doi.org/10.26434/chemrxiv.10271090.v1
Catalytic Resonance Theory: Parallel Reaction Pathway ControlM. Alexander Ardagh, Manish Shetty, Anatoliy Kuznetsov, Qi Zhang, Phillip Christopher, Dionisios Vlachos,Omar Abdelrahman, Paul Dauenhauer
Submitted date: 08/11/2019 • Posted date: 15/11/2019Licence: CC BY-NC-ND 4.0Citation information: Ardagh, M. Alexander; Shetty, Manish; Kuznetsov, Anatoliy; Zhang, Qi; Christopher,Phillip; Vlachos, Dionisios; et al. (2019): Catalytic Resonance Theory: Parallel Reaction Pathway Control.ChemRxiv. Preprint. https://doi.org/10.26434/chemrxiv.10271090.v1
Catalytic enhancement of chemical reactions via heterogeneous materials occurs through stabilization oftransition states at designed active sites, but dramatically greater rate acceleration on that same active site isachieved when the surface intermediates oscillate in binding energy. The applied oscillation amplitude andfrequency can accelerate reactions orders of magnitude above the catalytic rates of static systems, providedthe active site dynamics are tuned to the natural frequencies of the surface chemistry. In this work, differencesin the characteristics of parallel reactions are exploited via selective application of active site dynamics (0 <ΔU < 1.0 eV amplitude, 10-6 < f < 104 Hz frequency) to control the extent of competing reactions occurring onthe shared catalytic surface. Simulation of multiple parallel reaction systems with broad range of variation inchemical parameters revealed that parallel chemistries are highly tunable in selectivity between either pureproduct, even when specific products are not selectively produced under static conditions. Two mechanismsleading to dynamic selectivity control were identified: (i) surface thermodynamic control of one productspecies under strong binding conditions, or (ii) catalytic resonance of the kinetics of one reaction over theother. These dynamic parallel pathway control strategies applied to a host of chemical conditions indicatesignificant potential for improving the catalytic performance of many important industrial chemical reactionsbeyond their existing static performance.
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____________________________________________________________________________ Ardagh, et al. Page 1
Catalytic Resonance Theory: Parallel Reaction Pathway Control
M. Alexander Ardagh1,2, Manish Shetty1, Anatoliy Kuznetsov1, Qi Zhang1, Phillip Christopher2,3, Dionisios G. Vlachos2,5,
Omar Abdelrahman2,4, Paul J. Dauenhauer1,2* 1 University of Minnesota, Department of Chemical Engineering and Materials Science, 421 Washington Ave. SE,
Minneapolis, MN, 55455, USA. 2 Catalysis Center for Energy Innovation, University of Delaware, 221 Academy Street, Newark, DE, 19716, USA. 3University of California Santa Barbara, Department of Chemical Engineering, Engineering II Building, Santa
Barbara, CA 93106, USA 4University of Massachusetts Amherst, Department of Chemical Engineering, 686 N. Pleasant Street, Amherst, MA,
01003 USA 5University of Delaware, Department of Chemical and Biomolecular Engineering, 150 Academy Street, Newark, DE
19716 USA
*Corresponding author: [email protected]
1.0 Introduction. The core capability of catalysis
is the controlled steering of molecules through
preferred chemical pathways via manipulation of
surface intermediates and transition state
energies[1]. The complex reaction networks of even
small-molecule chemistries (e.g. methanol
synthesis, ethylene epoxidation) contain
energetically similar pathways to side products
such as CO2, which devalue chemical processes and
contribute to climate change[2,3,4,5,6]. Traditional
design aims for specific catalyst structures which
preferentially lower the transition states of
preferred pathways; catalyst binding strength and
configuration are tuned in the structural shape (e.g.
pores, pockets) and active site of materials[7,8,9,10].
The limit of this strategy derives from the
differences in competing pathway transition states,
for which competitive stabilization in many
important static catalytic systems has already
achieved maximum capability[11,12].
An alternative strategy for catalytic reaction
control proposes a dynamic catalytic surface,
whereby the binding energy (i.e., heat of
adsorption) of surface intermediates oscillate on the
time scale of the catalytic turnover frequency[13].
The heat of adsorption of hydrocarbons on metals
Abstract. Catalytic enhancement of chemical reactions via heterogeneous materials occurs through
stabilization of transition states at designed active sites, but dramatically greater rate acceleration on that
same active site is achieved when the surface intermediates oscillate in binding energy. The applied
oscillation amplitude and frequency can accelerate reactions orders of magnitude above the catalytic
rates of static systems, provided the active site dynamics are tuned to the natural frequencies of the
surface chemistry. In this work, differences in the characteristics of parallel reactions are exploited via
selective application of active site dynamics (0 < ΔU < 1.0 eV amplitude, 10-6 < f < 104 Hz frequency)
to control the extent of competing reactions occurring on the shared catalytic surface. Simulation of
multiple parallel reaction systems with broad range of variation in chemical parameters revealed that
parallel chemistries are highly tunable in selectivity between either pure product, even when specific
products are not selectively produced under static conditions. Two mechanisms leading to dynamic
selectivity control were identified: (i) surface thermodynamic control of one product species under strong
binding conditions, or (ii) catalytic resonance of the kinetics of one reaction over the other. These
dynamic parallel pathway control strategies applied to a host of chemical conditions indicate significant
potential for improving the catalytic performance of many important industrial chemical reactions
beyond their existing static performance.
____________________________________________________________________________ Ardagh, et al. Page 2
and metal oxides can be altered by several methods
including electric fields[14,15,16], photocatalysis[17],
surface strain[18,19], solid electrolytes[20,21,22,23,24],
catalytic diodes[25,26,27], and back-gated field effect
modulation[28,29,30]. For each combination of
catalyst material, chemical mechanism, and method
of external stimulus, the dynamic variables
including imposed surface binding energy
frequency f and amplitude ΔU comprise a narrow
set of conditions which achieves catalytic turnover
frequencies which are orders of magnitude above
the static Sabatier maximum (i.e., Balandin-
Sabatier volcano peak)[31].
The mechanism of ‘catalytic resonance’ for
enhanced catalytic turnover occurs by matching the
frequency of oscillating binding energies to the
natural frequencies of catalytic surface reactions.
As depicted in Figure 1a, a reaction is generally
comprised of three parts (adsorption, surface
reaction, and desorption), any one of which can be
rate determining. In Figure 1b, the Balandin-
Sabatier volcano curve depicts the system turnover
frequency as a function of a system descriptor; the
maximum observed turnover frequency delineates
the transition from one rate-limiting elementary
step to another[32,33,34]. An interpretation of catalytic
resonance is that the oscillation between surface
binding states on either side of the volcano peak
permits each elementary step of the catalytic
sequence to occur under conditions optimized for
that particular step. The amplitude ΔU of the
imposed surface binding energy oscillation
connects the two conditions as drawn in maroon in
Figure 1b: low binding energy, UL, and high
binding energy, UH. As the frequency of the
imposed surface binding energy oscillation
increases approaching the surface reaction
frequencies, the maximum overall turnover
frequency is achieved.
The introduction of two competing parallel
surface reactions raises the question of whether
selectivity to specific chemical products can be
controlled by prescribed tuning of the imposed
surface binding energy oscillation. Parallel
reversible reactions of A-to-B and A-to-C as shown
in Figure 1a can have different transition states and
different linear scaling relations. The transition
state energy of an elementary reaction is linearly
proportional to the surface energy by parameter α
and offset by parameter β (kJ mol-1)[35,36,37].
Additionally, the binding energies of surface
species B* and C* will exhibit different extents of
change relative to changes in the binding energy of
A*. A linear relationship between the binding
energies of any two species has proportionality
parameter γB/A (for the A-to-B reaction) and δB-A for
the energy offset (kJ mol-1)[31]. It remains to
identify parameter space from these operating and
chemical reaction variations that preferentially
enhance the rate of one elementary reaction over
another.
In this work, the parallel reversible elementary
reactions of A-to-B and A-to-C with thermoneutral
free energy (ΔHA-B = ΔHA-C = 0 kJ mol-1) are
evaluated under dynamic binding energy oscillation
of all three intermediate species with the goal of
-5.00
-4.00
-3.00
-2.00
-1.00
0.00
1.00
2.00
3.00
4.00
5.00
-0.25 0.00 0.25 0.50 0.75 1.00 1.25
Tu
rno
ver
Fre
qu
en
cy
to
B,
TO
FB
[s-1
]
U, Relative Binding Energy of B [eV]
Amplitude, ΔUAccessib
le R
eaction
Rate
s
Desorption Rate
Surface Reaction
Rate
XA~1%105
104
103
102
101
1
10-1
10-2
10-3
10-4
10-5
UL UH
(i) bA
A*
C
C*
ΔHA ΔHC
EA,2
B
B*
ΔHB
EA,1
a
Figure 1. (a) Parallel catalytic reversible reactions of A-to-B and A-to-C. (b) Volcano plot of a single reaction A-to-
B turnover frequency as a function of the relative binding energy of B at 1% conversion. Depicted is an oscillation
of amplitude ΔU of 1.0 eV.
____________________________________________________________________________ Ardagh, et al. Page 3
assessing the parameter space leading to selective
pathway control (i.e., more B than C, or more C
than B). Parallel reactions are simulated in a
continuous flow mixed reactor with varying
parameters of γB-A and γC-A, as well as δB-A and δC-A
in combination with different applied frequencies
and amplitudes of surface binding energy
oscillation to understand the conditions leading to
pathway tunability.
2.0 Results and Discussion. The competition
between parallel catalytic surface reactions under
dynamic conditions is most unique when the
product surface species vary differently in binding
energy. As depicted in Figure 2, competing
reactions of A-to-B and A-to-C are depicted with
inverse gamma parameters. The reaction to
produce B with γB/A of 0.5 has a multi-state energy
profile in Figure 2a, whereby B* changes only half
as much in binding energy relative to A*. In
contrast, the reaction to produce C with γC/A~2.0 has
a multi-state energy profile in Figure 2b, in which
C* changes twice as much in binding energy as A*.
𝛾𝐶/𝐴 = 𝛥𝐵𝐸𝐶
𝛥𝐵𝐸𝐴= 2.0 (1)
These two systems are depicted in the gamma-delta
plot of Figure 2c, with the values of slopes γ and
point of common binding energy δ between surface
reactant and surface product for each elementary
reaction. The state whereby B* and C* have the
same surface adsorption enthalpy occurs in the
gamma-delta plot of Figure 2c at the intersection of
the two reaction lines and is identified as δB-C.
For the case of inverse (2.0 and 0.5) gamma
parameters depicted in Figure 2, the reaction
kinetics were evaluated for the identical reaction
conditions (δB-A = 1.4 eV, δC-A = 1.4 eV). As
depicted in Figure 3a, variation of gamma (γB/A =
2.0, γC/A = 0.5) produces distinct volcano peak
positions and reaction activity. The low γC/A of 0.5
produces a volcano peak of ~5 s-1, while the high
γB/A of 2.0 volcano peak maximum is significantly
lower (5•10-3 s-1). The key transition in surface
coverage of the system occurs at zero relative
binding energy of A, at which the surface
transitions between high coverage of C and B as the
relative binding energy of A increases (Figure 3b).
Oscillation of the binding energy of A (ΔUA) by
0.6 eV was simulated over ten decades of
frequencies (10-6 < f < 104 Hz) and variation of the
amplitude position denoted by the position of the
weakest binding energy (i.e., left oscillation
endpoint, UL). As depicted in the results of Figure
3c, the selectivity is fully tunable to either product
B or C depending on the applied dynamic
conditions. At low oscillation frequencies (f < 10-3
Hz), the catalytic system achieves nearly perfect
selectivity to product C (blue) until about -0.2 eV
relative binding energy of A, after which selectivity
to both products is the same (SB ~ SC ~ 50%, green).
This low frequency behavior is consistent with the
activity predicted by the volcano plots of Figure 3a;
product C is dominant until UL of -0.2 eV, after
which both products are produced at equal rate.
This is consistent with the selectivity to B under
static catalyst conditions described in the bar above
Figure 3c. As the oscillation frequency increases, a
A CC*
A*
TS2
δA-C
A B
B*
A*
TS1
δA-B
a b c Heat of Adsorption of A, ΔHAH
eat o
f Ad
so
rptio
n
of B
, ΔH
B , or C
, ΔH
C
δA-B
δA-C
γB/A ~ 1/2
γC/A ~ 2
δB-C
Figure 2. Parameters of Parallel Reactions with Dynamic Heterogeneous Catalysis. (a) State-enthalpy diagram
of oscillating heterogeneous catalyst for the reversible reaction of A-to-B. (b) State-enthalpy diagram of oscillating
heterogeneous catalyst for the reversible reaction of A-to-C. (c) Variation of the binding energy of B* and C* linearly
scaling with the binding energy of A* with slopes γB-A and γC-A with common points δA-B and δA-C. Intersections of
the two reaction lines identifies δB-C.
____________________________________________________________________________ Ardagh, et al. Page 4
dramatic shift in product selectivity occurs at ~10-2
Hz. As depicted in Figure 3c, the transition from
high selectivity to C (blue) to high selectivity to B
(red) occurs in the range of -0.4 to -0.2 eV of UL
(lower oscillation endpoint). Notably, there is a
switch to ~100% selectivity towards product B at
these conditions that are not attainable under static
conditions or under low oscillation frequencies (<
10-3 Hz).
The transition between selective production of
B or C in Figure 3c is associated with dynamic rate
enhancement of either product. Figures 3d-3f
depict the rates of total conversion of A (TOFA),
total production rate of B formation (TOFB), and
total formation rate of C (TOFC), respectively. As
shown, TOFA exhibits two regions of high activity:
(i) above 100 Hz and oscillation endpoint UL < -
1.10 eV, and (ii) above 10 Hz and the oscillation
endpoint range of -0.5 < UL < -0.2 eV. By
comparison with the rates of the independent
reactions (TOFB in Fig. 3e and TOFC in Fig. 3f), the
regions of high activity of conversion of A can be
associated with acceleration of the independent
reactions to produce B and C, respectively.
The formation rate of C is enhanced at
oscillation amplitude endpoints of UL < -1.10 eV
(Fig. 3f), while the formation rate of B occurs at
oscillation amplitude endpoint range of -0.5 <UL <
-0.2 eV. The enhanced formation of C occurs in the
region of weak binding and a surface mostly
covered in C*. In this region under dynamic
conditions, the reaction is in resonance with the
desorption of C, and the overall formation rate is
enhanced over an order of magnitude.
-6.0
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2
Turn
ove
r F
requency t
o B
, C
& T
ota
l [s
-1]
Relative Binding Energy of A, UL Endpoint [eV]
A ↔ B
A ↔ C10-2
10-3
10-4
10-5
10-6
10-1
1
101
102
Amplitude, ΔU = 0.6 eV
0.0
0.0
0.0
0.0
0.1
1.0
10.0
-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2
Surf
ace C
ove
rage o
f A
, B
, C
& O
pen
[-]
Relative Binding Energy of A, UL Endpoint [eV]
θB
θCθA
θ*
Amplitude, ΔU = 0.6 eV
10-2
10-1
10-3
10-4
10-5
1
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
-1.64 -1.34 -1.04 -0.74 -0.44 -0.14 0.16
Osc
illat
ion
Fre
qu
en
cy
[Hz]
Left Oscillation Amplitude Endpoint [eV]Oscillation Endpoint, UL [eV]
Oscill
ation F
requency [
Hz]
104
103
102
101
1
10-1
10-2
10-3
10-4
10-5
10-6
-1.64 -1.34 -1.04 -0.74 -0.44 -0.14 0.16
Sele
ctivity
to B
[%]
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
-1.64 -1.34 -1.04 -0.74 -0.44 -0.14 0.16
Oscillation Endpoint, UL [eV]
TOFA, Rate of A Conversion [s-1]
10-2 10-1 101 1021
104
103
102
101
1
10-1
10-2
10-3
10-4
10-5
10-6
Oscill
ation F
requency [
Hz]
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
-1.64 -1.34 -1.04 -0.74 -0.44 -0.14 0.16
Oscillation Endpoint, UL [eV]
104
103
102
101
1
10-1
10-2
10-3
10-4
10-5
10-6
Oscill
ation F
requency [
Hz]
TOFB, Rate of B Formation [s-1]
10-2 10-1 101 1021
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
-1.64 -1.34 -1.04 -0.74 -0.44 -0.14 0.16
Oscillation Endpoint, UL [eV]
TOFC, Rate of C Formation [s-1]
10-2 10-1 101 1021
104
103
102
101
1
10-1
10-2
10-3
10-4
10-5
10-6
Oscill
ation F
requency [
Hz]
a b c
d e f
A ↔ B
↔
C
A ↔ B A
↔
C
A ↔ B
↔
C
Static Selectivity
UL
UL
Figure 3. Dynamic heterogeneous catalysis, using a fixed amplitude square waveform, for a parallel reaction
system with A-to-B and A-to-C chemistry. (a) Sabatier volcano plots for the consumption of A (black), production
of B (red), and production of C (blue), and (b) corresponding surface coverage plot with surface species * (black),
A* (black), B* (red), and C* (blue). (c) Selectivity enhancement towards the production of B with an oscillation
amplitude of 0.6 eV, varying oscillation endpoints (-1.64-0.16 eV), and varying oscillation frequencies (10-6-104 Hz)
and (d) corresponding rate enhancement for the consumption of A. Selectivity to B under static catalyst conditions
at varying relative binding energy of A in the above bar. (e) Rate enhancement towards the production of B in the A-
to-B single-reaction system, and (f) rate enhancement towards the production of C in the A-to-C single reaction
system. Conditions: T ~ 150 °C, 100 bar A feed pressure, 1% yield of B or C or 1% conversion of
A. Parameters: ΔHovr ~ 0 kJ mol-1 for both reactions, BEP parameters of α ~ 0.6, β ~ 100 kJ mol-1, surface binding
ratios of γB-A ~ 2.0, γC-A ~ 0.5, and δB-A ~ 1.4 eV, δC-A ~ 1.4 eV. Relative binding energies of A in all panels a-f can
be converted to absolute binding energies of A by adding 1.4 eV to the independent axis.
