Predicting a Sharp Decline in Selectivity for Catalytic Esterification of Alcohols from van der Waals Interactions

Article abstract of DOI:10.1002/anie.202001576

Controlling the selectivity of catalytic reactions is a critical aspect of improving energy efficiency in the chemical industry; thus, predictive models are of key importance. Herein the performance of a heterogeneous, nanoporous Au catalyst is predicted for the complex catalytic self-coupling of the series of C₂–C₄ alkyl alcohols, based solely on the known kinetics of the elementary steps of the catalytic cycle for methanol coupling, using scaling methods augmented by density functional theory. Notably, a sharp decrease in selectivity for ester formation with increasing molecular weight to favor the aldehyde due to van der Waals interactions of reaction intermediates with the surface was predicted and subsequently verified quantitatively by experiment. Further, the agreement between theory and experiment clearly demonstrates the efficacy of this approach for building a predictive model of catalytic behavior for a homologous set of reactants using a small set of experimental information.

Full text of DOI:10.1002/anie.202001576

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Accepted Article
Title: Predicting a dramatic decline in selectivity for catalytic
esterification of alcohols due to van der Waals interactions
Authors: Christian Reece, Mathilde Luneau, Cynthia M Friend, and
Robert J Madix
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Predicting a dramatic decline in selectivity for catalytic
esterification of alcohols from van der Waals interactions
Christian Reece,[b] Mathilde Luneau,[b] C.M. Friend,[b] and Robert J. Madix*[a]
Abstract: Controlling the selectivity of catalytic reactions is a critical
aspect of improving energy efficiency in the chemical industry; thus,
predictive models are of key importance. Herein the performance of a
heterogeneous, nanoporous Au catalyst is predicted for the complex
catalytic self-coupling of the series of C2-C4 alkyl alcohols, based
solely on the known kinetics of the elementary steps of the catalytic
cycle for methanol coupling, using scaling methods augmented by
density functional theory. Notably, a sharp decrease in selectivity for
ester formation with increasing molecular weight to favor the aldehyde
due to van der Waals interactions of reaction intermediates with the
surface was predicted and subsequently verified quantitatively by
experiment. Further, the agreement between theory and experiment
clearly demonstrates the efficacy of this approach for building a
predictive model of catalytic behavior for a homologous set of
reactants using a small set of experimental information.
The elementary steps for oxidative coupling of methanol on
gold were determined from fundamental studies on single-crystals
in ultrahigh vacuum.[3,4] The catalytic cycle requires dissociation
of O2 on the surface to initiate the catalytic cycle. Catalytic function
is achieved by seeding a small amount of silver into the gold host,
as demonstrated for support-free nanoporous Ag0.03Au0.97.
[1,2,7] On
this nanoporous gold catalyst selectivity exceeding 90% is
observed for production of methyl formate for at 1 atmosphere
pressure between 90 and 150 °C (363 – 423 K).[8,9] Further, both
the activity and selectivity for the esterification of methanol over
this catalyst are accurately predicted for flow reaction conditions
(1 atm, 423 K) by microkinetic analysis using the rate constants
from the fundamental studies.[5,6] The microkinetic analysis also
demonstrates that a subset of the reaction network determines
catalytic performance (Fig. 1).[5,6] The critical role of the surface
concentration of the methoxy intermediate (CH3O*) in determining
selectivity is specifically illustrated by the analysis.[5,6]
The ability to predict and control reaction selectivity for
catalytic reactions is a means of increasing energy efficiency in
chemical production. Hence, a central goal in designing catalytic
processes is to have models that can rapidly predict reaction
selectivity as a function of pressure and temperature regimes.
Recent studies of oxidative coupling of methanol over gold-based
catalysts have demonstrated the utility of using a reaction
mechanism and rate constants derived from fundamental
studies[1–4] to accurately predict reaction selectivity over a wide
pressure range.[5,6] While these prior studies demonstrated the
value of fundamental studies for constructing predictive models,
they also required intensive experimental effort.
