Surface Science 209 (1989) 243-289
North-Holland,
Amsterdam
243
CHEMISORPTION
OF OXYGEN, CHLORINE, HYDROGEN,
HYDROXIDE, AND ETHYLENE ON SILVER CLUSTERS:
A MODEL FOR THE OLEFIN EPOXIDATION REACTION *
Emily A. CARTER
* and William
Arthur Amos Noyes Laboratory
CA 91125, USA
Received
of Chemical
10 June 1988; accepted
A. GODDARD
Physics,
for publication
California
30 August
III
Institute
of Technology,
Pasadena,
1988
We have examined various postulated
pathways
for the catalytic epoxidation
of olefins by
silver using ab initio quantum mechanical methods to study likely intermediates
in this reaction.
In particular,
we predict preferred binding sites, geometries, vibrational
frequencies,
and binding
energies for 0, O,, Cl, H, OH, and C,H,
on a cluster model for Ag aggregates
present on
supported
catalysts. These calculations
suggest the presence of two nearly degenerate
states of
chemisorbed
atomic oxygen. The calculated
binding energy for these surface oxides are 78-79
kcal/mol
(experimental
values are 77-78 kcal/mol).
One surface oxide has the form of an
oxyradical anion and is predicted to be selective for olefin epoxidation.
The other surface oxide is
a closed shell state expected to be less active and nonselective for olefin epoxidation.
These results
lead to a detailed mechanistic
model that explains:
(i) why C,H, exhibits high selectivity for epoxide while higher olefins do not;
(ii) the difference in activity per surface site between the (110) and (111) surfaces of Ag; and
(iii) the role of both electropositive
(e.g. Cs) and electronegative
(e.g. Cl) promoters in increasing
selectivity.
A number of experiments
are proposed which would test key points of this new mechanism.
1. Introduction
The selective oxidation of ethylene to ethylene oxide (EO) is an exceedingly
important
industrial
catalytic reaction, providing
the feedstock chemical for
the production
of ethylene glycol, which is in turn used to synthesize polyesters and antifreeze
[l]. The industrial
reaction
is usually carried out at
pressures of lo-12 atm and at temperatures
of about 540 K, with a catalyst
consisting of silver dispersed on a-alumina,
+C02+H20
- 270 *C
* Contribution
no. 7582.
* Permanent
address: Department
Angeles, CA 90024-1569, USA.
of Chemistry
and Biochemistry,
0039-6028/89/$03.50
0 Elsevier Science Publishers
(North-Holland
Physics Publishing
Division)
University
B.V.
of California,
Los
244
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation
reaction
with trace quantities
of chlorine (usually in the form of 1,2-dichloroethane),
cesium (in the form of aqueous solutions of CsOH, CsNO,, or Cs,CO,)
[2],
and other promoters added in order to increase the activity and selectivity of
the catalyst. Total combustion
of the olefin to CO, and H,O is a competitive
process, and alkali metals and chlorine
(as well as other electronegative
elements) are known to inhibit this latter route.
The unique aspects of this partial oxidation [l] are the following [3-51:
(i) silver is especially
active, with other transition
metals yielding
only
products of total combustion;
(ii) chlorine, calcium, potassium, and cesium are among the known promoters of the reaction; and
(iii) epoxidation
is only efficient for ethylene, with higher olefins combusting mostly to CO, and H,O.
It is not well known why silver is so exceptional
nor is it fully understood
why olefins other than ethylene are combusted
rather than epoxidized.
In
addition,
despite the relative simplicity
of this system, there remains great
controversy over the precise nature of the active form of oxygen (atomic versus
molecular [3-61) and over the mechanism
by which both electropositive
(e.g.
alkali metals) and electronegative
elements (e.g. chlorine) act to promote the
formation of EO [7].
Much emphasis has been placed on achieving maximum
selectivity to EO
(i.e., minimal combustion),
since the production
of EO from ethylene is such a
high volume industry (several billion dollars/year).
Mechanism
is crucial in
this case, since a popular model in which chemisorbed
molecular
oxygen,
higher than 85.7% are
0 2(adj, is the active species suggests that selectivities
unattainable.
This mechanism
postulates
that an adsorbed peroxyradical
reacts with ethylene, forming EO with the outside oxygen and forming CO, with
the oxygen which remains behind. The stoichiometry
of the two competing
reactions
C,H,
+ O~(adj -+ C,H,O
C,H,
+ 60(,,,
+ 2C0,
+
O(ad)
+ 2H,O,
3
(2)
(3)
would then fix the maximum
selectivity at 6/7 or 85.7% [6]. (This scheme
assumes that the outer oxygen exclusively forms EO and the surface-bound
oxygen exclusively combusts ethylene.) While unpromoted
catalysts normally
achieve selectivities
in the range of 45% [6], a recent report indicates
that
adding NaCl to the catalyst leads to selectivities as high as 85-87s
(a result
right around the postulated
maximum)
[8]. Thus, if the above mechanism
is
correct, little practical incentive exists to pursue industrial optimization
of this
catalytic system. By contrast, a mechanism involving atomic oxygen would not
set a maximum on the selectivity to EO, providing encouragement
for further
refinement
of the epoxidation
catalyst.
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation reaction
245
Detailed experimental data exist to support either OCadjor OZCadjas the
active precursor to ethylene oxide [7f,9-131. However, all evidence supporting
molecular oxygen is indirect [7f,9-121, whereas direct evidence does exist for
the evolution of EO in the presence of Oca,,, [ 13 1. The most recent experiments
to be interpreted in terms of molecular oxygen as the active agent are due to
Campbell [7f,12], who found no direct correlation between the postreaction
coverage of monatomic oxygen (by varying the crystal face, the temperature,
or the coverage of chlorine) and the rate of EO production. He concluded
from these indirect results that diatomic oxygen must be the active species for
epoxidation. We present herein a two-state model for surface oxides on silver,
where one kind of chemisorbed oxygen atom [the surface atomic oxyradical
anion (SAO)] is selective for the formation of EO, while the other is unreactive
and nonselective. In section 4, we use this model to interpret the Campbell
data in terms of a specific type of O,,,,, the SAO, as the active species for
epoxidation.
The most convincing evidence to date supporting monatomic oxygen was
recently reported by van Santen and de Groot [13f]. Initially they adsorbed
1602 on Ag powder at high temperature (475 K) to produce monatomic 160cadj
(e.g., above 150 K, 0, adsorbs dissociatively on Ag(ll0)
[14]), with an
adsorbed oxygen to surface Ag ratio of - 1. (Separate experiments showed
that this precovered oxygen surface yielded epoxide when reacted with ethylene.) Then a gaseous mixture of “02 and C,H, was introduced at room
temperature to the ‘60-precovered surface, and the temperature was increased
at a rate of 2.3 K/mm. Under conditions where gaseous oxygen scrambling
was slow, ethylene first reacted to form exclusively C,H,‘60,
followed later by
the r*O analog. Unless the oxygen adatoms recombine immediately prior to
reaction (which cannot currently be ruled out), these experiments indicate that
Ocadj is the direct precursor to EO.
The promoters which have been studied most thoroughly experimentally are
Cl and Cs [7,8]. At high Cl coverages, Campbell and Koel observed an
increase in the selectivity toward EO production and concluded that Cl
promotes EO formation by an ensemble effect. The presumption here is that
CO, production requires a larger number of contiguous surface sites than does
EO formation [7a-7c]. In section 4, we suggest that Cl blocks the non-SAO
sites, putting a higher fraction of surface oxygen into the SAO form required
by our model for EO production. This provides an alternative explanation for
the promotional role of Cl (both effects could contribute).
Concerning Cs and other alkali metals, Lambert has reported that Cs
inhibits isomerization and hence the secondary combustion of EO on Ag(ll1)
[7g,7h,15]. On the same surface and under reaction conditions which produce
EO, Campbell found that cesium converts to a surface cesium oxide with
approximate composition CsO,. Again, Campbell suggested an ensemble
effect mechanism for the role Cs plays as a promoter [7d]. We propose instead
246
E.A. Carter, W.A. Goddard III /A
model
for the &fin epoxidation reaction
(section 4) that cesium aggregated with oxygen leads to both an electronic
effect that enhances
selectivity
and to site-blocking
of both selective and
nonselective
Ocad,.
In the present work, we designed a sequence of ab initio calculations
with
two objectives: (i) to obtain quantitative
accuracy for binding energies, vibrational frequencies,
and equilibrium
geometries for the interaction
of a silver
cluster with various adsorbates
likely to play a role in the epoxidation
chemistry ano(jii) to extract a qualitative
understanding
of the epoxidation
mechanism in order to suggest how to optimize this catalytic process.
We begin in section 2 with an overview of the qualitative
aspects of
bonding atomic and molecular species to a Ag, cluster. Reported in section 3
are results for H, Cl, 0, O,, OH, and C,H, interacting
with the l-coordinate
(pL1), 2-coordinate
(p2), and 3-coordinate
(pL3) sites of Ag,. Section 4 discusses
these results in the context of interpreting
experimental
data from extended
surfaces. We further describe
the implications
of these first quantitative
estimates for the energetics of various postulated
mechanistic
pathways. This
work suggests a detailed, comprehensive,
new mechanism
involving a special
form of chemisorbed
oxygen, the surface atomic oxyradical anion (SAO). In
this mechanism, the promoters play a role in enhancing
formation of the SAO
or in improving
selective interactions
between the SAO and the reactant
olefin. Section 5 concludes with a summary of the cluster results and their
impact on the mechanistic
details of the epoxidation
reaction over Ag. Section
6 provides calculational
details.
2. Qualitative aspects of bonding X to Ag,
Chemisorption
of a gaseous atom or molecule on a perfect surface gives rise
to strong localized interactions
and a breaking of the infinite two-dimensional
periodicity. For the nonmetallic
adsorbates considered here, the final chemical
bond between adsorbate and substrate is localized, and therefore may be well
represented
by the interaction
of an adsorbate
on a finite cluster. Some
properties
such as geometries
and vibrational
frequencies
should be well
described using such a model. However, the bond energy may differ for the
cluster versus the surface, since the metal-metal
bonds broken upon chemisorption may have different character. The cluster model chosen here is three
silver atoms in an equilateral
triangle with a Ag-Ag distance equal to the
nearest neighbor
distance
in bulk Ag (R(Ag-Ag)
= 2.89 A). The cluster
geometry is kept fixed, while the adsorbate degrees of freedom are optimized,
in order to mimic the interaction
of an adsorbate
with an unreconstructed
surface. For this cluster, we believe that the three-fold site may correspond
closely to the analogous site on Ag(ll1).
However, the other sites have steric
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation reaction
Ag,
t2A,)
241
Ag-f3Ag
4-+
Ag
a)
Ag
RADICAL
Ag-Ag
BOND
Fig. 1. The GVB one-electron
valence orbitals of Ag3(‘A,):
(a) the Ag3 singly-occupied
orbital
and (b) the Ag-Ag bond pair. Contours range from - 0.5 to + 0.5 a.u., incremented
by 0.01 a.u.
and electronic effects very different from the low index crystal faces and may
correspond only to defect sites on the infinite surface.
As in alkali metals [16], we find that the metal-metal bonding within the
Ag cluster is dominated by sp hybrid orbitals localized on each of the bond
midpoints. (With a valence electron configuration for Ag of 4d”5s’, the closed
shell Ag d-electrons do not participate directly in metal-metal bonding.) The
electrons localize in bond midpoints due to the greater strength of one-electron bonds over two-electron bonds in metallic systems [16d]. The ground
state of Ag, has two of the three bonding orbitals spin-paired, leaving one
bond-centered orbital singly occupied. This results is a ground state with 2E’
symmetry (D3,,). The valence orbitals for one component of the 2E’ state are
shown in fig. 1. Allowing the geometry to relax would result in C,, symmetry
(Jahn-Teller
effect) with 2E’ + 2A, and 2B, [17].
The presence of the radical orbital (singly occupied, unpaired) on Ag, (fig.
la) should lead to particularly strong bonds for adsorbates in a p2 coordination, since no Ag-Ag bonds need to be uncoupled. In contrast, some energy
must be expended to localize an occupied band orbital at the surface of bulk
248
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation reaction
Ag (in order to obtain the singly occupied orbital for bonding to adsorbates).
Thus, we expect that adsorbate-cluster
bonds in the p2 site (where the radical
orbital has the greatest amplitude)
will be especially
strong, with binding
energies larger than for an extended surface. The radical orbital of Ag, also
has considerable
amplitude
at the p, site, so that this site makes the second
strongest adsorbate-cluster
bond. Since the valence electron density of this
cluster is concentrated
near the bond midpoints,
the center of the cluster (the
pL3 site) is electron-deficient
and consequently
this site should give a lower
binding energy for most species.
The (vertical) ionization
potential (IP) for Ag, is calculated
to be 4.18 eV,
in good agreement
with the work function
of bulk Ag (4.26 eV) [18]. This
suggests that charge transfer to electronegative
atoms will be accounted
for
correctly. Bonding of electropositive
adsorbates
(e.g., K or Cs) will not be as
well described, since the (vertical) electron affinity of this Ag, cluster (1.94 eV)
is considerably
less than the work function of the infinite surface.
3. Results
Below we emphasize results for the ground state of each complex (generally
p2) and for the states arising from interaction
of the adsorbate
with the /.L~
binding
site (most appropriate
for comparison
to the (111) surface). Less
discussion focuses on adsorption
in the pi site, since it is generally neither the
ground state nor a good model for binding sites on aggregated Ag.
3.1. Ag,H
The three adsorption
schematically
by
sites for hydrogen
bound
to the Ag, cluster
are given
(4)
for the singlet states of Ag,H.
