Catalytic Resonance Theory: Parallel Reaction Pathway Control · Catalytic Resonance Theory:...

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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http://doi.org/10.26434/chemrxiv.10271090.v1

https://chemrxiv.org/authors/Omar_Abdelrahman/6419336

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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


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


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[-

]


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]

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


Oscill

atio

n F

reque

ncy

[Hz]

104

103

102

101

1

10-1

10-2

10-3

10-4

10-5

10-6


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]



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]



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]


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]


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]


102

104

1

10-2

10-4

10-6

0 10 20 30 40 50 60 70 80 90 100


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]


104

102

1

10-2

10-4

10-6

102101110-110-2


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]


102

104

1

10-2

10-4

10-6

0 10 20 30 40 50 60 70 80 90 100


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]


104

102

1

10-2

10-4

10-6

102101110-110-2


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]


102

104

1

10-2

10-4

10-6

0 10 20 30 40 50 60 70 80 90 100


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]


104

102

1

10-2

10-4

10-6

102101110-110-2


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

mailto:[email protected]


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


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;


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


function tf = targetfun(SV,Cf,k,T,x0,C) tspan = [0 5.0e100]; % s


[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;


% 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;


alpha = 0.6; % unitless beta = 100.0e3; % J/gmol


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


% 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) 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)


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];




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];


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


% 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);


alpha(1:2) = 0.6; % unitless beta(1:2) = 100.0e3; % J/gmol


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;


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


% 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


xsv = [xsv;x];




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) 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)


xsv = [xsv;x]; tsvm = [tsvm;t + tsv(end)];

xsvm = [xsvm;x];

else


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


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];


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


2752 LU decompositions

8256 solutions of linear systems Elapsed time is 0.228154 seconds.

Stats for ode23t: 699 successful steps

5 failed attempts


3 partial derivatives 243 LU decompositions

1019 solutions of linear systems


Stats for ode23tb:

543 successful steps 6 failed attempts





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.


Trial S2b. Solver Performance for Dynamic Catalysis

Stats for ode15s:





Elapsed time is 9.699912 seconds

Stats for ode23s:


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


1 partial derivatives 34 LU decompositions

182 solutions of linear systems


Stats for ode23tb:






ODE23tb was used throughout the manuscript for dynamic catalysis simulation because it required few

steps and was the fastest to converge.


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.


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


Table S2. Raw data for Figure 3D, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,


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.

04

-

0.9

8

-

0.9

2

-

0.8

6

-

0.8

0

-

0.7

4

-

0.

68

-

0.

62

-

0.

56

-

0.5

0

-

0.4

4

-

0.3

8

-

0.3

2

-

0.2

6

-

0.2

0

-

0.

14

-

0.

08

-

0.

02

0.

04

0.

10

0.

16

1.00E-06

7.3

3E

-

01

9.8

8E

-

01

1.1

9E

+0

0

1.4

2E

+0

0

1.5

6E

+0

0

1.5

8E

+0

0

1.2

3E

+0

0

8.0

5E

-01

5.

44

E-

01

4.

41

E-

01

4.

49

E-

01

5.4

3E

-01

7.0

7E

-01

9.2

1E

-01

1.1

1E

+0

0

1.0

9E

+0

0

7.

93

E-

01

4.

39

E-

01

2.

10

E-

01

9.5

1E

-02

4.2

1E

-02

1.8

5E

-02

8.2

2E

-03

4.2

0E

-03

2.6

5E

-03

1.

21

E-

03

4.

48

E-

04

1.

23

E-

04

1.

50

E-

05

8.

01

E-

07

3.

37

E-

08

3.16E-06

7.3

3E

-

01

9.5

1E

-

01

1.1

9E

+0

0

1.4

2E

+0

0

1.5

6E

+0

0

1.5

8E

+0

0

1.2

3E

+0

0

8.0

5E

-01

5.

44

E-

01

4.

41

E-

01

4.

49

E-

01

5.4

3E

-01

7.0

7E

-01

9.2

1E

-01

1.1

1E

+0

0

1.0

9E

+0

0

7.

93

E-

01

4.

39

E-

01

2.

10

E-

01

9.5

1E

-02

4.2

1E

-02

1.8

5E

-02

8.2

2E

-03

4.2

1E

-03

2.6

6E

-03

1.

21

E-

03

4.

49

E-

04

1.

23

E-

04

1.

51

E-

05

7.

86

E-

07

4.

10

E-

08

1.00E-05

7.3

3E

-

01

9.6

6E

-

01

1.1

9E

+0

0

1.4

2E

+0

0

1.5

6E

+0

0

1.5

8E

+0

0

1.2

3E

+0

0

8.0

5E

-01

5.

