NEW DOMAINS IN AUTOMATIC MECHANISM GENERATION

A Dissertation Presented

By

Belinda Leigh Slakman

To

The Department of Chemical Engineering

In partial fulfillment of the requirementsFor the degree of

Doctor of Philosophy

In the Field of

Chemical Engineering

Northeastern UniversityBoston, Massachusetts

August 2017

ii

Abstract

Deeper understanding of complex chemical systems can be aided by detailed kinetic mod-

eling, in which processes are broken down into their individual elementary reactions. An

important industrial goal is to move from postdictive to predictive modeling, where new

chemical vapor deposition (CVD) precursors, for example, can be tested for efficiency

without performing tedious and expensive experiments. Some of these microkinetic mod-

els may contain hundreds of reacting chemical species, and thousands of reactions; thus,

it is desirable to build the models automatically with a computer to speed up model gen-

eration and reduce errors. Automatic mechanism generation is now commonly used for

applications such as combustion, but extension to other systems presents challenges. This

dissertation describes the extension of the Reaction Mechanism Generator (RMG) soft-

ware to two less-studied chemical systems: the oxidation of liquid fuels and the gas-phase

decomposition of silicon hydrides.

To model liquid fuel oxidation, the software’s existing gas-phase thermodynamics

and kinetics databases needed to be supplemented, or corrected to account for solvated re-

actions. Existing correlations and data for solvation thermodynamics and diffusion were

improved and added to RMG. Solvation kinetics data were obtained by developing a ma-

chine learning algorithm to systematically predict the change in barrier height when going

from gas-phase to various solvents. The algorithm was trained with quantum chemistry cal-

culations on a simple set of hydrogen abstraction and intra-hydrogen migration reactions.

The method was used to change the rates in a model for the oxidation of dodecane/methyl

oleate blends, showing a marked change in the models prediction for the fuel’s induction

period.

iii

The second part of this dissertation involves gas-phase silicon hydride decomposi-

tion, for the application to CVD. Thermodynamic and kinetic data were added from liter-

ature to RMG’s database. Specifically focusing on radical reaction types, additional data

were calculated via quantum chemistry for hydrogen bond increment (HBI) values of sili-

con hydride species, as well as hydrogen abstraction reaction rates. A SiH4 decomposition

model was built with the updated RMG and compared to experiment, with good agreement.

This work provides new insight on both of these chemical systems and contributes

new calculated thermodynamics and kinetics parameters. Importantly, it also guides future

developers in adding capabilities for new phases or elements to mechanism generation

software.

iv

ACKNOWLEDGEMENTS

My dissertation work would not have been possible without the support of many

people, near and far.

Thank you to my advisor, Dr. Richard West, for supporting me these past five years.

Your intelligence and insights have been invaluable, but at the same time, you have always

let me run with the ideas I have had and let me make mistakes on my own- the marks of

a great advisor. Thanks for giving me the opportunities to travel and present my research,

teach, and mentor. I also want to thank my other committee members: Dr. Anand Asthagiri,

Dr. Carolyn Lee-Parsons, Dr. Mary Jo Ondrechen, and Dr. Harsono Simka for your time and

helpful discussions over the years. I would especially like to thank Harsono for mentoring

me throughout two internships at Intel Corporation and beyond, and for all of your personal

and professional advice.

I want to thank my other colleagues at Intel, particularly Karson Knutson, Dr. Har-

inath Reddy, and other members of the TCAD-IPAG group. I learned a lot from all of you,

and thanks for giving me the opportunity to come back and work with you a second time.

This dissertation would surely not have been possible without the hard work of past

and present RMG developers in the Green Group at MIT. I would especially like to thank

Dr. William Green for his insights over the years, and Dr. Amrit Jalan and Yunsie Chung

for helpful discussions on solvation in RMG.

This work could not have been completed without the help of Research Comput-

ing at Northeastern University, especially Nilay Roy, who helped maintain the Discovery

cluster.

v

I want to thank Michael Li, and my instructors and colleagues at The Data Incuba-

tor, for teaching me about data science, and providing guidance and friendship during the

spring of 2017. I would also like to acknowledge Lilian Tsang and the organizers of the

Combustion Energy Frontier Research Center summer school, which I attended in 2013

and 2014.

I would like to thank the current and former Northeastern Department of Chemical

Engineering staff for their support: Jessica, Brandon, Francesca, Kelly, Sarah and espe-

cially Pat and Rob. I also have to thank my 11 classmates and friends who started this

journey with me: Chris, Dan, Hunter, Luting, Mark, Negar, Oljora, Sue, Sydney, Tanya

and Taylor.

To Dr. Pierre Bhoorasingh and Dr. Fariba Seyedzadeh Khanshan: I couldn’t have

done this work without your guidance, good example, and levity, and thank you for the

friendship and advice you continue to provide. Thank you to Jason for being our “scientist”

and for all of your research assistance. I’d also like to thank Nate for letting me vent, not

just about kinetics. I also want to thank current West group members Yawei, Mike, Rasha

and Krishna and past members Jacob, Victor, Elliot, Claudia, and Drew for your useful

discussions and companionship; it’s been a pleasure to work with all of you.

I have to thank all of my friends, in Boston and beyond. In particular, I want to

thank Amanda for being my roommate for 4 years, Ina for sharing in the best friendship

that has ever come from Craigslist (#18westwood), Katarina for reminding me that my

Ph.D. project is not the only measure of my worth, and Jennifer for judgment-free support

of my decisions.

Last, and most importantly, I have to thank my family, who has patiently supported

me for the past 28 years. Mom, Dad, Jordan and Casey, thank you for standing with me as

I take this next step. I am lucky to have such love in my life.

vi

Contents

1 Introduction 1

1.1 Automatic mechanism generation . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Reaction Mechanism Generator (RMG) . . . . . . . . . . . . . . . 6

1.2 Parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.1 Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.2 Kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

1.2.3 Transition state geometries . . . . . . . . . . . . . . . . . . . . . . 13

1.3 Machine learning with decision trees . . . . . . . . . . . . . . . . . . . . . 13

1.3.1 Decision trees in chemistry and biology . . . . . . . . . . . . . . . 14

1.4 Dissertation overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2 Automatic calculation of solvation thermodynamics 17

2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2.1.1 Explicit thermodynamic calculations . . . . . . . . . . . . . . . . . 18

2.1.2 Estimation techniques . . . . . . . . . . . . . . . . . . . . . . . . 18

2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

2.2.1 Adaptation of solvation thermodynamics from RMG-Java . . . . . 22

2.2.2 New additions in RMG-Py . . . . . . . . . . . . . . . . . . . . . . 23

2.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27

2.3.1 Estimation of solute descriptors . . . . . . . . . . . . . . . . . . . 27

2.3.2 Calculation of solvation thermodynamics . . . . . . . . . . . . . . 28

vii

2.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

2.5.1 Temperature dependence of solvation thermodynamics . . . . . . . 30

2.5.2 Calculation of solvation thermodynamics for lone pair species . . . 30

2.5.3 Improved benchmarking of group additivity values . . . . . . . . . 30

2.5.4 Expansion and enhancement of solvents . . . . . . . . . . . . . . . 31

3 Implementing kinetic solvent effects in automatic mechanism generation 32

3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

3.1.1 Experimental techniques for determining reaction rates in liquids . 34

3.1.2 Computational chemistry . . . . . . . . . . . . . . . . . . . . . . . 35

3.1.3 Kinetic solvent effects within reaction families . . . . . . . . . . . 38

3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2.1 Diffusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

3.2.2 Intrinsic kinetics . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

3.2.3 Fuel oxidation model modification . . . . . . . . . . . . . . . . . . 54

3.2.4 Reactor simulations . . . . . . . . . . . . . . . . . . . . . . . . . . 54

3.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

3.3.1 Solvation kinetics trends . . . . . . . . . . . . . . . . . . . . . . . 55

3.3.2 New reactor simulations . . . . . . . . . . . . . . . . . . . . . . . 58

3.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.5 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

3.5.1 On-the-fly estimation of solvation kinetics . . . . . . . . . . . . . . 61

3.5.2 Benchmarking the estimates . . . . . . . . . . . . . . . . . . . . . 62

3.5.3 Check thermodynamic consistency with LSERs . . . . . . . . . . . 62

3.5.4 Data-driven approaches . . . . . . . . . . . . . . . . . . . . . . . . 63

viii

4 Automated silicon hydride mechanism generation 66

4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67

4.1.1 Experimental work on SiH4 chemistry . . . . . . . . . . . . . . . . 67

4.1.2 Detailed mechanisms for SiH4 CVD . . . . . . . . . . . . . . . . . 68

4.1.3 Importance of radical chemistry in silicon hydride thermal decom-

position . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

4.2.1 RMG source code . . . . . . . . . . . . . . . . . . . . . . . . . . 71

4.2.2 Updating RMG’s database . . . . . . . . . . . . . . . . . . . . . . 71

4.2.3 RMG model generation . . . . . . . . . . . . . . . . . . . . . . . . 74

4.2.4 Reactor modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

4.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

4.3.1 Kinetics of hydrogen abstraction reactions . . . . . . . . . . . . . . 75

4.3.2 Calculated thermodynamic data . . . . . . . . . . . . . . . . . . . 76

4.3.3 RMG generated mechanisms . . . . . . . . . . . . . . . . . . . . . 79

4.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

4.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

4.6 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88

4.6.1 Expansion of thermodynamic libraries for radical species . . . . . . 88

4.6.2 Calculation of rates . . . . . . . . . . . . . . . . . . . . . . . . . . 89

4.6.3 Sensitivity analysis . . . . . . . . . . . . . . . . . . . . . . . . . . 90

4.6.4 Surface chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

5 Conclusion 92

5.1 Liquid-phase fuel oxidation . . . . . . . . . . . . . . . . . . . . . . . . . . 92

5.2 Thermal decomposition of silicon hydrides . . . . . . . . . . . . . . . . . 94

5.3 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

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References 96

A Supplementary Info for Solvation Kinetics 114

A.1 Solvation kinetics molecular structure group trees and values . . . . . . . . 114