____________________________________________________________________________ Ardagh, et al. Page 5
Alternatively, the nearly 100% selectivity towards
B in the oscillation endpoint range of -0.5 < UL <
0.2 eV can be partially attributed to both the higher
surface coverage of species B (especially above a
UL value of 0 eV) and the resonance-enhanced rate
of the reaction to form product B.
The product selectivity results of Figure 3
indicate that there are at least two mechanisms for
selectivity control in a parallel reaction system: (i)
resonance rate enhancement with the individual
reaction pathways, and (ii) control of surface
coverage. These mechanisms are depicted in Figure
4a where conditions have been selected to indicate
both mechanisms. Surface species C* is
thermodynamically preferred, since it has lower
energy (i.e. stronger binding) than A* or B* in the
stronger binding (red) state. As shown in Figure 4b,
A* preferentially converts to C* resulting in a
surface covered in C*. The key transition
determining surface coverage dominance is
captured in the quantity, δB-C, which is the energy
whereby B* and C* have the same surface
adsorption enthalpy (identified in Figure 2c).
Alternatively, product B is kinetically favored,
since the desorption of B proceeds quickly relative
to C in the weaker binding (blue) state. As depicted
in Figure 4c, B* exhibits faster desorption kinetics.
The ultimately favored product in this scenario
depends on the overall balance of these two
mechanisms (thermodynamic versus kinetic),
which can shift as the binding energy of A* changes
over the range of the volcano plot.
The two mechanisms enhancing selectivity are
observed in the formation of product B in Figure 3c.
At stronger binding energies (oscillation endpoint
UL > 0 eV), the product B is produced due to
dominance of the surface coverage by B*.
However, the kinetic mechanism exists at relative
binding energies below 0 eV in the region of -0.5 <
UL < 0 eV. In this range the oscillation amplitude
55
B(g) A(g) C(g)
B* A* C*
Os
cil
lati
on
[A↔B]‡
Surface
Thermodynamic
Selectivity
Desorption
Kinetic
Selectivity
[A↔C]‡
C*B* C*C*C*A*C*
A(g)
C* C* C*B* C*C*C*A*C*
B(g)
C* C*
C(g) C(g)
b
a
c
Figure 4. Mechanisms of Dynamic Selectivity to Products in Parallel Chemistry. (a) Oscillation of surface
binding energies of A*, B*, and C* between strong (red) and weak (blue) enthalpy of adsorption occurs through two
transition states. Two general behaviors can produce high selectivity to specific products: weak surface binding
permitting reaction surface resonance to product B(g), or strong surface binding that dominates the catalyst surface
to C*. (b) The surface filling state. (c) The surface turnover state. Chemical dynamic parameters: γB/A = 1.3, γC/A =
0.6, and δB-A = 0.6 eV, δC-A = 1.5 eV, UA,lower = -0.5 eV, ΔU = 0.4 eV.
____________________________________________________________________________ Ardagh, et al. Page 6
(ΔUA = 0.6 eV) extends across the A-to-B reaction
volcano, and this reaction is kinetically resonance
enhanced. The reaction to form B increases from
10-3 s-1 under the static catalytic condition at the
volcano peak (Figure 3a) to a formation rate of 102
s-1 under dynamic conditions, even with the
existence of the parallel A-to-C reaction. This 105-
fold rate enhancement leads to high selectivity to B
even when B* does not dominate the surface
coverage.
More complicated behavior is observed when
oscillation amplitude becomes a variable. In Figure
3, the oscillation amplitude of A was fixed at ΔUA
of 0.6 eV. This amplitude was permitted to vary
between 0 < ΔUA < 1.0 eV as depicted in Figure 5a
for the same parallel reaction system (γB-A ~ 2.0, γC-
A ~ 0.5, and δB-A ~ 1.4 eV, δC-A ~ 1.4 eV). As
previously stated, this reaction system does not
select for product B in excess of 50% under any
condition when operated with a static catalyst, but
high selectivity to B becomes possible under
dynamic conditions. To assess the role of
amplitude in dynamic catalytic operation, the
oscillation amplitude was centered around the
volcano peak for the A-to-B reaction (-0.2 eV
relative binding energy of A); the reaction to form
B transitions between surface reaction (A*-to-B*)
control and desorption rate limitation (C*-to-C or
B*-to-B) at the peak. Here, the consumption of A
is limited by the desorption of C at the left
oscillation amplitude endpoint and the desorption
of B at the right amplitude endpoint.
The catalytic resonance of reaction A-to-B
under variable amplitude (0 < ΔUA < 1.0 eV) and
frequency (10-6 < f < 104 Hz) is depicted in figure
5b. As expected, the selectivity to B at low
oscillation frequencies is minimal due to the
relatively high production rate of C (the surface
coverage dominating species). Preferential
selectivity to B (>50 %B) is only achieved once the
oscillation frequency increases beyond ~0.01 Hz,
with a maximum selectivity of 93% achieved at
moderate oscillation amplitudes of 0.5-0.6 eV.
Generally, the consumption of A (Figure 5c)
increases with the oscillation amplitude, since the
lower amplitude endpoint, UL, rises to higher TOFs
as oscillation amplitude increases. However, a
larger oscillation amplitude is not more favorable
for selectivity enhancement, due to the tradeoff
between enhancing the production of B versus C.
Desorption of C proceeds quickly (1 < TOFC < 100
s-1) for all oscillation amplitudes, and higher
frequencies above 10 Hz begin to reduce selectivity
to product B. In addition, the consumption of A
decreases at higher oscillation frequencies as the
rate of B production decreases. Oscillation
-6.0
-5.0
-4.0
-3.0
-2.0
-1.0
0.0
1.0
2.0
-1.2 -1 -0.8 -0.6 -0.4 -0.2 0 0.2
Tu
rno
ver
Fre
qu
en
cy t
o B
, C
& T
ota
l [s
-1]
Relative Binding Energy of A, Endpoint [eV]
A ↔ B
A ↔ C
10-2
10-3
10-4
10-5
10-6
10-1
1
101
102
Variable Amplitude, ΔU
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
0.0 0.2 0.4 0.6 0.8 1.0
103
104
102
101
1
10-1
10-2
10-3
10-4
10-5
10-6
0 0.2 0.4 0.6 0.8 1.0
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
0.0 0.2 0.4 0.6 0.8 1.0
103
104
102
101
1
10-1
10-2
10-3
10-4
10-5
10-6
0 0.2 0.4 0.6 0.8 1.0
Oscillation Amplitude, ΔU [eV]O
scilla
tio
n F
req
uen
cy,
f[H
z]
Oscillation Amplitude, ΔU [eV]
Oscilla
tio
n F
req
uen
cy,
f[H
z]
Selectivity to B [%]
10 20 30 40 50 60 70 80 90 1000 10-3 10-2 10-1 1 101
Rate of Conversion of A, TOFA [s-1]
a b c
Figure 5. Dynamic heterogeneous catalysis, using a variable amplitude square waveform, for a parallel reaction
system with A-to-B and A-to-C chemistry. (a) Volcano plots for reactant consumption (black) and product
formation (red/blue) turnover frequency. Dynamic catalysis oscillations with varying oscillation amplitude are shown
as black horizontal bars. (b) Selectivity to the production of B (mol %) with varying oscillation frequency (10-6 to 104
Hz) and amplitude (0.0 to 1.0 eV). The oscillation midpoint was held constant at the volcano peak for product B
formation. (c) Consumption rate of A (s-1) with varying oscillation frequency and amplitude. Conditions: T ~ 150
°C, 100 bar A feed pressure, 1% yield of B or C or 1% conversion of A. Parameters: ΔHovr ~ 0 kJ mol-1 for both
reactions, BEP parameters of α ~ 0.6, β ~ 100 kJ mol-1, surface binding ratios of γB-A ~ 2.0, γC-A ~ 0.5, and δB-A ~ 1.4
eV, δC-A ~ 1.4 eV. Relative binding energies of A in all panels a-c can be converted to absolute binding energies of
A by adding 1.4 eV to the independent axis.
____________________________________________________________________________ Ardagh, et al. Page 7
frequencies above 10 Hz are too fast for the
desorption of B, which leads to incomplete
emptying of surface B* at the left oscillation
endpoint. Instead, C is produced but with minimal
rate enhancement as these oscillations do not reach
weak enough binding energies.
The linear scaling relationships of surface
intermediates A*, B* and C* strongly impact the
selectivity behavior of dynamic catalytic systems.
Throughout Figures 3 and 5, the linear scaling
relationships between the adsorbates were held
constant with γB-A of 2.0 and γC-A of 0.5. However,
studies of gas phase reactions over periodic metals
show that each adsorbate pair has quite different γ
and δ values, with γ ranging between -20 to 20 and
δ being -10-to-10 eV[37, 38,39,40]. In addition, density
functional theory (DFT) calculations of adsorbates
bound to common catalysts such as Pt(111) or
Ni(111) reveal that the linear scaling relationships
(γ and δ) for periodic metals can potentially vary for
different external stimuli (i.e. stress/strain, electric
field, lasers/light) applied to a single metal[40, 41,
42,43]. To account for these variations in catalyst-
stimulating methods, the effects of changing linear
scaling relationships were evaluated for product
selectivity and rate enhancement.
In two case studies, γB-A was decreased by a
factor of 2x and 8x to evaluate the impact on
selectivity trends if the ratio of γ between parallel
surface catalytic reactions (e.g. γB/A / γC/A) was
greater or less than one. Figure 6a and 6b depict the
volcano plots for the consumption of A (TOFA),
production of B (TOFB), production of C (TOFC),
and the surface coverage under static catalytic
1.E-08
1.E-07
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
-1.3 -0.8 -0.3 0.3
Turn
ove
r F
reque
ncy o
f A
, B
, &
C[s
-1]
Relative Binding Energy of A [eV]
0.0
0.2
0.4
0.6
0.8
1.0
-1.3 -0.8 -0.3 0.3
Surf
ace
Co
ve
rage
of A
, B
, &
C[-
]
Relative Binding Energy of A [eV]
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
-1.64 -1.34 -1.04 -0.74 -0.44 -0.14 0.16
Oscillation Endpoint, UL [eV]
Oscill
atio
n F
reque
ncy
[Hz]
104
103
102
101
1
10-1
10-2
10-3
10-4
10-5
10-6
Turnover Frequency of A [s-1]
10-4 10-3 10-2 10-1 1
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
-1.64 -1.34 -1.04 -0.74 -0.44 -0.14 0.16
Oscillation Endpoint, UL [eV]
Oscill
atio
n F
reque
ncy
[Hz]
104
103
102
101
1
10-1
10-2
10-3
10-4
10-5
10-6
Turnover Frequency of A [s-1]
10-2 10-1 1 101 102
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
-1.64 -1.34 -1.04 -0.74 -0.44 -0.14 0.16
Oscill
atio
n F
reque
ncy
[Hz]
Oscillation Endpoint, UL [eV]
Selectivity to B [%]
1009080706050403020100
104
103
102
101
1
10-1
10-2
10-3
10-4
10-5
10-6
Static Selectivity to B
1.E-06
1.E-05
1.E-04
1.E-03
1.E-02
1.E-01
1.E+00
1.E+01
1.E+02
1.E+03
1.E+04
-1.64 -1.34 -1.04 -0.74 -0.44 -0.14 0.16
Oscill
atio
n F
reque
ncy
[Hz]
Oscillation Endpoint, UL [eV]
Selectivity to B [%]
1009080706050403020100
104
103
102
101
1
10-1
10-2
10-3
10-4
10-5
10-6
Static Selectivity to B
γB/A = 1.00, γC/A = 0.5, Panels e,f
γB/A = 0.25, γC/A = 0.5, Panels c,d
a
b
c
d
e
f
Figure 6. Dynamic heterogeneous catalysis, using a fixed amplitude (ΔU = 0.6 eV) square waveform, for a
parallel reaction system with A-to-B and A-to-C chemistry with variable gammas. (a) Volcano plots of two
systems with variable gamma parameters. (b) Surface coverage of A*, B*, and C* for two systems. Turnover
frequency of A as a function of frequency and lower amplitude endpoint for system 1 (c,d) and system 2 (e,f). System
1: γB/A = 0.25, γC/A = 0.50, and δB-A = δC-A = 1.4 eV System 2: γB/A = 1.0, γC/A = 0.5, and δB-A = δC-A = 1.4 eV. Relative
binding energies of A in all panels a-f can be converted to absolute binding energies of A by adding 1.4 eV to the
independent axis.
____________________________________________________________________________ Ardagh, et al. Page 8
operation. In these two systems, the surface
coverage transition occurs at δB-C = δA-C = δA-B = 1.4
eV (which is 0 eV relative binding energy of A in
Figure 6). Generally, the product with a lower γ
dominates the surface coverage and production
until a UL of about -0.5 eV and -0.4 eV for Figure
6d and 6f, respectively. This occurs due to a shift
in the rate determining step from surface reaction to
desorption for the product with the higher γ. This
indicates that the selectivity challenge for dynamic
catalytic operation is to stimulate the rate of
production of the surface species more sensitive to
external stimuli (i.e., higher γ).
Figure 6c and 6d present heat maps for the TOF
for the consumption of A and selectivity to B when
γB-A < γC-A (0.25 and 0.50, respectively) as a
function of applied frequency (10-6 < f < 104 Hz)
and oscillation endpoint (UL) at fixed total
amplitude (ΔUA = 0.6 eV). In this scenario, the
selectivity to B is high only when its desorption is
enhanced at weak binding conditions (relative
binding energies of -1.64 to -1.0 eV). Once the
amplitude achieves an appreciable binding energy
(UL > -1.0 eV), the product C is heavily favored
over B for frequencies above ~1 Hz. However,
overall consumption rates of A do not increase
when both products exhibit γ < 1.0, due to the lack
of significant surface coverage for A* over a wide
range of binding energies. This is further
exacerbated by the stronger binding of both B* and
C* at the low γB-A and γC-A values that limit the
desorption rates of the products.
In the second scenario of Figure 6, γB-A is
increased to 1.0 revealing similar behavior to the
scenario in Figure 3 where γB-A was 2.0. Once γB-A
is higher than γC-A, selectivity to B is low (<10%)
across most binding energies less than -0.44 eV,
and rate enhancement can only be achieved at weak
binding (UL < -1.25 eV) and high frequencies (>100
Hz). This indicates that the ratio of γ between
reaction pathways (γB/C = γB/A / γC/A) is critical to
strategically controlling catalyst dynamics for
specific products. High selectivity with a γB/C ratio
less than one is readily achievable, while values
1.E-10
1.E-08
1.E-06
1.E-04
1.E-02
1.E+00
-1.4 -0.9 -0.4 0.1
Tu
rno
ver
Fre
qu
en
cy o
f A
]s
-1]
Relative Binding Energy of A [eV]
10-2
100
10-4
10-6
10-8
10-10
System 3
Panels g,hδC-A = 1.4
δB-A = 1.0
γC/A = γB/A = 2.0
System 1
Panels c,dδC-A = 1.4
δB-A = 0.8
γC/A = 0.5
γB/A = 2.0
System 2
Panels e,fδC-A = 1.4
δB-A = 2.0
γC/A = 0.5
γB/A = 2.0
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
-1.0 -0.8 -0.6 -0.4 -0.2 0.0
Su
rfa
ce
Co
vera
ge
[u
nitle
ss]
Relative Binding Energy of A [eV]
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
-1.64 -1.22 -0.80 -0.38 0.04
Oscilla
tio
n F
req
ue
ncy [
Hz]
Oscillation Endpoint, UL [eV]
102
104
1
10-2
10-4
10-6
0 10 20 30 40 50 60 70 80 90 100
Selectivity to B [%]
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
-1.64 -1.22 -0.80 -0.38 0.04
Oscilla
tio
n F
req
ue
ncy [
Hz]
Oscillation Endpoint, UL [eV]
104
102
1
10-2
10-4
10-6
102101110-110-2
Turnover Frequency of A [s-1]
c
d
a
b
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
-1.64 -1.22 -0.80 -0.38 0.04
Oscilla
tio
n F
req
ue
ncy [
Hz]
Oscillation Endpoint, UL [eV]
102
104
1
10-2
10-4
10-6
0 10 20 30 40 50 60 70 80 90 100
Selectivity to B [%]
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
-1.64 -1.22 -0.80 -0.38 0.04
Oscilla
tio
n F
req
ue
ncy [
Hz]
Oscillation Endpoint, UL [eV]
104
102
1
10-2
10-4
10-6
102101110-110-2
Turnover Frequency of A [s-1]
e
f
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
-1.64 -1.22 -0.80 -0.38 0.04
Oscilla
tio
n F
req
ue
ncy [
Hz]
Oscillation Endpoint, UL [eV]
102
104
1
10-2
10-4
10-6
0 10 20 30 40 50 60 70 80 90 100
Selectivity to B [%]
1.E-06
1.E-04
1.E-02
1.E+00
1.E+02
1.E+04
-1.64 -1.22 -0.80 -0.38 0.04
Oscilla
tio
n F
req
ue
ncy [
Hz]
Oscillation Endpoint, UL [eV]
104
102
1
10-2
10-4
10-6
102101110-110-2
Turnover Frequency of A [s-1]
g
h
B*
A*
C*
Static Selectivity to B Static Selectivity to B Static Selectivity to B
Figure 7. Dynamic heterogeneous catalysis, using a fixed amplitude (ΔU = 0.6 eV) square waveform, for a
parallel reaction system with A-to-B and A-to-C chemistry with variable deltas. (a) Volcano plots of three
systems with variable delta parameters. (b) Surface coverages of A*, B*, and C* for three systems. Turnover
frequency of A as a function of frequency and lower amplitude endpoint for system 1 (c,d), system 2 (e,f), and system
3 (g,h). The selectivity to B at static catalyst conditions for varying relative binding energy of A as bars below each
of the three systems. System 1: γB/A = 2.0, γC/A = 0.5, and δB-A = 0.8 eV, δC-A = 1.4 eV System 2: γB/A = 2.0, γC/A =
0.5, and δB-A = 2.0 eV, δC-A = 1.4 eV System 3: γB/A = 2.0, γC/A = 2.0, and δB-A = 1.0 eV, δC-A = 1.4 eV Relative
binding energies of A in all panels a-h can be converted to absolute binding energies of A by adding 1.4 eV to the
independent axis.
____________________________________________________________________________ Ardagh, et al. Page 9
greater than one require a precise selection of the
amplitude and frequency.