44

E-

01

4.

41

E-

01

4.

49

E-

01

5.4

3E

-01

7.0

7E

-01

9.2

1E

-01

1.1

1E

+0

0

1.0

9E

+0

0

7.

93

E-

01

4.

39

E-

01

2.

10

E-

01

9.5

1E

-02

4.2

1E

-02

1.8

5E

-02

8.2

3E

-03

4.2

1E

-03

2.6

6E

-03

1.

21

E-

03

4.

49

E-

04

1.

23

E-

04

1.

52

E-

05

8.

23

E-

07

6.

18

E-

08

3.16E-05

7.3

3E

-

01

9.5

1E

-

01

1.1

9E

+0

0

1.4

2E

+0

0

1.5

6E

+0

0

1.5

8E

+0

0

1.2

3E

+0

0

8.0

5E

-01

5.

44

E-

01

4.

41

E-

01

4.

49

E-

01

5.4

3E

-01

7.0

7E

-01

9.2

1E

-01

1.1

1E

+0

0

1.0

9E

+0

0

7.

93

E-

01

4.

39

E-

01

2.

10

E-

01

9.5

1E

-02

4.2

1E

-02

1.8

5E

-02

8.2

5E

-03

4.2

3E

-03

2.6

6E

-03

1.

21

E-

03

4.

50

E-

04

1.

24

E-

04

1.

51

E-

05

9.

00

E-

07

1.

29

E-

07

1.00E-04

7.3

3E

-

01

9.5

1E

-

01

1.1

9E

+0

0

1.4

2E

+0

0

1.5

6E

+0

0

1.5

8E

+0

0

1.2

3E

+0

0

8.0

5E

-01

5.

44

E-

01

4.

41

E-

01

4.

49

E-

01

5.4

3E

-01

7.0

8E

-01

9.2

1E

-01

1.1

1E

+0

0

1.0

9E

+0

0

7.

93

E-

01

4.

39

E-

01

2.

10

E-

01

9.5

2E

-02

4.2

2E

-02

1.8

6E

-02

8.3

3E

-03

4.2

9E

-03

2.6

8E

-03

1.

21

E-

03

4.

52

E-

04

1.

25

E-

04

1.

54

E-

05

1.

09

E-

06

9.

18

E-

07

3.16E-04

7.3

3E

-

01

9.5

2E

-

01

1.1

9E

+0

0

1.4

2E

+0

0

1.5

6E

+0

0

1.5

8E

+0

0

1.2

3E

+0

0

8.0

5E

-01

5.

44

E-

01

4.

41

E-

01

4.

49

E-

01

5.4

4E

-01

7.0

8E

-01

9.2

2E

-01

1.1

1E

+0

0

1.1

0E

+0

0

7.

94

E-

01

4.

39

E-

01

2.

11

E-

01

9.5

4E

-02

4.2

4E

-02

1.8

9E

-02

8.5

6E

-03

4.4

8E

-03

2.7

4E

-03

1.

22

E-

03

4.

55

E-

04

1.

27

E-

04

1.

62

E-

05

1.

80

E-

06

1.

01

E-

06

1.00E-03

7.3

4E

-

01

9.5

2E

-

01

1.1

9E

+0

0

1.4

2E

+0

0

1.5

6E

+0

0

1.5

8E

+0

0

1.2

3E

+0

0

8.0

5E

-01

5.

44

E-

01

4.

42

E-

01

4.

50

E-

01

5.4

5E

-01

7.0

9E

-01

9.2

3E

-01

1.1

1E

+0

0

1.1

0E

+0

0

7.

94

E-

01

4.

40

E-

01

2.

11

E-

01

9.6

1E

-02

4.3

2E

-02

1.9

6E

-02

9.2

8E

-03

5.0

6E

-03

2.9

1E

-03

1.

24

E-

03

4.

63

E-

04

1.

29

E-

04

1.

83

E-

05

3.

91

E-

06

3.

13

E-

06

3.16E-03

7.3

7E

-

01

9.5

4E

-

01

1.1

9E

+0

0

1.4

2E

+0

0

1.5

6E

+0

0

1.5

9E

+0

0

1.2

3E

+0

0

8.0

5E

-01

5.

45

E-

01

4.

43

E-

01

4.

53

E-

01

5.4

8E

-01

7.1

2E

-01

9.2

6E

-01

1.1

2E

+0

0

1.1

0E

+0

0

7.

95

E-

01

4.

41

E-

01

2.

13

E-

01

9.8

3E

-02

4.5

5E

-02

2.1

9E

-02

1.1

5E

-02

6.8

3E

-03

3.4

2E

-03

1.