Herein, a generalization of the prior work that enables rapid,
quantitative evaluation of selectivity trends for a homologous set
of catalytic transformations is demonstrated. Reactor
performance was predicted for oxidative coupling of C2-C4 alkyl
alcohols based solely on the kinetics for methanol coupling
combined with scaling relationships derived from density
functional theory (DFT). Central to the effects reported are van
der Waals interactions of the reaction intermediates with the
surface. The excellent agreement with experimental
measurements of reaction selectivity for this set of reactions over
a nanoporous Ag0.03Au0.97 catalyst demonstrates the efficacy of
this approach, taking one step closer to the goal of “catalysis by
design”.
Figure 1. Graphical representation of each elementary step comprising the
generalized reaction network for alcohol self-coupling. The elementary steps
are listed explicitly in Table S4. Reactions that increase in rate with
molecular weight of the alcohol are shown with increased line width (1,2,3,4)
and those that decrease (3r,4,6) are indicated with narrower line weight. The
coupling step (6) is a second order reaction between the isolated alkoxy RO*
and the isolated adsorbed aldehyde RCHO*.
species.
* designates adsorbed
Analogous oxidation of higher alcohols on gold single
crystals and over nanoporous Ag0.03Au0.97 catalysts suggest that
the ester production may be less significant under the same
reaction conditions.[10,11] The origin of this effect is unknown, since
the elementary steps are the same as methanol.[10,12] However,
the kinetic parameters have not been measured for these species
and to do so would be extremely time intensive. Thus, a full
microkinetic analysis that predicts the selectivities for the coupling
reactions of these higher alcohols is not currently possible.
[a]
[b]
Prof. R. J. Madix
School of Engineering and Applied Sciences
Harvard University
Cambridge, MA, 02138 (USA)
E-mail: rmadix@seas.harvard.edu
Dr. C. Reece, Dr. M. Luneau, Prof. C. M. Friend,
Department of Chemistry and Chemical Biology
Harvard University
Cambridge, MA, 02138 (USA)
An alternative approach is to use Density Functional Theory
(DFT) to estimate the rate constants for the selectivity-
Supporting information for this article is given via a link at the end of
the document.
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determining steps in the network. Unfortunately,
a
priori
The most common method of scaling activation energies is
the Brønsted–Evans–Polanyi (BEP) principle,[13,14] which asserts
that the activation energy is linearly related to the thermodynamic
energy of reaction (Equation 1); a and b are constants, Ea is the
activation energy, and Ereaction is the overall energy of reaction.
This method has been widely used by others to estimate, for
example, periodic trends in reaction rates.[15–17]
calculation of accurate rate constants using DFT is also
challenging and subject to substantial uncertainties. But
computation of the energies of initial and final states of reactions
and thereby the overall reaction energy is much more
straightforward and computationally less intensive. Further, even
though the quantitative values of rate constants obtained by DFT
are subject to errors, the relative values (trends) in overall reaction
energies determined by DFT are more robust. Therefore,
calculating the reaction energies by DFT, scaling them to estimate
the activation energies, and thus the relative rate constants of the
relevant elementary steps, circumvents these issues.