The other key surface chemistry parameter
controlling dynamic selectivity is δ (depicted in
Figure 2a-2c), which identifies the conditions of
common binding energy between surface species.
In the three scenarios of Figure 7, the offset for the
linear scaling relationship, δB-C, was varied (by
selecting δA-B and δA-C) to determine its effect on
catalytic selectivity to products under static and
dynamic conditions with a fixed amplitude (∆U =
0.6 eV) and varying oscillation frequency (10-6 < f
< 104 Hz). The three scenarios are depicted in
Figure 7a as volcano plots of the turnover frequency
of A and as the associated surface coverages in
Figure 7b. Systems 1 and 2 both have the same
gamma ratios (γC/A = 0.5, γB/A = 2.0) and delta for
the reaction of A-to-C (δA-C = 1.4 eV), but the delta
for the reaction of A-to-B differs (δA-B of 0.8 eV for
system 1 and δA-B of 2.0 eV for system 2). The third
system considers the case of similar delta values
(δA-C = 1.4 eV, δA-B = 1.0 eV) and identical gamma
values (γC/A = γB/A = 2.0).
System 1 of Figure 7c-7d only selects for
product C (UL < -0.4 eV) or an equimolar product
mixture of B and C under static catalyst conditions.
However, dynamic catalyst operation as square
waves of 0.6 eV amplitude leads to parameter space
with significant overall rate acceleration in addition
to a third selectivity regime which overwhelmingly
favors species B at higher frequencies. When δB-A
is 0.8 eV in system 1 as shown in Figure 7c, TOFA
exhibits two regimes of ~100x rate enhancement as
compared to the static optima (figure 7a). At -1.64
< UL < -1.22 eV, C* is the dominant surface species
under static conditions (Figure 7b), and resonance
with the desorption of C is achieved at oscillation
frequencies >100 Hz with ~100% selectivity
towards C. Alternatively, the selectivity towards B
is enhanced to nearly 100% at -0.75 < UL < 0 eV.
This regime is partially attributed to the enhanced
formation of B between -0.75 < UL < -0.4 eV, where
the system achieves resonance with the pathway to
B. At stronger binding energies above δB-C = -0.4
eV, high selectivity to B is attributed to the
dominant surface coverage of B*. This transition,
δB-C, can be predicted from the intersecting binding
energy lines of a gamma-delta plot comparable to
Figure 2c or from the following equation based on
the parameters of the independent elementary
reactions.
𝜹𝐵𝐶[𝑒𝑉] = (𝟏−𝜸𝑪/𝑨)𝜹𝑪𝑨−(𝟏−𝜸𝑩/𝑨)𝜹𝑩𝑨
𝜸𝑩/𝑨 − 𝜸𝑪/𝑨 (2)
Similar selectivity behavior is observed for
system 2 (Figure 7e-7f). When δB-A increases to 2.0
eV, the kinetic regime of high selectivity to B shifts
to stronger binding energies (UL > -0.4 eV) and
extends to lower oscillation frequencies (f > 10-2
Hz). This occurs due to the dominant surface
coverage transition at UL of 0 eV from species C*
to A* as the relative binding energy of A increases.
The surface coverage transition of the two products
only occurs at stronger binding energies associated
with δB-C of +0.4 eV (not shown). Additionally, the
enhancement in TOFA at weaker binding energies
due to resonance with the desorption of C is almost
identical to the behavior of system 1.
System 3 of Figure 7g-7h exhibited unique
behavior when γB/A and γC/A were both equal to 2.0
and δB-A and δC-A were 1.0 eV and 1.4 eV,
respectively. For static catalyst operation (Fig. 7h),
most conditions of amplitude position (UL)
produced equimolar selectivity to B and C; high
selectivity to B existed only for -0.9 < UL < -0.3 eV.
For square waveform oscillations at ΔUA of 0.6 eV,
the region of high selectivity to B expands to -1.4 <
UL < -0.4 eV where the surface coverage of B*
dominates. In this region, significant rate
enhancements of ~10,000x can be achieved at
oscillation frequencies greater than 100 Hz, as
shown in Figure 7g. With nearly 100% selectivity
to B, this kinetic regime resembles a single A-to-B
reaction whereby the system achieves ‘surface
resonance’ at these UL ranges. This particular
system is singular; because γB/A and γC/A are the
same, the quantity δB-C does not exist (Eq. 2), and
C* never exhibits high surface coverage. When
depicted as a gamma-delta plot similar to Figure 2c,
this system would have two parallel reaction lines
that never cross. Notably, selectivity of C is only
enhanced at higher frequencies (f > 1 Hz) and
strong binding energy (UL > 0 eV) where desorption
rates to C are higher.
3.0 Conclusions. The catalytic conversion of A via
parallel pathways to products B and C was
evaluated for selectivity control via applied
oscillation of the surface binding energy of A in the
form of square waves with variable amplitude and
frequency. Implementation of surface dynamics
leading to variation in the surface binding energies
____________________________________________________________________________ Ardagh, et al. Page 10
of all surface species (A*, B*, and C*) required
definition of linear scaling parameters (γ and δ) that
define the extent of variation of surface
intermediate and transition state binding energies.
Comparison of kinetically different parallel
reactions with broad variation in scaling parameters
indicated significant capability for targeting
specific products by selection of the dynamic
criteria (frequency, amplitude, etc.), even when
targeted chemical products (B or C) were not
possible to selectively produce under static catalyst
operation. Two mechanisms were identified
leading to dynamic operation for product
selectivity: (i) dominant surface coverage of a
single species in the strong binding state of the
oscillation, and (ii) catalytic resonance of one
elementary pathway to rates greater than the
competing pathway. Sampling of several disparate
combinations of chemical and dynamic parameters
indicates significant potential for controlling a wide
range of chemistries towards favorable products
beyond existing static catalytic methods.
4.0 Computational Methods. Parallel A-to-B and
A-to-C and single A-to-B or A-to-C reaction
network numerical simulations were conducted in
Matlab 2019a/b. Continuously stirred tank reactor
(CSTR) model equations were used and appropriate
model equations were implemented for three gas-
phase (A, B, and C) and surface species (A*, B*,
and C*). The conversion of the reactant A was held
at 1% throughout the static and dynamic
calculations. Pre-exponential factors for adsorption
and surface reaction/desorption were taken from
collision and transition state theory,
respectively[44,45]. Adsorption steps were assigned a
pre-exponential of 106 (bar-s)-1 and all other steps
were assigned 1013 s-1. Example differential
equations are shown below for the reactant A and
its adsorbed state A*. For either parallel or single
reaction systems, adsorption/desorption was
described as a mass balance:
𝑑[𝐴]
𝑑𝑡=
𝑞𝑑𝑜𝑡
𝑉([𝐴]𝑓𝑒𝑒𝑑 − [𝐴]) −𝑘𝑎𝑑𝑠[𝐴]𝑅𝑇𝜃∗ + 𝑘𝑑𝑒𝑠𝜃𝐴
∗ (3)
In parallel reaction systems, surface
reaction/desorption was described:
𝑑𝜃𝐴
∗
𝑑𝑡= 𝑘𝑎𝑑𝑠[𝐴]𝑅𝑇𝜃∗ − (𝑘𝑑𝑒𝑠 + 𝑘𝑠𝑟𝑓,𝐵 +
𝑘𝑠𝑟𝑓,𝐶)𝜃𝐴∗ + 𝑘𝑠𝑟𝑟,𝐵𝜃𝐵
∗ + 𝑘𝑠𝑟𝑟,𝐶𝜃𝐶∗ (4)
In single reaction systems, surface
reaction/desorption:
𝑑𝜃𝐴
∗
𝑑𝑡= 𝑘𝑎𝑑𝑠[𝐴]𝑅𝑇𝜃∗ − (𝑘𝑑𝑒𝑠 + 𝑘𝑠𝑟𝑓,𝐵)𝜃𝐴
∗ + 𝑘𝑠𝑟𝑟,𝐵𝜃𝐵∗ (5)
Activation energies for the surface reactions
were calculated using Brønsted-Evans-Polanyi
(BEP) relationships. The parameter ⍺ was set to a
typical value of 0.6, and β was set to a moderate
value of 100 kJ/mol based on literature of
calculated BEP relationships[36]. Binding energies
at each oscillation endpoint were calculated using
linear scaling relationships (LSRs) between the
surface adsorbates. Previously defined parameters
including γi/j and δi-j were used to fully specify the
binding energies of B* and C* relative to the
binding energy of A. The values of γi/j between
0.25-2.0 and δi-j between 0.8-2.0 eV were selected
to evaluate their effects on static and dynamic
reaction behavior. All binding energies were
restricted to positive values to avoid nonphysical
negative binding energies. Selectivity was defined
as the ratio of the rate of production for one product
(B or C) over the rate of consumption for the
reactant (A).
Volcano plots and surface coverage were
calculated for a given set of BEP and LSR
parameters at 1% conversion of A. The reaction
rates and coverage were sampled at intervals of
0.005 eV, and the built-in ‘fsolve’ function in
Matlab was used to obtain values that most closely
obtained 1% conversion of A. This calculation was
repeated across a binding energy span of 1.0-2.0
eV, and extrapolation was performed using
logarithmic extrapolation of rates and coverage.
Dynamic catalysis was implemented using
dynamic parameters including oscillation
amplitude (ΔUA), frequency (f), endpoints (UL, UH),
and waveform type (square waves). All simulations
in this manuscript were conducted using a
symmetric square waveform with assigned
endpoints and frequency. For each endpoint, a set
of adsorption, surface reaction, and desorption rate
constants were calculated. Then, the oscillation
frequency was used to allow the simulation to run
for an allotted amount of time at each endpoint.
Time-averaged conversion and turnover frequency
were calculated using the built in ‘trapz’ function in
Matlab over the final and one intermediate
____________________________________________________________________________ Ardagh, et al. Page 11
oscillation period. The simulation was converged if
it met two criteria: (i) time-averaged conversion of
A of 1.00 +- 0.01 % and (ii) <1.0% differences in
the time-averaged conversion of A sampled at the
end and middle of the simulation trial.
Heat maps were generated for the TOF of the
consumption of A and the selectivity towards B
production using the built in ‘heatmap’ function in
Matlab. Data was obtained at 175-650 discrete data
points and then subdivided by 80-130x to generate
a 2080 x 2080 grid. The makima (modified Akima
piecewise cubic Hermite interpolation) spline
fitting procedure was used to construct curves over
the discrete data points. A moving average
smoothing function was fitted to the data to remove
any fitting artifacts and outliers from the data set
with a smoothing factor between 0.00-0.25. The jet
color scheme was selected in most heat maps to
indicate low selectivity or TOF (dark blue) and high
selectivity or TOF (dark red). Raw data for all heat
maps are provided in the Supplementary
Information.
Acknowledgements. We acknowledge financial
support of the Catalysis Center for Energy
Innovation, a U.S. Department of Energy - Energy
Frontier Research Center under Grant DE-
SC0001004. The authors acknowledge the
Minnesota Supercomputing Institute (MSI) at the
University of Minnesota for providing resources
that contributed to the research results reported
within this paper. URL: http://www.msi.umn.edu/
Keywords. Catalysis, Sabatier, Dynamics,
Frequency, Resonance, Volcano, Ammonia
Supporting Information. Additional information
including computer code, time-on-stream data, and
simulation methods are included in the supporting
information.
____________________________________________________________________________ Ardagh, et al. Page 12
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download fileview on ChemRxivManuscript_Parallel_Rxn_Dynamics.pdf (1.58 MiB)
Ardagh, et al. Supporting Information Page S1
SUPPORTING INFORMATION
Catalytic Resonance Theory: Parallel Reaction Pathway Control
M. Alexander Ardagh1,2, Manish Shetty1, Anatoliy Kuznetsov1, Qi Zhang1, Phillip Christopher2,3,
Dionisios G. Vlachos2,5, Omar A. Abdelrahman2,4, Paul J. Dauenhauer1,2*
1 University of Minnesota, Department of Chemical Engineering and Materials Science, 421 Washington Ave. SE,
Minneapolis, MN, 55455, USA. 2 Catalysis Center for Energy Innovation, University of Delaware, 221 Academy Street, Newark, DE, 19716, USA. 3 University of California Santa Barbara, Department of Chemical Engineering, Engineering II Building, Santa
Barbara, CA 93106, USA 4 University of Massachusetts Amherst, Department of Chemical Engineering, 686 N. Pleasant Street, Amherst, MA,
01003 USA 5 University of Delaware, Department of Chemical and Biomolecular Engineering, 150 Academy Street, Newark,
DE 19716 USA
* Corresponding author: [email protected]
# of Figures: 1
# of Tables: 16
# of Equations: 8
Table of Contents:
Section S1. Matlab 2019a/b Code for A-to-B and A-to-B/A-to-C Systems ● Volcano Plots and Surface Coverage
● Dynamic Catalysis with a Square Waveform
Section S2. Matlab ODE Solver Performance for Static and Dynamic Catalysis
● ODE45
● ODE15s ● ODE23s
● ODE23t
● ODE23tb
Section S3. Static Catalysis Time on Stream Data at 1 % Conversion of A
Section S4. Data from Selectivity and TOF Heatmap Figures
Section S5. Linear Scaling Relationships Derivation
● Ɣ and δ ● δB-C
Ardagh, et al. Supporting Information Page S2
Section S1. Matlab 2019a/b Code
Code S1a. Volcano Plot and Surface Coverage for A-to-B/A-to-C
% Remove prior data and runs clear
clc
% Main program
% Constants: % Gas constant
R = 8.31446261815324; % J/gmol-K
Rg = R*10^-2; % L-bar/gmol-K
% Conditions:
% Temperature
Tc = 150.0; % deg C T = Tc + 273.15; % K
% Pressure (bar)
P(1) = 100.0; P(2:3) = 0.0;
% Concentration (M)
Cf = P/(Rg*T);
% Adsorbed species (gmol) Ns = zeros(3,1);
% Initial conditions
x0 = [Cf';Ns];
% Parameters:
% Number of active sites (gmol)
Nsites = 138.0/1000*20.0e-6;
% Reaction chemistry:
% Overall heat of reaction (J/gmol) delHovr = zeros(1,2);
% Bronsted-Evans-Polanyi relationship
alpha(1:2) = 0.6; % unitless beta(1:2) = 100.0e3; % J/gmol
% Linear scaling relationship
gamma(1) = 2.0; % unitless
gamma(2) = 0.5; % unitless delta(1:2) = 1.4; % eV
% Initial binding energy (eV) BEa0 = 1.4;
% Conversion target (mol %) C = 1.0;
% Initial space velocity
Ardagh, et al. Supporting Information Page S3
qsdot = 50.0; % mL/min qdot = qsdot/60000; % L/s
V = 138.0/1000*1/3.58*1/1000*1/(1 - 0.375); % L
SV0 = qdot/V; % 1/s
% ODE solver settings
tspan = [0 5.0e100]; % s
options = odeset('RelTol',1e-8,'AbsTol',1e-9);
% For loop bounds (eV)
is = -BEa0; ii = 0.005;
ie = BEa0;
% Preallocate matrices je = (ie - is)/ii + 1;
je = round(je);
delBEa = zeros(je,1); TOFa = delBEa;
TOFb = TOFa;
TOFc = TOFb; Theta_A_star = TOFc;
Theta_B_star = Theta_A_star;
Theta_C_star = Theta_B_star;
% Time volcano plot
tic
% Volcano plot generation
for i = is:ii:ie
% Loop index j = (i - is)/ii + 1;
j = round(j);
% Relative binding energy (eV)
delBEa(j) = i;
% Obtain rate constants (1/bar-s or 1/s)
k = rate_constants(BEa0,gamma,delta,delHovr,T,delBEa(j),alpha,beta);
% Solver for space velocity (1/s) SV = fsolve(@(SV) targetfun(SV,Cf,k,T,x0,C),SV0(j));
SV0(j + 1) = SV;