A.2 Script for modifying Chemkin files for solvation kinetics corrections . . . . 116

A.3 Modified Cantera input file for n-dodecane/ methyl oleate oxidation . . . . 116

A.4 Cantera script to simulate liquid fuel oxidation reactor . . . . . . . . . . . . 116

A.5 Code for automatic tree building . . . . . . . . . . . . . . . . . . . . . . . 116

B Supplementary Info for Silicon Hydrides 117

B.1 Geometries of reactants and transition states for hydrogen abstraction reac-

tions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

B.2 Geometries of silicon hydride species . . . . . . . . . . . . . . . . . . . . 119

B.3 Largest SiH4 decomposition mechanism . . . . . . . . . . . . . . . . . . . 122

B.4 Cantera script for simulating reactor . . . . . . . . . . . . . . . . . . . . . 122

B.5 Code for residence time comparison . . . . . . . . . . . . . . . . . . . . . 122

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List of Figures

1.1 Rules for the generation of an elementary reaction network in GRACE . . . 3

1.2 Lumped approach for the primary oxidation of n-pentane in MAMOX . . . 4

1.3 Template and recipe for the hydrogen abstraction reaction family . . . . . . 7

1.4 Part of hydrogen abstraction hierarchical tree in RMG . . . . . . . . . . . . 7

2.1 Examples of molecular structure fragments . . . . . . . . . . . . . . . . . 20

2.2 Entry in the solute group database . . . . . . . . . . . . . . . . . . . . . . 22

2.3 Molecular structure fragments in g-decalactone . . . . . . . . . . . . . . . 27

2.4 Comparison of calculated and experimental values for ∆Hsolv and ∆Gsolv . 28

3.1 Example of a potential energy surface . . . . . . . . . . . . . . . . . . . . 33

3.2 Concept of peroxyl radical clock . . . . . . . . . . . . . . . . . . . . . . . 35

3.3 Comparison between continuum and hybrid implicit/explicit solvation models 36

3.4 The solvent effect on hydrogen abstraction from α-tocopherol . . . . . . . 38

3.5 Example of the PCET mechanism . . . . . . . . . . . . . . . . . . . . . . 41

3.6 β-scission rates correlate with Dimroth-Reichardt parameter ET . . . . . . 43

3.7 Diels-Alder reaction of cyclopentadiene and (-)-menthyl acrylate . . . . . . 44

3.8 Acetylation mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

3.10 Possible mechanisms in the hydrolysis of formamide . . . . . . . . . . . . 48

3.11 ∆EA for the reaction XH + ·OH←→ ·X + H2O . . . . . . . . . . . . . . . 56

3.12 Illustration of the first few levels of group trees for hydrogen abstraction . . 57

xi

3.13 Comparison of experiments, original model and updated model with ki-

netic solvent effects for 0% methyl oleate. . . . . . . . . . . . . . . . . . . 59

3.14 Comparison of experiments, original model and updated model with ki-

netic solvent effects for 5% methyl oleate. . . . . . . . . . . . . . . . . . . 59

3.15 Comparison of experiments, original model and updated model with ki-

netic solvent effects for 10% methyl oleate. . . . . . . . . . . . . . . . . . 60

3.16 Comparison of experiments, original model and updated model with ki-

netic solvent effects for 30% methyl oleate. . . . . . . . . . . . . . . . . . 60

3.17 Algorithm for obtaining solvation energy estimation values from a large

transition state dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

4.1 G3//B3LYP calculations of ∆fH◦298 compared to high level calculations . . 77

4.2 Group additivity calculations of ∆fH◦298 and HBI corrections compared to

high level calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

4.3 Simulation results compared with SiH4 thermal decomposition experiment . 81

4.4 SiH4 concentration vs. temperature at different residence times . . . . . . . 82

4.5 Simulation results for full pressure dependent mechanisms generated by

RMG, compared with a mechanism generated without radical reaction fam-

ilies allowed . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83

4.6 Flux diagram for Si at 6× 104 seconds for full, pressure dependent mech-

anism generated by RMG and simulated at 613 K . . . . . . . . . . . . . . 83

4.7 Variation in concentration profiles of SiH4 and Si2H6 with initial SiH4 con-

centration at 873 K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

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List of Tables

2.1 Radical corrections to A for solvation thermodynamics calculations . . . . 25

2.2 Comparison of group additivity and experimental solute parameters . . . . 27

3.1 Training reactions used to deduce kinetic solvent effects . . . . . . . . . . . 52

3.2 Solvents used for single-point energy calculations on training reactions . . . 53

4.1 Reaction families used to generate mechanisms for silicon hydrides in RMG 73

4.2 Hydrogen abstraction rates calculated from M062X/6-311+(3d2f) and tran-

sition state theory using Cantherm . . . . . . . . . . . . . . . . . . . . . . 75

4.3 Hydrogen bond increment (HBI) corrections calculated with G3//B3LYP . . 78

A.1 Group tree for hydrogen abstraction reactions . . . . . . . . . . . . . . . . 114

B.1 Transition state geometries for silicon hydride hydrogen abstractions . . . . 117

B.2 Geometries of silicon hydride species . . . . . . . . . . . . . . . . . . . . 119

1

1 INTRODUCTION

Understanding the oxidation of fuels in the liquid phase is important, as autoxida-

tion during storage leads to a loss of reactivity and may cause fuels to fail national standards

of oxidative stability [1]. Over time, autoxidation also causes large increases in viscosity

[2], making the fuels more difficult and less cost-effective to use. On the other hand, oxi-

dation of fuels in the liquid-phase can also be used to produce higher-value petrochemical

products [3]. Fuel oxidation is a complex process, dependent upon the detailed chemistry of

fuel components and additives. Many of these details are unknown, particularly for newer,

biologically derived fuels [4]. Building microkinetic models can be an effective method for

studying these systems; however, since these models can be quite large (174 species and

3275 reactions for a recent n-dodecane/methyl oleate autoxidation model [4]), building the

models automatically using a computer is preferable to increase speed and reduce errors.

Another complex chemical system which can benefit from detailed kinetic model-

ing is chemical vapor deposition (CVD). CVD is an important process in the semiconductor

industry for making silicon wafers. Predictive models can guide experimentalists on how

to design new silicon precursors and choose process conditions that will improve the effi-

ciency of CVD and the quality of silicon produced. Modeling just the gas-phase portion of

CVD is complex; one large manually built model, for the application of silicon nanopar-

ticle formation, contains 220 chemical species and 2600 reactions [5]. Again, building

these models by hand is slow, error-prone and important pathways may be missed, so using

automatic mechanism generation is more desirable. Mechanism generation software was

utilized in one such study of silicon hydrides in the gas phase [6]. Proper modeling of gas-

2

phase chemistry of CVD using automatic mechanism generation leads the way for similar

modeling of gas-surface chemistry, which is integral to these systems.

This dissertation will address these two chemistry domains using automatic mecha-

nism generation, and will focus on one software package in particular, the Reaction Mech-

anism Generator (RMG) [7, 8]. Studying such systems using RMG (and automatic mecha-

nism generation in general) is novel; most applications of automatic mechanism generation

are in combustion and pyrolysis of hydrocarbon fuels, with recent extensions to oxygenated

biofuels [9] and fuels containing sulfur [10]. Extensions beyond combustion and pyrolysis

of fuels include refrigerant formation from chlorinated hydrocarbons [11] and the pyrolysis

of ethyl nitrite [12].

The completed work falls at the intersection of chemical kinetics, computational

chemistry, and machine learning, with the latter two used for parameter estimation in mi-

crokinetic models. Background on each of these facets of the dissertation will be discussed

in this chapter, including a brief history of automatic mechanism generation.

1.1 Automatic mechanism generation

As early as 1979, Ugi et al. introduced the idea of using matrices to represent chem-

ical species, reactions and distances [13]. The concept was extended to mechanism gen-

eration, defined as the problem of finding all possible sets of bond/electron matrices that

fit a given reaction matrix, and then using rules based on chemical knowledge to limit the

size of the mechanism. At the same time, Yoneda created GRACE, a network generator

based upon matrix theory using square matrices [14]. The reactant and product matrices

are also divided into atom groups, consisting of a center atom and its attached hydrogen

atoms. GRACE can handle both radical and ionic reactions but does not take into account

stereochemistry. The sub-systems of GRACE include decomposing an overall reaction into

a set of elementary reactions; gathering the Arrhenius parameters for these reactions; and

setting up the the material balances for each species. This mechanism generator also in-

3

cludes additional constraints; an example of these is given in Figure 1.1, reproduced from

the paper. The authors acknowledge that the constraints must be carefully chosen by an

experienced chemist, so that one does not generate unreasonable reactions or species.