In each case, two electrons are involved in the bond to H (indicated by the
line) and two electrons are localized at Ag-Ag bond midpoints
(singlet-coupled). Predicted properties
are listed in table 1 for Ag,H as a function
of
adsorption site and electronic state. The ground state involves spin pairing of a
hydrogen 1s orbital with the radical orbital on Ag, (in fig. 2a), leading to the
planar pLz site as the lowest energy configuration
(nonplanar
configurations
of
the cluster were found to be higher in energy). The Ag,-H
bond strength of
3B,
IA;
‘B,
‘A,
*B,
‘A’
3A”
l-fold
l-fold
2-fold
2-fold
2-fold (Ag,) 0
3-fold
3-fold
1.75
1.77
1.21
1.41
1.41
1.63
1.19
(A)
41.3
4.4
21.4
0.0
_
39.1
37.4
R I ,e')
Relative energy b,
(kcaI/mol)
R,Vk-W
1.75
1.77
1.88
2.02
2.02
2.33
2.05
(A)
leg%-W
1411
1357
1012
913
925
482
809
(cm-‘)
k(&-W
0.2705
0.2501
0.1389
0.1133
0.1162
0.03152
0.08887
(h/A’)
QWg,-Wd'
21.6
50.8
42.8
56.8
55.2
19.5
28.5
(kcal/mol)
- 112.77979
- 112.83656
-112.81369
-112.84613
- 150.25957
- 112.78672
- 112.79079
s’
h,
s)
h,
i,
h,
@
total energies e,
(hartree)
ccc1
a) Electronic state symmetry of the GVB wavefunction.
b, GVB(2/4)-PP energy relative to the ground state total energy of - 112.82983 hartree (1 hartree = 627.5096 kcal/mol = 27.21162 eV).
=’ R I = the perpendicular distance from H to the center of the cluster site (e.g., to the Ag-Ag bond midpoint for the 2-fold site, to the Ag atom for
the l-fold site, and to the center of the triangle for the 3-fold site).
d)
Adiabatic bond energies from CCC1 calculations (section 6).
C) Ref. [57]. See calculational details (section 6).
0
Properties for H bound to the 2-fold bridge site of Ag, (GVB-PP total energy = - 150.23336 hartree).
g) Bond energies for triplet states are calculated to the diabatic limit Ag,(4A2)+
H( *S) (HF total energies for Ag,( 4A2) and H( *S) are: - 112.19753
and -0.49994 hartree, respectively), followed by subtracting AE(4A, - *A,,Ag3) = 30.1 kcal/mol (see section 6) to obtain adiabatic bond energies
and
for the ground states Ag,(‘A,)
and H(*S). Total energies for the ‘A, and 4A, states of Ag, at the GVB(1/2)PP level are: -112.24550
- 112.19753 hartree, respectively.
Adiabatic bond energy calculated directly to the ground state of Ag,( ‘A,), with CCC1 total energy (corresponding to an RCI in the Ag-Ag bond
simultaneous with single excitations from the Ag, valence 5 sp orbitals) = - 112.25574 hartree.
CCC1 total energy for the ground state of Ag,( ‘E) = - 149.67160 hartree (CCC1 here is the same as described in footnote h).
State a’
Site
Table 1
Properties of AgjH as a function of adsite and electronic state
250
E.A. Carter, W.A. Goddard III / A model for the &fin
epoxidation
reaction
Ag3H (‘A,)
Ag
ONE
ONI E
a)
Ag3-H BOND
ONE
b)
ONE
E
I
Ag-Ag BOND
Fig. -2. The GVB OM:-e ,lectron orbitals of Ag3H(‘Al)
(for the 2-fold bridge
bond pair and (b) the Ag-Ag bond pair.
site): (a) the Ag,-H
kcal/mol is very similar to metal-hydrogen diatomic bond strengths for
second row, group VIII transition metals (D(Ru-H)
= 56 + 5, D(Rl-H)
= 59
+ 5, D(Pd-H) = 56 * 6 [19], and D(Ag-H) = 57.6 kcal/mol [20]). The metal
orbitals involved in the bond to H are quite similar in both the bond to the
cluster and to the metal atom in diatomic M-H (the radical orbital of Ag, has
90% s-character). For the p2 bridge site of tetrahedral Ag,, we calculate a
binding energy of 55.2 kcal/mol, in good agreement with the value of 54.6
kcal/mol from pseudopotential local density functional (LDF) calculations
[21a] for H bound to the same p2 bridge site on tetrahedral Ag,.
The one-electron GVB orbitals for the Ag-Ag and Ag,-H bonds are shown
in fig. 2, where we see that the Ag-Ag bond (fig. 2b) has moved out of the way
of the pL2site to avoid interaction with the Ag,-H bond. Fig. 2a indicates that
the Ag,-H bond is essentially covalent, with one electron localized on the
cluster and one electron in a 1s orbital on hydrogen, spin-paired to form the
56.8
E.A. Carier, W.A. Goddard III / A model for the okfin epoxidation
Table 2
Charge transfer
X
H
H
H
Cl
Cl
Cl
0
0
0
0
0
a)
b)
C)
d)
e)
f)
to atomic
Site
State/bond
character ‘)
‘A, ‘)
‘A, ”
‘A’
‘A, ‘)
‘A, f,
‘A’
*ZS+ radical
*fI radical
2fI radical
*Z: + radical
di-a bond
adsorbate
Mulliken
X
‘)
2-fold
l-fold
3-fold
2-fold
l-fold
3-fold
2-fold
2-fold
l-fold
3-fold
3-fold
X on Ag,,
- 0.30
- 0.23
-0.39
- 0.61
- 0.64
-0.55
- 0.70
-0.69
-0.61
-0.60
- 0.78
as a function
excess charge
b,
Agsurrace
Ag
+ 0.26
+ 0.03
+0.13
+ 0.36
+0.38
+0.18
+ 0.40
+ 0.41
+0.39
+ 0.20
+ 0.26
-0.22
+0.10
_
bulk
-0.12
+0.13
_
- 0.09
-0.13
-to.11
_
_
of adsite
Dipole
moment
(debye)
0.08
7.60
2.06
5.19
12.50
3.61
4.14
3.95
10.84
1.75
3.03
251
reaction
and bond character
‘)
Effective
charge on
x d’
d-band
shift e,
- 0.01
+ 0.09
- 0.20
-0.39
-0.36
- 0.80
-0.44
- 0.05
- 0.05
-0.51
+ 0.04
+ 0.02
-0.55
-0.26
-0.52
- 0.68
-0.32
-0.51
-0.57
- 0.71
- 0.20
- 0.47
See table 4 for Ag,O.
“Surface” Ag = Ag atoms directly attached
Obtained from Mulliken populations.
and “bulk” Ag = Ag atoms beneath the surface atoms.
Magnitude of the dipole moment along bond axis.
Effective adsorbate point charge corresponding
to the predicted dipole moment.
Averaged shift of Ag d-orbital energies upon adsorption.
Ground state.
(ev)
to adsorbate
Ag,-H
bond. The degree of ionic character is assessed quantitatively
in table
2, where Mulliken population
analysis suggests that hydrogen pulls 0.3 electron off of the cluster. Despite this apparent charge transfer, we see that the
net dipole moment is small (0.08 debye), indicating
only 0.01 electron transferred to H. Consistent
with this small electron transfer,
the shift in the
average energies of the Ag d orbitals is only +0.09 eV. (This represents
the
shift in the Fermi energy for the bulk atoms.) On the other hand, we find a
substantial
dipole moment for H in the p, and pj sites. This reflects the large
charge transfer required
to rearrange
the Ag orbitals to overlap the H Is
orbital for these geometries.
Examining
the excited states in table 1, we see that the p, binding site lies
above the ground state by about 5 kcal/mol
[4.4 kcal/mol
(GVB-PP) or 6.0
kcal/mol
(GVB-CCCI)].
In the pi geometry, the H is attached to only one of
the Ag atoms, within the plane of the cluster. Although
the perpendicular
distance to the cluster (RI)
is shorter for the p2 site, the actual Ag-H
distance is longer for pL2 than for ~1, (R(Ag-H)
= 2.02 A versus R(Ag-H)
=
1.77 A). The geometric factors lead to a vibrational
frequency for pz Ag,-H
only 63% of that for pL1(913 versus 1357 cm-‘).
The binding energy of H to the p3 site (3A” state) is only 28.5 kcal/mol,
half of the value for the ground state of the cluster (pz site). The pL3 site is
252
E.A. Carter, W.A. Goddard III / A model for the olejin epoxidation
reaction
poor for covalent bonding to an adsorbate because the highest lying cluster
orbitals have low electron density in the center of the cluster, leading to low
overlap in the Ag,-H
bond. On an extended surface or for larger clusters, we
expect much larger electron density in the p3 hollows [16], and hence larger
binding
energies. Indeed, LDF calculations
on tetrahedral
Ag, predict a
binding energy of 49.8 kcal/mol
for H adsorbed on the pj face [21a].
In sum, the bond energy calculated
at the pX site, 56.8 kcal/mol,
is
probably an upper bound to the Ag-H bond energy on the Ag surface (since
bonding
to the cluster radical orbital requires no substantial
Ag-Ag
bond
weakening),
while the value calculated
for the pj site, 28.5 kcal/mol,
is
undoubtedly
a lower bound. Consistent
with this value is an experimental
estimate [21b] of 40 kcal/mol
for the binding energy of H to polycrystalline
Ag, where H is expected to occupy primarily three-fold sites.
3.2. Ag,CI
The three high symmetry
Ag$a
adsorption
cl+
AOlAQ
c’t
AQ
ccl
cl2
sites for Cl on Ag,
are given by
4
(5)
AQNAo
4%
Table 3 lists predicted properties
of Ag,Cl for both the singlet and triplet
states (these correspond
to bonds to doublet Ag, and to the quartet (4A2)
excited state, 30.1 kcal/mol
higher). Unlike H, the singlet states are much
Table 3
Properties
Site
l-fold
l-fold
2-fold
2-fold
3-fold
3-fold
‘)
h,
‘)
‘)
of Ag,Cl
State
‘B,
‘A,
3B,
‘A,
3A”
‘A’
as a function
of adsite and electronic
state
Relative
R I,e
KG%-Cl)
dAg,-Cl)
ke
energy ‘)
(kcal/
mol)
(A)
(4
(cm-‘)
@/‘A2
1 (kcal/
50.7
9.3
35.1
0.0
44.4
22.0
2.43
2.45
2.15
2.23
2.21
2.38
2.43
2.45
2.59
2.66
2.77
2.91
258
246
230
211
203
161
0.2868
0.2622
0.2278
0.1918
0.1782
0.1116
DC
ccc1
mol) b
total energies
(hartree)
50.0
85.0
61.8
91.0
55.2
73.2
- 571.77595
-571.84196
- 571.79476
- 571.85149
- 571.78427
- 571.82316
‘)
d’
”
d,
e,
‘)
‘)
GVB(2/4)-PP
energy relative to the ground state total energy of - 571.82622 hartree.
See table 1, footnote d).
Section 6 and ref. [57].
See table 1, footnote g). Total energy for Cl(*P) at the CCC1 level (single excitations from the
3sp orbitals from the HF reference configuration)
= - 459.45077 hartree.
‘) See table 1. footnote h).
E.A. Carter, W.A. Goddard III / A model
for the &fin epoxidation reaction
253
more stable than the triplet states (for the p2 site, AEs, = E,,,,,,,
E SINGLET
= 35 kcal/mol for Cl and 21 kcal/mol for H). This occurs because
the bond between Ag, and Cl is more ionic than the Ag,-H bond (for the p2
site, q = -0.61 for Cl and q = -0.30 for H, where q is the amount of charge
transfered). For separated Cl- and Ag: fragments, the triplet excitation
energy is AE,, = 50.5 kcal/mol.
At@
( ‘A,,
---.\
*‘,-._
~
: ,;;i::\ I
_--
ONE
ONE
a)
b)
Ag-Ag
BOND
Cl 2p LONE
PAIR
Fig. 3. The GVB one-electron orbitals of Ag,Cl(‘A,)
(for the 2-fold bridge site): (a) the Ag3-Cl
bond pair; (b) the Ag-Ag bond pair; and (c) the Cl doubly-occupied, in-plane p-like orbital. (A
second doubly-occupied p-like orbital is not shown.)
254
E.A. Carter, W.A. Goddard III / A model
for the olefin epoxidaiion reaction
The ground state has Cl in the cl1 site (‘A,), with a Ag-Cl distance of 2.66
A (R I = 2.23 A), very close to that observed for Cl on Ag(ll1) from SEXAFS
experiments
(Cl was found to reside in p3 sites with R(Ag-Cl)
= 2.70 f 0.01
A [22]). The Ag,-Cl vibration frequency is calculated to be 211 cm-’ and the
bond energy is calculated
to be 91.0 kcal/mol.
As a calibration
of our
theoretical methods, we calculate for AgCl diatomic (GVB-CCC1 total energy
= -496.97280
hartree for AgCl; HF total energy for Ag(*S) = -37.40668
hartree) R, = 2.43 A, tie = 287 cm-‘, and De = 72.4 kcal/mol,
whereas the
experimental
values are R, = 2.28 A, w, = 343 cm-‘, and De = 75.2 kcal/mol
WI.
The orbitals for the ground state of Ag,Cl (fig. 3) indicate a large amount
of ionic character in the Ag,-Cl
bond, with the Ag-Ag bond pair moving out
of the way of the Ag,-Cl
bond (as for Ag,H). Table 2 supports the assertion
that the bonding is ionic, with approximately
0.6 electron removed from the
cluster by Cl in all three sites. In the pLz site, the calculated dipole moment of
5.2 debye suggests a charge transfer of -0.52 electrons. The shift in the 4d
energy by -0.36 eV is also consistent with the large charge transfer.
The dipole moments as a function of adsite for electronegative
groups such
as Cl and 0 (vide infra) show the following trend: pL1 exhibits the largest
dipole moment,
p2 a moderate dipole moment, and p3 the smallest dipole
moment. Since the pi site has the most dispersive charge distribution,
with the
adsorbate
negatively-charged
and all three Ag atoms positively-charged,
it
exhibits the largest dipole moment. The p2 site has the next most widespread
charge distribution,
but the small, negative image charge on the “bulk” Ag
atom induces a dipole moment less than half of the size of the p, dipole
moment. The closest approach of the adsorbate is in the p3 site, leading to the
smallest dipole moment. A trend is also apparent
in the d-band shifts: for
clusters where the “bulk” Ag atoms are positively-charged,
the d-band shifts
are quite large (i.e., for the p, site). Decreasing the occupation
of the sp-band
(the valence Ag orbitals) stabilizes the d-band by lowering electron-electron
repulsion.