% Generate optimal solution
[t,x] = ode15s(@(t,x) xdot(t,x,SV,Cf,k,T),tspan,x0,options);
% Store data
TOFa(j) = (Cf(1) - x(end,1))*SV*V/Nsites;
TOFb(j) = (x(end,2) - Cf(2))*SV*V/Nsites;
Ardagh, et al. Supporting Information Page S4
TOFc(j) = (x(end,3) - Cf(3))*SV*V/Nsites; Theta_A_star(j) = x(end,4)/Nsites;
Theta_B_star(j) = x(end,5)/Nsites;
Theta_C_star(j) = x(end,6)/Nsites;
% Remove prior data
clear t x
end
% Stop timer
toc
% Plot results
semilogy(delBEa,[TOFa TOFb TOFc])
plot(delBEa,[Theta_A_star Theta_B_star Theta_C_star])
% Rate constants
function k = rate_constants(BEa0,gamma,delta,delHovr,T,delBEa,alpha,beta)
R = 8.31446261815324; % J/gmol-K
BE0(1) = BEa0; % A*
BE0(2:3) = gamma*BE0(1) + (1 - gamma).*delta + delHovr/96.485e3;
BE(1) = BE0(1) + delBEa; % A* BE(2:3) = BE0(2:3) + gamma*delBEa;
% Restrict to positive values
BE = max(0,BE)*96.485e3;
delH(1) = -BE(1); % A(g) + * <--> A*
delH(2:2:5) = delHovr + BE(1) - BE(2:3);
delH(3:2:5) = BE(2:3);
K(1) = 1.0e-7*exp(-delH(1)/(R*T)); % A(g) + * <--> A*
K(2:2:5) = 1.0*exp(-delH(2:2:5)/(R*T)); K(3:2:5) = 1.0e7*exp(-delH(3:2:5)/(R*T));
A(1) = 1.0e6; % 1/bar-s A(2:5) = 1.0e13; % 1/s
Ea(1) = 0.0e3; % A(g) + * --> A*
Ea(2:2:5) = alpha.*delH(2:2:5) + beta; Ea(3:2:5) = delH(3:2:5);
% Restrict to positive values
Ea = max(0,Ea);
k(1:2:10) = A.*exp(-Ea/(R*T));
k(2:2:10) = k(1:2:10)./K; end
% Target Function
Ardagh, et al. Supporting Information Page S5
function tf = targetfun(SV,Cf,k,T,x0,C) tspan = [0 5.0e100]; % s
options = odeset('RelTol',1e-8,'AbsTol',1e-9);
[t,x] = ode15s(@(t,x) xdot(t,x,SV,Cf,k,T),tspan,x0,options);
tf = ((Cf(1) - x(end,1))/sum(Cf)*100 - C)^2; end
% Derivative function dx = xdot(t,x,SV,Cf,k,T)
R = 8.31446261815324; % J/gmol-K
Rg = R*10^-2; % L-bar/gmol-K Nsites = 138.0/1000*20.0e-6; % gmol
V = 138.0/1000*1/3.58*1/1000*1/(1 - 0.375); % L
dx(1,1) = SV*(Cf(1) - x(1)) - k(1)*Rg*T*x(1)*(Nsites - sum(x(4:6)))/V + k(2)*x(4)/V; % M/s
dx(2,1) = SV*(Cf(2) - x(2)) - k(6)*Rg*T*x(2)*(Nsites - sum(x(4:6)))/V + k(5)*x(5)/V; % M/s dx(3,1) = SV*(Cf(3) - x(3)) - k(10)*Rg*T*x(3)*(Nsites - sum(x(4:6)))/V + k(9)*x(6)/V; % M/s
dx(4,1) = k(1)*Rg*T*x(1)*(Nsites - sum(x(4:6))) - k(2)*x(4) - k(3)*x(4) + k(4)*x(5) - k(7)*x(4) +
k(8)*x(6); % gmol/s dx(5,1) = k(6)*Rg*T*x(2)*(Nsites - sum(x(4:6))) - k(5)*x(5) + k(3)*x(4) - k(4)*x(5); % gmol/s
dx(6,1) = k(10)*Rg*T*x(3)*(Nsites - sum(x(4:6))) - k(9)*x(6) + k(7)*x(4) - k(8)*x(6); % gmol/s
end
Code S1b. Dynamic Catalysis in an A-to-B System with Square Waveform
% Remove prior runs and data clear
clc
% Step test for Model 1 - CSTR
% Constants:
% Gas constant (L-bar/gmol-K) Rg = 8.31446261815324e-2;
% Conditions: % Temperature
Tc = 150.0; % deg C
T = Tc + 273.15; % K
% Parameters:
% Feed pressure (bar)
Pf(1) = 100.0; % A(g) Pf(2) = 0.0; % B(g)
% Feed concentration (M)
Cf = Pf/(Rg*T);
% Volumetric flowrate
qsdot = 50.0; % mL/min qdot = qsdot/60000; % L/s
% Number of active sites (gmol)
Nsites = 138.0/1000*20.0e-6;
Ardagh, et al. Supporting Information Page S6
% CSTR volume (L) V = 138.0/1000*1/3.58*1/1000*1/(1 - 0.375);
% Space velocity (1/s)
SV = qdot/V;
% Steady State Initial Conditions for the States
C_ss = Cf'; % M
N_ss = zeros(2,1); % gmol x_ss = [C_ss;N_ss];
% Reaction chemistry: % Heat of reaction (J/gmol)
delHovr = 0.0;
% Bronsted-Evans-Polanyi relationship
alpha = 0.6; % unitless beta = 100.0e3; % J/gmol
% Linear scaling relationship
gamma = 2.0; % unitless delta = 1.4; % eV
% Initial binding energy of A (eV) BEa0 = mean(delta);
% Dynamic catalysis:
% Oscillation time constants (s) tau(1) = 5e5;
taur = 1.0;
tau(2) = taur*tau(1); % Oscillation frequency (Hz)
fosc = 1/sum(tau);
% Number of oscillations (unitless)
Nosc = max(11,fosc);
% Oscillation amplitude (eV)
delU = 0.6; % Oscillation endpoints (eV)
UL = -0.20;
UR = UL + delU; % Obtain rate constants (1/bar-s or 1/s)
kR = cstr1_constants(BEa0,gamma,delta,delHovr,UR,T,alpha,beta);
kL = cstr1_constants(BEa0,gamma,delta,delHovr,UL,T,alpha,beta);
% Solver options
options = odeset('RelTol',1e-8,'AbsTol',1e-9);
% Time Matlab code
tic
% Iterate until convergence
for n = 1:inf
% Empty matrices
Ardagh, et al. Supporting Information Page S7
tsvm = []; xsvm = [];
tsve = [];
xsve = [];
% Simulate all oscillations for i = 1:Nosc
% Odd numbered runs if mod(i,2) == 1
% Generate ODE solution [t,x] = ode23tb(@(t,x) cstr1(t,x,SV,Cf,kR,T),[0 tau(1)],x_ss(:,i),options);
% Store data
if i == 1
tsv = t; xsv = x;
else
if round(i) == round(Nosc/2.0) || round(i) == round(Nosc/2.0 + 1.0) tsv = [tsv;t + tsv(end)];
xsv = [xsv;x];
tsvm = [tsvm;t + tsv(end)]; xsvm = [xsvm;x];
else
if round(i) == round(Nosc - 1.0) || round(i) == round(Nosc)
tsv = [tsv;t + tsv(end)]; xsv = [xsv;x];
tsve = [tsve;t + tsv(end)];
xsve = [xsve;x]; else
tsv = [tsv;t + tsv(end)];
xsv = [xsv;x];
end end
end
x_ss(:,i + 1) = x(end,:)';
% Clean up matrices
clear t x
% Even numbered runs
else
% Generate ODE solution
[t,x] = ode23tb(@(t,x) cstr1(t,x,SV,Cf,kL,T),[0 tau(2)],x_ss(:,i),options);
% Store data if round(i) == round(Nosc/2.0) || round(i) == round(Nosc/2.0 + 1.0)
tsv = [tsv;t + tsv(end)];
xsv = [xsv;x]; tsvm = [tsvm;t + tsv(end)];
xsvm = [xsvm;x];
else
Ardagh, et al. Supporting Information Page S8
if round(i) == round(Nosc - 1.0) || round(i) == round(Nosc) tsv = [tsv;t + tsv(end)];
xsv = [xsv;x];
tsve = [tsve;t + tsv(end)];
xsve = [xsve;x]; else
tsv = [tsv;t + tsv(end)];
xsv = [xsv;x]; end
end
x_ss(:,i + 1) = x(end,:)';
% Clean up matrices
clear t x
end end
% Parse out the state values (M) Casvm = xsvm(:,1); % A(g)
Casve = xsve(:,1); % A(g)
% Measure reactor performance (mol %)
Xasvm = (Cf(1) - Casvm)/sum(Cf)*100;
Xasve = (Cf(1) - Casve)/sum(Cf)*100;
% Midpoint Riemann sums
Xainte = zeros(size(tsve));
Xaintm = zeros(size(tsvm)); for k = 2:size(Xainte,1)
Xainte(k) = (tsve(k) - tsve(k - 1))*mean([Xasve(k),Xasve(k - 1)]);
end
for l = 2:size(Xaintm,1) Xaintm(l) = (tsvm(l) - tsvm(l - 1))*mean([Xasvm(l),Xasvm(l - 1)]);
end
% Time averaged conversion
Xaavge = sum(Xainte)*fosc;
Xaavgm = sum(Xaintm)*fosc;
% Converge on C conversion of A (mol %)
C = 1.0;
if abs(Xaavge - Xaavgm) > 0.01 plot(tsv,xsv)
x_ss(:,1) = xsv(end,:)';
nt = n; nt
clear tsv xsv Casvm Casve Xasvm Xasve
else if abs(Xaavge - C) > 0.01
SV = SV*Xaavge/C;
x_ss(:,1) = [C_ss;N_ss];
Ardagh, et al. Supporting Information Page S9
nq = n; nq
clear tsv xsv Casvm Casve Xasvm Xasve
else
toc break
end
end end
% Parse out the state values (M) Cbsve = xsve(:,2); % B(g)
% Measure reactor performance (1/s)
TOFae = (Cf(1) - Casve)*SV*V/Nsites; TOFbe = (Cbsve - Cf(2))*SV*V/Nsites;
% Midpoint Riemann sums TOFaint = zeros(size(tsve));
TOFbint = TOFaint;
for m = 2:size(TOFaint,1) TOFaint(m) = (tsve(m) - tsve(m - 1))*mean([TOFae(m),TOFae(m - 1)]);
TOFbint(m) = (tsve(m) - tsve(m - 1))*mean([TOFbe(m),TOFbe(m - 1)]);
end
% Time averaged TOF (1/s)
TOFaavg = sum(TOFaint)*fosc;
TOFbavg = sum(TOFbint)*fosc;
% Check data visually
plot(tsv,xsv)
% Collect results
Results = [SV,TOFaavg,TOFbavg];
Code S1c. Dynamic Catalysis in a Parallel A-to-B/A-to-C System with Square Waveform
% Remove prior runs and data clear
clc
% Step test for Model 1 - CSTR
% Constants:
% Gas constant (L-bar/gmol-K) Rg = 8.31446261815324e-2;
% Conditions: % Temperature
Tc = 150.0; % deg C
T = Tc + 273.15; % K
Ardagh, et al. Supporting Information Page S10
% Parameters:
% Feed pressure (bar)
Pf(1) = 100.0; % A(g)
Pf(2:3) = 0.0; % Feed concentration (M)
Cf = Pf/(Rg*T);
% Volumetric flowrate
qsdot = 50.0; % mL/min
qdot = qsdot/60000; % L/s % Number of active sites (gmol)
Nsites = 138.0/1000*20.0e-6;
% CSTR volume (L)
V = 138.0/1000*1/3.58*1/1000*1/(1 - 0.375); % Space velocity (1/s)
SV = qdot/V;
% Steady State Initial Conditions for the States
C_ss = Cf'; % M
N_ss = zeros(3,1); % gmol x_ss = [C_ss;N_ss];
% Reaction chemistry:
% Heat of reaction (J/gmol) delHovr = zeros(1,2);
% Bronsted-Evans-Polanyi relationship
alpha(1:2) = 0.6; % unitless beta(1:2) = 100.0e3; % J/gmol
% Linear scaling relationship
gamma(1) = 2.0; % unitless
gamma(2) = 0.5; % unitless delta(1:2) = 1.4; % eV
% Initial binding energy of A (eV) BEa0 = 1.4;
% Dynamic catalysis: % Oscillation time constants (s)
tau(1) = 5e5;
taur = 1.0;
tau(2) = taur*tau(1); % Oscillation frequency (Hz)
fosc = 1/sum(tau);
% Number of oscillations (unitless) Nosc = max(11,fosc);
% Oscillation amplitude (eV) delU = 0.60;
% Oscillation endpoints (eV)
UL = -0.50;
Ardagh, et al. Supporting Information Page S11
UR = UL + delU; % Obtain rate constants (1/bar-s or 1/s)
kR = parallel_cstr1_constants(BEa0,gamma,delta,delHovr,UR,T,alpha,beta);
kL = parallel_cstr1_constants(BEa0,gamma,delta,delHovr,UL,T,alpha,beta);
% Solver options
options = odeset('RelTol',1e-8,'AbsTol',1e-9);
% Time Matlab code
tic
% Iterate until convergence
for n = 1:inf
% Empty matrices
tsvm = []; xsvm = [];
tsve = [];
xsve = []; % Simulate all oscillations
for i = 1:Nosc
% Odd numbered runs
if mod(i,2) == 1
% Generate ODE solution [t,x] = ode23tb(@(t,x) parallel_cstr1(t,x,SV,Cf,kR,T),[0 tau(1)],x_ss(:,i),options);
% Store data
if i == 1 tsv = t;
xsv = x;
else
if round(i) == round(Nosc/2.0) || round(i) == round(Nosc/2.0 + 1.0) tsv = [tsv;t + tsv(end)];
xsv = [xsv;x];
tsvm = [tsvm;t + tsv(end)]; xsvm = [xsvm;x];
else
if round(i) == round(Nosc - 1.0) || round(i) == round(Nosc) tsv = [tsv;t + tsv(end)];
xsv = [xsv;x];
tsve = [tsve;t + tsv(end)];
xsve = [xsve;x]; else
tsv = [tsv;t + tsv(end)];
xsv = [xsv;x]; end
end
end x_ss(:,i + 1) = x(end,:)';
% Clean up matrices
Ardagh, et al. Supporting Information Page S12
clear t x
% Even numbered runs
else
% Generate ODE solution
[t,x] = ode23tb(@(t,x) parallel_cstr1(t,x,SV,Cf,kL,T),[0 tau(2)],x_ss(:,i),options);
% Store data if round(i) == round(Nosc/2.0) || round(i) == round(Nosc/2.0 + 1.0)
tsv = [tsv;t + tsv(end)];
xsv = [xsv;x]; tsvm = [tsvm;t + tsv(end)];
xsvm = [xsvm;x];
else
if round(i) == round(Nosc - 1.0) || round(i) == round(Nosc) tsv = [tsv;t + tsv(end)];
xsv = [xsv;x];
tsve = [tsve;t + tsv(end)]; xsve = [xsve;x];
else
tsv = [tsv;t + tsv(end)]; xsv = [xsv;x];
end
end
x_ss(:,i + 1) = x(end,:)';
% Clean up matrices
clear t x end
end
% Parse out the state values (M) Casvm = xsvm(:,1); % A(g)
Casve = xsve(:,1); % A(g)
% Measure reactor performance (mol %)
Xasvm = (Cf(1) - Casvm)/sum(Cf)*100;
Xasve = (Cf(1) - Casve)/sum(Cf)*100;
% Time averaged conversion
Xaavge = trapz(tsve,Xasve)*fosc;
Xaavgm = trapz(tsvm,Xasvm)*fosc;
% Converge on C conversion of A (mol %)
C = 1.0; if abs(Xaavge - Xaavgm) > 0.01
plot(tsv,xsv)
x_ss(:,1) = xsv(end,:)'; nt = n;
error = abs(Xaavge - Xaavgm)/max([Xaavge,Xaavgm])*100;
nt
Ardagh, et al. Supporting Information Page S13
error clear tsv xsv Casvm Casve Xasvm Xasve
else
if abs(Xaavge - C) > 0.01
SV = SV*Xaavge/C; x_ss(:,1) = [C_ss;N_ss];
nq = n;
conversion = Xaavge; nq
conversion
clear tsv xsv Casvm Casve Xasvm Xasve else
toc
break
end end
end
% Parse out the state values (M)
Cbsve = xsve(:,2); % B(g)
Ccsve = xsve(:,3); % C(g)
% Measure reactor performance (1/s)
TOFae = (Cf(1) - Casve)*SV*V/Nsites;
TOFbe = (Cbsve - Cf(2))*SV*V/Nsites; TOFce = (Ccsve - Cf(3))*SV*V/Nsites;
% Time averaged TOF (1/s) TOFaavg = trapz(tsve,TOFae)*fosc;
TOFbavg = trapz(tsve,TOFbe)*fosc;
TOFcavg = trapz(tsve,TOFce)*fosc;
% Check data visually
plot(tsv,xsv)
% Collect results
Results = [SV,TOFaavg,TOFbavg,TOFcavg];
Ardagh, et al. Supporting Information Page S14
Section S2. Matlab ODE Solver Performance
ODE45 is Matlab’s general purpose solver and we attempted to use it for both static and dynamic
catalysis in the parallel reaction system. Since ODE45 was slow, stiff solvers including ODE15s,
ODE23s, ODE23t, and ODE23tb were used to compare performance. A relative tolerance of 10-8 and absolute tolerance of 10-9 were used throughout the performance tests.
Trial S2a. Solver Performance for Static Catalysis
Stats for ode15s:
632 successful steps 9 failed attempts
774 function evaluations
3 partial derivatives
149 LU decompositions 752 solutions of linear systems
Elapsed time is 0.034665 seconds.
Stats for ode23s:
1621 successful steps
1131 failed attempts 16853 function evaluations
1621 partial derivatives
2752 LU decompositions
8256 solutions of linear systems Elapsed time is 0.228154 seconds.
Stats for ode23t: 699 successful steps
5 failed attempts
1041 function evaluations
3 partial derivatives 243 LU decompositions
1019 solutions of linear systems
Elapsed time is 0.041602 seconds.
Stats for ode23tb:
543 successful steps 6 failed attempts
1278 function evaluations
3 partial derivatives
208 LU decompositions 1803 solutions of linear systems
Elapsed time is 0.019131 seconds.
ODE23tb was used throughout the manuscript for static catalysis simulation (i.e. volcano plots and
surface coverage) because it required the fewest number of steps and was the fastest to converge.
Ardagh, et al. Supporting Information Page S15
Trial S2b. Solver Performance for Dynamic Catalysis
Stats for ode15s:
101 successful steps
1 failed attempts 144 function evaluations
1 partial derivatives
22 LU decompositions 135 solutions of linear systems
Elapsed time is 9.699912 seconds
Stats for ode23s:
295 successful steps
166 failed attempts
2990 function evaluations 295 partial derivatives
461 LU decompositions
1383 solutions of linear systems Elapsed time is 63.131786 seconds
Stats for ode23t: 148 successful steps
0 failed attempts
191 function evaluations
1 partial derivatives 34 LU decompositions
182 solutions of linear systems
Elapsed time is 15.923910 seconds
Stats for ode23tb:
109 successful steps
0 failed attempts 266 function evaluations
1 partial derivatives
30 LU decompositions 366 solutions of linear systems
Elapsed time is 5.758628 seconds
ODE23tb was used throughout the manuscript for dynamic catalysis simulation because it required few
steps and was the fastest to converge.
Ardagh, et al. Supporting Information Page S16
Section S3. Example CSTR Time-on-Stream Data
Figure S1. Time on Stream Data for a Parallel Reaction System. Gas phase concentrations ([=] M) for A, B, and C are shown on the left. Surface coverage for A*, B*, and C* are displayed on the right panel.
Ardagh, et al. Supporting Information Page S17
Section S4. Raw Data for Manuscript Heatmaps
Table S1. Raw data for Figure 3C, heatmap for the selectivity of B ([=] mol %). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 2.0,
ɣC-A of 0.5, δB-A of 1.4 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency. Fixed oscillation amplitude of 0.6 eV.
Oscillation endpoint
(eV), oscillation
frequency (Hz)
-
1.
64
-
1.
58
-
1.
52
-
1.
46
-
1.
40
-
1.
34
-
1.
28
-
1.
22
-
1.
16
-
1.
10
-
1.
04
-
0.
98
-
0.
92
-
0.
86
-
0.
80
-
0.