Figure 1.1: Rules imposed for the generation of an elementary reaction network, repro-duced from [14].

The matrix theory above is also applied in the 1992 network generator KING [15].

A combinatorial approach is taken, in which the set of products to be formed or possible

reactions are unknown. In this way, a large network is formed, but it may be possible

to discover new reaction types. It is suggested that constraints, including the number of

species that are allowed to interact and the number of bonds that can be broken or formed,

be implemented in order to reduce the size of the networks formed.

Ranzi et al. used a lumping method in their mechanism generator, MAMOX, de-

veloped in Fortran for oxidation and pyrolysis of fuels [16]. In this procedure, the de-

composition of the primary products are simply“lumped” and products beyond this first

decomposition are ignored. An overall rate constant is given for each type of reaction of

the primary products (see the reproduced Figure 1.2). Lumping reduces the number of

species and reactions to a manageable number, but one may miss important pathways or

products.

Alternatively, NetGen is a mechanism generator which, instead of lumping, in-

4

Figure 1.2: Lumped approach for the primary oxidation of n-pentane, reproduced from[16]. Intermediates and products are grouped together, with k1 - k9 representing lumpedrate constants for each step of the mechanism.

cludes the reactions deemed important in the network and removes the ones which are not

[17]. If a species has a production rate that is greater than some minimum rate, it is in-

cluded in the reaction network. This minimum rate is determined by a user-specified factor

multiplied by a characteristic rate, defined as

Rchar =amount of reactant converted

time it takes for conversion

If a species exceeds the minimum rate, it is included in the network and then re-

acted with all other species, and these reactions added to the mechanism. The mechanism

generation stops when no more species exist which have a rate greater than the minimum

rate and the desired conversion of a starting species has been achieved. The concept of

characteristic rate is included in several other mechanism generators, including Genesys

and RMG, to be described in the following sections.

EXGAS is a software for generating mechanisms of alkane and ether fuels [18].

The mechanisms created consist of a reaction base which involves all unimolecular or bi-

molecular reactions of molecules C0 to C2; a primary mechanism with only initial species

and oxygen as reactants; and a secondary mechanism, which is lumped. The lumping is

5

done by grouping the species formed in the primary mechanism that contain the same func-

tional groups and have the same chemical formula. A distinguishing feature of EXGAS is

that internally, non-cyclic species are represented as treelike structures. Thus, species can

be compared for redundancy using an algorithm which is called the “algorithm of canon-

icity”, based on graph theory. The concept of graph representation of species was used in

all future automatic mechanism generators (with additional layers of complexity added in

some cases).

A mechanism generator developed in 2003 by Ratkiewicz et al., COMGEN, uses

chemical graphs to represent species both internally and externally [19]. Information such

as atomic charges, valences and bond types can also be included in these graphs. To gen-

erate reactions, the program relies on reaction patterns, which are matched with the same

pattern in the reacting molecules.

The Rule Input Network Generator (RING) takes not only the initial species and

network analysis instructions as user inputs, but also the chemistry rules it uses to gener-

ate reactions [20]. The language used to provide input to RING is English-like and the

compiler “proofreads” this in order to communicate between the user and network genera-

tion. RING has the ability to represent intermediates and also has a post-processing module

which analyzes the network topologically to enable lumping of pathways and mechanisms.

This mechanism generator also implements a lumping scheme that groups together isomers

with the same functional groups. For a network representing the dehydration of fructose to

form hydroxymethylfurfural, for example, lumping reduced the number of reactions by a

factor of two. RING has the ability to represent user-defined entities that the program does

not automatically identify, such as inorganic atoms or active sites on catalysts. It can also

represent non-bonded interactions such as partial bonds and hydrogen bonds.

Genesys, developed at Ghent University, is similar to NetGen and RING in that it

uses only elementary reactions, limiting the network size by characteristic rate and uses a

rule-based approach for defining how molecules react. However, it differs in its internal

6

representation of chemical species; rather than using a graph, it utilizes the Chemistry De-

velopment Kit (CDK). The representation allows for different stereo-isomers to be uniquely

identified, which connectivity graphs cannot distinguish [21]. This capability is beneficial,

since different conformers may have different reactivity.

1.1.1 Reaction Mechanism Generator (RMG)

The mechanism generator utilized in this work is the Reaction Mechanism Gener-

ator (RMG) [7, 8, 22]. RMG is an open-source program with two versions, one written in

the Java programming language and the other in Python. The Python version will be used

and modified in this work, due to its simplicity of use and code readability as compared

to the Java version. Given a set of starting species, temperature, and pressure, RMG uses

the literature and chemical knowledge to propose a network of elementary reactions, their

rates, and thermodynamic properties.

In RMG, like several of the aforementioned mechanism generators, chemical species

are represented by graphs, with nodes as atoms and edges as bonds. Graph theory can then

be used to compare species and ensure uniqueness in the network. The network is built

by expanding a ‘core’ set of species, starting with the user input. When a reaction results

in a new species, that species is put on the ‘edge’. When a species flux reaches a critical

amount, determined by a user-defined tolerance and the characteristic rate of the core, it is

brought into the core. The simulation ends when there are no more edge species which fit

this criteria for a given simulation time or species conversion [23]. The concept of charac-

teristic rate has been previously described [17].

A unique aspect of RMG is its way of estimating reaction rates. Reaction families

in RMG have a specific “recipe” that defines the change in radicals, lone pairs and bond

order occurring in a reaction. Figure 1.3 gives an example of the template and recipe for the

hydrogen abstraction reaction family. Starred atoms indicate the reacting atoms. Kinetic

groups include the reacting atom in the family’s recipe and the structures surrounding that

7

Figure 1.3: Example of the template and recipe for the hydrogen abstraction reaction fam-ily. In the recipe, starred atoms participate in each action; ‘S’ refers to a single bond beingformed or broken, and ‘1’ indicates that the radical count increases or decreases by 1.

Figure 1.4: An example of part of the hierarchical tree for the hydrogen abstraction reactionclass from RMG documentation

8

atom. These groups are defined in RMG in a tree-like structure. The root of each tree is the

most generic group which follows the reaction recipe, while nodes make up more specific

groups. An example of a hierarchical tree is given in Figure 1.4. When a combination

of groups reacts, a rule describes its kinetic parameters. If a rule exactly matches the

combination of groups in the reaction it will be returned, but if not, the nearest neighbors

in the hierarchical trees will be averaged to determine the reaction’s kinetic parameters.

One way new kinetics can be added to RMG’s database is as part of a reaction

library. Rates in a reaction library, such as GRI-mech [24], are used without modification

whenever the reactant or product species are found in the model core. This method of

addition to RMG’s database should be used for reactions that do not belong to a reaction

family. For example, reactions with small molecules may not follow the same trend as

others in the reaction family, or reactions may not match an existing recipe at all. Also, if

a pressure-dependent reaction rate is known, this reaction should be added to a library in

order bypass RMG’s Master Equation code for pressure dependence, explained below.

Reaction kinetics added as training reactions to a reaction family are placed into

the hierarchical tree of estimate rules, using the most specific functional group definitions

possible for those reactants. They are then used when completing the more general nodes

in the tree by averaging. Training reaction rates must provide high-pressure limit kinetics

for an elementary reaction of a specific reaction family, and will influence the estimates of

other similar reactions generated by the reaction family. This is the preferred way to add

kinetic data to RMG’s rule-based estimation database [8].

In the case of unimolecular reactions, when the number of nonreactive collisions

with a third body is rate-limiting, rate coefficients are dependent on both temperature and

pressure. RMG contains a methodology for using the high-pressure limit kinetics to esti-

mate these pressure dependent rate coefficients, which is described in ref. 25.

When a new chemistry domain is studied with RMG, new reaction libraries, fami-

lies and rate estimates should be added. This poses particular challenges when extending

9

to new elements, and especially when extending to a new phase. Prior to this work, all

reaction rates included in RMG’s database, as well as its methods for rate estimation, were

based upon data for gas-phase reactions. Additionally, RMG previously contained capa-

bility for chemical species containing only carbon, hydrogen, oxygen, nitrogen, sulfur and

chlorine.

1.2 Parameter estimation

Most parameters in microkinetic models are estimated, due to a lack of known and

trusted kinetic and thermodynamic parameters from experimental or high level theoretical

calculations [26]. The following sections will outline estimation techniques that are used to

calculate these kinetics and thermodynamics values at low computational cost. These esti-

mation techniques have been incorporated into automatic mechanism generation software

and form the basis for the some of the work in this dissertation.

1.2.1 Thermodynamics

Thermodynamic values can be calculated using group additivity, with radical chem-

ical species adding more complexity. When group additivity is insufficiently accurate, the

parameters can also be calculated using quantum chemistry.

1.2.1.1 Benson’s group additivity scheme

Benson developed a scheme in which chemical species are decomposed into groups,

defined as a central atom connected to its ligands. Group values for enthalpy and entropies

of formation, and heat capacity as a function of temperature, can then be summed to obtain

these thermodynamic values for the overall species [27]. Group values exist for molecules

containing a variety of atoms and also for open-shell species, but groups do not yet exist for

every single type of chemical species that might be present in a microkinetic model. Group

values can either be derived from experimental data, or high level quantum calculations

10

can be used to calculate new group values. The accuracy of the group additivity method is

dependent on the accuracy of the methods used to derive the group values, and also how

similar the chemical species to be estimated are to the species from which the groups were

derived. For example, many group additivity values exist for stable molecules, but less for

radicals or ions, meaning that less appropriate or analogous values are sometimes applied

to calculate their thermodynamic properties [26].