The pi site lies 9.3 kcal/mol
above the p2 site, with the pL3 site 22.0
kcal/mol
up, (table 3). The p3 site has an Ag-Cl bond length of 2.91 A
(RI = 2.38 A) and a bond energy of 73.2 kcal/mol.
This is 0.25 A longer than
for the p2 site and 0.21 A longer than the experimental
value for Cl/Ag(lll).
(The Ag-Cl distance in bulk AgCl is 2.77 A.) This suggests that Cl adsorbed
on Ag(ll1) is held more tightly than the theoretically-predicted
properties for
p,-coordination.
The bond energy of Cl to Ag, in the I”~ site is therefore
expected to be a lower bound on the surface-Cl
binding
energy (as with
Ag,H). Thus, we believe that the Ag-Cl surface bond energy lies between the
values of 91.0 kcal/mol
for the p2 site (an upper bound as discussed for pL2
Ag,H) and 73.2 kcal/mol
for the p3 site. This suggests dissociative
chemisorption of Cl, is very exothermic, downhill by at least 88 kcal/mol
(assuming
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation reaction
255
no weakening of the Ag lattice occurs). Recent Xa-SW calculations for Cl on
an Ag, cluster are consistent with our findings, where an Ag-Cl bond energy
of 72.2 kcal/mol was reported [20b].
Although Cl, dissociates readily on Ag, no binding energies for Cl on Ag
have been reported, primarily because of uncertainty as to whether Cl desorbs
as Cl,, Cl., or AgCl[23a-23d].
Assuming Cl, desorbs at 750 K [23a-23d], a
Redhead analysis [23e] for second-order desorption yields a Cl-Ag,,, bond
energy of 52 kcal/mol (with an activation energy for desorption of 46
kcal/mol). Desorption of Cl. at 750 K implies an Cl-Ag,,, bond energy of
only 45 kcal/mol. A Redhead analysis for AgCl desorption would yield an
activation energy of 46 kcal/mol, the same as for Cl,. However, using the
heats of formation (at 298 K) for AgCl(,, of + 22.3 kcal/mol and for Cl,,, . of
28.9 kcal/mol [24a], along with the theoretically predicted range of binding
energies for Cl on Ag,,, (73.2-91.0 kcal/mol), leads to an (average) activation
energy of - 75 kcal/mol to desorb AgCl,,,. In addition, the theoretical
endothermicities (lower bounds on activation energies) for the formation of
Cl 2(g) and Cl,,, . (calculated from the average theoretical binding energy for
Ag,-Cl of 82.1 kcal/mol) are 106 kcal/mol and 83 kcal/mol, respectively.
Since desorption of AgCl,,, has the theoretical endothermicity closest to that
obtained from experiment, we conclude that AgCl,,, is the most likely
desorbing species, with Cl. the next most likely.
3.3. Ag,O
The orbitals for the low-lying states of oxygen on Ag, adsorbed in the p2
site are displayed in figs. 4-6, while the three low-lying states of oxygen on the
p3 site of Ag, are represented as
(6)
OXYRADICAL
(‘II)
di- 0
OXYRADICAL
(‘Z+)
where we find that the UT double-bonded description for the ps site on Ag, is
equivalent in energy to a description where two equivalent u bonds are formed
between 0 and the cluster (di-a bonding).
Table 4 displays the properties for the three low-lying states of Ag,O
binding to all three sites. Again, the p2 site is favored, with the ionic bonding
configurations shown in figs. 4 and 5 (‘Z+ and ‘II) separated by only 2.7
kcal/mol, while the UT double-bonded state lies 29.8 kcal/mol higher in
energy (fig. 6). The ground state has an Ag-0
bond length of 2.26 A
(R I = 1.74 A), an Ag,-0
vibrational frequency of 332 cm-‘, and a bond
256
E.A. Carter, W.A. Goddard III /A
22
Ag,O
model for the &fin
..
STATE
4%
Ag
c2A,)
epoxidation
reaction
..
Ag
sr?;
Ag
+
ONI
I
L-L--
0 2p u RADICAL
ONE 1
ONE]
b)
0 2p LONE PAIR
Ag-Ag
BOND
Fig. 4. The GVB one-electron orbitals of ground state Ag,O( ‘A,) with 2Z O- character (for the
2-fold bridge site): (a) the 0 2~0 radical; (b) the 0 in-plane 2p lone pair; and (c) the Ag-Ag bond
pair. (A second oxygen 2p lone pair out of the plane is not shown.)
strength of 92.9 kcal/mol. Again, this bond energy is expected to be an upper
bound to the surface-0
binding energy, because both the slightly smaller
(vertical) IP of Ag, (4.18 eV) relative to the bulk work function of Ag (4.26
eV) and the localized hole (positive charge) on the cluster work to create a
stronger ionic bond. The ‘II state (2.7 kcal/mol up) has a longer bond length
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation reaction
*II
257
STATE
AsJO
fB2)
_-- . .
,’ ,,-_--_:\~
AS---AS
ONE
I --.
-_..
ONE
a)
0 2pu
PAIR
b)
0 2p r RADICAL
ONI
ONE
I
I
J
Ag-Ag BOND
Fig. 5. The GVB one-electron
orbitals of Ag,O( *B,) with *rI O- character (for the 2-fold bridge
site): (a) the 0 2~0 pair; (b) the 0 2pv radical, and (c) the Ag-Ag bond pair. (An oxygen 2p lone
pair out of the plane is not shown.)
(RI = 1.91 A or R,(Ag-0)
= 2.40 A), a smaller vibrational frequency (289
cm-‘), and a slightly smaller bond energy (90.2 kcal/mol) than the ground
state. This is due to the doubly-occupied 0 pa orbital which prevents a close
approach of 0 to the cluster. On the other hand, the ground state can form a
shorter, stronger ionic bond to the cluster because the 0 pa orbital is
258
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation
UT
reaction
DOUBLE BOND
Ag30
(*A,)
a)
Ag3-0
a- BOND
b)
Ag<O
T BOND
ONIE
A% RADICAL
Fig. 6. The GVB one-electron
orbitals of excited state Ag30(‘A1)
with m double bond character
(for the 2-fold bridge site): (a) the Ag3-0
bond pair; (b) the Ag,-0
71 bond; and (c) the Ag,
singly-occupied
orbital.
singly-occupied. In contrast, the p1 211 state (3.1 kcal/mol above the ground
state) is much more stable (20.3 kcal/mol) than the p1 ‘Z+ state. The bonding
for pL1resembles AgO diatom& since the oxygen is bound to only one Ag
atom. AgO has a similar ordering of states, with a 21X ground state [20] and a
*Z+ excited state - 15 kcal/mol higher (table 5).
Bond
Site
*rJ radical
‘Z: ’ radical
*II radical
a~/di-a
bond
‘I: + radical
2-fold
2-fold
S-fold
3-fold
3-fold
14.9
14.0
19.9
2.7
0.0
‘A’
2A’
R i.e
1.80
1.91
1.74
1.92
1.37
2.11
2.13
2.14
1.54
‘)
53.9
23,4
3.1
29.8
energy
f=%
Relative
(kcal/moJ)
2A”
2J%
2AI
2A,
%;
2&
2A,
State
of adsitc and bond character
2.45
2.40
2.26
2.54
2.16
2.11
2.13
2.14
2.11
(A)
R,@HV
299
289
332
252
412
415
318
399
380
--1
f
d&,-Q
&m
0.1838
0.1718
0.2248
5.1313
0.3504
0.3541
0.2939
0.3283
0.2971
(h/A2 )
ke
78.7
-1X7.18795
d,
d,
- 187.16450
90.2
92.9
72.8
77.8
d,
- 187.09362
18.6
69.5
89.8
63.1
CCCI
total energies
(hartfee)
0, c,
jkcalfmof)
‘) Bond character refers to either two bonds from 0 to Ag, (on or di-a) or an ionic bond between W and Ag; (*Z+ for radical electron along the
symmetry axis or 2zI for radicai eIectron perpendicular
to the symmetry axis}; see section 3.3.
bt GVB(2/4)-PP
energy relative to the ground state total energy of -- 187.10445 hartree.
‘) Bond energies for the double-bonded-states
are from CCCI calculations
(see section 6); bond energies for the radical states are obtained by adding
the difference in relative GVB-PP energies (column 4) of the radical and double-bonded
states (for a given adsite) to the CCC1 bond energy for the
double-bonded
state.
d, Adiabatic bond energies calculated by dissociation
to HF Ag3(4A2) and HF times sing&z excitations from 0 2sp valence orbitals (total energy for
0(3P) at HF*S,,
level = -74.81842
&tree),
followed by subtracting
AE(4A,-.2A,,
Ag,) = 30.1 kcaI/mal.
See table I, footnote g).
a~ bond
‘): * radical
211 radical
(TT band
a>
as a function
I-fold
l-fold
l-fold
2-fold
character
of Ag,Q
Table 4
Properties
260
Table 5
Properties
E.A. Curter, W.A. Goddard III / A model for the &fin epoxidation reaction
of AgO
Level of
calculation
Experiment
Hartree-Fock
HF*SD
GVB(1/2)-PP
GVB-RCI(2)
GVB-RCI(2)
‘)
”
*SD,
* SD,* S,,
R,(‘ff)
No. config./
R,(22’)
AE(2Z+-
q.(Ag-0,
De(2n)
(A)
no. SEF h,
(A)
*ff)
(kcal/mol)
2ff)
(cm
(kcal/
mol)
_
15.6
14.0
_
_
_
490
447
422
416
410
467
2.00
_
2.13
2.26
2.16
2.17
2.20
l/l
877/2380
2/2
129/226
2849/9476
2.12
2.18
_
-
’)
52.8
6.5
34.5
20.7
26.2
45.8
‘) SD = all single and double excitations
from the Ag-0
bond and the oxygen 2p orbitals
virtual orbitals. SD, = singles and doubles from the 0 2po( 2Zt ) or the Ag-0
o bond
only. SD,* S,, = SD,, simultaneous
with all single excitations
from all 0 2p orbitals.
‘) SEF = spin eigenfunctions.
‘) Ref. [20a], p. 14.
to all
(*fI)
The two lowest states of oxygen in the ps site are of primary importance
to
the discussion in section 4, since they represent the most realistic binding site
on Ag, to compare with an extended surface. We see from table 4 that the two
lowest states in the 1*.s site are nearly degenerate,
separated by 0.9 kcal/mol
(up 14 kcal/mol
from the p2 ground state). These near degenerate states have
very different properties, however, with the 2IS+ radical state exhibiting a long
bond length (R I = 1.80 A and R,(Ag-0)
= 2.45 A) and a small vibrational
frequency (299 cm-‘),
while the aa/di-t
state (0.9 kcal/mol
higher) has a
= 2.16 A) and a
much shorter bond length (RI = 1.37 A and R,JAg-0)
higher vibrational
frequency (412 cm-‘). The Ag-0 bond distance in the di-a
oxide state (2.16 A) is close to that observed by surface extended
X-ray
absorption
fine structure (SEXAFS) for p-(2 x 1)-O on Ag(ll0):
R(Ag-0)
=
2.06-2.17 A [24b]. The vibrational
frequency for O/Ag(llO)
is known from
electron energy loss spectroscopy
(EELS) [25a] to be 315 cm-’ while EELS
data for O/Ag(lll)
reveal a loss at 220 cm-’ [26c]. The difference in Ag-0
frequencies
(6~ = 100 cm-‘)
on the two surfaces is in excellent agreement
with 60 predicted
for the p3 di-a oxide and oxyradical
states (60 = 110
cm-‘), suggested a possible change in the electronic state of OCadjwith surface
structure (see section 4).
The bond energies for the two pj states are predicted to be 78.7 and 77.8
kcal/mol.
This is in excellent agreement with thermal desorption
(TD) data
from O/Ag(llO),
where 0, exhibits a double peak in the TD spectrum
(discussed further in section 4) with peak temperatures
of 565 and 617 K
[26a,26b]. A second-order
Redhead analysis [23e] for both peaks yields activation energies for desorption
of 34.0 and 37.0 kcal/mol
for the high coverage,
low temperature
peak (0, = 0.67) and for the higher temperature
peak (do4
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation reaction
261
OS), respectively.
These activation
energies translate
into surface-oxygen
binding energies of 76.6 and 78.1 kcal/mol,
in excellent agreement with the
theory. 0, desorbs at 579 K from Ag(ll1)
[26b], implying
an Ag-0
bond
energy of 76.6 kcal/mol,
the same as found for the high coverage oxide state
on Ag(llO), and in excellent agreement
with the ~~-0 states on Ag,. Our
results are in contrast to Hartree-Fock
calculations
reported for 0 on Ag,,.
For the four-fold
bridge site on Ag(llO),
[27], Martin and Hay obtained
excellent agreement with experiment
for the vibrational
frequency (327 cm-‘)
and distance from the surface (0.3 A versus O.O?i:i A experimentally
[25b]),
but the Ag-0 bond energy was only 9 kcal/mol,
too low by 8X%! Hartree-Fock
theory neglects all electron correlation
effects, leading to a poor description
of
the entire potential
energy surface (e.g., ionic dissociation
limits) and to an
extremely weak bond. Our method, on the other hand, properly accounts for
the electron correlation
effects dominant
during chemisorption
(see section 6)
so that the Ag-0 interaction
potential is accurately calculated and an accurate
bond energy is obtained.
higher than the two p3
The 211 radical state in the /_L~site is - 5 kcal/mol
states discussed above, with the oxygen less tightly bound, as indicated by the
frequency
(252
long bond length (RI = 1.92 A) and the low vibrational
cm-‘). Even higher in energy are the 2X+ radical state for the /.Q site and the
two U~Tdouble-bonded
states for the p, and p2 sites. The (77~double-bonded
states in the pLz and p, sites are destabilized
because they involve very weak r
bonds due to the low overlap between the cluster valence b, orbital and the
oxygen pi orbital:
for the pZ site, the 7~ bond resolves this problem
by
ionizing the cluster, while the r bond in the p, site involves two weakly
coupled, singly occupied orbitals with an overlap of 0.06! This explains why
the pI UT double-bonded
state is so high in energy (53.9 kcal/mol
up). The p3
analog forms high overlap ionic bonds (1.60 electrons on 0 in each bond) with
some back-donation
from the 0 lone pair to the Ag, cluster, leading to a large
stabilization
of the p3 ar/di-a
state over the p2 and p, 0~ states.