74
-
0.6
8
-
0.6
2
-
0.5
6
-
0.5
0
-
0.4
4
-
0.3
8
-
0.3
2
-
0.2
6
-
0.2
0
-
0.1
4
-
0.0
8
-
0.0
2
0.0
4
0.1
0
0.1
6
1.00E-06
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
08
0.
11
0.
06
0.0
3
0.0
1
0.0
0
0.0
0
0.0
1
0.1
4
1.7
6
16.
62
43.
66
49.
50
49.
97
50.
00
50.
00
50.
00
50.
00
3.16E-06
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
08
0.
11
0.
06
0.0
3
0.0
1
0.0
0
0.0
0
0.0
2
0.1
5
1.7
9
16.
65
43.
67
49.
50
49.
97
50.
00
50.
00
50.
00
50.
00
1.00E-05
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
08
0.
11
0.
06
0.0
3
0.0
1
0.0
1
0.0
1
0.0
3
0.1
9
1.8
7
16.
76
43.
70
49.
50
49.
97
50.
00
50.
00
50.
00
50.
00
3.16E-05
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
08
0.
11
0.
06
0.0
3
0.0
2
0.0
1
0.0
3
0.0
9
0.3
1
2.1
2
17.
10
43.
81
49.
52
49.
97
50.
00
50.
00
50.
00
50.
00
1.00E-04
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
08
0.
11
0.
06
0.0
3
0.0
2
0.0
3
0.1
0
0.2
4
0.6
7
2.9
1
18.
14
44.
13
49.
58
49.
99
50.
00
50.
00
50.
00
50.
00
3.16E-04
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
08
0.
11
0.
06
0.0
3
0.0
3
0.1
0
0.3
1
0.7
5
1.8
0
5.3
1
21.
28
45.
11
49.
77
50.
02
50.
01
50.
01
50.
00
50.
00
1.00E-03
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
08
0.
11
0.
06
0.0
3
0.0
6
0.3
1
0.9
6
2.2
9
5.2
1
12.
14
29.
73
48.
02
50.
35
50.
15
50.
05
50.
02
50.
01
50.
01
3.16E-03
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
08
0.
11
0.
06
0.0
4
0.1
6
0.9
8
2.9
8
6.8
6
14.
50
28.
29
47.
53
55.
57
52.
16
50.
54
50.
15
50.
06
50.
03
50.
02
1.00E-02
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
08
0.
11
0.
06
0.0
6
0.4
6
3.0
0
8.7
9
18.
73
34.
54
54.
56
70.
90
69.
62
57.
09
51.
73
50.
48
50.
18
50.
09
50.
06
3.16E-02
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
07
0.
10
0.
06
0.1
3
1.4
1
8.8
1
23.
11
41.
89
62.
34
78.
94
87.
93
84.
85
67.
66
55.
19
51.
50
50.
57
50.
29
50.
18
1.00E-01
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
02
0.
07
0.
10
0.
07
0.3
5
4.1
7
23.
03
48.
46
69.
41
83.
93
92.
20
95.
78
94.
18
82.
01
63.
68
54.
60
51.
82
50.
92
50.
56
3.16E-01
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
01
0.
05
0.
08
0.
11
0.9
6
11.
78
48.
37
74.
77
87.
77
94.
31
97.
41
98.
63
98.
07
92.
12
78.
25
63.
42
56.
00
53.
03
51.
80
1.00E+00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
01
0.
04
0.
07
0.
21
2.7
9
27.
05
72.
07
90.
06
95.
78
98.
15
99.
18
99.
58
99.
43
97.
85
92.
41
81.
89
69.
42
60.
52
56.
12
3.16E+00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
01
0.
04
0.
08
0.
48
5.1
6
34.
76
78.
50
94.
56
98.
29
99.
37
99.
75
99.
88
99.
87
99.
62
98.
73
96.
07
89.
56
79.
10
69.
45
1.00E+01
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
01
0.
03
0.
09
0.
60
4.7
6
28.
71
73.
69
94.
31
98.
73
99.
65
99.
90
99.
97
99.
98
99.
95
99.
85
99.
50
98.
32
95.
02
88.
47
3.16E+01
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
01
0.
02
0.
06
0.
31
2.0
1
13.
05
48.
56
88.
63
98.
22
99.
70
99.
94
99.
99
99.
99
99.
99
99.
97
99.
91
99.
75
99.
25
97.
80
1.00E+02
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
01
0.
03
0.
12
0.7
3
4.9
3
29.
72
80.
27
97.
82
99.
79
99.
97
10
0.0
0
10
0.0
0
10
0.0
0
99.
99
99.
97
99.
93
99.
81
99.
52
3.16E+02
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
01
0.
06
0.3
8
3.0
9
24.
83
78.
82
97.
90
99.
83
99.
99
10
0.0
0
10
0.0
0
10
0.0
0
10
0.0
0
99.
99
99.
98
99.
94
99.
84
1.00E+03
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
01
0.
05
0.3
1
2.8
6
23.
72
78.
78
97.
95
99.
84
99.
99
10
0.0
0
10
0.0
0
10
0.0
0
10
0.0
0
10
0.0
0
99.
99
99.
98
99.
95
3.16E+03
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
01
0.
04
0.3
1
2.8
3
24.
21
78.
82
97.
97
99.
85
99.
99
10
0.0
0
10
0.0
0
10
0.0
0
10
0.0
0
10
0.0
0
10
0.0
0
99.
99
99.
98
1.00E+04
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
00
0.
01
0.
04
0.3
1
2.8
3
24.
21
78.
83
97.
98
99.
85
99.
99
10
0.0
0
10
0.0
0
10
0.0
0
10
0.0
0
10
0.0
0
10
0.0
0
10
0.0
0
99.
99
Ardagh, et al. Supporting Information Page S18
Table S2. Raw data for Figure 3D, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 2.0,
ɣC-A of 0.5, δB-A of 1.4 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation endpoint
(eV), oscillation
frequency (Hz)
-
1.6
4
-
1.5
8
-
1.5
2
-
1.4
6
-
1.4
0
-
1.3
4
-
1.2
8
-
1.2
2
-
1.
16
-
1.
10
-
1.
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01
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01
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01
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01
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01
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03
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04
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04
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05
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01
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01
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01
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01
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01
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01
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01
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01
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03
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04
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04
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05
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07
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01
9.6
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01
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1.4
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01
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01
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01
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01
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01
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01
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03
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04
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04
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05
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07
6.
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08
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01
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01
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1.4
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01
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01
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01
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01
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01
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01
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03
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04
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04
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05
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07
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01
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01
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1.4
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01
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01
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01
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01
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01
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10
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01
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1.8
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8.3
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2.6
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03
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04
1.
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04
1.
54
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05
1.
09
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06
9.
18
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07
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7.3
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01
9.5
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01
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1.4
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44
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01
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01
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01
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94
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01
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01
2.
11
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01
9.5
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4.2
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1.8
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8.5
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4.4
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2.7
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03
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55
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04
1.
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04
1.
62
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05
1.
80
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06
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06
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7.3
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01
9.5
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01
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0
1.4
2E
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1.5
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5.
44
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01
4.
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01
4.
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01
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01
4.
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01
2.
11
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01
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4.3
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1.9
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9.2
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5.0
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2.9
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1.
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03
4.
63
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04
1.
29
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04
1.
83
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05
3.
91
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06
3.
13
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06
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7.3
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01
9.5
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01
1.1
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0
1.4
2E
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1.5
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1.5
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1.2
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5.
45
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01
4.
43
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01
4.
53
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01
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01
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01
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01
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6.8
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3.4
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03
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04
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04
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05
8.
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05
9.
94
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06
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01
9.6
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01
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1.4
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1.5
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1.5
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5.
46
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01
4.
48
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01
4.
61
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01
5.5
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7.2
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9.3
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99
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01
4.
44
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01
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18
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01
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5.2
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2.8
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1.8
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1.2
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4.9
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1.
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03
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04
1.
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04
4.
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05
3.
18
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05
3.
13
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05
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7.7
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01
9.8
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01
1.2
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0
1.4
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1.5
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50
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01
4.
62
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01
4.
85
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01
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7.5
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9.6
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09
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01
4.
53
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01
2.
35
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01
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5.0
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3.9
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2.9
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9.8
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1.
94
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03
5.
95
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04
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24
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04
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14
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04
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96
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05
9.
83
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05
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01
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1.2
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1.4
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1.6
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62
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01
5.
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01
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56
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01
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8.
43
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01
4.
80
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01
2.
84
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01
1.9
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1.4
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1.0
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8.5
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2.5
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95
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03
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04
2.
23
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04
1.
08
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04
9.
94
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05
9.
86
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05
3.16E-01
1.0
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0
1.2
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0
1.4
2E
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0
1.6
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1.7
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1.6
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7.7
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5.
88
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01
5.
81
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01
6.
79
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01
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1.3
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11
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01
5.
36
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01
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28
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01
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2.5
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26
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03
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90
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03
2.
28
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04
9.
98
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05
9.
92
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05
9.
88
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05
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1.4
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1.6
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0
1.8
6E
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0
1.9
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01
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01
6.
25
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01
7.
61
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01
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1.5
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1.7
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1.4
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9.
49
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01
6.
40
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01
7.
89
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01
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1.0
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9.9
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8.1
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2.3
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2.
51
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02
4.
98
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03
2.
18
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04
1.
04
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04
9.
90
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05
9.
86
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05
3.16E+00
1.3
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0
1.5
0E
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0
1.7
4E
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0
2.0
0E
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0
2.0
7E
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0
1.7
5E
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0
1.1
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0
7.6
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6.
12
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01
6.
32
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01
8.
06
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01
1.0
3E
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0
1.3
4E
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0
1.6
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0
1.7
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0
1.4
5E
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0
9.
08
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01
6.
65
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01
9.
92
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01
1.7
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2.4
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0
2.8
5E
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0
3.0
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0
2.5
3E
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7.2
3E
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7.
48
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02
1.
42
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02
2.
01
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04
9.
80
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05
9.
88
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05
9.
84
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05
1.00E+01
1.3
6E
+0
0
1.5
3E
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0
1.8
2E
+0
0
2.1
4E
+0
0
2.2
0E
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0
1.8
7E
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0
1.2
5E
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0
7.9
9E
-01
6.
85
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01
6.
97
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01
8.
63
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01
1.0
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0
1.3
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0
1.6
1E
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0
1.6
6E
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0
1.3
6E
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0
8.
48
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01
5.
71
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01
7.
41
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01
1.6
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0
3.1
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0
4.9
2E
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0
6.3
9E
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0
6.4
4E
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0
2.0
0E
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0
1.
38
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01
3.
78
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02
2.
09
E-
04
1.
04
E-
04
1.
04
E-
04
1.
04
E-
04
Ardagh, et al. Supporting Information Page S19
3.16E+01
1.4
1E
+0
0
1.6
6E
+0
0
1.9
8E
+0
0
2.3
5E
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0
2.4
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0
2.0
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8.4
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6.
56
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01
6.
50
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01
7.
67
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01
9.6
3E
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1.1
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0
1.4
5E
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0
1.5
2E
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0
1.2
5E
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7.
94
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01
4.
58
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01
3.
73
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01
8.3
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2.3
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0
5.6
4E
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0
1.0
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1.5
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1
3.6
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2.
13
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01
3.
54
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02
2.
82
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04
1.
40
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04
1.
39
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04
1.
40
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04
1.00E+02
1.6
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1.9
6E
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0
2.5
3E
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0
3.1
2E
+0
0
3.3
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0
2.8
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0
1.7
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9.9
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6.
74
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01
6.
01
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01
6.
92
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01
8.7
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1.1
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0
1.3
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0
1.4
7E
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0
1.2
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0
7.
55
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01
4.
05
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01
3.
35
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01
4.8
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1.8
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0
7.9
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0
2.4
3E
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1
4.2
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1
5.0
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0
2.
34
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01
3.
39
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02
2.
79
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04
2.
53
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04
2.
51
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04
2.
53
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04
3.16E+02
2.0
6E
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0
2.9
1E
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0
4.1
7E
+0
0
5.5
7E
+0
0
6.2
3E
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0
5.1
1E
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0
2.8
3E
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0
1.2
8E
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0
6.
80
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01
5.
57
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01
6.
39
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01
8.1
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1.0
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0
1.3
2E
+0
0
1.4
2E
+0
0
1.1
8E
+0
0
7.
30
E-
01
3.
95
E-
01
2.
62
E-
01
4.5
1E
-01
1.9
4E
+0
0
9.8
2E
+0
0
4.2
2E
+0
1
7.9
8E
+0
1
5.7
1E
+0
0
2.
47
E-
01
3.
32
E-
02
2.
54
E-
04
2.
52
E-
04
2.
51
E-
04
2.
52
E-
04
1.00E+03
3.6
0E
+0
0
5.9
3E
+0
0
9.1
8E
+0
0
1.3
0E
+0
1
1.4
9E
+0
1
1.0
3E
+0
1
4.2
2E
+0
0
1.5
0E
+0
0
7.
07
E-
01
5.
45
E-
01
6.
44
E-
01
8.0
1E
-01
1.0
7E
+0
0
1.3
2E
+0
0
1.4
5E
+0
0
1.1
8E
+0
0
7.
47
E-
01
3.
94
E-
01
3.
15
E-
01
4.5
0E
-01
1.9
9E
+0
0
1.0
7E
+0
1
5.2
8E
+0
1
9.1
4E
+0
1
5.9
1E
+0
0
2.
49
E-
01
3.
32
E-
02
2.
54
E-
04
2.
52
E-
04
2.
52
E-
04
2.
52
E-
04
3.16E+03
8.5
1E
+0
0
1.5
2E
+0
1
2.5
4E
+0
1
3.7
2E
+0
1
3.5
2E
+0
1
1.5
5E
+0
1
5.0
3E
+0
0
1.6
2E
+0
0
7.
13
E-
01
5.
40
E-
01
6.
19
E-
01
7.9
7E
-01
1.0
4E
+0
0
1.3
1E
+0
0
1.4
1E
+0
0
1.1
8E
+0
0
7.
29
E-
01
3.
94
E-
01
2.
60
E-
01
4.5
1E
-01
2.0
1E
+0
0
1.1
0E
+0
1
5.5
9E
+0
1
9.2
9E
+0
1
5.9
4E
+0
0
2.
50
E-
01
3.
33
E-
02
2.
54
E-
04
2.
52
E-
04
2.
51
E-
04
2.
52
E-
04
1.00E+04
2.3
6E
+0
1
4.5
1E
+0
1
7.7
9E
+0
1
1.0
1E
+0
2
5.5
0E
+0
1
1.8
1E
+0
1
5.3
4E
+0
0
1.6
5E
+0
0
7.
14
E-
01
5.
39
E-
01
6.
18
E-
01
7.9
5E
-01
1.0
4E
+0
0
1.3
1E
+0
0
1.4
1E
+0
0
1.1
8E
+0
0
7.
29
E-
01
3.
94
E-
01
2.
60
E-
01
4.5
1E
-01
2.0
2E
+0
0
1.1
1E
+0
1
5.6
3E
+0
1
9.3
0E
+0
1
5.9
4E
+0
0
2.
50
E-
01
3.
33
E-
02
2.
54
E-
04
2.
52
E-
04
2.
51
E-
04
2.
52
E-
04
Ardagh, et al. Supporting Information Page S20
Table S3. Raw data for Figure 3E, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 2.0,
and δB-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency. Fixed oscillation amplitude of
0.6 eV.
Oscillation frequency (Hz), oscillation
endpoint (eV) -1.64 -1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04 0.16
1E-06
9.87E
-04
7.09E
-04
1.08E
-04
8.46E
-05
2.23E
-04
2.57E
-03
1.20E
-02
1.90E
-02
8.52E
-04
2.31E-
04
1.59E-
03
1.13E-
02
1.88E-
02
8.19E
-04
8.55E
-06
1.63E
-08
1E-05
9.87E
-04
7.09E
-04
1.08E
-04
8.46E
-05
2.23E
-04
2.57E
-03
1.20E
-02
1.90E
-02
8.53E
-04
2.38E-
04
1.60E-
03
1.13E-
02
1.88E-
02
8.20E
-04
8.67E
-06
2.23E
-08
1E-04
9.87E
-04
7.09E
-04
1.08E
-04
8.46E
-05
2.23E
-04
2.57E
-03
1.20E
-02
1.90E
-02
8.67E
-04
3.06E-
04
1.69E-
03
1.14E-
02
1.89E-
02
8.25E
-04
8.66E
-06
8.23E
-08
1E-03
9.87E
-04
7.09E
-04
1.08E
-04
8.46E
-05
2.23E
-04
2.58E
-03
1.20E
-02
1.90E
-02
9.67E
-04
9.81E-
04
2.59E-
03
1.23E-
02
1.91E-
02
8.37E
-04
9.30E
-06
6.80E
-07
1E-02
9.54E
-04
7.09E
-04
1.08E
-04
8.46E
-05
2.23E
-04
2.58E
-03
1.21E
-02
1.93E
-02
1.87E
-03
7.73E-
03
1.15E-
02
2.12E-
02
2.14E-
02
8.48E
-04
1.53E
-05
6.65E
-06
1E-01
6.80E
-04
4.18E
-04
7.19E
-05
4.96E
-05
2.23E
-04
2.55E
-03
1.21E
-02
1.95E
-02
1.09E
-02
7.52E-
02
1.00E-
01
1.10E-
01
4.21E-
02
1.01E
-03
7.44E
-05
6.63E
-05
1E+00
6.80E
-04
5.55E
-05
7.19E
-05
4.96E
-05
2.80E
-04
1.96E
-03
1.26E
-02
2.22E
-02
1.00E
-01
7.48E-
01
9.89E-
01
9.94E-
01
2.48E-
01
2.71E
-03
6.73E
-04
6.65E
-04
1E+01
6.80E
-04
5.55E
-05
7.19E
-05
4.96E
-05
2.80E
-04
1.33E
-03
1.86E
-02
4.80E
-02
4.60E
-01
3.31E
+00
9.47E
+00
9.84E
+00
2.15E
+00
1.30E
-02
6.66E
-03
6.64E
-03
1E+02
6.80E
-04
5.55E
-05
7.19E
-05
4.96E
-05
2.80E
-04
1.33E
-03
3.75E
-02
1.01E
-01
6.10E
-01
4.25E
+00
2.70E
+01
8.81E
+01
5.35E
+00
3.39E
-02
2.53E
-02
2.53E
-02
1E+03
6.80E
-04
5.55E
-05
7.19E
-05
4.96E
-05
2.80E
-04
1.33E
-03
3.43E
-02
1.07E
-01
6.25E
-01
4.36E
+00
3.10E
+01
1.99E
+02
5.97E
+00
3.32E
-02
2.52E
-02
2.52E
-02
1E+04
6.80E
-04
5.55E
-05
7.19E
-05
4.96E
-05
2.80E
-04
1.33E
-03
2.92E
-02
1.08E
-01
6.27E
-01
4.37E
+00
3.15E
+01
2.12E
+02
5.99E
+00
3.33E
-02
2.52E
-02
2.52E
-02
Ardagh, et al. Supporting Information Page S21
Table S4. Raw data for Figure 3F, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC, P
of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣC-A of 0.5, and
δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency. Fixed oscillation amplitude of 0.6
eV.