1.2.1.2 Hydrogen Bond Increment method

An alternative method to Benson’s group additivity for determining the thermody-

namic properties of radical species was proposed by Lay et al. [28] and is known as the Hy-

drogen Bond Increment (HBI) method. The approach uses the thermodynamic properties

of parent molecules and a single group value to account for loss of a hydrogen atom. For

enthalpy of formation, ∆fH◦298, the group value for a radical R∗ is simply the bond strength

of the R–H bond. The HBI values for Cp(T ) and S◦298 are obtained from molecular struc-

ture differences between the radical and parent molecule using the rigid-rotor/harmonic

oscillator (RRHO) approximation, which essentially means that translations, rotations, and

vibrations of the species are treated as uncoupled when solving the Schrodinger equation.

The S◦298 value calculated for the radical does not include symmetry corrections, which

should be added in later based on the point group of the radical.

The equations for the thermodynamic properties are as follows:

∆fH◦298(R∗) = HBI(∆fH

◦298) + ∆fH

◦298(RH)−∆fH

◦298(H)

C◦p(R∗) = HBI(C◦p) + C◦p(RH)

S◦298(R∗) = HBI(S◦298) + S◦298(RH)

where R∗ is the radical chemical species, RH is the parent molecule created by saturating

the radical chemical species with hydrogen atoms, and HBI are the group values for each

11

of enthalpy, entropy and heat capacity.

1.2.1.3 Quantum Mechanics Thermodynamic Property estimation

RMG contains a module for calculating thermodynamics known as Quantum Me-

chanics Thermodynamic Property (QMTP) estimation. During the course of a simulation,

if this option is turned on, RMG will send information about the molecule’s 2D graph to

a computational chemistry program to obtain the 3D geometry and eventually the species’

vibrational frequencies and enthalpy. Other thermodynamic properties can be calculated

from the computational chemistry output files using statistical mechanics. Typically, this

option is only used for cyclic and polycyclic species. QMTP uses the RRHO approxi-

mation and it was built for semi-empirical methods such as PM3, PM6 and PM7. While

these methods are not as accurate as other quantum chemistry methods, such as density

functional theory (DFT), they are sufficient when group additivity estimates are very inac-

curate, at low computational cost [29].

1.2.2 Kinetics

Similar to thermodynamics, unknown reaction kinetics can be calculated using esti-

mation techniques. Kinetic parameters can also be calculated directly using transition state

theory; these are used to formulate rate rules for a given type of reaction [30].

1.2.2.1 Evans-Polanyi

One estimation correlation, which relates reaction rates to enthalpy of reaction, is

the Evans-Polanyi relationship [31]:

k(T ) = A exp

((E0 + α∆H◦)

RT

)The correlation trends with reaction family; parameters A, α and E0 are fitted for a

given reaction family. While computationally efficient, the relationship is not accurate for

12

all classes of reactions.

1.2.2.2 Transition State Theory

With increases in computing power, more reaction rates can be calculated using

quantum chemistry and statistical mechanics concepts in a framework known as transi-

tion state theory [32]. Transition state theory says that a quasi-equilibrium exists between

reactant and activated complexes, or transition states. Classical transition state theory is

described by the following equation:

k(T ) =kBT

hexp

(−∆G‡

RT

)kB is the Boltzmann’s constant, T is temperature, h is Planck’s constant, R is the

ideal gas constant, and ∆G‡ is the difference in Gibbs free energy between transition state

and reactant. The equation can also be expressed in terms of partition functions, which can

be calculated using statistical mechanics and molecular parameters from quantum chem-

istry calculations. CanTherm, included as part of the RMG software but often used stand-

alone, is an automated kinetics calculator that calculates reaction rates via classical transi-

tion state theory (and also can calculate thermodynamic properties) from quantum chem-

istry output files [33]. Classical transition state theory is only appropriate for reaction types

with a clear reaction barrier; variational transition state theory should be used when the di-

viding surface between reactant and product is less clear. Other kinetics calculators include

POLYRATE [34], Variflex [35], and MultiWell [36].

13

1.2.3 Transition state geometries

To allow kinetics to be calculated via transition state theory, a transition state ge-

ometry is required. This is often the bottleneck of kinetics calculations, as a very close

estimate is needed for computational chemistry programs to correctly optimize the transi-

tion state geometry, which lies at a first order saddle point on the potential energy surface.

Double ended methods have been developed, which require the user to provide the reactant

and product geometries and use these to find the transition state. These methods fall under

the categories of interpolation, nudged elastic band, or string methods. Some of these dou-

ble ended methods have been automated, such as an algorithm developed by Zimmerman

[37], and KinBot [38], but the computational cost of these programs is prohibitive for use

in detailed kinetic models that may require thousands of rate parameter estimates.

Bhoorasingh and West developed a group contribution algorithm for creating the

transition state geometry estimate directly. It uses a machine learning approach to train key

distances in the transition state geometry, based on the molecular structure of the reactants

and products. Once these distances are known, correct transition states can be optimized

about 70% of the time, for three reaction families [39]. The algorithm was recently inte-

grated with computational chemistry packages, as well as CanTherm, for a fully automated

method to calculate reaction rates. This automated kinetics algorithm, known as AutoTST,

was used to generate some of the transition states and reaction rates used in this work [40].

1.3 Machine learning with decision trees

Thermodynamics, kinetics, and transition state geometry estimation using group

contribution is essentially a regression problem. Group values, based on molecular struc-

ture, are calculated by “regressing”, or minimizing the overall error (based on some cost

function) between estimated and true values from a training set. The way these regres-

sions are currently set up in RMG are in the format of decision tree regressors, which are

14

retrained when new reaction rates or transition state geometries are added to the training

set.

Decision trees can be applied to classification or regression problems. The class

label, or value in the case of regression, is chosen based on a set of questions about features

of data items. The tree is constructed by training on data items whose class label or value

is known, and then used on new data points. Decision trees are advantageous because they

are easier to understand than other, more complex machine learning models, such as neural

networks, but are more robust than linear or logistic regressions. The predictions can also

be improved by combining the results of multiple decision trees, known as ensembling

[41]. Depending on the application, the decision tree method is sometimes preferable over

simpler methods such as cluster analysis or data partitioning, which are used to develop

quantitative structure activity relationships (QSAR), because of its applicability to large

sets of diverse compounds which may also contain erroneous data [42]. Some examples of

using decision trees in chemistry and biology are described below.

1.3.1 Decision trees in chemistry and biology

There are many examples of bioinformatics and cheminformatics problems that

have been approached with decision trees. Han et al. describe a method for choosing

biologically interesting compounds for drug discovery from a high throughput screening

(HTS) data set. The decision tree was formulated based on the PubChem chemical struc-

ture fingerprint system, and the C4.5 algorithm was used to construct the decision trees

[43]. 10-fold cross validation was used to verify the validity of the decision tree model.

It was shown that the model can be used to determine commonalities in an HTS data set,

select compounds, and eliminate selections which arise from noisy data [42].

DNA sequencing is also a promising area for use of decision trees. Decision tree

regression was used by Thornley et al. for prediction of unknown bases in a sequence. The

decision tree was trained on all the peak heights near the base to be predicted, as well as

15

the bases in the neighborhood of those peaks. A neural network was further used to regress

the information that was most successful for the decision tree regressor. [44]

Decision tree regression has also been used for environmental applications. Hu and

Cheng used a decision tree method known as the conditional inference tree (CIT) to under-

stand which factors are important for predicting heavy metal distribution among the surface

soils of the Pearl River Delta in China. They used a random forest approach, a bootstrap-

ping algorithm where the CITs are subsampled without replacement. They combined the

CIT approach with a finite mixture distribution model (FMDM), which can be used to dis-

tinguish between natural and arthropogenic causes of heavy metal concentration in soils

[45].

Decision tree classification and regression have proved useful for several applica-

tions in chemistry and biology. Diverse features and data sets can be used with ease of

understanding and dealing with missing data. They are also more robust than other ma-

chine learning techniques. Furthermore, decision tree regressors are already implemented

for some estimation in RMG, and can be extended to applications in this dissertation. As it

stands, these trees are built by hand from chemical intuition, and the structure of these trees

also influence the accuracy of the predictive models. Automated decision tree generation

will be briefly discussed in Chapter 3.

1.4 Dissertation overview

The dissertation will apply automatic mechanism generation, quantum chemical

calculations and machine learning to two new domains: silicon hydride chemistry and

liquid-phase fuel chemistry. Chapter 2 of the dissertation discusses the implementation

of solvation thermodynamic corrections to the gas phase data and methods in the Python

version of RMG (RMG-Py). The implementation draws largely from the implementation

in RMG-Java, with several improvements and additional data. Chapter 3 continues on the

liquid-phase application, introducing a new method which uses machine learning to predict

16

a change in reaction rate between gas and liquid-phase. The method is used to modify the

rates of an existing fuel oxidation model. Chapter 4 introduces a different application:

the use of automatic mechanism generation to generate detailed kinetic models for silicon

hydrides. The process of calculating and adding thermodynamic and kinetic data for silicon

hydrides to RMG is outlined, and a new model for gas-phase thermal decomposition of

SiH4 is generated and discussed. Chapter 5 concludes by wrapping up the previous chapters

and recommending some future directions for the research.