Summarizing,
we find that the atomic oxyradical states are preferred for the
pI and p2 sites, while two very different states [with stark contrasts in both
predicted properties and reactivity (section 4)] are competitive
for the p3 site:
one with radical character on oxygen and one with the 0 2p electrons tied up
in bonds to the cluster, leaving no unpaired electrons on oxygen.
The orbitals for the three states of 0 on Ag, in the p2 site are shown in
figs. 4-6. Fig. 4 shows the ground state (‘A,) of Ag,O, with fig. 4a depicting
the singly-occupied
0 2p radical [oriented
perpendicular
to the cluster
“surface”
(i.e., the two Ag atoms)], fig. 4b shows the in-plane,
doubly-occupied 0 2pr lone pair, and fig. 4c displays the Ag-Ag bond. Fig. 5 shows the
2B2 excited state, in which the radical orbital (fig. 5b) now is oriented parallel
to the cluster surface, with the doubly-occupied
0 2p orbital perpendicular
to
the surface. Comparison
of the Ag-Ag bonds in figs. 4c and 5c reveai that the
E.A. Carter, W.A. Goddard III / A model for the ok/in epoxidation
262
reaction
Ag-Ag bond delocalizes towards the surface of the pLz site more in the ‘A, (or
*Z+) radical state than in the *B, (or ‘II) radical state, presumably
because
the 0 2p orbital of the 2A1 radical is only singly-occupied.
This delocalization
may explain why the 2X+ orientation
is preferred over the 211 orientation
for
the p2 site.
The orbitals for the “UT double-bonded”
state (also ‘Ar) are shown in fig.
6, where we see that the 71 bond (fig. 6b) is very ionic and strongly resembles
the doubly-occupied
oxygen pr in the ‘A1 ground state (fig. 4b). Hence,
although this *A, excited state is derived from a covalent
UT double bond
description,
the x bond is in reality extremely ionic (with 1.67 electrons on the
oxygen and only 0.33 on the cluster). This excited state is very high in energy
(29.8 kcal/mol
up) since the Ag-Ag bond has been broken in the cluster. It is
also destabilized because it must be orthogonal to the ground state of the same
symmetry (2A1). The major difference
between these two 2A, states is the
location of the unpaired electron: the ground state has a radical electron on
the oxygen, while the excited state has radical character on the cluster.
In table 2 we see that all of the low-lying states of oxygen pull 0.6-0.7
electron off the cluster, leading to large dipole moments which follow the same
trend as discussed above for Cl and H (i.e., the pL1site has the largest dipole
moment due to the larger distance over which charge is distributed,
the /.L*
states have more moderate dipoles due to the negative image charge on the
“bulk” Ag atom, and the p3 states have the smallest dipoles since they have
the most compact charge distributions).
The Ag d-band is largely unaffected
by adsorption
of 0, except for the p, site where the large polarization
of the
s-electrons induces a d-band shift, as discussed for Cl.
3.4. Ag,O,
The two lowest energy configurations
for 0, on Ag,
are
O-0’
A0 ---A!3
+
k#
Ag
(7)
with the ground state having the parallel 0,
structure
(denoted
as q* to
indicate that both oxygen atoms are bound to the surface), with the 17’ peroxy
(only one oxygen bound to the surface) lying 4.1 kcal/mol
higher. Except for
the ~~-7’ peroxy species, only high symmetry orientations
of 0, on all three
sites were considered
(table 6). For the p2 site, we examined
the following
orientations:
(i) q* 2-coordinate: 0; is bound parallel to the p2 surface and in the Ag,
plane (ground state);
8’ end-on
q2
$ bridge
nt end-on
q’ peroxy
n2
n’ end-on
11”
*)
2A2
2A”’
2A”
2*”
2B,
2A,
2Aa
2B,
State
(A)
2.10
2.22
1.99
1.76
2.22
2.18
1.85
2.24
25.9
13.2
16.2
9.8
4.1
0.0
29.7
26.4
R I .e ‘)
(kcal/moi)
Relative energy b,
as a Function of adsite and orientation
1.35
1.33
1.34
2.37
1.33
1.32
1.39
1.34
(A)
R,(O-Q)
303
290
226
251
306
286
195
211
Ags-0,
We(cm-‘)
- 261.93097
-261.95126
- 261.94638
- 261.95665
- 261.95529
- 261.91224
- 261.92494
- 261.93f)lZ
1005
1200
1179
949
921
1264
856
912
Cl
total energies
(hartree)
d)
O-U
21.1
33.8
30.7
37.2
36.3
47.0
17.3
20.5
D,(kcal/mol)
+
6).
b, GVB(2/4)-PP
energy relative to the ground state total energy of - 261.94443 hartree.
” Perpendicular
distance from the center of the cluster site to the bond midpoint of 0, for n2 and to the nearest 0 for n’.
‘) Adiabatic bond energies from a valence level CI (section 6). Bond energies calculated
to ionic fragments Ag; (‘At) and 0, (*If,),
subtraction
of IP(Ag,) - EA(0,) = 86.2 kcal/moi.
cl Total energies for Agl and 0; (R,(CVB - PP) = 1.34 A) at this valence CI level are - 112.09179 and - 149.66806 hartree, respectivcfy
by
(see section
followed
‘) High symmetry orientations
except for q’ peroxy (see section 3.4 for details of peroxy geometry). 7’ and n2 refer to the number of oxygen atoms
directly bound to the cluster. End-on has only one oxygen bound to the cluster, with 0, oriented straight up from the I-, 2-, or 3-fold sites. l- and
2-fold Ag,Oa orientations
are all planar except for the 2-fold perpendicular
bridge (0, in Zfold site, oxygens equivalent
with O-O axis
perpendicular
to Ag-Ag axis).
l-fold
l-fold
2-fold
Zfold
2-fold
2-fold
3-fold
3-fold
Bond
site
orientation
of Ag,O,
Table 6
Properties
2
2
3
,?
&
P
264
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidatlon
reaction
(ii) 7’ peroxy: one oxygen is bound to the surface with the other oxygen
free (the optimum C, symmetry geometry, assuming the attached oxygen binds
above the Ag-Ag bond midpoint, has R L,e(Ag2-0)
= 2.24 A, R,(O-0)
= 1.33
A, and the outer oxygen displaced by 1.7’ off the horizontal
and toward the
cluster) (4.1 kcal/mol
up);
(iii) 17’ end-on: all atoms are coplanar
with one oxygen bound
to the
surface, and the O-O axis perpendicular
to the Ag-Ag pLz site and along the
C, axis of the molecule (9.8 kcal/mol
up); and
(iv) q2 2-coordinate I bridge: the O-O axis is perpendicular
to the Ag-Ag
axis, with the oxygen atoms above and below the Ag, plane (the O-O bond
midpoint is coplanar with Ag, and lies on the C, axis of the molecule) (16.2
kcal/mol
up).
Two orientations
were examined for each of the p, and p3 sites:
(v) n2 Z-coordinate: all atoms are coplanar, with the O-O axis parallel to
the two “bulk” Ag atoms and the O-O bond midpoint lies along the C, axis,
with the 0 atoms equidistant
from the “surface” Ag atom (13.2 kcal/mol
up);
(vi) 71’ end-on Z-coordinate: all atoms are coplanar,
with the O-O axis
perpendicular
to the “bulk” Ag atoms and along the C, axis of the molecule
(25.9 kcal/mol
up);
(vii) n2 3-coordinate: the O-O axis is parallel to the Ag, plane, lying
directly above a perpendicular
bisector of the Ag, triangle, with the O-O bond
midpoint directly above the center of the cluster (26.4 kcal/mol
up); and
(viii) 77’ end-on 3-coordinate: the O-O axis is perpendicular
to the Ag,
plane and directly above the center of the cluster (29.7 kcal/mol
up).
The properties of isomers (i)-(viii)
are listed in table 6. The ground state
(‘A,) has an O-O bond length and vibrational
frequency of 1.32 A and 1264
respectively,
with a very large bond energy of 47.0 kcal/mol.
The
cm-‘,
peroxy state, which has been proposed
as a possible intermediate
in
the
0
synthesis of EO, has a similar O-O bond length of 1.33 A but a lower
vibrational
frequency of 921 cm-’ and a smaller bond energy of 36.3 kcal/mol.
These values differ sharply from observed binding
energies for 0, on Ag
(ranging from 10 to 13 kcal/mol
[14,26b], depending on crystal face) and from
the observed O-O vibrational
frequency of 639 cm-’ on Ag(ll0)
[25a,28a],
but resembles quite closely a vibrational
frequency
observed for O,,,,
on
polycrystalline
Ag (- 1300 cm-‘) [28b]. The w, (O-O) observed on Ag(ll0) is
unusually
small, which has led many workers to assign the OZcadj species a
charge of - 2. However, 0, 2- is a highly unstable dianion and is likely to exist
on a surface (which can accept charge). We believe a more reasonable
description
of O,/Ag(llO)
involves
a cis-dimetallaperoxide
(M-O-O-M)
where the substituents
attached
to O2 are so heavy that they induced an
anomalously
low w,(O-0).
For all geometries examined, we find that the bond between 0, and Ag, is
very ionic (e.g., 0.70 electron is transferred
from the cluster to 0, in the
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation
reaction
265
ground
state). Thus Ag,O,
is best thought
of as Ag:O;,
with binding
energies much larger than those found on extended
surfaces because the
localized positive charge on the cluster (not present on the surface) induces an
anomalously
strong ionic bond. The average O-O vibrational
frequency of all
the geometries listed in table 6 is 1036 cm-‘, which is close to the O-O stretch
in 0;
(0, = 1090 cm-‘) [20]. The O-O bond length for 0, on Ag(ll0)
has
recently
been estimated
from near edge X-ray absorption
fine structure
(NEXAFS) experiments
to be 1.47 * 0.05 A [29], very close to the bond length
of 1.48 A in (CH,),CO-OC(CH,),
[30], but very much longer than the
1.32-1.39 A range which we find for 0, on Ag,.
While our Ag, model does not describe the states of dioxygen observed on
Ag single crystals, we may conclude that 0, prefers a symmetric configuration
rather than TJ’ peroxy or end-on orientations.
This is consistent
with X-ray
photoelectron
spectroscopy
(XPS) data for 0, on Ag(llO), in which only one
sharp 0 Is peak is observed, indicating
that the 0, is lying parallel to the
surface [31]. A recent XPS study of 0, on Ag(ll1)
indicates the oxygens may
not be equivalent
[32], which could be interpreted
either as 0, being tilted
with respect to the surface (as in the 17’ peroxy species) or as the 0, lying
parallel to the surface but with each oxygen sitting over inequivalent
sites.
3.5. Ag,OH
Table 7 displays properties for OH binding to the pL1, p2, and pj sites on
Ag,. We find that OH prefers to bind in a linear fashion in the p3 site, but is
tilted by 30” from the surface normal in the pZ site (out of the cluster plane).
However, the energy to deform the OH to a linear configuration
in the pZ site
is only 0.2 kcal/mol.
Experimentally,
OH formed from the interaction
of H,O
with a p(2 x 2)-O layer on Pt(ll1)
is thought to be bent with respect to the
surface (deduced from the strong intensity of the energy loss peak in EELS at
1015 cm-‘) [33,34a], but electron stimulated
desorption-ion
angular distribution (ESDIAD)
data for OH,,,, on Ag(ll1)
indicate a linear geometry where
the OH is perpendicular
to the surface, presumably
residing in p3 sites [34b].
Recent ESDIAD data for OHcad) on Ag(ll0) find the OH bent - 30” off the
surface normal, consistent either with a bent geometry in the pL2bridge sites or
a linear geometry in the pd3 sites along the sides of the troughs (along the [liO]
direction) [35c]. Our results suggest bent p2 geometries and linear p3 geometries, consistent with all of the ESDIAD results on Ag [34b,35c]. The linear
configuration
is favored for the cluster because of the ionic character of the
Ag,-OH
bond, in which 0.6-0.8 electron (table 7) is transferred
to OH from
the cluster. Therefore the bonding in Ag,OH is best viewed as OH- interacting with Ag: . The pL2site is again lowest in energy, with the bond energy of
65.4 kcal/mol
providing an upper bound to the bond energy on an extended
surface. The p3 site is 18.8 kcal/mol
higher in energy, with the bond energy of
266
E.A. Carter, W.A. Goddard III / A model
for the &fin epoxidation reaction
E.A. Carter, W.A. Goddard III / A model
for the olefin epoxidation
reaciion
261
45.7 kcal/mol
expected to be a lower bound on the binding energy for OH
bound in a pj site on a single crystal face of Ag. The CL,site lies slightly higher
in energy (20.2 kcal/mol
up) and has a bond energy of 55.9 kcal/mol.
Bange
et al. [35c] have calculated
a lower bound of 54 kcal/mol
for the binding
and
energy of OHcad) on Ag(llO), halfway in between our upper (65 kcal/mol)
lower (46 kcal/mol)
limits for the infinite surface.
As before, the relative energies are calculated at a different level than the
bond energies (section 6). Since the bond energies were calculated
using CI
methods and the relative energies shown in table 7 are from the lower level
GVB-PP calculations,
it may be that a more reliable ordering of states is
obtainable
from the relative bond energies. This would lead to the pL3 site
being 19.8 kcal/mol
above the pL2 site (in good agreement with the GVB-PP
result) and to the p, site being only 9.5 kcal/mol
above the ground state. The
GVB-PP energies for p, and pX are close in energy, so that the dynamic
correlations
included in a CI calculation
could very well change the ordering
of the excited states.
The vibrational
frequencies
for Ag,OH
(Ag-0:
300-450
cm-‘,
OH:
3640-3800 cm-‘) may be compared to values for OH adsorbed on Ag(ll0)
[35c], where the O-H stretch is 3380 cm-’ and the Ag-0 stretch is 280 cm-‘.