Oscillation frequency (Hz), oscillation
endpoint (eV) -1.64 -1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04 0.16
1E-06
7.33E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.44E
-01
4.49E
-01
7.07E-
01
1.11E
+00
7.93E
-01
2.10E
-01
4.21E
-02
8.07E
-03
1.48E
-03
2.28E
-04
2.20E
-05
1.16E
-06
1E-05
7.33E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.44E
-01
4.49E
-01
7.07E-
01
1.11E
+00
7.93E
-01
2.10E
-01
4.21E
-02
8.07E
-03
1.48E
-03
2.29E
-04
2.20E
-05
1.16E
-06
1E-04
7.33E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.44E
-01
4.49E
-01
7.07E-
01
1.11E
+00
7.93E
-01
2.10E
-01
4.21E
-02
8.08E
-03
1.49E
-03
2.32E
-04
2.20E
-05
1.22E
-06
1E-03
7.34E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.44E
-01
4.50E
-01
7.09E-
01
1.11E
+00
7.94E
-01
2.10E
-01
4.22E
-02
8.13E
-03
1.51E
-03
2.33E
-04
2.24E
-05
1.83E
-06
1E-02
7.45E-
01
1.19E
+00
1.57E
+00
1.23E
+00
5.46E
-01
4.61E
-01
7.23E-
01
1.12E
+00
7.98E
-01
2.11E
-01
4.26E
-02
8.23E
-03
1.51E
-03
2.37E
-04
2.81E
-05
7.67E
-06
1E-01
8.55E-
01
1.27E
+00
1.61E
+00
1.22E
+00
5.62E
-01
5.56E
-01
8.52E-
01
1.23E
+00
8.39E
-01
2.17E
-01
4.28E
-02
8.19E
-03
1.56E
-03
2.95E
-04
8.76E
-05
6.74E
-05
1E+00
1.31E
+00
1.64E
+00
1.93E
+00
1.17E
+00
6.01E
-01
7.61E
-01
1.28E
+00
1.72E
+00
9.18E
-01
2.07E
-01
4.09E
-02
8.37E
-03
1.63E
-03
8.55E
-04
6.77E
-04
6.65E
-04
1E+01
1.36E
+00
1.81E
+00
2.18E
+00
1.22E
+00
6.11E
-01
7.62E
-01
1.28E
+00
1.63E
+00
7.64E
-01
1.75E
-01
4.17E
-02
1.30E
-02
7.30E
-03
6.71E
-03
6.66E
-03
6.65E
-03
1E+02
1.60E
+00
2.53E
+00
3.37E
+00
1.75E
+00
6.58E
-01
6.73E
-01
1.09E
+00
1.44E
+00
7.31E
-01
1.94E
-01
6.20E
-02
3.15E
-02
1.31E
-02
2.53E
-02
2.53E
-02
2.53E
-02
1E+03
3.60E
+00
9.18E
+00
1.49E
+01
4.22E
+00
7.08E
-01
6.24E
-01
1.05E
+00
1.41E
+00
7.26E
-01
1.94E
-01
6.16E
-02
3.13E
-02
2.57E
-02
2.51E
-02
2.52E
-02
2.51E
-02
1E+04
2.36E
+01
7.79E
+01
5.50E
+01
5.34E
+00
7.14E
-01
6.18E
-01
1.04E
+00
1.41E
+00
7.26E
-01
1.94E
-01
6.16E
-02
3.13E
-02
2.57E
-02
2.51E
-02
2.51E
-02
2.52E
-02
Ardagh, et al. Supporting Information Page S22
Table S5. Raw data for Figure 5B, heatmap for the selectivity of B ([=] mol %). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 2.0,
ɣC-A of 0.5, δB-A of 1.4 eV, and δC-A of 1.4 eV. Dynamics: various oscillation amplitude and frequency.
The oscillation midpoint is fixed at the volcano peak for B production.
Oscillation amplitude (eV), oscillation
frequency (Hz)
0.0
0
0.0
5
0.1
0
0.1
5
0.2
0
0.2
5
0.3
0
0.3
5
0.4
0
0.4
5
0.5
0
0.5
5
0.6
0
0.6
5
0.7
0
0.7
5
0.8
0
0.8
5
0.9
0
0.9
5
1.0
0
1.00E-06
40.
68
36.
25
25.
53
14.
56
7.1
9
3.2
7
1.4
1
0.5
7
0.2
1
0.0
7
0.0
2
0.0
1
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
3.16E-06
40.
68
36.
25
25.
53
14.
56
7.1
9
3.2
7
1.4
1
0.5
7
0.2
1
0.0
7
0.0
2
0.0
1
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
1.00E-05
40.
68
36.
25
25.
53
14.
56
7.1
9
3.2
7
1.4
1
0.5
8
0.2
2
0.0
8
0.0
3
0.0
2
0.0
1
0.0
1
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
0.0
0
3.16E-05
40.
68
36.
25
25.
53
14.
56
7.1
9
3.2
8
1.4
2
0.5
9
0.2
4
0.1
0
0.0
6
0.0
4
0.0
3
0.0
2
0.0
1
0.0
1
0.0
1
0.0
1
0.0
0
0.0
0
0.0
0
1.00E-04
40.
68
36.
25
25.
53
14.
56
7.2
0
3.2
9
1.4
5
0.6
3
0.3
0
0.1
8
0.1
4
0.1
1
0.0
8
0.0
6
0.0
5
0.0
3
0.0
3
0.0
2
0.0
1
0.0
1
0.0
1
3.16E-04
40.
68
36.
25
25.
52
14.
56
7.2
1
3.3
3
1.5
3
0.7
7
0.5
0
0.4
3
0.3
9
0.3
3
0.2
6
0.2
0
0.1
5
0.1
1
0.0
8
0.0
6
0.0
5
0.0
4
0.0
3
1.00E-03
40.
68
36.
24
25.
50
14.
55
7.2
6
3.4
6
1.7
8
1.2
0
1.1
3
1.2
0
1.1
9
1.0
3
0.8
2
0.6
2
0.4
6
0.3
4
0.2
5
0.1
9
0.1
5
0.1
2
0.1
0
3.16E-03
40.
68
36.
23
25.
48
14.
58
7.4
2
3.8
7
2.5
7
2.5
1
3.0
5
3.5
6
3.6
1
3.1
8
2.5
5
1.9
4
1.4
4
1.0
7
0.8
0
0.6
0
0.4
7
0.3
8
0.3
2
1.00E-02
40.
68
36.
24
25.
54
14.
82
8.0
6
5.1
9
4.9
7
6.4
2
8.5
9
10.
26
10.
48
9.3
4
7.5
9
5.8
5
4.4
0
3.2
8
2.4
6
1.8
7
1.4
6
1.1
9
1.0
1
3.16E-02
40.
68
36.
34
25.
80
15.
65
10.
06
9.1
8
11.
88
16.
93
22.
52
26.
30
26.
77
24.
32
20.
39
16.
24
12.
55
9.5
7
7.2
8
5.6
0
4.4
0
3.5
9
3.0
5
1.00E-01
40.
66
36.
63
26.
91
18.
41
15.
98
19.
87
28.
34
38.
70
47.
71
52.
89
53.
47
50.
19
44.
46
37.
63
30.
77
24.
58
19.
39
15.
29
12.
23
10.
04
8.5
8
3.16E-01
40.
67
37.
10
29.
09
25.
30
30.
12
41.
54
54.
94
66.
47
74.
21
77.
98
78.
38
76.
07
71.
60
65.
46
58.
16
50.
27
42.
43
35.
22
29.
11
24.
35
20.
89
1.00E+00
40.
73
38.
37
35.
69
41.
21
54.
27
68.
01
78.
34
84.
91
88.
65
90.
47
90.
92
90.
21
88.
38
85.
41
81.
27
75.
99
69.
70
62.
68
55.
42
48.
53
42.
60
3.16E+00
40.
69
41.
91
48.
40
60.
45
71.
72
79.
80
85.
13
88.
58
90.
73
92.
22
93.
04
93.
35
93.
14
92.
37
90.
98
88.
92
86.
12
82.
57
78.
31
73.
46
68.
33
1.00E+01
41.
97
47.
78
58.
23
66.
76
73.
06
77.
80
80.
29
83.
43
85.
13
87.
32
89.
06
90.
37
91.
25
91.
72
91.
77
91.
35
90.
44
89.
03
87.
20
85.
02
82.
62
3.16E+01
41.
51
51.
71
62.
53
67.
77
70.
51
72.
30
73.
70
75.
06
75.
27
78.
30
79.
11
80.
90
83.
01
84.
91
86.
48
87.
64
88.
31
88.
52
88.
27
87.
67
86.
88
1.00E+02
41.
67
51.
80
63.
68
67.
62
69.
77
70.
46
70.
73
70.
84
71.
14
71.
46
71.
94
73.
12
74.
10
75.
43
76.
44
78.
37
80.
39
82.
31
83.
96
85.
26
86.
19
3.16E+02
41.
68
52.
44
63.
94
68.
55
70.
13
70.
63
70.
73
70.
65
70.
59
70.
53
70.
60
70.
78
71.
14
71.
71
72.
46
73.
49
74.
79
76.
40
78.
22
80.
26
82.
42
1.00E+03
41.
67
52.
44
63.
96
68.
20
70.
25
70.
73
70.
78
70.
68
70.
59
70.
50
70.
55
70.
70
71.
01
71.
51
72.
17
73.
09
74.
22
75.
66
77.
26
79.
11
81.
16
3.16E+03
41.
68
52.
44
63.
21
68.
62
70.
27
70.
76
70.
80
70.
70
70.
60
70.
52
70.
56
70.
72
71.
03
71.
55
72.
23
73.
18
74.
34
75.
83
77.
48
79.
38
81.
46
1.00E+04
41.
67
52.
44
67.
20
68.
62
70.
27
70.
77
70.
81
70.
70
70.
61
70.
52
70.
57
70.
73
71.
05
71.
58
72.
27
73.
23
74.
42
75.
93
77.
61
79.
55
81.
67
Ardagh, et al. Supporting Information Page S23
Table S6. Raw data for Figure 5C, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 2.0,
ɣC-A of 0.5, δB-A of 1.4 eV, and δC-A of 1.4 eV. Dynamics: various oscillation amplitude and frequency.
The oscillation midpoint is fixed at the volcano peak for B production.
Oscillation amplitude (eV),
oscillation frequency (Hz) 0.00 0.05 0.10 0.15 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 0.75 0.80 0.85 0.90 0.95 1.00
1.00E-06
5.92
E-
03
5.84
E-
03
5.89
E-
03
6.53
E-
03
8.02
E-
03
1.06
E-
02
1.44
E-
02
2.00
E-
02
2.80
E-
02
3.94
E-
02
5.53
E-
02
7.76
E-02
1.09
E-01
1.52
E-01
2.10
E-01
2.89
E-01
3.91
E-01
5.19
E-01
6.68
E-01
8.24
E-01
9.71
E-01
3.16E-06
5.92
E-
03
5.84
E-
03
5.89
E-
03
6.53
E-
03
8.02
E-
03
1.06
E-
02
1.44
E-
02
2.00
E-
02
2.80
E-
02
3.94
E-
02
5.53
E-
02
7.76
E-02
1.09
E-01
1.52
E-01
2.10
E-01
2.89
E-01
3.91
E-01
5.19
E-01
6.68
E-01
8.24
E-01
9.71
E-01
1.00E-05
5.92
E-
03
5.84
E-
03
5.89
E-
03
6.53
E-
03
8.02
E-
03
1.06
E-
02
1.44
E-
02
2.00
E-
02
2.80
E-
02
3.94
E-
02
5.53
E-
02
7.76
E-02
1.09
E-01
1.52
E-01
2.10
E-01
2.89
E-01
3.91
E-01
5.19
E-01
6.68
E-01
8.24
E-01
9.71
E-01
3.16E-05
5.92
E-
03
5.84
E-
03
5.89
E-
03
6.53
E-
03
8.02
E-
03
1.06
E-
02
1.44
E-
02
2.00
E-
02
2.80
E-
02
3.94
E-
02
5.53
E-
02
7.77
E-02
1.09
E-01
1.52
E-01
2.10
E-01
2.89
E-01
3.91
E-01
5.19
E-01
6.68
E-01
8.24
E-01
9.71
E-01
1.00E-04
5.92
E-
03
5.84
E-
03
5.89
E-
03
6.53
E-
03
8.03
E-
03
1.06
E-
02
1.44
E-
02
2.00
E-
02
2.81
E-
02
3.94
E-
02
5.54
E-
02
7.77
E-02
1.09
E-01
1.52
E-01
2.10
E-01
2.89
E-01
3.91
E-01
5.19
E-01
6.68
E-01
8.24
E-01
9.71
E-01
3.16E-04
5.92
E-
03
5.84
E-
03
5.90
E-
03
6.54
E-
03
8.04
E-
03
1.06
E-
02
1.44
E-
02
2.01
E-
02
2.81
E-
02
3.95
E-
02
5.55
E-
02
7.79
E-02
1.09
E-01
1.52
E-01
2.11
E-01
2.89
E-01
3.92
E-01
5.19
E-01
6.69
E-01
8.25
E-01
9.71
E-01
1.00E-03
5.92
E-
03
5.85
E-
03
5.90
E-
03
6.56
E-
03
8.07
E-
03
1.06
E-
02
1.45
E-
02
2.02
E-
02
2.84
E-
02
3.99
E-
02
5.61
E-
02
7.86
E-02
1.10
E-01
1.53
E-01
2.12
E-01
2.90
E-01
3.92
E-01
5.20
E-01
6.70
E-01
8.26
E-01
9.73
E-01
3.16E-03
5.92
E-
03
5.85
E-
03
5.92
E-
03
6.59
E-
03
8.14
E-
03
1.08
E-
02
1.47
E-
02
2.06
E-
02
2.91
E-
02
4.10
E-
02
5.77
E-
02
8.05
E-02
1.12
E-01
1.55
E-01
2.14
E-01
2.93
E-01
3.95
E-01
5.23
E-01
6.73
E-01
8.30
E-01
9.77
E-01
1.00E-02
5.92
E-
03
5.85
E-
03
5.93
E-
03
6.62
E-
03
8.22
E-
03
1.10
E-
02
1.52
E-
02
2.17
E-
02
3.11
E-
02
4.45
E-
02
6.26
E-
02
8.66
E-02
1.19
E-01
1.63
E-01
2.22
E-01
3.01
E-01
4.04
E-01
5.33
E-01
6.84
E-01
8.43
E-01
9.92
E-01
3.16E-02
5.92
E-
03
5.86
E-
03
5.95
E-
03
6.69
E-
03
8.41
E-
03
1.15
E-
02
1.65
E-
02
2.45
E-
02
3.70
E-
02
5.47
E-
02
7.74
E-
02
1.05
E-01
1.40
E-01
1.85
E-01
2.46
E-01
3.27
E-01
4.32
E-01
5.63
E-01
7.17
E-01
8.81
E-01
1.04
E+0
0
1.00E-01
5.92
E-
03
5.91
E-
03
6.01
E-
03
6.93
E-
03
8.90
E-
03
1.29
E-
02
2.03
E-
02
3.33
E-
02
5.49
E-
02
8.59
E-
02
1.23
E-
01
1.61
E-01
2.03
E-01
2.53
E-01
3.17
E-01
4.02
E-01
5.13
E-01
6.52
E-01
8.17
E-01
9.96
E-01
1.17
E+0
0
3.16E-01
5.92
E-
03
6.29
E-
03
6.32
E-
03
7.68
E-
03
1.10
E-
02
1.77
E-
02
3.22
E-
02
6.08
E-
02
1.11
E-
01
1.84
E-
01
2.64
E-
01
3.36
E-01
3.98
E-01
4.59
E-01
5.31
E-01
6.22
E-01
7.41
E-01
8.95
E-01
1.08
E+0
0
1.30
E+0
0
1.51
E+0
0
1.00E+00
5.92
E-
03
7.31
E-
03
8.12
E-
03
1.09
E-
02
1.76
E-
02
3.29
E-
02
6.71
E-
02
1.35
E-
01
2.52
E-
01
4.23
E-
01
6.26
E-
01
8.18
E-01
9.71
E-01
1.09
E+0
0
1.19
E+0
0
1.29
E+0
0
1.42
E+0
0
1.59
E+0
0
1.80
E+0
0
2.06
E+0
0
2.35
E+0
0
3.16E+00
5.92
E-
03
1.07
E-
02
1.05
E-
02
1.59
E-
02
2.80
E-
02
5.16
E-
02
9.56
E-
02
1.75
E-
01
3.05
E-
01
5.12
E-
01
8.07
E-
01
1.19
E+0
0
1.63
E+0
0
2.06
E+0
0
2.44
E+0
0
2.78
E+0
0
3.09
E+0
0
3.40
E+0
0
3.73
E+0
0
4.09
E+0
0
4.48
E+0
0
1.00E+01
5.92
E-
03
1.05
E-
02
1.19
E-
02
1.47
E-
02
3.91
E-
02
5.42
E-
02
7.32
E-
02
1.18
E-
01
1.87
E-
01
3.09
E-
01
5.05
E-
01
8.08
E-01
1.25
E+0
0
1.86
E+0
0
2.62
E+0
0
3.49
E+0
0
4.39
E+0
0
5.27
E+0
0
6.15
E+0
0
7.04
E+0
0
7.95
E+0
0
3.16E+01
5.92
E-
03
9.50
E-
03
1.06
E-
02
1.86
E-
02
4.39
E-
02
5.44
E-
02
6.99
E-
02
9.29
E-
02
1.15
E-
01
1.83
E-
01
2.58
E-
01
3.96
E-01
6.25
E-01
9.86
E-01
1.54
E+0
0
2.35
E+0
0
3.44
E+0
0
4.81
E+0
0
6.38
E+0
0
8.03
E+0
0
9.72
E+0
0
1.00E+02
5.92
E-
03
8.20
E-
03
1.25
E-
02
1.80
E-
02
4.93
E-
02
5.89
E-
02
7.21
E-
02
9.06
E-
02
1.05
E-
01
1.44
E-
01
1.98
E-
01
2.92
E-01
4.09
E-01
5.84
E-01
8.49
E-01
1.26
E+0
0
1.88
E+0
0
2.83
E+0
0
4.18
E+0
0
6.02
E+0
0
8.27
E+0
0
3.16E+02
5.92
E-
03
8.21
E-
03
1.24
E-
02
1.69
E-
02
4.93
E-
02
5.91
E-
02
7.22
E-
02
9.02
E-
02
1.17
E-
01
1.52
E-
01
2.05
E-
01
2.74
E-01
3.78
E-01
5.17
E-01
7.23
E-01
1.00
E+0
0
1.40
E+0
0
1.94
E+0
0
2.72
E+0
0
3.82
E+0
0
5.37
E+0
0
1.00E+03
5.92
E-
03