17

2 AUTOMATIC CALCULATION OF SOLVATION THERMODYNAMICS

Several environmentally, medically, and industrially relevant chemical systems in-

volve liquid-phase reactions, including secondary organic aerosol formation, oxidation

of fuels in the condensed phase, and radical scavenging in the body [4, 46–49]. When

these systems are large and complex, containing thousands of radical-radical and radical-

molecule reactions, it is difficult to elucidate all reaction pathways by hand. It is much

easier and less error-prone to generate these mechanisms automatically. Thermodynamic

solvation corrections are one necessary component in automatic mechanism generation for

liquid-phase systems. It is important to have correct thermodynamics, because the equi-

librium constant, Keq, is calculated from ∆Grxn. The accuracy of these Keq and therefore

∆Grxn can change the reaction mechanism dramatically. Because of solute/solvent interac-

tions, the thermodynamics for individual chemical species, which are used to calculate the

overall reaction thermodynamics, are different in gas and liquid phase. Experimental in-

formation is not available for every species (and is especially sparse for radicals), so there

exists a need for some other way to estimate the thermodynamic parameters. Literature

data and estimation methods are already implemented into the Reaction Mechanism Gen-

erator for gas-phase thermodynamics [7, 8, 22]. Using these gas-phase data, we can make

so-called “corrections” to the thermodynamic data for the liquid-phase. Such methods exist

in the Java version of RMG [50]. I have implemented these methods in the Python version

of RMG, and extended the capabilities further as part of this dissertation.

18

2.1 Background

Below is a review of methods used by chemists to calculate the liquid-phase ther-

modynamics parameters that are necessary for mechanism generation. The parameters can

either be calculated explicitly using computational chemistry, or they can be estimated us-

ing empirical relationships.

2.1.1 Explicit thermodynamic calculations

Calculation of thermodynamic parameters in solution is performed using a variety

of methods, including discrete models such as quantum mechanical (QM), molecular me-

chanical (MM) and hybrid (QM/MM) models [51], and continuum models [52]. Discrete

solvation models treat each solvent molecule separately and can be computationally ex-

pensive, especially in the case of pure QM methods. These methods also cannot represent

long-range, bulk phenomena in solvent. Continuum methods, including the polarizable

continuum methods (PCM), multipole expansion (MPE) and Generalized Born (GB), are

less expensive when taking a QM approach. However, they have the disadvantage of ne-

glecting local interactions between solute and solvent. A more thorough description of

these methods can be found in Jalan et al. [53], and in Chapter 3.

2.1.2 Estimation techniques

Another approach to calculating solvation thermodynamics are estimation meth-

ods, such the linear solvation free energy relationship method (LSER). This approach is

based on the assumption that the solvation thermochemistry of a single species can be bro-

ken down into individual contributions from solute/solvent properties such as cavitation,

dispersion, hydrogen bonding and polarizability. Kamlet and Taft suggested that these con-

tributions could be quantified in terms of electronic transitions, such as π to π? and p to

p?, which occur when a solute is solvated. Kamlet and Taft’s observations along with other

19

contributions resulted in the solvatochromatic equation [54]:

SP = SP0 + sπ?1 + dδ + aα1 + bβ1 + h(δh)2

SP refers to any solvation parameter (with SP0 an intercept); for example, one solvation

property to be calculated is the logarithm of the partition coefficient between gas and sol-

vent (logK). The lowercase parameters are fitted parameters for a given solvent, while the

other parameters represent the following: π?1 is the electrostatic contribution due to dipo-

larity/polarizability, α1 is hydrogen bond donation, β1 is hydrogen bond acceptance, δh

represents cavity formation, and δ is a polarizability correction factor [55].

Abraham et al. [56] later refined this equation:

SP = c+ eE + sS + aA+ bB + lL

where the capital letters purely represent solute properties and again, the lowercase letters

are fitted solvent parameters. These solvent parameters have been previously tabulated and

published for many solvents; for example, those for water and 1-octanol can be found in

[57]. Of the solute descriptors, S represents the solute’s electrostatic interactions due to

dipolarity and polarizability and was derived from the π? parameter; L is a representation

of size based upon the solute’s gas-hexadecane partition coefficient; E is derived from the

Kamlet-Taft δ parameter and serves as a correction to S; A represents hydrogen bond do-

nation ability/acidity of the solute; and B is the hydrogen bond acceptance ability/basicity

[55].

Some correlations are used to find the solute (uppercase) Abraham parameters indi-

vidually (reviewed in [53]), but molecular structure group additivity methods can be used

to calculate all of the parameters at once. In particular, Platts et al. devised 81 molecular

structure fragments to be used in the calculation of S,B,E and L, and another 51 frag-

ments for A [58]. These fragments include atom-centered contributions, such as a carbon

20

(a) (b)

Figure 2.1: Examples of molecular structure fragments. (a) An atom-centered methylgroup, consisting of a carbon atom with three single bonds to hydrogen atoms. (b) Anon atom-centered ester group, specified by several atoms.

atom attached to four non-hydrogen atoms; group-based corrections, such as fused rings;

and intra-atomic interactions, such as ortho, meta and para interactions. Examples of some

of these groups are given in Figure 2.1. The contributions for each of these fragments are

added together to obtain a value for each solute descriptor. Then, the Gibbs free energy of

solvation, ∆Gsolv at 298 K can be found from the partition coefficient with the following:

∆Gsolv = −RT lnK

Mintz et al. found solvent descriptors to utilize the solvatochromatic approach with

the Abraham solute descriptors for the prediction of the enthalpy of solvation, ∆Hsolv [59]:

∆Hsolv = ch + ehE + shS + ahA+ bhB + lhL

where the subscripts h denote that these solvent descriptors refer to the fitted parameters

corresponding to the enthalpy of solvation relationship.

To obtain ∆Gsolv at other temperatures, a method of linear extrapolation is com-

monly used. ∆Gsolv and ∆Hsolv at 298 K are used to calculate the entropy of solvation,

∆Ssolv:

∆Ssolv =∆Hsolv −∆Gsolv

T

Assuming that ∆Hsolv and ∆Ssolv are independent of temperature, ∆Gsolv at a given tem-

perature can be found with:

21

∆Gsolv(T ) = ∆Hsolv(298K)− T∆Ssolv(298K)

Other methods for treating the temperature dependence of ∆Gsolv can be used, as

in [60]; however, the Mintz method is both fast and useful in that the solute properties, cal-

culated via group additivity, can be used for both the partition coefficient and the enthalpy

of solvation.

The errors in the outlined linear solvation method for molecules at 298 K are com-

parable to those of the discrete and continuous methods, about 1 kcal/mol typically, but

higher for large molecules and ions [61]. However, the computational time required is

much shorter as compared to the more expensive QM and MM methods [53].

A study comparing force field (MM) calculations of solvation free energy with

SM6, a continuum QM method [62], and LSER, for nitroaromatic compounds, found that

the LSER method performs as well as the best force field methods. The LSER method had a

mean unsigned error of 0.59 kcal/mol as compared with experimental data, with all energies

slightly too negative. The deviation increased with increasing number of nitro functional

groups on the molecules. The SM6 method, in comparison, yielded a mean unsigned error

of 0.50 kcal/mol, was unaffected by the number of nitro groups, and is faster than MM

calculations. However, the error was highly affected by the level of theory used for the

geometry optimizations [63].

2.2 Methods

As mentioned, while solvation thermodynamics had been previously implemented

in the Java version of RMG [50], in this dissertation these capabilities were adapted for use

in RMG-Py. Additionally, several improvements to the prior implementation of solvation

thermodynamics were made in this work.

22

2.2.1 Adaptation of solvation thermodynamics from RMG-Java

(a) (b)

Figure 2.2: (a) Example of an entry in the solute group database, and (b) the molecularstructure of the corresponding group.

The estimation methods of Abraham and Platts which are described in the Back-

ground, using linear solvation energy relationships along with group additivity, were newly

implemented in this work. Specifically, the RMG-database [64] project, which is coupled

with the Python version of RMG, was modified. The addition of solute molecular struc-

ture groups consisted of adding two group databases, one for atom-centered groups and

one for non atom-centered groups. The groups are specified such that each atom (besides

hydrogen) in a molecule must belong to exactly one atom-centered group, and may also

belong to one non atom-centered group. An example entry in the solute group database

and its corresponding structure is shown in Figure 2.2. Each group is defined by a label, an

adjacency list specifying the atom types and bonds included in the group, and the Abraham

solute parameters S,B,E, L and A. The starred atom is the one matched against atoms in

the solute molecule in RMG, and “Cs” indicates that it is a carbon atom with only single

bonds.

23

A solvent database also was added, where the solvent is defined by either an adja-

cency list or its SMILES string identifier. The parameters included in the solvent database

are the solvent coefficients for the logK and ∆Hsolv linear solvation energy relationships.

Each entry also contains the A-E coefficients of the viscosity-temperature correlation to be

used in diffusion corrections. Some entries also store the solvent’s dielectric constant and

its solute A and B parameters for potential use in kinetic solvent corrections. The diffusion

and other kinetic solvent corrections will be explained in the following chapter.