ꢀꢁ = ꢂꢀꢃꢄꢁꢅꢆꢇꢈꢉ + ꢊ
(1)
Since the activation energy for each of the elementary steps
in the reaction network for methanol has been experimentally
determined (Table S4), and each Ereaction is calculable by DFT
(Tables 1,S3),[5,6] the values of the second scaling parameter, b,
for each step could be determined by using a generalised value
for the scaling constant, a, of 0.4 (Table 1).[18–21] The activation
energies for each elementary step in the reaction networks of
longer-chain alcohols were then calculated using a, b and the
corresponding overall reaction energy (Table 2). By scaling the
activation energies utilizing experimentally determined activation
energies as a reference, it is possible to circumvent the inherent
difficulty and significant computational cost of locating transition
states
Table 1. Calculated reaction energies for key steps in the alcohol coupling
network. BEP parameter b is estimated using a value of 0.4 for the BEP
parameter a. The reaction energy for alkoxy formation is calculated using
the binding energy of the adsorbed alcohol. The reaction energy
calculations are listed in Table S3
Reaction Energies (eV)
Reaction
b
Methanol
-0.38
Ethanol
-0.46
1-Propanol
-0.59
1-Butanol
-0.67
Alkoxy
formation
32.2
Aldehyde
formation
97.7
32.4
74.4
-0.67
0.21
-1.01
0.43
-1.07
0.55
-1.05
0.63
Aldehyde
desorption
Aldehyde
oxidation
-1.01
-0.72
-0.67
-0.59
Carboxylate
decomposition
-0.32
50.8
1.01
0.72
0.67
0.59
Coupling
-0.86
-0.38
-0.40
-0.18
Table 2. Activation energies, for key steps in the alcohol coupling network
derived for the higher alcohols by scaling the experimental value for
methanol. Reaction energies calculated from DFT are listed in Table 1.
Figure 2. Reaction energy diagram for alkoxy formation over Au(111)
surface for methanol, ethanol, 1-propanol, and 1-butanol. The formation of
alkoxy is limited by the surface lifetime of the alcohol, and therefore the
activation energy scales relative to the binding energy of the adsorbed
alcohol. The decrease in scaled activation energies are directly related to
the increased van der Waals binding of the adsorbed alcohol (Fig. S1). All
energies are in eV.
Activation Energy (kJ/mol)
Reaction
Methanola
17.0
Ethanol
13.0
1-Propanol
11.2
1-Butanol
8.3
Alkoxy
Formation
Aldehyde
Formation
66.7
40.6
34.4
53.8
49.1
45.8
51.5
53.8
47.7
52.3
56.8
50.8
For example, previous work demonstrates that the
differences in the binding energies for these alkoxides is due to
differences in the van der Waals interactions of the pendant R
groups.[22–25] The increase in the binding energies of surface
bound intermediates and molecules with increasing alkyl chain
length thus leads to corresponding changes in the activation
energies (Table 1). Thus, for example, the energetics of alkoxy
formation by adsorbed O* (Fig. 1, step 1) increase with increasing
alkyl chain length, driven by differences in the corresponding
Eadsorption of the alcohol (Table 1). Consequently, with increasing
alkyl chain length the activation energies for both alkoxy formation
(Fig. 2) and aldehyde formation (Fig, 1, steps 1 and 2) decrease
due to the increased van der Waals stabilization of the surface
Aldehyde
Desorption
Aldehyde
Oxidation
Carboxylate
Decomposition
38.7
17.6
27.3
36.2
25.4
35.3
22.4
44.0
Coupling
[a] Experimentally measured values
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bound alkoxy and aldehyde intermediates (Fig. S1). In contrast,
the same van der Waals stabilization of the aldehyde leads to an
increase in the activation energies for both aldehyde oxidation
(Fig. 1, steps 4 and 5) and the coupling (Fig. 1, step 6) pathway.
Since no significant differences are expected in the
preexponential factors from those of the corresponding reactions
for methanol coupling[26] (see SI), these changes in activation
energies indicate that with increasing molecular weight, steps 1
and 2, increase in rate, whereas steps 4, 5 and 6 decrease (Fig.
1, Table S2), short circuiting the reaction network. Therefore, the
higher alcohols are more likely to form their respective aldehydes.
Table 3. Conversions recorded for self-coupling of primary alcohols over
nanoporous gold catalyst, both experimentally and theoretically. Reaction
conditions 2% alcohol, 4% oxygen balanced in He at 423 K, 50 mL/min flow.
Product distributions are shown in Fig. 3.
Conversion (%)
Alcohol
Methanol
Ethanol
Experiment
8.5
Simulation
8.7
16.9
12.8
1-Propanol
1-Butanol
24.6
20.5
21.7
18.8
Furthermore, the scaled rate constants and the network of
elementary reactions accurately predict measured changes in
selectivity and activity with molecular weight when used in a
microkinetic model (Fig. 3, Table 3).[5,6] There are two clear
effects as alkyl chain length increases: (1) the alcohol conversion
increases and (2) the selectivity for aldehyde production
increases sharply at the expense of coupling and combustion.
