusters, computed with the r-PBE functional.
Neutral
Cation
n
Agn
Aun
Agn
Aun
1
2
3
4
5
0.03
0.24
0.47
0.52
0.18
0.38
1.01
1.27
1.19
0.69
1.72
1.14
0.92
0.83
0.74
3.13
2.18
1.77
1.53
1.70
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9928
J. Chem. Phys., Vol. 121, No. 20, 22 November 2004
FIG. 3. Desorption energies of propene 共left column兲 and absolute value of
the energy of the LUMO of the naked Ag clusters 共right column兲 as a
function of cluster size. The upper and lower rows correspond, respectively,
to the cationic and neutral cluster. All energies are in eV and were calculated
with the r-PBE functional.
propene to bind more strongly to gold. Moreover, propene
should bind more strongly to a positive cluster than to the
neutral one 共for a given cluster size兲. Indeed, this is what the
DFT calculations show 共see Table I兲.
However, it turns out that the electron affinity of the
cluster is not an adequate predictor of propene bond strength.
The electron affinity of a naked cluster oscillates with the
number of electrons in the cluster: it is large for clusters with
an odd number of electrons, and small when the number of
electrons is even.22,23 The desorption energy of electron acceptors 共i.e., oxygen兲 oscillates with the electron affinity of
the cluster,43– 48 but that of electron donors 共propene,18 CO,38
propene oxide, and acetone49兲 does not. Therefore, we cannot
use the electron affinity to predict how the desorption energy
varies with the number of atoms in the cluster.
There is however a good correlation between the desorption energy of propene 共from the lowest energy isomer of
关 M n (C3 H6 ) 兴 q ) and the energy of the LUMO of the naked
M qn cluster: the plot of the desorption energy of propene in
关 M n (C3 H6 ) 兴 q versus n is very similar to the plot of the
LUMO energy of M qn versus n 共see Fig. 3兲.
In making the above corelation we have ignored, for the
clusters with odd number of electrons, the SOMO. Had we
assumed that propene binding engages the SOMO and that
the bond energy correlates with the SOMO energy, we would
have predicted that the desorption energy oscillates with the
number of electrons in the bare cluster. This would be in
disagreement with the DFT results. Our disregard of the
SOMO can be justified by the following simple physical
argument.38 There is some electronic repulsion between the
␲ electrons of propene and the partially occupied SOMO of
the Au and Ag clusters. This repulsion is absent when the
accepting orbital is empty 共LUMO兲.
The similarity between propene binding to the Ag and to
the Au clusters is due to the similarity between the LUMOs
of the naked clusters. To describe qualitatively the properties
of an orbital ␸ i (x,y,z) we use plots of the surface on which
the orbital wave function square, 兩 ␸ i (x,y,z) 兩 2 , takes a con-
Chrétien, Gordon, and Metiu
FIG. 4. LUMO orbital density plots 兩 ␸ i 兩 2 for the two most stable Ag4
clusters. The orbital energies ␧ are in eV, and the plots show an equal
density surface of 0.025 e/Å3.
stant value. We call these, orbital density surfaces or LUMO
plot. As an example we show, in Fig. 4, the orbital density of
the LUMOs of two Ag4 clusters 共the ones having the lowest
energies兲.
In our previous study of propene binding to Au clusters18
we have shown that the most stable bond is formed at the
sites where the orbital density of the LUMO sticks out in the
vacuum, to ensure a good overlap with the ␲ MO of propene.
⫹
clusters examined
The same is true for all Agm and Agm
here.
For example, propene will bind to the cluster shown in
the upper panel of Fig. 4 in position 1 or 3 共which are
equivalent兲, since the LUMO protrudes in space at those positions. Propene binds to the Ag4 cluster, shown in the lower
pannel, to the position 1 or 3, for a similar reason.
In our previous work with Au clusters18 we have also
found that the desorption energy of propene correlates with
the energy of the LUMO of the naked cluster. This rule can
be used to predict to which Auqn isomer propene will make
the strongest bond. For example, the LUMO energies of the
Ag3 clusters having a triangular and a bent configuration are
⫺3.2 and ⫺2.6 eV, respectively. As we can see from Fig. 1,
propene binds more strongly to the isomer with the triangular
shape 共structure 1C兲 than the bent one 共structure 1D兲 by 0.28
eV, in agreement with the rule.
The rules predict other features that have been found by
DFT calculations. Propene does not bind to the flat faces of
q
the Agm
clusters because the LUMO density allong these
facets is very small. We have found that it cost very little
energy to rotate propene around an axis going through the
atom to which the propene is bound. This happens because
the plot of the LUMO density is spherically symmetric and
rotating the molecule does not change the overlap of its ␲
orbital with the cluster’s LUMO. Finally, propene does not
adsorb perpendicularly to a Ag–Ag bond on the edge of the
silver clusters, because of the lack of good overlap between
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J. Chem. Phys., Vol. 121, No. 20, 22 November 2004
the frontier orbitals 共the ␲ of propene and the LUMO of the
cluster兲 of the two fragments.
Adsorption of propene on metal clusters
9929
Initiative on Nanotechnology 共DURINT兲 grant is gratefully
acknowledged. We are grateful to Greg Mills for helpful discussions.
D. Exceptions to the rules
The rule works for all Ag clusters studied here with relatively few exceptions. One example of failure is provided by
the isomers 1G and 1H in Fig. 1, in which propene binds to
a trapezoidal Ag5 cluster. According to our rules, the binding
of propene at the long base of the trapeze 共1H in Fig. 1兲
involves LUMO1, while the binding of propene at the
shorter base of the trapeze 共1G in Fig. 1兲 involves the
LUMO2 of the naked trapezoidal Ag5 cluster. Based on the
LUMOs energy, the rules suggest that the most stable isomer
is obtained when propene binds to the corner of the long base
of the trapeze 共1H in Fig. 1兲. The DFT calculations say that
this is not the case: the bond to the top edge of the trapeze
共1G of Fig. 1兲 is stronger by 0.03 eV. However, the orbital
energies of the two LUMOs 共⫺2.6 and ⫺2.4 eV兲 and the
desorption energies to the two sites 共0.15 and 0.18 eV兲 are
very close to each other. These energy differences are rather
small and it would be very surprising if our empirical rules
had the high accuracy needed to discriminate between these
two cases.
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