The experimental
lower limit on the OH,,,, binding energy of 54 kcal/mol
and our theoretical upper bound of 65 kcal/mol,
along with the Ocadj binding
energy of 79 kcal/mol,
can be used to bracket
the thermodynamics
of
hydroxyl disproportionation
to H *Ocadj + Ocadj. A first-order Redhead analysis
[23e] of H,O desorption
in the presence of 0 on Ag(ll0)
yields a binding
energy for H,O of 14 kcal/mol
(H,O desorbs at 240 K under such conditions
[35]). Combining
this with the binding energies of Ocadj and OHcad) suggests
that hydroxyl disproportionation
is up to 21 kcal/mol
endothermic,
in good
agreement
with recent work by Madix and co-workers,
who followed the
kinetics of hydroxyl disproportionation
on oxygen-covered
Ag(ll0) and found
an activation energy of 22.2 k 0.3 kcal/mol
[36].
3.6. Ag,(C,
H4) +
Calculations
on ethylene interacting
with neutral Ag, yielded only repulsive
potential curves. (We did not include the simultaneous
single excitations
on
the cluster and on C,H,
required
to describe van der Waals attractive
interactions.)
This is consistent with experiments
that show little adsorption
of
ethylene
on clean Ag surfaces [37]. However,
oxygen-precovered
surfaces
readily adsorb C,H,, presumably
at Ag sites that are more electrophilic
[37].
As a model for these electrophilic
sites, we have examined five high-symmetry
orientations
of ethylene bound to Ag: , shown schematically
in fig. 7. They are
depicted in terms of decreasing energy, with the 3-coordinate
bridge being the
least-favored
while both l-coordinate
sites are nearly degenerate in energy (so
268
E.A. Carter, W.A. Goddard III / A model
a) 3F SITE
for the &fin epoxidation reaction
Ag
Ag
Ag
H\,/H
‘I
b) 2F SITE (1)
A,/-+Ag
H/‘\H
c) 2F SITE (II)
d) IF SITE (II)
/
Ag
1
AQ \
HNC/
fH
co,
H
H
Li //q
e)lF
SITE (1)
,Ag
p
Ag
Fig. 7. Adsorption sites for C,H, on Ag ; : (a) the 3-fold site; (b) the 2-fold perpendicular bridge
site; (c) the 2-fold parallel bridge site; (d) the l-fold parallel site; and (e) the l-fold perpendicular
site (the ground state). The + signs for Ag: have been omitted for clarity.
that the ground state should have essentially no barrier to rotation about the
Ag-C,H,
bond).
Table 8 shows the properties calculated for these five orientations. We find
an 8.7 kcal/mol bond energy for ethylene in the l-coordinate site, in excellent
agreement with the experimental heat of adsorption of - 10 kcal/mol for
C,H,
adsorption on an oxygen precovered Ag(ll0)
surface [37]. (It was
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation
Table 8
Properties
Orientation
C-C II
c-c I
C-C II
C-C II
c-c I
of Agz (C,H,I
a)
Site
3-fold
a-fold
2-fold
l-fold
l-fold
as a function
Relative
reaction
269
of adsite and orientation
energy
b,
R I ,e
(A) c’
we(Agx-CzH4)
(cm-‘)
D, d,
(kcal/mol)
1.6
6.1
5.8
0.1
0.0
4.95
3.64
3.58
2.71
2.70
21
34
31
107
110
1.0
2.5
2.8
8.6
8.7
(kcal/mol)
‘) Gives orientation
of C-C axis relative to the Ag, plane, where the C-C bond midpoint lies in
the Ag, plane for the l- and 2-fold sites.
‘) GVB(3/6)-PP
energy relative to the ground state total energy of - 190.15705 hartree.
distance from the center of the cluster site to C-C bond midpoint.
” R I ,e = perpendicular
d, Adiabatic bond energies from GVB(3/6)PP
calculations
(section 6).
concluded
that ethylene binds directly to Ag, since no change in the Ag-0
stretch is observed in the EEL spectrum; thus this is the heat of adsorption
for
ethylene on Ag, not ethylene on OcadJ.)
The bond lengths for the five adsorption
sites increase for less favored
binding
sites, with the vibrational
frequencies
tracking
the bond lengths
consistently.
Only a r-bonded
form of ethylene was considered,
since this
should have the best Lewis acid-Lewis
base interaction.
This structure
is
consistent with EEL spectra for C,H, and C,D, on Ag(llO), which reveal no
change in the out-of-plane
bending vibrations
from the gas phase values. This
indicates that no substantial
rehybridization
occurs upon adsorption
[37a].
In sum, the predictions
of this section are mostly in good agreement with
experimental
data, lending credence to the use of a metal cluster to represent
the localized interactions
present on an extended metal surface.
4. Implications for olefin epoxidation
In this section we address the major reaction steps involved in the partial
oxidation
of olefins, predicting
both the thermodynamic
feasibility
and the
qualitative
nature of each reaction. We will develop a perspective
allowing a
reinterpretation
of a series of experimental
studies, leading to a comprehensive
description
of the types of oxygen which exist on the surface, how promoters
work to stabilize the active form of oxygen, and how decomposition
pathways
occur [38a,38b].
4.1. Thermodynumics
of orefin oxidation
on silver
4.1. I. Predominant adsorbed oxygen species
From the experimental
and theoretical heats of adsorption
of oxygen, we
conclude that 0, dissociation
is facile, proceeding through a chemisorbed
0;
270
E.A. Carter, W.A. GoddardIII / A model for the olefin epoxidatron reaction
species (heat of adsorption
- 10 kcal/mol
[26b]) which decomposes above 170
K to form a monatomic
oxide [25,26]. From the results of section 3.3, we
predict that two near-degenerate
states of oxygen can populate high coordination sites on Ag surfaces. One we refer to as the “di-a ” state, with both
singly-occupied
2p-orbitals
on 0 (‘P) spin-paired
to the surface, forming two
bonds. The other we refer to as the surface atomic oxyradical anion (SAO)
state, to indicate the presence of a singly-occupied
pa orbital on O-:
(8)
di-u
OXYRADICAL
The di-o species isOpredicted to have a short bond length (R i = 1.37 k and
R,(Ag-0)
= 2.16 A), a vibrational
frequency
of 412 cm-‘, and a binding
energy of 77.8 kcal/mol,
in excellent agreement with experimental
values from
SEXAFS (R(Ag-0)
= 2.16 A) [24b], EELS (w(Ag-0)
= 315 cm-‘) [25a], and
TDS (D(Ag-0)
= 78.1 kcal/mol)
[26]. Since all of the electrons of the di-a
oxygen are intimately
involved with the surface, we expect this species to be
relatively
inert and it should not be active for the formation
of EO. In
contrast, the oxyradical species is predicted to have a much longer bond length
(R I = 1.80 A and R,(Ag-0)
= 2.45 A), a smaller Ag-0 vibrational
frequency
(299 cm-‘),
but essentially
the same binding
energy to the surface (78.7
kcal/mol).
The lower vibrational
frequency
for the oxyradical
is consistent
with the observation
by Benndorf
et al. [26c] of We(Ag-0) = 220 cm-’ for
0 Cadjon Ag(ll1).
Indeed, we predict a difference in w,(Ag-0)
for the di-a
oxide and the oxyradical species of 113 cm-‘, close to the difference found for
O/Ag(llO)
versus O/Ag(lll).
In section 4.2, we will identify the low coverage
(commonly
observed) state of O/Ag(llO)
with the di-a oxide and the state of
O/Ag(lll)
with the SAO. Hence the observed shifts in vibrational
frequencies
can be understood
in terms of a change in the ground electronic state of OCadJ
with surface structure. Indeed, these frequency shifts may be fingerprints
for
these two states of adsorbed oxygen (vida infra).
An experiment
to search for this oxyradical
state of monatomically
adsorbed oxygen would be to use NEXAFS with - 530 eV photons to excite the
0 Is -+ 0 2p transition.
If polarized
light is focused in the plane of the
O-surface
bond and the angle of incidence is varied from the surface normal
(0 = 0 o ) to grazing incidence
(0 = 90 “), one should see an increase in the
intensity of the X-ray absorption
from nearly zero at normal incidence
to a
maximum at grazing incidence. This would indicate the presence of a singly
occupied p orbital oriented perpendicular
to the surface, as postulated
for the
oxyradical state.
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation
reaction
271
Another probe for the SAO state would be electron paramagnetic resonance
(EPR). However, the only EPR studies of oxygen on silver have been on
supported catalysts, since their high surface area provides a sufficiently high
concentration of unpaired spins for facile detection [10,38c]. Unfortunately,
accurate determinations of oxygen coverage on supported catalysts are not as
easy to obtain as for single crystal adsorption. Shimizu et al. [38c] did not
report oxygen coverages at all, while Clarkson and Cirillo [lo] estimated 19, in
their experiments to be - 0.44. As we will explain in section 4.2, we expect the
oxyradical to exist primarily for t$, > 0.5, with the di-a oxide to prevail for
0,s 0.5. Therefore, we do not expect an EPR signal to be observed for Ocadj in
Clarkson and Cirillo’s experiments where the di-a oxide should predominate,
and Shimizu et al.‘s work was probably carried out under similar conditions.
Indeed, no O- EPR signal was observed by either group (although small
amounts of 0, were observed). In order to independently probe for O& with
EPR, conditions must be utilized to ensure 0, > 0.5 for the catalyst under
observation.
4.1.2. Epoxidation and combustion of ethylene
A common view of the epoxidation mechanism assumes the addition of gas
phase ethylene to an 02jadj oriented parallel to the surface (an O2 geometry
consistent with both experiment [31,32] and theory). Formation of the incipient C-O bond requires localization of the oxygen 2p electron originally
delocalized in an 0;
4 orbital. This localization costs - 14 kcal/mol, as
estimated from the relative O-H bond strengths in H,O, (loss of this same r
resonance in HO,. upon formation of H,O,) versus CH,OH (no energy cost
to bind H. to CH,O a) [24c-24f]: AD(O-H) = D(CH,O-H)
- D(HO,-H)
=
103.6 - 89.7 = 13.9 kcal/mol [24a]. Once the 0 2p orbital is localized, radical
addition to ethylene has a typical barrier of 0 to 2 kcal/mol [38d]. Hence the
intrinsic minimum barrier of adding O,,,,
to gas phase C,H,
is - 15
kcal/mol (the barrier will be higher by the binding energy of C,H,
if a
Langmuir-Hinshelwood
mechanism is operative). This assumes that the C,H,
and 0, are oriented to obtain the best overlap between the C 2p and 0 2p
orbitals comprising the new C-O bond,
(9)
272
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation
reaction
and that the binding energies of the dioxygen moiety for both the reactant
(O,(,,,) and the intermediate (O,CH,CH,
scadJ) are identical due to their
parallel orientation. This 15 kcal/mol estimate of the minimum barrier is
corroborated by gas phase information about the thermodynamics of adding
0; to C,H, (AH = 14.6 kcal/mol) [39a]. Since the barrier for OZcadjdissociation to 20(,,, is < 10 kcal/mol (dissociative chemisorption is not activated on
Ag), we expect O2 to dissociate rather than to attack ethylene. In addition,
under typical reaction conditions (1 atm 02(sj and T = 540 K), we calculate
that the steady state coverage of OZcadjwill be no more than 1.2 X 10e9, while
= 0.67 [39b]. Hence,
due both to high barriers and negligible concentra00
tions, we rule out OlcadJ as the active precursor to EO.
Instead we propose that the SAO state with its u radical character is the
active oxidizing agent for EO formation. The oxygen radical orbital can easily
break into the C=C T bond of an olefin, forming a radical center on the outer
olefinic carbon, followed by rapid collapse to the epoxide.
The following mechanism
implies the possible loss of stereochemistry at one of the carbon atoms
(depending on relative rates of rotation and closure). In fact, both cis- and
trans-ethylene-1,2-d,
randomize ( - 92% equilibrated) when oxidized to EO
under actual catalytic reaction conditions [40], lending support to the above
mechanism. The production of epoxide is predicted to be thermodynamically
favorable for ethylene (AH,,, = -6 kcal/mol) [39c]. Indeed, each step of the
reaction
is predicted to be exothermic (except for desorption of epoxide), with little or
no barriers expected [38d] for radical addition to the 7~ bond of the olefin
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation reaction
213
(downhill by 5 kcal/mol for C,H,) or for closure to form epoxide (downhill
by 11 kcal/mol). Desorption of epoxide is expected to be uphill by 10
kcal/mol, consistent with the heat of adsorption of ethylene oxide on Ag(llO)
as measured by Campbell and Paffett [41].
Next we must consider pathways to combustion. In addition to the steps in
(ll), the surface atomic oxyradical state might also abstract a hydrogen atom
from the olefin to form OHcad) and a vinyl radical. With excess oxygen on the
surface, the vinylic species should be highly reactive and decompose rapidly,
leading to CO, and H,O. However, we predict that direct ethylene combustion is inhibited, since hydrogen abstraction from ethylene (eq. (12)) is
endothermic by - 39 kcal/mol and subject to a barrier of - 44 kcal/mol
[38d,42]:
-
OXIDATION PRODUCTS
CO,+
I
H,O
39 KCAL
................
4.1.3. Epoxidation and combustion of propene
The SAO state nicely explains the selectivity for EO formation. We must
now consider the oxidation of propene over Ag. Propylene oxide (PO) is
produced in yields ranging from O-6% from propene and oxygen over Ag
catalysts [6,43a,43b], with the balance leading to combustion products. First
274
E.A. Carter, W.A. Goddard III / A model
for the olefin epoxidation reaction
we consider the energetics of PO formation:
(13)
Here we see that the selective oxidation pathway analogous to (11) is favorable
for both olefins. The combustion pathway via hydrogen abstraction from
propene by the SAO is much more accessible than for ethylene, with a
predicted endothermicity of 9 kcal/mol and an expected barrier of only - 16
kcal/mol [38d,44] (eq. (13)) rather than 44 kcal/mol (eq. (12)).
The sharp contrast in combustion energetics is due to the difference in C-H
bond strengths for the two olefins. In the case of ethylene, the vinylic C-H
bond strength is extremely strong (Q9s = 118 kcal/mol [42]), whereas the
allylic C-H bond is much weaker ( DZ9s = 88 kcal/mol [44]). The difference in
C-H bond strengths may be understood in terms of the stability of the
subsequent radical formed: in the case of C,H,,
the product is a highly
unstable vinyl radical, while a resonance-stabilized ally1 radical is formed from
C,H,.