2.2.2 New additions in RMG-Py

Once the solute and solvent parameters are obtained or calculated based on the

Platts group fragments, the functions to calculate partition coefficient K, ∆Hsolv, and ulti-

mately ∆Gsolv(T ) were implemented using the equations in the Background. These meth-

ods were added to a new solvation module in RMG-Py, with modifications also made to

the source code in the thermo and molecule modules to calculate and apply the solvation

correction during an RMG simulation. Modifications also were made to the main RMG-Py

execution in order to load the user-specified solvent at the start of the so that the proper sol-

vent descriptors would be loaded. Furthermore, in this work, several important updates and

improvements were made to the implementation of solvation thermodynamics in RMG-Py,

which are not present in RMG-Java

2.2.2.1 Treatment of radicals and Abraham A value

No Abraham parameters for logK or ∆Hsolv exist for radical species. Therefore, we

must devise a method to calculate solvation thermodynamics of radicals using the available

data. By comparison, for gas phase thermodynamics, radical species (R∗) data are calcu-

lated using the saturated species (RH) data and hydrogen bond increment (HBI) theory,

explained in Chapter 1 [28]. One can similarly use the saturated species data to calculate

the solvation thermodynamics of radicals by calculating the solute descriptors, and then

24

correcting the Abraham A solute descriptor to account for the effect on hydrogen bonding

caused by removing a hydrogen atom. For example, the effect of creating a peroxyl radical

from a peroxide group by removing a hydrogen is a 0.345 decrease in A [58]. 14 Platts

groups for this A descriptor correction have been added to a “radical” database in the cur-

rent RMG-Py. These A descriptor corrections were obtained from Table 5 of [58], with

slight modifications made to adhere to the RMG format of adjacency lists and to ensure

that the correction is not double counted for groups where there are two hydrogen bonded

atoms. The sign of the values were flipped from those provided in the table since the cor-

rection is applied when a hydrogen is removed. With these changes, the implementation of

radical groups in RMG-Py is shown in Table 2.1.

2.2.2.2 Treatment of lone pairs in solvation thermodynamics

Currently, there exist no Platts groups to account for lone pairs on atoms above their

normal bonded configuration (i.e., 0 for carbon, 2 for oxygen). Similarly, there also exist

no gas-phase Benson groups for carbon centered groups with one or more lone pairs. Since

these groups would not match existing Platts or Benson groups, in both cases, would be

estimated by RMG incorrectly. For example, since 1CH2 is only singly bonded to 2 groups,

in this case hydrogen atoms, it would not match any Platts groups that are sp3 carbon atoms

bonded to 4 groups, or any sp2 or sp groups. Therefore, it would fall up RMG’s molecular

structure group tree to a generic sp3 carbon atom. This generic group is filled in with the

data for a carbon atom bonded to 4 other carbon atoms (as in neopentane), which would

have very different thermodynamic properties than 1CH2. When this situation occurs, rather

than using this erroneous data, I devised and implemented a new method to convert these

lone pairs to unpaired electrons, therefore converting 1CH2 to 3CH2. RMG would then

proceed with the algorithm in the prior section; that is, it would saturate these unpaired

electrons, creating CH4, and calculate the solute descriptors for that molecule. While not

relevant in this example, if removing these two hydrogen atoms would change the A solute

25

Radical fragment Hydrogen bonding correction to A

-0.345

-0.345

-0.243

-0.087

-0.371

-0.543

-0.247

-0.275

-0.281

0.091

0.0825*

0.119

-0.17

Table 2.1: Hydrogen bonding parameters from [58], adapted for corrections to the solvationthermodynamics of radical species when saturating the radical with hydrogens causes ahydrogen bonding effect. *the value was divided in half since there are two hydrogen-bonded nitrogen atoms in this molecule.

26

descriptor, it would also be updated as in the true radical electrons case. Similarly, the gas-

phase thermodynamics methods were analogously updated to convert lone pairs to radicals

when we do not have data for the specific lone pair group.

2.2.2.3 Additional Platts groups

Carbon, hydrogen and oxygen atom-containing Platts groups for calculating solute

descriptors were originally included in the Java version of RMG. To adapt to increasing

capabilities of RMG-Py, in this work, additional published Platts groups were added to the

database of RMG-Py. Specifically, these were groups including nitrogen and sulfur atoms

[58]. In the future, halogen groups calculated by Platts should be added to the database, as

capabilities for chlorine and fluorine are currently being added to RMG. Additionally, sili-

con atom-containing groups should be added, but must first be calculated, as these groups

were not previously published.

2.2.2.4 Solute database

Using group additivity to calculate the five solute parameters for every species in

every reaction increases the time needed for mechanism generation. For many molecules,

the solute descriptors have already been calculated and tabulated [65]. Thus, in this work a

solute database was created from this published data, which currently contains 152 values.

If RMG can find the molecule of interest in this solute database, it will use the values given.

If it cannot, then it will use group additivity to calculate the solute descriptors.

27

2.3 Results

The calculations of solvation thermodynamics were validated to ensure that both

the group additive scheme for estimating solute descriptors as well as the Abraham and

Mintz correlations for logK and ∆Hsolv are sufficiently accurate.

2.3.1 Estimation of solute descriptors

Figure 2.3: g-decalactone structure, with atom-centered groups circled in green and nonatom-centered groups in blue.

For verification that the algorithm to predict solute descriptors is implemented cor-

rectly into RMG, the Abraham solute parameters for g-decalactone (Figure 2.3), a molecule

consisting of several atom-centered and non-atom-centered groups, are compared to exper-

imental values from ACD/Labs [66]. Table 2.2 displays the results of the comparison. The

values predicted by RMG-Py and the experimental values closely agree, showing that RMG

can identify molecular structure fragments via their adjacency list and count them correctly

for groups containing carbon, hydrogen and oxygen atoms. The groups containing nitrogen

and sulfur have been implemented, but not yet tested.

Solute Parameter Experimental Predicted by RMG-PyS 1.26 1.26B 0.55 0.54E 0.32 0.39L 6.27 6.33A 0 0

Table 2.2: Abraham solute parameters for g-decalactone calculated by group additivity inRMG-Py, shown with experimental values from from ACD/Labs [66]

28

(a) (b)

Figure 2.4: Comparison of solvation thermodynamics values for 20 solutes in water calcu-lated by RMG-Py to those in databases. (a) ∆Hsolv, compared to values in Mintz et al. [59](b) ∆Gsolv, compared to values from the University of Minnesota solvation database [67].

2.3.2 Calculation of solvation thermodynamics

The logarithm of the partition coefficient, logK and ∆Hsolv are calculated with

linear solvation energy relationships. These relationships utilize the solute descriptors,

which we showed can be calculated via group additivity in the previous section, along with

the solvent descriptors. Then, ∆Gsolv was obtained from K. For 20 solutes in water at

298 K, the calculated values of ∆Hsolv were compared to those in Mintz et al. [59] and

those of ∆Gsolv were correlated with those from the University of Minnesota solvation

database [67]. The mean absolute deviation was 4.2 kJ/mol for ∆Hsolv and 2.9 kJ/mol for

∆Gsolv. The results of this comparison are illustrated in Figure 2.4. Because the Minnesota

solvation database was likely used to train the values for the Platts group contributions,

the similarity in values should be interpreted as a demonstration of reproducibility (also

acknowledged in Jalan et al. [50]).

29

2.4 Summary

In this chapter of the dissertation, solvation thermodynamics was enabled in the

Python version of the Reaction Mechanism Generator (RMG). The calculation methods,

involving linear solvation energy relationships and a group additivity method for determin-

ing solute descriptors, were adapted into RMG-Py, with the source code updated with these

changes. In addition, treatment for the solvation thermodynamics of radicals was improved

by using saturated species thermodynamics and the Abraham A value, more of which were

added to RMG’s database. Solvation thermodynamics for species with lone pairs were

treated by converting the lone pairs into unpaired electrons. More group additivity values

were added to RMG’s database for species containing nitrogen and sulfur, and estimation

was sped up and improved by incorporating a database of known solute descriptors. It

was ensured that group additivity was implemented properly by comparison of ∆Gsolv and

∆Hsolv to the values in University of Minnesota’s solvation database [67]. Solute descrip-

tors for a complex molecule were also successfully compared to experimental values from

ACD/Labs [66]. The progress made in these areas make it possible to correct gas-phase

thermodynamics to account for reactions in different solvents, and ultimately are the first

step to generating detailed kinetic models for liquid-phase systems using RMG-Py.

2.5 Recommendations

The recommendations outlined below will further improve the estimation of solva-

tion thermodynamics in RMG-Py. These involve improving the temperature dependence

of ∆Gsolv, refining treatment of the solvation chemistry of species with lone pairs, better

benchmarking, and expanded solvent list.

30

2.5.1 Temperature dependence of solvation thermodynamics

The linear extrapolation method used for calculating ∆Gsolv at temperatures other

than 298 K, i.e., by assuming that ∆Hsolv and ∆Ssolv are constant, is not always an ac-

curate assumption for temperatures far from 298 K. For example, it was shown to be very

inaccurate for O2 in water; while the RMG estimation method would have ∆Gsolv increase

monotonically with temperature, the experimental values only increase slightly, and begin

to decrease near 450 K [68, 69], (Chung, unpublished work). Other methods for treating

the temperature dependence have been previously suggested and implemented [53, 60].