The shift in selectivity away from the coupling product arises from
the increased binding energy of the aldehyde due to higher van
der Waals interactions between the alkyl chain and the metal (Fig.
S1). Generally, these results demonstrate that van der Waals
interactions direct both the catalytic activity and selectivity.
Contour plots for the selectivity for self-coupling show
significant dependence on the partial pressure of the reactants at
the reactor temperature of 423 K (Fig. 4). Much like methanol self-
coupling (Fig. 4a) there is a general trend toward increasing
selectivity to the self-coupling product with an increase in reactant
pressure (both alcohol and oxygen) and with an increase in
alcohol pressure at higher oxygen pressures.[5] At sufficiently high
pressures of both reactants, the reaction becomes highly
selective towards self-coupling for all of the alcohols. This result
suggests that higher selectivity may be possible for reactions in
the liquid phase or reactions and above atmospheric pressure for
higher molecular weight alcohols.
Figure 3. Product distributions for the coupling of the primary alcohols a)
from plug flow simulation, b) experimental measurements. Reaction
conditions 2% alcohol, 4% oxygen balanced in He at 423 K, 50 mL/min flow
rate, 20mg of catalyst. Conversions are listed in Table 2.
Previous analysis of methanol coupling shows that the high
selectivity to methyl formate is strongly associated with the
dominance of the surface concentration of methoxy.[5,6] Though
the increased rate of alkoxy formation (Tables 2, S2) suggests
that the selectivity for ester formation might increase with
molecular weight of the alcohol, its increase is outweighed by the
much larger increase in its rate of decomposition, driven by the
increasing stability of the adsorbed aldehyde with molecular
weight. Due to the exponential dependence of rate on these
activation energies, the rate of alkoxy decomposition is increased
100-fold from methanol to 1-butanol, whereas its rate of formation
is increased only 10-fold at 423 K (Table S2). The steady-state
alkoxy concentration is thus sharply reduced with increasing
alcohol chain length, significantly diminishing its availability for
coupling. Further adding to the inhibition to coupling, the
activation energy for the coupling step itself increases 27 kJ/mol
from methanol to 1-butanol, effecting a 1000-fold decrease in its
rate at 423 K (Table S2).
Figure 4. Selectivity to the coupling product for methanol to 1-butanol as a
function of alcohol and oxygen reaction pressures from microkinetic reactor
analysis. Reaction conditions from 10-7 to 101 bar alcohol/oxygen pressure,
423 K. The conditions of high selectivity for ester formation (red regions)
move toward higher reactant pressures with increasing molecular weight.
In conclusion, dramatic changes in catalytic selectivity are
predicted among a homologous set of catalytic reactions using a
combination of well-established, experimentally measured rate
constants for a single species from within the series and overall
reaction energetics from DFT. This surprising shift is attributable
to differences in the van der Waals interactions of adsorbed
reaction intermediates with the surface. We demonstrate that a
capacity of DFT to predict trends combined with a few selected
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quantitative experiments can efficiently recreate the catalytic
behaviour for a large group of reactants, drastically reducing the
amount of experimental work required. Similar analysis may be
applicable to better predicting the catalytic behavior of other
homologous reactions.
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Entry for the Table of Contents (Please choose one layout)
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van der Waals interactions control selectivity
More efficient kinetics: By
Christian Reece, Mathilde Luneau,
C.M. Friend, and Robert J. Madix*
combining experimentally measured
kinetic parameters with Density
Functional Theory to compute van der
Waals interactions, it is possible to
efficiently scale a whole set of rate
constants for the homologous set of
alcohol self-coupling reactions. The
strong van der Waals interactions
between the higher alcohol
Page No. – Page No.
Predicting a dramatic decline in
selectivity for catalytic esterification
of alcohols due to van der Waals
interactions
intermediates and the surface are
found to drive the decrease in
selectivity to coupling.
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