This is not an adequate explanation for the combustion of propene,
however, since reactions involving hydrogen abstraction experience barriers of
5 to 10 kcal/mol (in addition to the endothermicity), while radical additions
to olefins experience barriers of 0 to 2 kcal/mol [38d]. Hence, the lack of
selectivity for higher olefins is not explained by direct hydrogen abstraction
from the olefin (since epoxidation is kinetically preferred in general).
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation
reaction
275
On the other hand, the oxyalkyl radical intermediate formed upon addition
of the SAO to the 7~ bond of propene has an alternative route to combustion:
(14)
1
-wo.+n,o
Since radical addition occurs readily, we propose that this intermediate can
undergo rapid y-hydrogen abstraction to form adsorbed ally1 alkoxide (downhill by 37 kcal/mol), which can subsequently react with surface oxygen to
form such products as acrolein (CH,CHCHO),
CO,, and H,O. Thus, we
suggest that oxyalkyl radicals are common intermediates en route to expoxidation and combustion products.
This mechanism involving y-hydrogen abstraction requires accessible surface
oxides (in next-nearest-neighbor
sites) and hence the yield of combustion
products should depend upon oxygen coverage. Thus, a test for this pathway
would be to examine selectivity on Ag(ll1) as a function of oxygen coverage,
with the expectation that higher selectivity to PO should be observed at low
coverages of oxygen. (Observing variations in coverage for O/Ag(llO) will not
be conclusive, since we believe that only the di-a oxide species (not oxyradicals) will be present at low coverage, whereas we wish to probe varying
coverages of the SAO.) A second test of this mechanism is to compare the rate
and products of combustion of adsorbed ally1 alcohol on an 0-precovered Ag
surface (we predict that dissociative adsorption of ally1 alcohol to form
adsorbed ally1 alkoxide and OH,,,, is - 29 kcal/mol exothermic) with the
combustion rate of propene. Indeed, Solomon and Madix have recently
studied [43c] the oxidation of ally1 alcohol on Ag(ll0) with 0, I 0.25. They
observed formation of acrolein, water, and hydrogen as primary products and,
similar to our work, invoked an ally1 alkoxy group as the primary intermediate
in the oxidation. Consistent with our mechanism, they also suggest that water
is formed from OH,,,, disproportionation, where the OH,,,, was formed by
dissociative adsorption of ally1 alcohol on O/Ag(llO). Although CO, was not
produced for low coverages of Ocadj on the low surface area single crystal
276
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation
reaction
produced
for low coverages of Ocadj on the low surface area single crystal
[Ag(llO)], it has been observed as a product in the oxidation of ally1 alcohol
on a high surface area silver sponge catalyst
[43d], consistent
with our
expectation
that total combustion
requires high coverages of oxygen.
Allylic intermediates
obtained
by y-H abstraction
have been proposed
previously
for the oxidation
of propene over supported
Ag-Au
alloys by
Geenen et al. [43b]. Such intermediates
were suggested in order to explain the
efficient production
of acrolein by these alloy catalysts. Alternatively,
acrolein
may be produced within our mechanism
as a subsequent
oxidation of the ally1
alkoxide intermediate.
We estimate that an a-H abstraction
from adsorbed
ally1 alkoxide by Ocadj
+ Ocadj -+ CH,=CHCHO,gJ
CH,=CHCH,O(,,
+ OHcad)
is exothermic by 9 kcal/mol.
These energetics are entirely consistent with the
findings of Solomon and Madix [43c].
In our model, any olefin with y-hydrogens
will combust; this explains why
the epoxidation
reaction
over Ag is specific to ethylene.
A test of this
hypothesis is to study selectivity for olefins lacking allylic (or y) hydrogens,
with the prediction
that substrates such as styrene or t-butylethylene,
H
H
H
(15)
H
styrcne
H
will lead to greater
tert-butytcthylcne
selectivity
toward
epoxide.
4.1.4. Alternative combustion pathways
Since C,H,
has no y-hydrogens,
ethylene cannot participate
in process
(14). Both propene and ethylene could possibly undergo a-hydrogen
abstraction from the oxyalkyl radical intermediate
(AH,,, = - 41 and - 39 kcal/mol
for C,H,
and C,H,, respectively),
but this would require oxygen atoms in
highly unfavorable
nearest-neighbor
sites. P-hydrogen
abstraction
from this
intermediate
is ruled out, since the product would be an unstable
carbene
for ethylene) [38a]. We propose that ethylene combus(uphill - 36 kcal/mol
tion may occur via combustion
of the ethylene oxide product (with a predicted
for H abstraction
from EO):
endothermicity
of - 16 kcal/mol
H
I4
(16)
E.A. Carier, W.A. Goddard III / A model for the olefin epoxidation
reaction
211
This can be tested by exposing EO to oxide-covered
Ag single crystals, in
order to distinguish
between direct EO hydrogen
abstraction
and the side
reaction thought to occur on supported
catalysts:
isomerization
of EO to
acetaldehyde,
followed by rapid combustion
of the aldehyde to CO, + H,O
[4]. In fact, experimental
evidence exists for both combustion
pathways, even
on single crystal surfaces [3a].
4. I. 5. Water formation
After hydrogen abstraction
from the olefin occurs to form surface-bound
should
not
form,
since the incipient
Ag-H bond is much
hydroxyls ]H(,,,
weaker than the incipient
O-H bond (30 to 50 kcal/mol
versus 80 to 90
kcal/mol)],
water is produced as one of the final products of combustion.
As
discussed
in section 3.5, the energetics
for the formation
of H,O from
surface-bound
hydroxyl groups can be predicted from the theoretical
values
for the binding energies of OH (I 65 kcal/mol)
and 0 (79 kcal/mol)
and the
heat of adsorption of H,O on Ag (- 14 kcal/mol)
[35]. Converting
these bond
energies
to heats of formation
by using AH&,,(OH,,,)
= 9.4 kcal/mol,
AH,P,,,(O(,,) = 59.6 kcal/mol,
and AHf&8(H20~gj) = - 57.8 kcal/mol
[24a]
to disproportionate
two
leads to a predicted endothermicity
of - 21 kcal/mol
surface-bound
hydroxyls
to one adsorbed
oxygen atom and one adsorbed
molecule of H,O,
(17)
in good agreement with the activation energy of 22.2 f 0.3 kcal/mol
observed
for OH disproportionation
on Ag(ll0)
[36]. Since the predicted
Ag,,,-OH
bond energy (65 kcal/mol)
is expected to be an upper bound to the true
binding energy of OH,,,,, 21 kcal/mol
is expected to be an upper limit to the
endothermicity
for disproportionation.
4.2. Identification
of the active oxygen
As discussed in the introduction,
many investigations
have been carried out
to determine the nature of the oxygen that produces epoxide, in order to find
ways to optimize its concentration.
Van Santen and de Groot’s recent labelling
studies involving the exposure of a gaseous mixture of C,H, and “02 to an
Ag surface pre-covered with 160cadj,
(18)
278
EA. Carter, W.A. Goddard III /A
modelfor the olefin epoxidation reaction
provides compelling evidence that adsorbed oxygen atoms are responsible
for
the production
of EO, since initially only r60-labeled
EO is formed [13f].
On the other hand, Campbell has shown that the rate of EO production
is
uncorrelated
with the postreaction
concentration
of atomic oxygen, a conclusion based on the following two facts:
(i) For low coverages of oxygen (0o 2 OS), the probability
for dissociative
adsorption
is about two orders of magnitude
smaller on Ag(l11)
than on
Ag(ll0) at 490 K [2Sbf. Correspondingty,
the coverage of Ocadi (determined
by
postreaction
analysis) is a factor of - 18 smaller on Ag{fll) than on Ag(llO),
while the activities for EO production
on the two surfaces differ only by a
factor of two [12c].
(ii) Coadsorption
of Cl and 0 on AgflfO) and Ag(ll1)
produced
EO at
rates nearly independent
of chlorine coverage (up to 6,, = 0.5) but under
conditions
where the postreaction
concentration
of Ocadj decreases dramatically with increasing B,, [7a-7cj.
Since the rate was found to be independent
of the measured coverage of
monatomic
oxygen, Campbell concluded
that diatomic oxygen must be the
active precursor to EO.
Herein we present a new interpretation
of the kinetic trends discussed
above, in terms of atomic oxygen as the active species for epoxidation.
The
difference in saturation coverages of Ocadj between the (110) and (111) faces of
Ag is due to the presence of more than one binding site for 0 on Ag(l10).
While the close-packed
(111) surface has only 3-coordinate
binding
sites
available, the corrugated (1X0) surface has two d~$t~~~t~y
different binding sites
with undoubtedly different stabilities. These two sites are shown in fig. 8, where
fig. 8a depicts the 4-coordinate
site in the bottom of troughs (between the first
and second layer Ag atoms), while fig.. 8b displays the 3-coordinate
site
located on the side of the troughs. This 3-coordinate
site is analogous
to the
3-coordinate
site present on the (111) plane of Ag.
We expect the oxygen in the 4-coordinate
site to have d&-type
bonding
(eq. (g)), resulting in a relatively
unreactive
oxide since all of the oxygen
electrons are tied up with the surface. After saturating
the 4-coordinate
sites
a
b
Fig. 8. The two high-symmetry adsorption sites on Ag(l10f: (a) the 4-f&d site down in the trough
and (b) the 3-fold site along the sides of the trough.
E.A.Carter, W.A. Goddard III / A model for the olefin epoxidation reaction
219
with oxygen (/3= OS), any remaining oxygen must go into 3-coordinate sites
(or possibly into 2-coordinate bridge sites on the crests) which favor the SAO
state. The oxygens in the 4-coordinate hollows of Ag(ll0)
have binding
energies of - 78 kcal/mol, whereas the 3-coordinate oxygens on Ag(ll1) are
bound by - 77 kcal/mol [26b]. Indeed, a Redhead analysis [23e] of the
second-order desorption kinetics for the thermal desorption spectra of Campbell [26] leads to identical binding energies (76.6 kcal/mol) for Ocadj on
Ag(ll1) (local 0, = 0.41) and for a high coverage form of Ocad, on Ag(ll0)
(local So = 0.67), with a higher binding energy (78.1 kcal/mol) for Ocad, on
Ag(ll0) at or below 0, = 0.5. The identical binding energies for Ocad,on the
two different crystal faces suggests identical binding sites and/or forms of
0 (adj, namely oxyradicals in p3 sites on Ag(ll1)
and on the sides of the
troughs of Ag(ll0). The higher binding energy for the lower coverage Ocadjon
Ag(ll0) is expected for the di-o oxide species. The evidence for two states on
Ag(ll0)
is glaringly apparent from the asymmetry of the high coverage
thermal desorption spectrum [26a], a feature absent on Ag(lll)
(suggesting
only one species is present for the latter surface). An experimental test of our
suggestion that the high coverage state of Ocad, on Ag(ll0) is the SAO state
would be to examine the high coverage EEL spectrum. If the SAO exists at
high coverages on Ag(ll0) [and at any coverage on Ag(lll)], we expect to see
losses at both - 220 and 315 cm-‘. This would provide further evidence of
the similarity between O/Ag(lll)
and high coverage O/Ag(llO), as well as
indicating the presence of two distinct forms of Ocad,on Ag(ll0).
In comparison to 0 on Ag,, the strength of the di-a bond in the 4-coordinate site is essentially identical to the di-a/ar bond strength in the 3-coordinate site of Ag, (77.8 kcal/mol). The O- radical in the 3-coordinate site of
Ag, has a binding energy of 78.7 kcal/mol, also in excellent agreement with
the stability (D(Ag,,,-0)
= 76.6 kcal/mol) found for oxygen in the 3-coordinate sites on Ag(ll1) [26a,26b].
At oxygen coverages below 0.5, p-( n X 1) (n decreasing continuously from 7
to 2 as the oxygen coverage increases) low-energy electron diffraction (LEED)
patterns form, which have been interpreted as oxygens residing in the four-fold
sites of the troughs [6,25]. At a pressure of 50 Torr and a temperature of 485
K, a high coverage (0, = 0.67) form of oxygen has been recently observed on
the (110) surface, exhibiting a c-(6 x 2) LEED pattern [26a]. This high coverage form was shown to be five times more reactive for CO oxidation to CO,
than the low coverage 0 (adj species, but once the oxygen coverage decreased to
0.5 (~(2 X 1) LEED pattern), the reaction probability for CO oxidation
dropped precipitously.
Several conclusions may be drawn from these observations:
(i) the 4-coordinate site on Ag(ll0) (fig. 8a) is filled first (probably the
most stable site for oxygen adatoms) with di-a oxide-type Ocadj;
(ii) higher exposures of oxygen on Ag(ll0) allow another site to fill which
280
E.A. Carter, W.A. Goddard III / A model for the okfin epoxidatron
reaction
we interpret
to be the 3-coordinate
site (fig. 8b) expected to have the same
character as O/Ag(lll),
namely, oxyradical character: and
(iii) the 4-coordinate
site is less reactive than the 3-coordinate
site, as
indicated by the CO titration studies [26a].
Thus we interpret the differences in activity with coverage of Ocadj between
Ag(ll0) and Ag(l11) to be due to the unreactive 4-coordinate
sites on Ag(ll0)
filling first, followed by filling the reactive 3-coordinate
sites on Ag(ll0).
Ag(ll1)
only has 3-coordinate
sites and therefore the activity per adsorbed
oxygen atom is higher than that found for Ag(ll0).
In our SAO mechanism
[38a,38b] the crucial concentration
is not the overall concentration
of Ocadj but
rather the concentration
of Ocadj in the atomic oxyradical
state (in 3- or
2-coordinate
sites). We suggest that the concentration
of SAO is similar on
both crystal faces, resulting in similar activities for the formation of EO.