32

E-

03

4.

67

E-

04

1.

32

E-

04

2.

52

E-

05

8.

66

E-

05

9.

94

E-

06

1.00E-02

7.4

5E

-

01

9.6

1E

-

01

1.1

9E

+0

0

1.4

2E

+0

0

1.5

7E

+0

0

1.5

9E

+0

0

1.2

3E

+0

0

8.0

4E

-01

5.

46

E-

01

4.

48

E-

01

4.

61

E-

01

5.5

8E

-01

7.2

3E

-01

9.3

7E

-01

1.1

3E

+0

0

1.1

0E

+0

0

7.

99

E-

01

4.

44

E-

01

2.

18

E-

01

1.0

5E

-01

5.2

7E

-02

2.8

9E

-02

1.8

3E

-02

1.2

4E

-02

4.9

8E

-03

1.

46

E-

03

4.

79

E-

04

1.

55

E-

04

4.

66

E-

05

3.

18

E-

05

3.

13

E-

05

3.16E-02

7.7

1E

-

01

9.8

6E

-

01

1.2

1E

+0

0

1.4

4E

+0

0

1.5

8E

+0

0

1.5

9E

+0

0

1.2

2E

+0

0

8.0

2E

-01

5.

50

E-

01

4.

62

E-

01

4.

85

E-

01

5.8

8E

-01

7.5

6E

-01

9.6

9E

-01

1.1

5E

+0

0

1.1

2E

+0

0

8.

09

E-

01

4.

53

E-

01

2.

35

E-

01

1.2

7E

-01

7.4

5E

-02

5.0

6E

-02

3.9

6E

-02

2.9

8E

-02

9.8

6E

-03

1.

94

E-

03

5.

95

E-

04

2.

24

E-

04

1.

14

E-

04

9.

96

E-

05

9.

83

E-

05

1.00E-01

8.5

5E

-

01

1.0

5E

+0

0

1.2

7E

+0

0

1.4

9E

+0

0

1.6

1E

+0

0

1.6

0E

+0

0

1.2

2E

+0

0

7.9

2E

-01

5.

62

E-

01

5.

05

E-

01

5.

56

E-

01

6.7

6E

-01

8.5

2E

-01

1.0

7E

+0

0

1.2

4E

+0

0

1.1

8E

+0

0

8.

43

E-

01

4.

80

E-

01

2.

84

E-

01

1.9

1E

-01

1.4

2E

-01

1.1

9E

-01

1.0

7E

-01

8.5

0E

-02

2.5

5E

-02

3.

95

E-

03

9.

00

E-

04

2.

23

E-

04

1.

08

E-

04

9.

94

E-

05

9.

86

E-

05

3.16E-01

1.0

7E

+0

0

1.2

3E

+0

0

1.4

2E

+0

0

1.6

2E

+0

0

1.7

2E

+0

0

1.6

3E

+0

0

1.2

0E

+0

0

7.7

3E

-01

5.

88

E-

01

5.

81

E-

01

6.

79

E-

01

8.4

4E

-01

1.0

6E

+0

0

1.2

9E

+0

0

1.4

5E

+0

0

1.3

3E

+0

0

9.

11

E-

01

5.

36

E-

01

4.

28

E-

01

3.9

1E

-01

3.5

5E

-01

3.3

4E

-01

3.1

9E

-01

2.5

9E

-01

7.4

9E

-02

8.

26

E-

03

1.

90

E-

03

2.

28

E-

04

9.

98

E-

05

9.

92

E-

05

9.

88

E-

05

1.00E+00

1.3

1E

+0

0

1.4

4E

+0

0

1.6

4E

+0

0

1.8

6E

+0

0

1.9

3E

+0

0

1.7

0E

+0

0

1.1

7E

+0

0

7.5

8E

-01

6.

01

E-

01

6.

25

E-

01

7.

61

E-

01

9.9

0E

-01

1.2

8E

+0

0

1.5

8E

+0

0

1.7

3E

+0

0

1.4

8E

+0

0

9.

49

E-

01

6.

40

E-

01

7.

89

E-

01

9.9

0E

-01

1.0

2E

+0

0

1.0

1E

+0

0

9.9

1E

-01

8.1

1E

-01

2.3

1E

-01

2.

51

E-

02

4.

98

E-

03

2.

18

E-

04

1.

04

E-

04

9.

90

E-

05

9.

86

E-

05

3.16E+00

1.3

3E

+0

0

1.5

0E

+0

0

1.7

4E

+0

0

2.0

0E

+0

0

2.0

7E

+0

0

1.7

5E

+0

0

1.1

8E

+0

0

7.6

5E

-01

6.