Because they are slower than the current method, other methods should only be imple-

mented in RMG where the inaccuracy is expected to be high; for example, only above

certain temperatures or for certain chemical systems.

2.5.2 Calculation of solvation thermodynamics for lone pair species

A fix has been implemented to convert lone pairs to radical electrons in order to

compute solute descriptors; however, it would be preferable to directly calculate Platts

groups for lone pair species. Though there is a lack of experimental data for these molecules,

quantum chemistry calculations could be done to obtain solvation thermochemistry and

derive solute descriptors for these species. These descriptors could simply be put into the

solute library, or several calculations could be further processed to derive Platts group ad-

ditivity values.

2.5.3 Improved benchmarking of group additivity values

The solvation thermodynamic parameters calculated in this work were only com-

pared to values in the Minnesota solvation database, which were originally used to train

the molecular structure group values used to calculate the solute descriptors. While ex-

perimental ∆Hsolv and ∆Gsolv are not widely available, the calculated parameters could

be compared to high level quantum calculations to get a better feel for the accuracy of

31

the estimates. This type of comparison is often done to gauge the accuracy of gas-phase

thermodynamic values calculated by group additivity [28, 70].

2.5.4 Expansion and enhancement of solvents

The current list of 26 solvents available for calculating solvation thermodynam-

ics could be further expanded in the future. For example, there exist published Abraham

solvent descriptors for biological solvents such as blood in the brain [71], which would

facilitate kinetic modeling of even more diverse processes using RMG. Another useful

addition would be the ability to select mixtures of solvents for a RMG simulation, thus re-

quiring a method of interpolation between the solvent descriptors of two or more solvents.

Ben Amara et al. use dodecane as the single solvent in their RMG simulations, despite

investigating different mixtures of dodecane and methyl oleate as biodiesel surrogates, for

example [4]. Furthermore, if a solvent is also a reacting chemical species, the identity of

the solvent changes throughout the RMG simulation. Capability to make the solvent de-

scriptors similarly change as a simulation progresses would make the RMG simulations

more realistic.

32

3 IMPLEMENTING KINETIC SOLVENT EFFECTS IN AUTOMATIC

MECHANISM GENERATION

The previous chapter dealt with corrections to gas-phase thermodynamics to ac-

count for solvation, which is necessary in calculating the overall ∆Grxn and thus reverse

reaction rates. However, learning about complex liquid-phase systems also requires knowl-

edge of solvent effects on the forward rates of elementary chemical reactions. Many of

the reactions in liquid-phase mechanisms of interest, including fuel oxidation, are radical-

molecule and radical-radical reactions. Depending on the solvent, rates of reaction can vary

by orders of magnitude, thus changing likely pathways and product distributions. Further-

more, knowledge of kinetic solvent effects not only helps with generation of liquid-phase

reaction mechanisms, but can aid in the design of solvents to promote a desired reaction

pathway or product [72]. Two main effects must be understood: physical diffusion and

intrinsic kinetics effects.

To account for diffusion limitations on reaction kinetics, we calculate an effective

rate constant for each reaction, which depends on the intrinsic gas-phase reaction rate and

the diffusivities of reacting species. Diffusivities, diameters of reacting species, and solvent

viscosities are all calculated using empirical correlations. The specifics of these calcula-

tions will be outlined in this chapter.

Modifying reaction rates to account for a solvent’s intrinsic effect on the gas-phase

kinetics is more challenging. This intrinsic effect changes the chemical environment of

reactants and modifies the reaction barrier, as opposed to a solvent’s physical diffusion

limitation, which modifies the effective rate [73]. Solvent effects on the reaction rate de-

33

pend on both the nature of the solvent and the type of reaction occurring.

The intrinsic effect of the solvent on the reaction rate will be investigated using

quantum mechanical methods to find the energy difference between the reactant and transi-

tion states of chemical reactions, i.e. Figure 3.1. Several reactions within specific families

in RMG that are relevant to oxidation chemistry, such as hydrogen abstraction, will be

analyzed. Trends in solvent effect will be illustrated, based upon properties of the react-

ing species, for example, carbon chain length or presence of an alcohol group. Using these

trends, a scheme can be created to predict the change in rate with solvation based on molec-

ular structure and properties of the solvent.

Figure 3.1: Example of a potential energy surface for a reaction in gas-phase (black) and asolvent (blue). A solvent may have a different effect on the energy of reactants, transitionstates, and products in a chemical reaction. Reproduced from [73]

3.1 Background

Prior studies on intrinsic solvent effects employ a number of experimental and the-

oretical approaches, which will be outlined below. Previous solvent effect discoveries will

then be organized and discussed based on reaction family.

34

3.1.1 Experimental techniques for determining reaction rates in liquids

Experimentally determining reaction rates for radical reactions in solution can be

difficult due to the short-lived nature of some radicals; however, some methods have been

developed over the last century and are commonly used for measuring these kinetics.

In an early method pioneered by Briers and Chapman known as rotating sector, or the

intermittent-illumination method (IIM), a sample is exposed to a constant intensity of light

for intermittent periods of time, such that the amount of time spent in light and in the dark

remains constant [74–76]. The average reaction rate, WM, can be calculated by:

WM =kp√2kt

[M ]√φI(1 + r)−1

where kp and kt are the propagation and termination rates, respectively, [M ] is the concen-

tration of the compound under investigation, M , reacting with a radical, φ is the quantum

yield of photoinitiation, I is the light intensity, and r is the ratio of time in the dark to

time in the light [76]. This method has been applied to reactions in gas phase and solution,

including polymerization and radical recombination [77–79]. This method, however, can

only be used for some specific types of radical chain reactions, with one requirement being

that they can be photochemically initiated. [80]

A very common method for measuring the reaction rate of radical reactions in both

gas and liquid-phase is laser flash photolysis. In this method a sample is excited by a

pulse from a laser, and radical species are monitored by measurement of their spectral

absorption. The spectral absorption can be measured with electron spin resonance, in which

the unpaired electron of the radical interacts with the nuclei in the molecule leading to a

mapping of electron density [81].

An indirect way of measuring the rate constants for radical-molecule reactions is the

radical clock method, which uses a known unimolecular reaction rate and a measured prod-

uct distribution to determine an unknown radical-molecule reaction rate.[80] For example,

35

Roschek and co-workers developed radical clocks for peroxyl radical reactions using the

competition between a beta-fragmentation of a peroxyl radical and a bimolecular H-atom

transfer [82]. This concept is shown in Figure 3.2. Jha and Pratt point out some limitations

Figure 3.2: Concept of peroxyl radical clock from Roschek et al.[82]

to the type of molecule R1-H from which the hydrogen atom is abstracted [83]. If R1 is

either persistent or highly stabilized, it cannot carry the chain reaction, and a large con-

centration of substrate is required. They describe a modification the radical clock method

using peroxyesters, making it possible to study a wider range of reactions.

3.1.2 Computational chemistry

Another approach to computing intrinsic kinetic solvent effects is by comparing

reaction barriers calculated in both gas and solution using quantum chemistry. Differen-

tial solvation between reactants and transition states affects the reaction rate according to

transition state theory, which says that a quasi-equilibrium exists between reactant and ac-

tivated complexes, or transition states [32]. Several computational methods are commonly

utilized for obtaining geometries of reactants and transition states and their energies.

3.1.2.1 Density functional theory

One set of methods used to solve the Schrodinger equation numerically is based on

density functional theory (DFT), an approximation to the wave function with only three

variables used to obtain electronic structures of molecules, radicals and activated com-

plexes [84, 85]. The DFT method chosen has a significant impact on whether the species’

36

geometries and energies are accurate, and it was previously found that the accuracy of den-

sity functionals for predicting barrier height is correlated with their accuracy for transition

state geometries [86]. In addition, approximate functionals such as DFT predict the tran-

sition state energies too low because they incorrectly delocalize electrons [87]. However,

when comparing transition states in gas and liquid, this discrepancy matters less since it

will be present in both cases and some cancellation of error will occur. When DFT is used

to compute solvent effects, comparison to experimental rates shows that it provides a high

enough level of theory to capture the desired effects [88, 89].

3.1.2.2 Solvation models

Figure 3.3: Comparison between a continuum solvation model (left, figure from [90]) anda hybrid implicit/explicit model (right, figure from[91])

Computational methods for estimating solvation energies are reviewed briefly in

the previous chapter and in [53] and generally fall into two categories: those that represent

solute and solvent molecules explicitly, and those that represent only solute molecules ex-

plicitly and the solvent molecules somewhere in between explicit and continuous. Explicit

treatment is done either quantum mechanically (QM) or with molecular mechanics (MM),

or some combination of both, as in QM/MM.

One hybrid implicit/explicit solvation method is the shells theory proposed by Pliego

[92]. In this solvation treatment, the solvent shell closest to the solute (S1), representing

solute-solvent interaction, is treated either fully quantum mechanically or with molecular

dynamics based on classical force fields. The remaining solvent, S2, is treated with contin-

uum solvation. When the number of solvent molecules in S1 becomes infinite, this theory

37

converges to the full discrete solvent representation. This approach is also known as the

cluster-continuum model, mixed discrete-continuum model, or quasichemical theory [93].