Summarizing,
our SAO mechanism
suggests that the key to increasing
the
activity of the catalyst is to saturate the 4-coordinate,
nonselective
sites, and
then to maximize the oxygen concentration
in the selective SAO sites. Consistent with this idea is the observation
that a ratio of O/Ag above 1 : 2 is
needed to obtain EO on Ag powders [13f]; i.e., a high coverage of oxygen is
necessary to form the active oxygen species. Finally, we note that while other
workers such as Twigg [45a], Hayes [45b], Force and Bell [13a,13b], Grant and
Lambert [13d,13e], Backx et al., [13c,25a,45c], and van Santen et al. [3a,13f]
precursor, we are the first to
have also proposed Ocad, as the active epoxidation
predict the detailed electronic nature of the two types of Otadj, one active for
epoxidation
at high coverage and one leading only to combustion
at low
coverage.
4.3. The role of electronegative
promoters
Chlorine is the prototypical
electronegative
promoter, but other such elements also act to increase the activity and selectivity for EO formation
[3-51.
Campbell
and Koel have observed that high coverages of Cl (ec, 2 0.4) on
Ag(ll0) inhibit the formation of CO, [7b]. They have interpreted
this result as
an ensemble effect, where the number of open surface sites required for total
combustion
is presumed higher than the number of sites necessary for epoxidation. While the relative site requirements
may indeed differ, we believe that
it is the specific sites blocked by chlorine which increase the selectivity of the
catalyst.
In particular, a p-(2 x 1) structure is observed by LEED above 19,~= 0.4 on
Ag(ll0)
[7b], coinciding
with the increase
in selectivity
towards
EO. A
comparison
of the ab initio binding energies of Cl versus 0 suggests [46] that
Cl may compete with 0 for the most stable sites on the (110) surface (the
4-coordinate
site in the troughs). The p-(2 x l)-Cl LEED pattern is consistent
with this analysis, since the p-(2 X 1)-O LEED pattern found for oxygen on
E.A. Carter, W.A. Goddard III / A model for the &fin
epoxidatmn
reuction
281
Ag(ll0)
is associated with oxygen in these 4-coordinate
sites. Furthermore,
Winograd and co-workers used angle-resolved
secondary ion mass spectrometry (SIMS) to show that as the Cl coverage increases, the surface-Cl
distance
decreases
significantly,
indicating
that Cl probably
falls into the troughs
(occupying the 4-coordinate
sites) at high coverage [47].
Our interpretation
of Campbell and Koel’s results is that Cl saturates the
4-coordinate
hollows, forcing 0 to occupy the slightly less stable but more
reactive 3-coordinate
sites. Thus the role of Cl (or S, Se, Br, etc.) is simply to
block the nonselective
4-coordinate
hollows, thereby increasing the population
of reactive oxygen species in the selective SAO state (in the 3-coordinate
sites).
Indeed,
Campbell
and Koel’s experiments
indicate
that the postreaction
coverage of Ocadj drops dramatically
with increasing &.,. Since the postreaction
measurement
observes the amount of unreacted oxygen, we conclude
that
increasing
t$, leads to an increase in reactive SAO and a decrease in
unreactive di-a oxide.
4.4. The role of electropositive promoters
Salts of alkali metals and alkaline earths are also known promoters of the
EO reaction [3-51. Cesium is one of the most common dopants and has been
studied on single crystals by both Lambert
and Campbell
[7d,7e,7g,7h].
Thermal desorption
and LEED studies of the coadsorption
of Cs and 0 on
Ag(ll1)
have revealed [7d] that aggregates are formed with the approximate
stoichiometry
CsO,. The promotional
effect of Cs was attributed
in this work
by Campbell [7d] to be exactly analogous to the role proposed for Cl: that of a
site-blocker which suppresses CO, formation.
We now offer a new interpretation
of the role of Cs, based on our results
for the interaction
of ethylene with Ag, and Ag_T. Since Cs and the other
electropositive
promoters are added to the catalyst as salts, they are likely to
be present as M+. Aggregates such as Cs+O;
should be favorable, since the
oxygen adatoms are partially negatively charged (section 3.3). Ethylene binds
only weakly to the clean Ag surface [37], consistent
with our results of a
repulsive interaction
with the neutral Ag, cluster (section 3.6). However, we
find that the positively-charged
Ag: cluster does bind ethylene with a bond
energy of - 9 kcal/mol.
We propose that Cs+ sits on top of the oxygens
present in the 4-coordinate
trough sites (since they may be more negatively
charged than the radical oxygens in the 3-coordinate
sites), and then Cs+ helps
to direct olefins down to the Ag surface via a Lewis acid-Lewis
base
interaction,
increasing the overall adsorption probability
for ethylene on Ag. If
ethylene adsorption
occurs on Cs + in the troughs, nearby oxygen radicals in
the 3-coordinate
sites on the sides of the troughs may be more readily
accessible to the ethylene, increasing the rate of reaction, as shown schemati-
282
tally
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation
below for a generic
reaction
surface:
Indeed, an increase in selectivity upon addition of Cs may be explained by this
Lewis acid-Lewis
base bonding,
since the olefin will be held parallel to the
surface to maximize this interaction.
As a result, the hydrogens of the olefin
will also be parallel
to the surface, reducing
the chances
for hydrogen
abstraction
by adsorbed oxygen (inhibiting
the direct combustion
pathway).
Instead, the C-C r-bond
of the olefin is held perpendicular
to the surface,
increasing the probability
for reaction to form epoxide.
In this section we have addressed many of the issues involved in the olefin
epoxidation
reaction as catalyzed by silver. In the next section we summarize
our findings.
5. Conclusions
Ab initio GVB-CCC1 calculations
of the interaction
of various adsorbates
on Ag, indicate the following:
(i) All adsorbates
except ethylene (which prefers one-fold coordination)
favor binding
to the 2-coordinate,
in-plane
site of the cluster, with bond
energies much stronger
than those expected
for adsorbate-surface
bond
energies (providing
upper bounds
to the Ag,,,-X
binding
energies).
The
unpaired
electron on this cluster helps to preserve the Ag-Ag bond (bulk
diamagnetic
Ag should incur some Ag-Ag bond weakening upon adsorption).
(ii) Adsorbate
binding
energies to the 3-coordinate
site of the cluster
provide estimates of the actual binding energies on an extended surface (lower
bounds due to the lack of electron density in the p3 site of Ag,), with values
as a function of adsite reported for H (29 < D(Ag,,,-H)
< 57 kcal/mol),
Cl
(73 < D(Ag,,,-Cl)
< 91 kcal/mol),
0 (79 < D(Ag,,,-0)
< 93 kcal/mol),
and
0, (17 kcal/mol
as an upper bound),
and OH (46 < D(Ag,,,-OH)
< 65
E.A. Caner,
W.A. Goddurd III / A model for rhe
&fin epoxidationreaction
283
kcal/mol).
The binding energy of ethylene to Ag: is found to be 9 kcal/mol
in the l-coordinate
site. The values for C,H, and 0 are in excellent agreement
with experiment and the experimental
lower bound for OH (54 + 3 kcal/mol)
falls right in the middle of our range of theoretical values. Experimental
values
for H and Cl remain undetermined.
Implications
from this work for understanding
the detailed mechanistic
aspects of the Ag-catalyzed
olefin epoxidation
reaction are as follows:
(iii) Two near-degenerate
states of Ocadj are predicted to have drastically
different properties
and reactivity,
with a surface atomic oxyradical
anion
(SAO) predicted to be the active precursor to epoxide. This suggests that the
control of catalyst selectivity and activity is directly related to the relative
populations of the SAO and the nonselective, di-o-bound oxygen. Specifically, we
propose that the key to high epoxidation
yields is to keep the oxygen coverage
above 0, = 0.5 to ensure a large concentration
of the SAO.
(iv) These two oxygen species are used in section 4 to propose
new
interpretations
of the trends observed in single crystal studies of EO formation, with the result that the radical oxygen is predicted to reside in 3-coordinate sites on both Ag(l11) and Ag(llO), while the unreactive,
di-a oxygen is
expected to prefer the 4-coordinate
binding site in the valleys of the (110)
surface.
(v) The role of electronegative
promoters
such as Cl is attributed
to
blocking the 4-coordinate
sites, forcing surface oxygen into the SAO state,
while the role of electropositive
promoters is to increase the concentration
of
adsorbed ethylene and to increase selectivity by holding the olefin parallel to
the surface.
(vi) Epoxide formation is exothermic for both ethylene and propylene, but
olefins larger than ethylene combust due to the ease with which y-hydrogens
may be abstracted from the olefin to form surface-bound
hydroxyl groups and
adsorbed ally1 alkoxide. Disproportionation
of OHcad) to adsorbed 0 and H,O
is predicted to be endothermic
by 5 21 kcal/mol,
in good agreement
with
experiment.
(vii) Combustion
of ethylene probably occurs after EO is formed, since the
primary C-H bonds in EO are weaker than the vinyl C-H bonds of ethylene.
(viii) We propose that the uniqueness
of Ag (versus the other coinage
metals) as an epoxidation
catalyst is due primarily to the extreme sensitivity of
the reaction to the relative stabilities of various forms of adsorbed oxygen;
namely, oxygen adatoms are readily formed on Ag, whereas a large barrier to
dissociative
adsorption
exists on Au [48a], and Ocad) on Ag is much less
strongly bound (and thus more reactive) than on Cu [48b]. In particular,
the
SAO may only form on Ag, due to the barrier on Au and surface oxide
formation on Cu.
284
E.A. Curter, W.A. Goddard III / A model
6. Calculational
for the
olefin epoxidation
reaction
details
6. I. Basis sets
The eleven valence electrons of Ag (4d’“5s’) were treated explicitly within
the (3s3p4d/3s2p2d)
Gaussian basis of Hay and Wadt, with the core electrons
represented by an effective core potential [49]. The Dunning valence double-[
contractions
[50] of the Huzinaga Gaussian primitive bases [51] for hydrogen
(4s; exponents
scaled by 1.2) oxygen (9s5p), and carbon (9~5~) were used,
with a 3d-polarization
function added to oxygen (ld = 0.95) [52]. For Ag,H,
the more extensive triple-l contraction
of Huzinaga’s
6s primitive basis [51]
along with a 2p-polarization
function
(5, = 0.6) were used on H. Cl was
described using the SHC effective core potential
and valence double-l
basis
set of Rappt et al. [53], along with one 3d-polarization
function ({, = 0.6) and
one set of s and p diffuse functions (la = I,, = 0.049). For Ag,O and Ag,OH,
one set of s and p diffuse functions [52] was added to the 0 basis described
above (2, = 0.088 and 5, = 0.060) and the (6s/3s) basis used on H in Ag,H
was also used on Ag,OH.
6.2. GVB and CCCI calculations
All geometries and vibrational
frequencies were optimized for all molecules
(with the Ag, cluster constrained
to be an equilateral triangle with side length
2.89 A (the nearest neighbor value in bulk Ag [54]) and the ethylene molecular
geometry fixed at the experimental
geometry [55]) at the GVB-PP level (two
pairs were correlated for Ag,H, Ag,Cl, Ag,O, Ag,OH, Ag,O,, while three
bond pairs were correlated for C,H, bound to Ag,) [56]. The relative energies
reported in each table were calculated at the GVB-PP level. The bond energies
for H, Cl, OH, and the doubly-bonded
states of 0 were calculated using the
correlation-consistent
configuration
interaction
(CCCI) approach [57], which
allows full correlation
(single and double excitations)
from the bond that is
breaking, along with single excitations
from all valence orbitals to all unoccupied orbitals, to account for orbital shape changes important
during bond
breakage. These excitations
are allowed from the RCI reference states, in
which all three occupations
of two electrons in the two orbitals of each GVB
pair are included. For example, calculation
of the bond energy for the di-a/ar
state of 0 in the pJ site involved all single and double excitations out of each
Ag-0
bond (separately)
plus all single excitations
from all valence orbitals
(from the RCI reference states). This involves a CI expansion of 5856 spatial
configurations
and 17196 spin eigenfunctions.
The doubly-bonded
states of
Ag,O dissociate diabatically
to the 4A, excited state of Ag,. We calculated the
diabatic bond energy, then subtracted
the 4A2-2A, energy splitting in Ag,
(30.1 kcal/mol
at the GVB(1/2)PP
level) to obtain the adiabatic bond energy.
E.A. Carwr, W.A. Goddard III / A model for the olefm epoxldarm
reacrion
285
The bond energies for the ionic radical states of 0 on Ag, were determined
indirectly by subtracting
or adding the GVB-PP energy difference between the
radical state and the double-bonded
state for each adsite. The binding energies
for 0, to Ag, were determined
using a valence level CI to describe the
resonance in the 7~orbitals of 0,. Since 0, on Ag, is best described as 0,) we
calculated the ionic bond energy, then subtracted the theoretical IP(Ag,) = 4.18
eV and added the experimental
EA(0,) = 0.44 eV [20] to obtain a covalent
bond energy. The valence level CI consisted of an RCI within the Ag-Ag and
O-O u bond pairs simultaneous
with both configurations
of the 0, threeand 7~,$gz). The bond energies for Ag,OH
were
electron 71 system (7r$j
calculated by allowing all single and double excitations out of the 0 2s and 2p
lone pairs from the RCI configurations
for the O-H and Ag-Ag GVB bond
pairs. The ethylene binding energies to Agl were calculating at the GVB(3/6)PP level (Ag-Ag and the two C-C bonds were correlated as GVB pairs).
Acknowledgements
This work was initiated and supported by the Shell Development
Corporation (198221985)
and the Shell Companies
Foundation
(1985-1987).
We
would particularly
like to thank Drs. Charles Adams, Rutger van Santen, and
John Cole for initiating
and continuing
their industrial
support
for our
research. Further support was provided by the National
Science Foundation
[Grant
No. DMR82-15650
(1983-1986)
and Grant
No. CHE83-18041
(1986-1987)].
EAC acknowledges
a National Science Foundation
Predoctoral
Fellowship
(1982-1985)
a research grant award from the International
Precious Metals Institute
and Gemini
Industries
(1985-1986)
and a SOHIO
fellowship in Catalysis (1986-1987).
We would also like to thank Professors
C.T. Campbell and B.E. Koel for lively and helpful discussions.
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(b) E.L. Force and A.T. Bell, J. Catalysis 40 (1975) 356;
(c) C. Backx, J. Moolhuysen,
P. Geenen and R.A. van Santen, J. Catalysis 72 (1981) 364;
(d) R.B. Grant and R.M. Lambert, J. Chem. Sot. Chem. Commun. (1983) 662;
(e) R.B. Grant and R.M. Lambert, J. Catalysis 92 (1985) 364;
(f) R.A. van Santen and C.P.M. de Groot, J. Catalysis 98 (1986) 530.