12

E-

01

6.

32

E-

01

8.

06

E-

01

1.0

3E

+0

0

1.3

4E

+0

0

1.6

7E

+0

0

1.7

9E

+0

0

1.4

5E

+0

0

9.

08

E-

01

6.

65

E-

01

9.

92

E-

01

1.7

8E

+0

0

2.4

7E

+0

0

2.8

5E

+0

0

3.0

0E

+0

0

2.5

3E

+0

0

7.2

3E

-01

7.

48

E-

02

1.

42

E-

02

2.

01

E-

04

9.

80

E-

05

9.

88

E-

05

9.

84

E-

05

1.00E+01

1.3

6E

+0

0

1.5

3E

+0

0

1.8

2E

+0

0

2.1

4E

+0

0

2.2

0E

+0

0

1.8

7E

+0

0

1.2

5E

+0

0

7.9

9E

-01

6.

85

E-

01

6.

97

E-

01

8.

63

E-

01

1.0

5E

+0

0

1.3

7E

+0

0

1.6

1E

+0

0

1.6

6E

+0

0

1.3

6E

+0

0

8.

48

E-

01

5.

71

E-

01

7.

41

E-

01

1.6

1E

+0

0

3.1

8E

+0

0

4.9

2E

+0

0

6.3

9E

+0

0

6.4

4E

+0

0

2.0

0E

+0

0

1.

38

E-

01

3.

78

E-

02

2.

09

E-

04

1.

04

E-

04

1.

04

E-

04

1.

04

E-

04


3.16E+01

1.4

1E

+0

0

1.6

6E

+0

0

1.9

8E

+0

0

2.3

5E

+0

0

2.4

7E

+0

0

2.0

7E

+0

0

1.3

9E

+0

0

8.4

5E

-01

6.

56

E-

01

6.

50

E-

01

7.

67

E-

01

9.6

3E

-01

1.1

8E

+0

0

1.4

5E

+0

0

1.5

2E

+0

0

1.2

5E

+0

0

7.

94

E-

01

4.

58

E-

01

3.

73

E-

01

8.3

9E

-01

2.3

0E

+0

0

5.6

4E

+0

0

1.0

1E

+0

1

1.5

0E

+0

1

3.6

8E

+0

0

2.

13

E-

01

3.

54

E-

02

2.

82

E-

04

1.

40

E-

04

1.

39

E-

04

1.

40

E-

04

1.00E+02

1.6

0E

+0

0

1.9

6E

+0

0

2.5

3E

+0

0

3.1

2E

+0

0

3.3

8E

+0

0

2.8

0E

+0

0

1.7

5E

+0

0

9.9

5E

-01

6.

74

E-

01

6.

01

E-

01

6.

92

E-

01

8.7

1E

-01

1.1

2E

+0

0

1.3

5E

+0

0

1.4

7E

+0

0

1.2

0E

+0

0

7.

55

E-

01

4.

05

E-

01

3.

35

E-

01

4.8

2E

-01

1.8

7E

+0

0

7.9

4E

+0

0

2.4

3E

+0

1

4.2

0E

+0

1

5.0

5E

+0

0

2.

34

E-

01

3.

39

E-

02

2.

79

E-

04

2.

53

E-

04

2.

51

E-

04

2.

53

E-

04

3.16E+02

2.0

6E

+0

0

2.9

1E

+0

0

4.1

7E

+0

0

5.5

7E

+0

0

6.2

3E

+0

0

5.1

1E

+0

0

2.8

3E

+0

0

1.2

8E

+0

0

6.

80

E-

01

5.

57

E-

01

6.

39

E-

01

8.1

4E

-01

1.0

6E

+0

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


Table S3. Raw data for Figure 3E, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,


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


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


Table S5. Raw data for Figure 5B, heatmap for the selectivity of B ([=] mol %). Conditions: T of 150 oC,


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


Table S6. Raw data for Figure 5C, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,


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


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


Table S7. Raw data for Figure 6C, heatmap for the selectivity of B ([=] mol %). Conditions: T of 150 oC,




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






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


Table S9. Raw data for Figure 6E, heatmap for the selectivity of B ([=] mol %). Conditions: T of 150 oC,




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


Table S10. Raw data for Figure 6F, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,




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


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.


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






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


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



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


Table S14. Raw data for Figure 7F, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,




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


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



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


Table S16. Raw data for Figure 7H, heatmap for the consumption of A ([=] 1/s). Conditions: T of 150 oC,




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


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

download fileview on ChemRxivSupporting_Information_Parallel_Rxn_Dynamics.pdf (895.86 KiB)



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