8.20
E-
03
1.30
E-
02
1.86
E-
02
4.94
E-
02
5.89
E-
02
7.22
E-
02
9.02
E-
02
1.17
E-
01
1.52
E-
01
2.04
E-
01
2.78
E-01
3.76
E-01
5.13
E-01
7.15
E-01
9.85
E-01
1.36
E+0
0
1.86
E+0
0
2.55
E+0
0
3.47
E+0
0
4.70
E+0
0
Ardagh, et al. Supporting Information Page S24
3.16E+03
5.92
E-
03
8.14
E-
03
1.19
E-
02
1.69
E-
02
4.95
E-
02
5.89
E-
02
7.23
E-
02
9.02
E-
02
1.17
E-
01
1.52
E-
01
2.05
E-
01
2.78
E-01
3.76
E-01
5.14
E-01
7.17
E-01
9.89
E-01
1.37
E+0
0
1.88
E+0
0
2.59
E+0
0
3.54
E+0
0
4.84
E+0
0
1.00E+04
5.92
E-
03
8.13
E-
03
1.27
E-
02
1.69
E-
02
4.95
E-
02
5.89
E-
02
7.23
E-
02
9.03
E-
02
1.17
E-
01
1.52
E-
01
2.05
E-
01
2.79
E-01
3.76
E-01
5.14
E-01
7.17
E-01
9.91
E-01
1.37
E+0
0
1.89
E+0
0
2.61
E+0
0
3.59
E+0
0
4.94
E+0
0
Ardagh, et al. Supporting Information Page S25
Table S7. Raw data for Figure 6C, heatmap for the selectivity of B ([=] mol %). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 0.25,
ɣC-A of 0.50, δB-A of 1.4 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation endpoint (eV), oscillation frequency (Hz) -1.64
-
1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04 0.16
1E-06 98.94
98.1
1 96.69 94.08 89.54 91.87
95.1
6
94.6
1
89.8
2
71.8
1
53.9
3
50.3
8
50.0
3
50.0
0
50.0
0
50.0
0
1E-05 98.94
98.1
1 96.68 94.08 89.54 91.87
95.1
6
94.6
0
89.8
0
71.7
9
53.9
2
50.3
8
50.0
3
50.0
0
50.0
0
50.0
0
1E-04 98.94
98.1
1 96.68 94.08 89.56 91.88
95.1
3
94.5
3
89.5
7
71.5
6
53.8
8
50.3
7
50.0
3
50.0
0
50.0
0
50.0
0
1E-03 98.93
98.1
0 96.66 94.05 89.73 91.98
94.9
3
93.7
9
87.4
0
69.3
7
53.4
5
50.2
8
50.0
1
50.0
0
50.0
0
50.0
0
1E-02 98.86
98.0
0 96.43 93.80 90.79 92.42
93.0
8
87.3
9
70.5
0
52.7
3
49.1
7
49.3
7
49.7
8
49.9
6
50.0
1
50.0
2
1E-01 98.76
97.8
7 96.29 93.49 90.17 87.34
77.8
7
52.0
0
23.5
5
14.8
9
27.8
6
41.7
6
47.6
1
49.5
7
50.0
9
50.1
6
1E+00 98.72
97.8
3 96.07 92.94 88.10 79.16
54.4
6
18.0
9 4.85 5.37
16.3
2
29.8
8
39.4
6
46.7
9
50.9
9
51.8
6
1E+01 98.68
97.0
2 91.55 93.21 88.59 76.20
48.1
3
18.5
2 6.97
11.1
2
16.1
6
22.6
9
33.5
6
44.1
1
52.4
3
58.6
3
1E+02 98.68
96.3
4 94.29 93.19 88.50 78.74
59.6
7
35.4
0
19.9
4
16.7
1
16.8
1
16.9
8
17.2
5
19.4
5
29.8
7
49.3
6
1E+03 98.69
97.5
9 95.51 93.19 87.62 75.80
78.6
0
51.8
4
24.3
5
17.6
7
16.8
2
16.7
4
16.7
4
16.7
5
16.9
3
18.1
9
1E+04 98.61
97.7
0 96.21 84.07 91.80 92.28
83.1
0
54.8
6
24.6
6
17.7
1
16.8
2
16.7
4
16.7
4
16.7
2
16.7
2
16.7
3
Ardagh, et al. Supporting Information Page S26
Table S8. Raw data for Figure 6D, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 0.25,
ɣC-A of 0.50, δB-A of 1.4 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation endpoint (eV), oscillation
frequency (Hz) -1.64 -1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04 0.16
1E-06
3.24E
-02
4.03E
-02
2.86E
-02
1.95E
-02
1.87E
-02
2.53E
-02
3.16E
-02
2.29E
-02
1.18E
-02
6.57E
-03
3.73E
-03
1.65E
-03
6.37E
-04
2.01E
-04
3.40E
-05
2.25E
-06
1E-05
3.24E
-02
4.03E
-02
2.86E
-02
1.95E
-02
1.87E
-02
2.53E
-02
3.16E
-02
2.29E
-02
1.18E
-02
6.57E
-03
3.73E
-03
1.65E
-03
6.37E
-04
2.01E
-04
3.43E
-05
2.26E
-06
1E-04
3.24E
-02
4.04E
-02
2.86E
-02
1.95E
-02
1.88E
-02
2.54E
-02
3.17E
-02
2.29E
-02
1.19E
-02
6.60E
-03
3.74E
-03
1.65E
-03
6.41E
-04
2.03E
-04
3.45E
-05
2.51E
-06
1E-03
3.26E
-02
4.04E
-02
2.84E
-02
1.94E
-02
1.91E
-02
2.62E
-02
3.24E
-02
2.33E
-02
1.23E
-02
6.85E
-03
3.80E
-03
1.67E
-03
6.47E
-04
2.04E
-04
3.76E
-05
5.43E
-06
1E-02
3.44E
-02
4.11E
-02
2.71E
-02
1.86E
-02
2.18E
-02
3.28E
-02
3.81E
-02
2.65E
-02
1.55E
-02
9.04E
-03
4.12E
-03
1.70E
-03
6.53E
-04
2.33E
-04
6.62E
-05
3.30E
-05
1E-01
3.74E
-02
4.24E
-02
2.65E
-02
1.85E
-02
2.31E
-02
4.05E
-02
5.10E
-02
4.55E
-02
4.55E
-02
2.91E
-02
6.78E
-03
2.25E
-03
9.80E
-04
5.06E
-04
1.73E
-04
3.13E
-04
1E+00
4.05E
-02
4.54E
-02
2.95E
-02
2.17E
-02
2.79E
-02
4.81E
-02
7.34E
-02
1.24E
-01
1.85E
-01
6.57E
-02
6.60E
-03
5.59E
-03
3.83E
-04
3.27E
-04
3.15E
-05
3.10E
-04
1E+01
4.16E
-02
6.17E
-02
6.18E
-02
2.08E
-02
2.60E
-02
9.17E
-02
1.08E
-01
1.30E
-01
1.54E
-01
4.93E
-02
4.09E
-03
3.37E
-03
3.18E
-04
3.12E
-04
3.11E
-04
3.12E
-04
1E+02
4.17E
-02
7.72E
-02
4.07E
-02
2.07E
-02
2.53E
-02
3.96E
-02
7.70E
-02
6.07E
-02
7.17E
-02
5.01E
-02
3.57E
-03
2.88E
-03
1.31E
-04
2.53E
-04
1.26E
-04
2.54E
-04
1E+03
4.48E
-02
5.47E
-02
3.56E
-02
1.85E
-02
1.24E
-02
1.26E
-02
5.63E
-02
5.92E
-02
6.40E
-02
4.90E
-02
1.56E
-03
1.58E
-03
2.55E
-04
2.51E
-04
2.51E
-04
2.51E
-04
1E+04
8.80E
-02
9.83E
-02
5.30E
-02
1.71E
-02
9.04E
-03
1.17E
-02
1.16E
-01
5.73E
-02
4.85E
-02
4.89E
-02
1.56E
-03
1.57E
-03
2.55E
-04
2.52E
-04
2.51E
-04
2.52E
-04
Ardagh, et al. Supporting Information Page S27
Table S9. Raw data for Figure 6E, heatmap for the selectivity of B ([=] mol %). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 1.0,
ɣC-A of 0.5, δB-A of 1.4 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation endpoint (eV), oscillation frequency (Hz) -1.64 -1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04 0.16
1E-06 0.02 0.04 0.12 0.28 0.59 1.29 0.96 0.27 0.42 1.47 12.08 44.12 49.78 50.00 50.00 50.00
1E-05 0.02 0.04 0.12 0.28 0.59 1.29 0.96 0.27 0.42 1.47 12.09 44.12 49.78 50.00 50.00 50.00
1E-04 0.02 0.04 0.12 0.28 0.59 1.29 0.96 0.27 0.42 1.49 12.16 44.17 49.79 50.00 50.00 50.00
1E-03 0.02 0.04 0.12 0.28 0.59 1.29 0.96 0.28 0.44 1.65 12.87 44.59 49.90 50.03 50.01 50.01
1E-02 0.02 0.04 0.12 0.28 0.59 1.26 0.95 0.32 0.67 3.24 19.33 48.50 50.94 50.33 50.12 50.05
1E-01 0.02 0.04 0.12 0.29 0.57 1.05 0.89 0.70 2.73 16.33 53.72 70.34 59.66 53.28 51.22 50.53
1E+00 0.02 0.05 0.13 0.32 0.54 0.77 1.05 2.86 15.22 61.44 91.09 94.93 87.09 73.53 62.11 55.60
1E+01 0.02 0.05 0.13 0.33 0.60 0.89 1.73 3.22 16.69 56.98 92.35 97.10 95.86 93.37 88.57 81.22
1E+02 0.02 0.05 0.14 0.34 0.57 0.46 0.53 0.94 3.70 27.62 85.44 96.00 96.44 96.42 96.33 95.89
1E+03 0.02 0.05 0.14 0.36 0.59 0.22 0.20 0.46 2.27 24.58 85.08 95.99 96.45 96.46 96.46 96.45
1E+04 0.02 0.05 0.14 0.36 0.59 0.19 0.16 0.43 2.24 24.54 85.08 95.99 96.47 96.46 96.46 96.46
Ardagh, et al. Supporting Information Page S28
Table S10. Raw data for Figure 6F, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 1.0,
ɣC-A of 0.5, δB-A of 1.4 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation endpoint (eV), oscillation
frequency (Hz) -1.64 -1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04 0.16
1E-06
7.33E-
01
1.19E
+00
1.57E
+00
1.23E
+00
5.49E
-01
4.60E
-01
7.20E-
01
1.12E
+00
7.97E
-01
2.14E
-01
4.80E
-02
1.44E
-02
2.81E
-03
3.69E
-04
2.66E
-05
1.23E
-06
1E-05
7.33E-
01
1.19E
+00
1.57E
+00
1.23E
+00
5.49E
-01
4.60E
-01
7.20E-
01
1.12E
+00
7.97E
-01
2.14E
-01
4.80E
-02
1.44E
-02
2.81E
-03
3.69E
-04
2.69E
-05
1.23E
-06
1E-04
7.33E-
01
1.19E
+00
1.57E
+00
1.23E
+00
5.49E
-01
4.60E
-01
7.20E-
01
1.12E
+00
7.98E
-01
2.14E
-01
4.81E
-02
1.45E
-02
2.82E
-03
3.72E
-04
2.70E
-05
1.53E
-06
1E-03
7.34E-
01
1.19E
+00
1.57E
+00
1.23E
+00
5.49E
-01
4.61E
-01
7.22E-
01
1.12E
+00
7.98E
-01
2.14E
-01
4.85E
-02
1.46E
-02
2.85E
-03
3.75E
-04
2.98E
-05
4.40E
-06
1E-02
7.45E-
01
1.19E
+00
1.57E
+00
1.23E
+00
5.51E
-01
4.71E
-01
7.36E-
01
1.13E
+00
8.05E
-01
2.19E
-01
5.30E
-02
1.59E
-02
2.91E
-03
4.01E
-04
5.79E
-05
3.22E
-05
1E-01
8.55E-
01
1.27E
+00
1.62E
+00
1.22E
+00
5.67E
-01
5.65E
-01
8.65E-
01
1.25E
+00
8.68E
-01
2.61E
-01
9.33E
-02
2.71E
-02
3.74E
-03
6.95E
-04
1.65E
-04
3.12E
-04
1E+00
1.31E
+00
1.64E
+00
1.94E
+00
1.17E
+00
6.06E
-01
7.75E
-01
1.30E
+00
1.79E
+00
1.11E
+00
5.66E
-01
4.71E
-01
1.30E
-01
1.07E
-02
3.61E
-03
3.14E
-03
3.10E
-03
1E+01
1.37E
+00
1.81E
+00
2.19E
+00
1.23E
+00
6.58E
-01
8.14E
-01
1.40E
+00
1.72E
+00
9.82E
-01
4.77E
-01
5.25E
-01
1.90E
-01
4.10E
-02
3.14E
-02
3.11E
-02
3.13E
-02
1E+02
1.60E
+00
2.53E
+00
3.38E
+00
1.76E
+00
6.63E
-01
6.78E
-01
1.13E
+00
1.47E
+00
7.69E
-01
2.77E
-01
2.90E
-01
1.52E
-01
3.58E
-02
2.57E
-02
1.27E
-02
2.53E
-02
1E+03
3.60E
+00
9.19E
+00
1.49E
+01
4.25E
+00
7.15E
-01
6.26E
-01
1.05E
+00
1.42E
+00
7.49E
-01
2.66E
-01
2.84E
-01
1.51E
-01
3.55E
-02
2.55E
-02
2.52E
-02
2.52E
-02
1E+04
2.37E
+01
7.80E
+01
5.52E
+01
5.37E
+00
7.22E
-01
6.20E
-01
1.05E
+00
1.42E
+00
7.49E
-01
2.66E
-01
2.84E
-01
1.51E
-01
2.28E
-02
2.55E
-02
2.52E
-02
2.51E
-02
Ardagh, et al. Supporting Information Page S29
Table S11. Raw data for Figure 7C, heatmap for the selectivity of B ([=] mol %). Conditions: T of 150 oC, P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of
2.0, ɣC-A of 0.5, δB-A of 0.8 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation frequency (Hz), Oscillation endpoint (eV) -1.64 -1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04
1E-06 0.00 0.00 0.00 0.08 1.13 5.98 0.04 0.01 0.11 2.78 43.61 50.45 50.05 50.01 50.00
1E-05 0.00 0.00 0.00 0.08 1.13 5.98 0.05 0.01 0.11 2.78 43.62 50.45 50.05 50.01 50.00
1E-04 0.00 0.00 0.00 0.08 1.13 5.98 0.06 0.01 0.12 2.82 43.65 50.46 50.06 50.01 50.00
1E-03 0.00 0.00 0.00 0.08 1.13 5.98 0.18 0.10 0.23 3.23 43.98 50.53 50.09 50.02 50.01
1E-02 0.00 0.00 0.00 0.08 1.12 5.97 1.37 0.88 1.34 7.07 47.09 51.18 50.39 50.18 50.09
1E-01 0.00 0.00 0.00 0.08 1.09 6.02 9.45 7.17 10.51 32.80 68.65 58.43 53.62 51.78 50.90
1E+00 0.00 0.00 0.00 0.09 1.02 6.95 17.13 21.70 43.67 81.21 95.70 86.74 77.16 67.86 60.02
1E+01 0.00 0.00 0.01 0.09 1.14 8.68 20.53 28.13 60.16 92.04 98.79 97.16 95.75 93.29 88.60
1E+02 0.00 0.00 0.01 0.09 1.07 5.20 16.76 30.34 62.71 94.94 99.38 98.03 96.77 96.53 96.38
1E+03 0.00 0.00 0.01 0.10 1.12 2.58 9.78 43.25 82.22 99.21 99.92 99.63 98.22 96.83 96.58
1E+04 0.00 0.00 0.01 0.10 1.13 2.15 7.86 54.43 96.53 99.92 99.99 99.96 99.10 97.11 96.73
Ardagh, et al. Supporting Information Page S30
Table S12. Raw data for Figure 7D, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 2.0,
ɣC-A of 0.5, δB-A of 0.8 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation frequency (Hz), Oscillation
endpoint (eV) -1.64 -1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04
1E-06
7.33E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.53E
-01
4.91E
-01
6.92E-
01
1.11E
+00
7.94E-
01
2.17E-
01
6.57E
-02
5.88E
-04
8.64E
-07
2.45E
-09
1.25E
-09
1E-05
7.33E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.53E
-01
4.91E
-01
6.92E-
01
1.11E
+00
7.94E-
01
2.17E-
01
6.57E
-02
5.88E
-04
8.78E
-07
1.36E
-08
1.26E
-08
1E-04
7.33E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.53E
-01
4.91E
-01
6.92E-
01
1.11E
+00
7.94E-
01
2.17E-
01
6.57E
-02
5.92E
-04
1.18E
-06
1.26E
-07
1.26E
-07
1E-03
7.34E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.53E
-01
4.92E
-01