[14] M.A. Barteau and R.J. Madix, Surface Sci. 97 (1980) 101.
[15] R.B. Grant and R.M. Lambert, J. Catalysis, to be published.
[16] (a) M.H. McAdon and W.A. Goddard
111, J. Non-Cryst.
Solids 75 (1985) 149;
(b) M.H. McAdon and W.A. Goddard III, Phys. Rev. Letters 55 (1985) 2563:
(c) M.H. McAdon and W.A. Goddard
III, J. Phys. Chem. 91 (1987) 2607;
(d) in systems where the orbitals have low overlap (S = 0.4) the one-electron
bond is often
stronger than the two-electron
bond (e.g., Da(Li; ) = 1.44 eV whereas D,(Li *) = 1.05 eV).
[17] Distortion
from D,, symmetry leads to an obtuse angle geometry for the 2B, state and an
acute angle geometry for the 2A, state of Ag,. ESR studies have yielded conflicting
results,
with the ‘B, state lower in a C,D, matrix [J.A. Howard, K.F. Preston and B. Mile, J. Am.
Chem. Sot. 103 (1981) 62261, while the ‘A, state prevails in an N, matrix [K. Kernisant, G.A.
Thompson
and D.M. Lindsay, J. Chem. Phys. 82 (1985) 47391, indicating
that all three
structures
are very close in energy. (The equilateral
triangle is the low-lying saddle point
For a recent
( - 400 cm-‘)
between these two near-degenerate,
C,, symmetry structures.)
theoretical study of this distortion,
see S.P. Walch, J. Chem. Phys. 85 (1986) 5900.
[18] R.C. Weast, Ed. CRC Handbook
of Chemistry and Physics (CRC Press, Boca Raton, 1981)
p. E-79.
[19] M.A. Tolbert and J.L. Beauchamp.
J. Phys. Chem. 90 (1986) 5015.
[20] (a) K.P. Huber and G. Herzberg,
Constants
of Diatomic
Molecules (Van Nostrand,
New
York, 1979);
(b) Tian Zeng-ju, Zhang Kai-ming and Xie Xi-de, Surface Sci. 163 (1985) 1.
[21] (a) J. Flad, Cr. Igel-Mann, M. Dolg, H. Preuss and H. Stall, Surface Sci. 163 (1985) 285;
(b) K.W. Frese, Jr., Surface Sci. 182 (1987) 85.
[22] G.M. Lamble. R.S. Brooks, S. Ferrer and D.A. King, Phys. Rev. B 34 (1986) 2975.
[23] (a) M. Bowker and K.C. Waugh, Surface Sci. 134 (1983) 639;
(b) D.E. Taylor, E.D. Williams and R.L. Park, preprint;
E.A. Carter, W.A. Goddard III / A model for the olefin epoxidation
P4l
[25]
[26]
[27]
[28]
[29]
[30]
[31]
[32]
[33]
[34]
[35]
[36]
[37]
[38]
[39]
reaction
287
(c) M. Kitson and R.M. Lambert, Surface Sci. 100 (1980) 368;
(d) P.J. Goddard
and R.M. Lambert, Surface Sci. 67 (1977) 180;
(e) P.A. Redhead, Vacuum 12 (1962) 203.
are taken from: JANAF Thermochemical
Tables, J. Phys. Chem. Ref. Data 14
(a) AH,P,,,
Suppl. 1 (1985) and from SW. Benson, Thermochemical
Kinetics (Wiley, New York, 1976);
(b) A. Puschmann
and J. Haase, Surface Sci. 144 (1984) 559;
(c) W.R. Wadt and W.A. Goddard
III, J. Am. Chem. Sot. 96 (1974) 1689;
(d) W.R. Wadt and W.A. Goddard III, J. Am. Chem. Sot. 97 (1975) 3004;
(e) L.B. Harding and W.A. Goddard III, J. Chem. Phys. 67 (1977) 2377;
(f) L.B. Harding and W.A. Goddard
III, J. Am. Chem. Sot. 100 (1978) 7180.
(a) C. Backx, C.P.M. de Groot and P. Biloen, Surface Sci. 104 (1981) 300;
(b) A.M. Bradshaw, H.A. Engelhardt
and D. Menzel, Ber. Bunsenges. Phys. Chem. 76 (1972)
501;
(c) H.A. Engelhardt and D. Menzel, Surface Sci. 40 (1973) 140;
(d) W. Heiland, F. Iberl, E. Taglauer and D. Menzel, Surface Sci. 53 (1975) 383;
(e) H.A. Engelhardt
and D. Menzel, Surface Sci. 57 (1976) 591;
(f) H.A. Engelhardt,
A.M. Bradshaw and D. Menzel, Surface Sci. 40 (1973) 410.
(a) CT. Campbell and M.T. Paffett, Surface Sci. 143 (1984) 517;
(b) CT. Campbell, Surface Sci. 157 (1985) 43;
(c) C. Benndorf, M. Franck and F. Thieme, Surface Sci. 128 (1983) 417.
R.L. Martin and P.J. Hay, Surface Sci. 130 (1983) L283.
(a) B.A. Sexton and R.J. Madix, Chem. Phys. Letters 76 (1980) 294;
(b) K. Prabhakaran
and C.N.R. Rao, Surface Sci. 186 (1987) L575.
D.A. Outka, J. St&r, W. Jark, P. Stevens, J. Solomon and R.J. Madix, Phys. Rev. B 35 (1987)
4119.
J. Marsden, L.S. Bartell and P. Diodati, J. Mol. Struct. 39 (1977) 253.
K.C. Prince, G. Paolucci and A.M. Bradshaw, Surface Sci. 175 (1986) 101.
C.T. Campbell, Surface Sci. 173 (1986) L641.
G.B. Fisher and B.A. Sexton, Phys. Rev. Letters 44 (1980) 683.
(a) P.R. Norton, in: The Chemical Physics of Solid Surfaces and Heterogeneous
Catalysis,
Vol. 4, Eds. D.A. King and D.P. Woodruff (Elsevier, Amsterdam,
1982) ch. 2;
(b) M. Klana and T.E. Madey, Surface Sci. 136 (1984) L42.
(a) E.M. Stuve and R.J. Madix, Surface Sci. 111 (1981) 11;
(b) I. Pockrand, Surface Sci. 122 (1982) L569:
(c) K. Bange, T.E. Madey, J.K. Sass and E.M. Stuve, Surface Sci. 183 (1987) 334.
S.W. Jorgensen, A.G. Sault and R.J. Madix, Langmuir 1 (1985) 526.
(a) C. Backx, C.P.M. de Groot, and P. Biloen, Appl. Surface Sci. 6 (1980) 256;
(b) C. Backx, C.P.M. de Groot, P. Biloen and W.M.H. Sachtler, Surface Sci. 128 (1983) 81.
(a) E.A. Carter and W.A. Goddard
III, J. Catalysis 112 (1988) 80;
(b) preliminary
theoretical
results may be found in: W.A. Goddard
III, J.J. Low, B.D.
Olafson, A. Redondo, Y. Zeiri, M.L. Steigetwald, E.A. Carter, J.N. Allison and R. Chang, in:
Proc. Symp. on the Chemistry
and Physics of Electrocatalysis,
Vol. 84-12, Eds. J.D.E.
McIntyre, M.J. Weaver and E.B. Yeager (The Electrochemical
Society, Pennington,
NJ, 1984)
pp. 63-95;
(c) N. Shimizu,
K. Shimokoshi and I. Yasumori, Bull. Chem. Sot. Japan 46 (1973) 2929;
(d) F. Westley, Table of Recommended
Rate Constants for Chemical Reactions Occurring in
Combustion,
NSRDS-NBS
67 (1980).
(a) The energetics for 0, +C,H,
+
OzCHzCH,.
are derived from AH,,,,,(O,,,)
= - 10.1
kcal/mol,
AHr,,,s(C,H,(,,)
= 12.1 kcal/mol,
AH r.aas(( OzCH,CHz.t,,)
=16.6 kcal/mol,
as
derived from ref. [24a] and using the EA(HO,.)
= 27.4 kcal/mol
[V.M. Bierbaum,
R.J.
Schmitt and C.H. DePuy, J. Am. Chem. Sot. 103 (1981) 62621 as an approximation
to
EA(.O,CH,CH,.);
288
E.A. Carter. W.A. Goddard III / A model for the &fin
epoxidation
reaction
(b) Assuming
adsorption-desorption
equilibrium.
Bo, may be calculated
using Boz=
S’F/N,k,
[26b], where S” = the probability
for molecular adsorption
and S” = 5 x 10mh for
0, chemisorption
on clean Ag(ll1) at 147 K [26b] (we expect So < 5 x 10mh for the higher
temperature
and due to repulsive interactions
on the oxygen-precovered
surface);
F=
“* = the flux of 0, impinging on the surface = 2.04 X 10” molecules/cm*.s;
Po,/(2amkT)
N,=1.38~10’~
molecules/cm2;
and k, = 10” exp( - E,/kT),
where E, is taken to be 3
kcal/mol
(the heat of physisorption
of 0,): an upper bound on the heat of adsorption
for 0,
on O/Ag;
(c) We have used the theoretical
value for the Ag-0
binding energy (79 kcal/mol)
in
conjunction
with the heats of formation
of the olefins (A H,P,,, = 12.1 kcal/mol
for C,H,
and 4.9 kcal/mol
for C,H,),
epoxides [AH;,,,
= - 12.6 kcal/mol
for EO and -22.6
kcal/mol
for propylene oxide (PO)], and oxygen atom (AH:*,, = 59.6 kcal/mol)
to predict
the heats of reaction [24a].
[40] (a) A.L. Larrabee and R.L. Kuczkowski,
J. Catalysis 52 (1978) 72:
(b) N.W. Cant and W.K. Hall, J. Catalysis 52 (1978) 81.
[41] CT. Campbell and M.T. Paffett, Surface Sci. 177 (1986) 417.
kcal/mol
for hydrogen
abstraction
from ethylene
is derived
from
[421 AfL = +39.1
D&(C2H3-H)
=118.2 kcal/mol
(obtained
by correcting
Dt by 1.5 kcal/mol
(GRT) for
finite temperature,
where Dt = 116.7* 1.2 kcal/mol
[H. Shiromaru,
Y. Achiba, K. Kimura
and Y.T. Lee, J. Phys. Chem. 91 (1987) 17]), and the theoretically-predicted
binding energies
of OH (an averaged value of 55 kcal/mol
is used: (65 + 45)/2) and 0 (79 kcal/mol)
to the
Ag surface.
[43] (a) M.A. Barteau and R.J. Madix, J. Am. Chem. Sot. 105 (1983) 344, and references therein;
(b) P.V. Geenen, H.J. Boss and G.T. Pott, J. Catalysis 77 (1982) 499;
(c) J.L. Solomon and R.J. Madix, J. Phys. Chem. 91 (1987) 6241;
(d) M. Imachi, N.W. Cant and R.L. Kuczkowski,
J. Catalysis 75 (1982) 404.
is derived from the same quantities
listed in ref. [42] except for the
WI AH,,, = + 9 kcal/mol
C-H bond energy in propene of 87.8 kcal/mol
(obtained from ref. [24a]).
[451 (a) G.H. Twigg, Trans. Faraday Sot. 42 (1946) 284; Proc. Roy. Sot. (London) A 188 (1946)
92;
(b) K.E. Hayes, Can. J. Chem. 38 (1960) 2256;
(c) C. Backx, C.P.M. de Groot and P. Biloen, Surface Sci. 115 (1982) 382.
[461 See tables 3 and 4: Cl may be slightly more stable than 0 on Ag surfaces, with predicted
binding energies of 79.7 kcal/mol
for Cl and 78.7 kcal/mol
for 0 in 3-coordinate
sites.
[471 D.W. Moon, R.J. Bleiler and N. Winograd, J. Chem. Phys. 85 (1986) 1097.
[481 (a) A.G. Sault, R.J. Madix and C.T. Campbell, Surface Sci. 169 (1986) 347;
(b) T. Inui, T. Ueda and M. Suehiro, J. Catalysis 65 (1980) 166.
[491 P.J. Hay and W.R. Wadt, J. Chem. Phys. 82 (1985) 270.
[501 T.H. Dunning, J. Chem. Phys. 53 (1970) 2823.
[511 S. Huzinaga, J. Chem. Phys. 42 (1965) 1293.
[521 R.A. Bair and W.A. Goddard III, unpublished.
[531 A.K. Rappe. T.A. SmedIey and W.A. Goddard III, J. Phys. Chem. 85 (1981) 1662. Note that
the second p exponent for the Cl basis listed in table 1 of this reference should read 0.641.
not 0.691, and the s orbital energy for Cl in table 4 of this reference should read - 1.0675. not
~ 0.1068.
[541 N.W. Ashcroft and N. David Mermin, Solid State Physics (Holt, Rinehart, and Winston,
Philadelphia,
1976).
R.H. Schwendeman,
D.A Kamsay, I-.J.
[55] M.D. Harmony,
V.W. Laurie, R.L. Kuczkowski,
Lovas. W.J. Lafferty and A.G. Maki, J. Phys. Chem. Ref. Data 8 (1979) 619.
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III, Chem. Phys. Letters 3 (1969) 606;
W.A. Goddard III. T.H. Dunning, Jr. and W.J. Hunt, Chem. Phys. Letters 4 (1969) 231:
E.A. Carter, W.A. Goddard III / A model for the &fin epoxidatton reaction
289
W.J. Hunt, W.A. Goddard
III and T.H. Dunning, Jr., Chem. Phys. Letters 6 (1970) 147;
W.J. Hunt, P.J. Hay and W.A. Goddard
III, J. Chem. Phys. 57 (1972) 738;
F.W. Bobrowicz and W.A. Goddard
III, in: Methods of Electronic Structure Theory, Eds.
H.F. Schaefer (Plenum, New York, 1977) pp. 79-127;
(b) L.G. Yaffe and W.A. Goddard
III, Phys. Rev. A 13 (1976) 1682.
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III, J. Chem. Phys. 88 (1988) 3132.