6.95E-
01
1.11E
+00
7.96E-
01
2.18E-
01
6.60E
-02
5.96E
-04
3.95E
-06
1.25E
-06
1.25E
-06
1E-02
7.45E-
01
1.19E
+00
1.57E
+00
1.23E
+00
5.55E
-01
5.04E
-01
7.27E-
01
1.14E
+00
8.12E-
01
2.28E-
01
6.92E
-02
6.03E
-04
3.16E
-05
1.25E
-05
1.25E
-05
1E-01
8.55E-
01
1.27E
+00
1.61E
+00
1.22E
+00
5.71E
-01
6.06E
-01
9.96E-
01
1.40E
+00
9.61E-
01
3.27E-
01
9.72E
-02
8.32E
-04
3.11E
-04
1.25E
-04
1.25E
-04
1E+00
1.31E
+00
1.64E
+00
1.93E
+00
1.17E
+00
6.11E
-01
8.36E
-01
1.71E
+00
2.44E
+00
1.76E
+00
1.18E
+00
1.89E
-01
1.61E
-03
3.13E
-03
1.25E
-03
1.25E
-03
1E+01
1.37E
+00
1.82E
+00
2.18E
+00
1.22E
+00
6.62E
-01
8.81E
-01
1.77E
+00
2.72E
+00
2.38E
+00
2.72E
+00
2.41E
-01
3.14E
-02
3.12E
-02
1.25E
-02
1.25E
-02
1E+02
1.60E
+00
2.53E
+00
3.37E
+00
1.75E
+00
6.67E
-01
7.51E
-01
1.58E
+00
2.83E
+00
2.61E
+00
4.25E
+00
2.45E
-01
1.29E
-02
2.53E
-02
1.26E
-02
1.26E
-02
1E+03
3.60E
+00
9.18E
+00
1.49E
+01
4.23E
+00
7.21E
-01
6.55E
-01
1.32E
+00
4.05E
+00
6.02E
+00
2.42E
+01
2.50E
-01
2.55E
-02
2.52E
-02
1.25E
-02
1.25E
-02
1E+04
2.36E
+01
7.79E
+01
5.50E
+01
5.35E
+00
7.28E
-01
6.44E
-01
1.26E
+00
5.89E
+00
3.32E
+01
1.02E
+02
2.51E
-01
2.54E
-02
2.52E
-02
1.25E
-02
1.25E
-02
Ardagh, et al. Supporting Information Page S31
Table S13. Raw data for Figure 7E, heatmap for the selectivity of B ([=] mol %). Conditions: T of 150 oC, P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of
2.0, ɣC-A of 0.5, δB-A of 2.0 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation endpoint (eV), Oscillation frequency (Hz)
-
1.64
-
1.52
-
1.40
-
1.28
-
1.16
-
1.04
-
0.92
-
0.80
-
0.68
-
0.56
-
0.44 -0.32 -0.20 -0.08 0.04 0.16
1E-06 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.02 3.25 46.60 50.00
1E-05 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.02 3.60 47.70 50.15
1E-04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.05 6.93 56.89 51.62
1E-03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.00 0.29 30.91 84.39 62.64
1E-02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.02 2.67 80.69 97.90 88.61
1E-01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.00 0.18 21.39 97.68 99.79 98.59
1E+00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.01 0.02 1.85 74.46 99.80 99.98 99.88
1E+01 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.07 13.35 97.64 99.99 100.00 100.00
1E+02 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.11 25.77 98.81 99.99 100.00 100.00
1E+03 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.23 31.73 98.91 99.99 100.00 100.00
1E+04 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.00 0.26 32.46 98.92 99.99 100.00 100.00
Ardagh, et al. Supporting Information Page S32
Table S14. Raw data for Figure 7F, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 2.0,
ɣC-A of 0.5, δB-A of 2.0 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation endpoint (eV), Oscillation
frequency (Hz) -1.64 -1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04 0.16
1E-06
7.33E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.44E
-01
4.49E
-01
7.07E-
01
1.11E
+00
7.93E
-01
2.10E
-01
4.21E
-02
8.07E
-03
1.48E
-03
2.36E
-04
4.07E
-05
2.32E
-06
1E-05
7.33E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.44E
-01
4.49E
-01
7.07E-
01
1.11E
+00
7.93E
-01
2.10E
-01
4.21E
-02
8.07E
-03
1.48E
-03
2.37E
-04
4.19E
-05
2.34E
-06
1E-04
7.33E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.44E
-01
4.49E
-01
7.07E-
01
1.11E
+00
7.93E
-01
2.10E
-01
4.21E
-02
8.08E
-03
1.49E
-03
2.49E
-04
5.12E
-05
2.63E
-06
1E-03
7.34E-
01
1.19E
+00
1.56E
+00
1.23E
+00
5.44E
-01
4.50E
-01
7.09E-
01
1.11E
+00
7.94E
-01
2.11E
-01
4.22E
-02
8.13E
-03
1.51E
-03
3.38E
-04
1.43E
-04
6.13E
-06
1E-02
7.45E-
01
1.19E
+00
1.57E
+00
1.23E
+00
5.46E
-01
4.61E
-01
7.23E-
01
1.12E
+00
7.98E
-01
2.11E
-01
4.26E
-02
8.24E
-03
1.57E
-03
1.19E
-03
1.04E
-03
4.08E
-05
1E-01
8.55E-
01
1.27E
+00
1.61E
+00
1.22E
+00
5.62E
-01
5.56E
-01
8.52E-
01
1.23E
+00
8.39E
-01
2.17E
-01
4.28E
-02
8.42E
-03
2.23E
-03
9.92E
-03
1.01E
-02
3.93E
-04
1E+00
1.31E
+00
1.64E
+00
1.93E
+00
1.17E
+00
6.01E
-01
7.61E
-01
1.28E
+00
1.72E
+00
9.18E
-01
2.06E
-01
4.35E
-02
1.10E
-02
8.55E
-03
9.71E
-02
1.00E
-01
3.88E
-03
1E+01
1.37E
+00
1.82E
+00
2.18E
+00
1.22E
+00
6.53E
-01
8.06E
-01
1.37E
+00
1.63E
+00
8.05E
-01
2.16E
-01
7.02E
-02
3.89E
-02
6.04E
-02
4.39E
-01
4.64E
-01
3.89E
-02
1E+02
1.60E
+00
2.53E
+00
3.37E
+00
1.75E
+00
6.58E
-01
6.73E
-01
1.09E
+00
1.44E
+00
7.31E
-01
1.94E
-01
6.20E
-02
3.41E
-02
7.47E
-02
5.32E
-01
5.75E
-01
4.64E
-02
1E+03
3.60E
+00
9.18E
+00
1.49E
+01
4.22E
+00
7.08E
-01
6.24E
-01
1.05E
+00
1.41E
+00
7.26E
-01
1.94E
-01
6.17E
-02
3.37E
-02
7.86E
-02
5.45E
-01
5.95E
-01
4.76E
-02
1E+04
2.36E
+01
7.79E
+01
5.50E
+01
5.34E
+00
7.14E
-01
6.18E
-01
1.04E
+00
1.41E
+00
7.26E
-01
1.94E
-01
6.17E
-02
3.39E
-02
7.88E
-02
5.46E
-01
5.96E
-01
4.74E
-02
Ardagh, et al. Supporting Information Page S33
Table S15. Raw data for Figure 7G, heatmap for the selectivity of B ([=] mol %). Conditions: T of 150 oC, P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of
2.0, ɣC-A of 2.0, δB-A of 1.0 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation frequency (Hz), Oscillation endpoint (eV) -1.64 -1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04 0.16
1E-06
50.0
0
50.0
0
95.6
9
99.4
8
99.6
6
99.7
6
97.1
5
94.1
5
99.8
6
99.8
6
99.8
5
98.1
5
56.3
9
50.0
4
50.0
0
50.0
0
1E-05
50.0
0
50.0
0
95.6
9
99.4
8
99.6
6
99.7
6
97.1
5
94.1
6
99.8
6
99.8
6
99.8
5
98.1
5
56.4
0
50.0
4
50.0
0
50.0
0
1E-04
50.0
0
50.0
0
95.7
0
99.4
8
99.6
6
99.7
6
97.1
6
94.3
1
99.8
6
99.8
6
99.8
5
98.1
5
56.4
6
50.0
4
50.0
0
50.0
0
1E-03
50.0
0
50.0
0
95.7
2
99.4
8
99.6
6
99.7
6
97.1
9
95.4
8
99.8
6
99.8
6
99.8
5
98.1
5
56.4
9
50.0
4
50.0
0
49.9
7
1E-02
50.0
0
50.0
0
95.7
6
99.4
9
99.6
6
99.7
6
97.4
9
98.5
0
99.9
0
99.8
7
99.8
5
98.1
6
56.5
2
50.0
2
49.9
0
49.5
5
1E-01
50.0
0
50.0
0
95.8
4
99.5
1
99.6
7
99.7
6
98.7
1
99.7
8
99.9
7
99.9
1
99.8
6
98.2
0
56.4
9
49.7
3
48.7
9
45.7
1
1E+00
50.0
0
50.0
0
95.7
6
99.5
4
99.6
8
99.7
6
99.6
8
99.9
5
99.9
9
99.9
5
99.8
7
98.2
0
55.7
2
46.8
8
39.9
1
25.5
4
1E+01
50.0
0
50.0
0
95.7
7
99.4
9
99.7
0
99.7
7
99.8
4
99.9
5
99.9
2
99.8
8
99.8
6
98.1
6
48.8
4
29.7
1
13.8
0 4.42
1E+02
50.0
0
50.0
0
95.7
7
99.4
9
99.6
7
99.7
7
99.8
5
99.8
8
99.8
7
99.8
6
99.8
5
98.1
5
50.6
6
33.3
2
17.1
6 5.81
1E+03
50.0
0
50.0
0
95.7
7
99.4
9
99.6
7
99.7
7
99.8
6
99.8
6
99.8
6
99.8
6
99.8
5
98.1
5
50.6
6
33.2
9
17.1
6 5.81
1E+04
50.0
0
50.0
0
95.7
7
99.4
9
99.6
5
99.7
7
99.8
6
99.8
6
99.8
6
99.8
6
99.8
5
98.1
5
50.6
6
33.2
7
17.1
4 5.81
Ardagh, et al. Supporting Information Page S34
Table S16. Raw data for Figure 7H, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,
P of 100 bar, 1 % conversion of A. Parameters: ΔHovr of 0 kJ/mol, ⍺ of 0.6, β of 100 kJ/mol, ɣB-A of 2.0,
ɣC-A of 2.0, δB-A of 1.0 eV, and δC-A of 1.4 eV. Dynamics: various oscillation endpoints and frequency.
Fixed oscillation amplitude of 0.6 eV.
Oscillation frequency (Hz),
Oscillation endpoint (eV) -1.64 -1.52 -1.40 -1.28 -1.16 -1.04 -0.92 -0.80 -0.68 -0.56 -0.44 -0.32 -0.20 -0.08 0.04 0.16
1E-06
1.96E
-03
1.44E
-03
3.21E
-03
2.23E
-02
1.60E
-01
1.05E
+00
6.81E-
02
3.36E-
03
2.22E-
02
1.60E-
01
1.05E
+00
6.67E
-02
1.81E
-04
2.89E
-07
3.56E
-09
3.10E
-09
1E-05
1.96E
-03
1.43E
-03
3.22E
-03
2.23E
-02
1.60E
-01
1.05E
+00
6.81E-
02
3.37E-
03
2.22E-
02
1.60E-
01
1.05E
+00
6.67E
-02
1.82E
-04
3.13E
-07
3.14E
-08
3.10E
-08
1E-04
1.96E
-03
1.44E
-03
3.21E
-03
2.23E
-02
1.60E
-01
1.05E
+00
6.82E-
02
3.46E-
03
2.23E-
02
1.60E-
01
1.05E
+00
6.67E
-02
1.83E
-04
5.95E
-07
3.11E
-07
3.12E
-07
1E-03
1.98E
-03
1.44E
-03
3.24E
-03
2.24E
-02
1.60E
-01
1.05E
+00
6.91E-
02
4.36E-
03
2.32E-
02
1.61E-
01
1.05E
+00
6.67E
-02
1.82E
-04
1.54E
-06
3.12E
-06
3.10E
-06
1E-02
1.97E
-03
1.45E
-03
3.23E
-03
2.25E
-02
1.60E
-01
1.05E
+00
7.77E-
02
1.33E-
02
3.23E-
02
1.70E-
01
1.06E
+00
6.72E
-02
2.08E
-04
3.15E
-05
3.13E
-05
3.11E
-05
1E-01
1.69E
-03
1.17E
-03
2.96E
-03
2.26E
-02
1.62E
-01
1.06E
+00
1.58E-
01
1.03E-
01
1.22E-
01
2.60E-
01
1.14E
+00
6.81E
-02
4.93E
-04
3.10E
-04
3.13E
-04
3.13E
-04
1E+00
7.19E
-04
1.81E
-04
2.02E
-03
2.01E
-02
1.61E
-01
1.07E
+00
9.55E-
01
9.99E-
01
1.02E
+00
1.16E
+00
1.96E
+00
6.94E
-02
3.26E
-03
3.13E
-03
3.13E
-03
3.10E
-03
1E+01
8.40E
-04
2.89E
-04
9.21E
-04
1.03E
-02
1.33E
-01
1.09E
+00
5.49E
+00
9.94E
+00
1.00E
+01
1.02E
+01
1.00E
+01
8.63E
-02
3.13E
-02
3.11E
-02
3.12E
-02
3.12E
-02
1E+02
8.40E
-04
2.89E
-04
7.38E
-04
1.00E
-02
1.39E
-01
1.11E
+00
8.06E
+00
4.56E
+01
9.88E
+01
1.00E
+02
4.15E
+01
8.88E
-02
2.55E
-02
2.54E
-02
2.53E
-02
2.53E
-02
1E+03
8.40E
-04
2.89E
-04
7.38E
-04
1.02E
-02
1.37E
-01
1.13E
+00
8.40E
+00
5.91E
+01
3.55E
+02
9.57E
+02
5.31E
+01
8.91E
-02
2.55E
-02
2.51E
-02
2.52E
-02
2.52E
-02
1E+04
8.40E
-04
2.89E
-04
7.38E
-04
1.02E
-02
1.21E
-01
1.13E
+00
8.44E
+00
6.07E
+01
4.29E
+02
2.69E
+03
5.45E
+01
8.91E
-02
2.55E
-02
2.51E
-02
2.52E
-02
2.51E
-02
Ardagh, et al. Supporting Information Page S35
Section S5. Derivation of Linear Scaling Relationship Parameters
1. Nomenclature:
a. General reactant (R) and product (P)
b. Manuscript specific reactant (A) and products (B and C)
c. Note: this derivation is valid for any reaction system where two products are referenced
to one other reactant or product
2. ɣ definition
𝑑𝐵𝐸𝑃
𝑑𝐵𝐸𝑅≡ 𝛾𝑃−𝑅 (S1)
3. δ definition
In words: when BER = δP-R, BEP = δP-R + ΔHP-R
In equations: 𝑑𝐵𝐸𝑃
𝑑𝐵𝐸𝑅≡ 𝛾𝑃−𝑅
Integrating the definition of ɣ: 𝐵𝐸𝑃 = 𝛾𝑃−𝑅𝐵𝐸𝑅 + 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (S2)
Using the definition of δ: 𝛿𝑃−𝑅 + 𝛥𝐻𝑃−𝑅 = 𝛾𝑃−𝑅𝛿𝑃−𝑅 + 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 (S3)
Rearranging: 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 = (1 − 𝛾𝑃−𝑅)𝛿𝑃−𝑅 + 𝛥𝐻𝑃−𝑅
Therefore: 𝐵𝐸𝑃 = 𝛾𝑃−𝑅𝐵𝐸𝑅 + (1 − 𝛾𝑃−𝑅)𝛿𝑃−𝑅 + 𝛥𝐻𝑃−𝑅 (S4)
4. δB-C derivation
We can substitute in symbols for our specific reactant (A) and products (B and C) to complete the
derivation.
For product B: 𝐵𝐸𝐵 = 𝛾𝐵−𝐴𝐵𝐸𝐴 + (1 − 𝛾𝐵−𝐴)𝛿𝐵−𝐴 + 𝛥𝐻𝐵−𝐴 (S5)
For product C: 𝐵𝐸𝐶 = 𝛾𝐶−𝐴𝐵𝐸𝐴 + (1 − 𝛾𝐶−𝐴)𝛿𝐶−𝐴 + 𝛥𝐻𝐶−𝐴 (S6)
In words: when BEC = δB-C, BEB = δB-C + ΔHB-C
Plug in: 𝛾𝐵−𝐴𝐵𝐸𝐴 + (1 − 𝛾𝐵−𝐴)𝛿𝐵−𝐴 + 𝛥𝐻𝐵−𝐴 − 𝛥𝐻𝐵−𝐶 = 𝛾𝐶−𝐴𝐵𝐸𝐴 + (1 − 𝛾𝐶−𝐴)𝛿𝐶−𝐴 + 𝛥𝐻𝐶−𝐴 (S7)
Rearranging: (𝛾𝐵−𝐴 − 𝛾𝐶−𝐴) 𝐵𝐸𝐴 = (1 − 𝛾𝐶−𝐴)𝛿𝐶−𝐴 − (1 − 𝛾𝐵−𝐴)𝛿𝐵−𝐴 + 𝛥𝐻𝐶−𝐴 − 𝛥𝐻𝐵−𝐴 + 𝛥𝐻𝐵−𝐶
Simplifying: 𝐵𝐸𝐴 = (1−𝛾𝐶−𝐴)𝛿𝐶−𝐴−(1−𝛾𝐵−𝐴)𝛿𝐵−𝐴
𝛾𝐵−𝐴−𝛾𝐶−𝐴 (S8)
5. Final answer
At δB-C: 𝑩𝑬𝑨 = (𝟏−𝜸𝑪−𝑨)𝜹𝑪−𝑨−(𝟏−𝜸𝑩−𝑨)𝜹𝑩−𝑨
𝜸𝑩−𝑨−𝜸𝑪−𝑨
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