Continuum solvation models represent solvation as a solute placed inside a cavity

within an implicit solvent, which is modeled as a continuum with a constant property such

as conductivity or dielectric constant. See Figure 3.3 for a pictoral comparison between

continuum and a more explicit method. The solute cavity can be shaped like a sphere or

ellipsoid, or as in more modern methods, based upon a superposition of atom-centered

spheres [93]. However, representing a solvent this way does not account for local solute-

solvent interactions, and the assumption that the dielectric constant near the solute surface

is equal to the bulk dielectric constant is inaccurate.

A recommended method for calculating liquid-phase energies, which takes into

account contributions from the first solvation shell, is SMD [94]. This model, like the

authors’ other SMx methods, include a term for non-electrostatic effects due to cavity for-

mation, dispersion interactions, and solvent structure. The contribution is dependent upon

the solvent-accessible surface area (SASA) of each solute atom. The main feature distin-

guishing SMD from the other SMx methods is that it utilizes a continuous charge density of

the solute, rather than a discrete representation. In the Gaussian computational chemistry

program [95], the method is combined with the polarizable continuum method (PCM) [96]

for single-point energy calculations on a solute in a solvent. However, it can be used with

other algorithms such as COSMO [97] and COSab [98].

A recent method developed by Pomogaeva and Chipman, known as the composite

method for implicit representation of solvent (CMIRS), uses six parameters to describe

interactions between solute and solvent including dispersion, exchange, hydrogen bonding,

and long range electrostatic interactions. Because of low level of parameterization, this

model is believed to capture a higher level of physical truth. For hydration energy, the

mean unsigned error may be as low as 0.8 kcal/mol for neutral solutes and 2.4 kcal/mol

for ionic solutes and has been parametrized for the B3LYP and Hartree-Fock quantum

38

chemistry methods [99]. With regards to solvation kinetics, Silva et al. parametrized the

CMIRS model for methanol in order to predict activation free energy barriers for SN2 and

SNAr reactions. Both CMIRS and SMD were compared to experimental data of solvation

free energies and while they perform similarly for neutral species, the MUE for CMIRS is

lower in the case of anion and cation solutes. For free energy barriers, CMIRS performs

similarly to COSMO-RS while SMD is slightly worse [100].

3.1.3 Kinetic solvent effects within reaction families

Kinetic solvent effects are usually deduced, and are most generalizable, within a

particular reaction type. However, as will be shown, the kinetic solvent effect can vary

within a reaction family and across solvents.

3.1.3.1 Hydrogen abstraction

Figure 3.4: The solvent effect on hydrogen abstraction from α-tocopherol is independent ofthe radical (DPPH (x-axis) or TOH (y-axis)) Each number from 1-13 represents a differentsolvent. Reproduced from [101]

The largest body of literature on solvent effects on reaction rates is in bimolecular

hydrogen abstraction reactions. Das et al. used laser flash photolysis to study the reaction

39

of tert-butoxyl radicals with phenols in six solvents [102]. The rate decreased in polar sol-

vents, explained by the capability of the phenolic OH group to hydrogen bond with solvent

molecules. Ingold and co-workers have attempted since to further deduce these solvent

effects in hydrogen abstraction reactions. Valgimigli et al. found that the solvent effect on

abstraction of the phenolic hydrogen from α-tocopherol by both tert-butoxyl radical and

2,2,-diphenyl-1-picrylhydrazyl (DPPH·) is independent of the radical in almost every sol-

vent they tested [101] (see Figure 3.4). This result is especially surprising, since for these

two radicals, the reaction rate in the same solvent differs by over 106. Any deviation from

this behavior, as in tert-butyl alcohol, is thought to be due to the reaction being partially

diffusion controlled. The reaction of α-tocopherol with tert-butoxyl was further investi-

gated in four solvents; the rate constant decreased with increasing βH2 value [103]. The

βH2 parameter represents the hydrogen bond acceptance ability/basicity of the solvent. Fi-

nally, discrepancies between the data obtained and another study on the reaction of Trolox

with Cl3COO· [104] are explained by a mechanistic shift from hydrogen atom abstraction

to electron transfer in solvents with high dielectric constants and basicities. This electron

transfer mechanism may also be accompanied by a solvent-assisted proton loss, known as

sequential proton loss electron transfer (SPLET):

Cl3COO ·+ArOH −→ Cl3COO− + ArO ·+H+(1)

Cl3COO ·+ArOH + S −→ Cl3COO− + ArO ·+SH+(2)

Thus, the electron transfer mechanism can account for rates which are higher than

the rate expected from simply using a correlation with a solvent property. Foti et al. also

discovered this fast electron-transfer reaction between phenols and DPPH [105]. While hy-

drogen atom transfer was dominant in nonpolar solvents most of the time, electron transfer

still occurred if the radical was strongly oxidizing, as with Cl3COO·. Reactions proceeding

via the electron-transfer mechanism should be faster in polar solvents. But surprisingly, the

40

rate constant was higher in ethanol than methanol despite methanol having a higher dielec-

tric constant; they attributed this inconsistency to solvent impurities.

The Snelgrove-Ingold correlation for hydrogen abstraction reactions relates the dif-

ference in rate constant between the reaction in gas and in solvent to the solvent’s αH2 and

βH2 (hydrogen bonding) parameters [106]:

log10

kgasksolvent

= 8.3αH2 β

H2

Later, it was found that this single empirical equation could not describe an entire

reaction family [107–109]. In solvents which support ionization, some hydrogen abstrac-

tion reactions, for example that of 2,2’-methylene-bis(4-methyl-6-tert-butylphenol) (BIS)

with DPPH·, proceeded by the SPLET mechanism [109]. This led to a reaction which is

zero-order in DPPH·. Because this is not true for the reactions of all phenols with DPPH·,

it was suggested that properties of the reacting phenol play a role. One such property is the

intramolecular H-bond in BIS, which may slow the reverse proton-transfer reaction, thus

leading to the unusual effect observed. Furthermore, Nielsen and Ingold found that the βH2

scale does not account for solvents’ anion solvating properties, and thus reactions involving

proton transfer do not quite follow the Snelgrove-Ingold correlation [110]. The Taft β scale

[54] gives better correlations for this type of reaction. An experimental study by Warren

and Mayer also note the failure of the generalized Snelgrove-Ingold correlation. They stud-

ied the effect of small amounts of solvent additives on the oxidation of ascorbate (vitamin

C) by TEMPO radical. Their results indicate that solvent effect on hydrogen abstraction

reactions is better explained by local solvent effects, as the effects are much greater than

can be explained by bulk solvent properties [111].

In some types of hydrogen abstraction reactions, the effect of changing the solvent

is low. The reaction between ascorbate and 2,2,6,6-tetramethylpiperidine-1-oxyl radical

was studied experimentally [112]. The mechanism was best explained by proton-coupled

electron transfer (PCET) (Figure 3.5), where an electron and proton are transferred simul-

41

Figure 3.5: Example of the PCET mechanism, reproduced from [112]

taneously but between different sets of orbitals. The solvent was varied between water

and mixtures of water and dioxane, decreasing the polarity. The quantity investigated was

the kinetic isotope effect (KIE), which is defined as the ratio of the rates of hydrogen ab-

straction in water and in D2O. KIE was found to only slightly increase with decreasing

solvent polarity. Interestingly, hydrogen tunneling was suspected to take place in all sol-

vents studied, because the experimental KIEs were larger than expected by semiclassical

theory.

From these studies it has generally been understood that solvent effects on hydro-

gen abstraction reactions are significant when looking at O-H bond abstraction, primarily

because of the O-H bond’s ability to participate in hydrogen bonding networks, but that

the effect on C-H bond abstraction is negligible. Despite this assumption, Koner and co-

workers generalized these effects to C-H and Sn-H bonds [113]. They explain the results as

a stabilization of the abstracting species in polar solvents, rather than the hydrogen donor

(which is the case for abstraction from the O-H bond). Thus, the nature of the abstracting

species has a large effect on the reaction rate in solvents. They still hypothesize that the

reaction of a non-polar hydrogen donor and non-polar abstracting radical will have little

solvent effect, but acknowledge this is hard to test due to the high activation barrier of these

reactions.

42

3.1.3.2 Radical addition to multiple bonds

Kinetic solvent effects on the addition of radicals to multiple bonds has mainly been inves-

tigated theoretically and has been extensively studied by the groups of Fouassier [114–116]

and Radom [117–120]. When various radicals were added to methyl acrylate using DFT

calculations, the rate of reaction in various solvents correlated well with the dipole mo-

ment of the solvents; however, it was argued that a multipole approach was still needed

[115]. Polar solvents still had a small effect on the rate if the charge transfer from the

reactants to transition states, calculated using a Mulliken charge analysis [121], was low.

Wong and Radom performed calculations using the self-consistent isodensity polarizable

continuum model (SCIPCM) [52, 117]. In the case of radicals with saturated substituents

adding to alkenes with saturated substituents, addition of any solvent increases the barrier.

Solvent decreases the barrier in the unsaturated case. The higher the dielectric constant of

the solvent, the greater this effect. Finally, Garcia et al. investigated the addition of sev-

eral radicals to methyl aminoacrylate with DFT and found that for an unspecified solvent,

barriers increase with solvation for electrophilic radicals (phenyl and trifluoromethyl) and

decrease for nucleophilic radicals (methoxymethyl and methyl) [122]. From these studies,

it can be concluded that the chemical nature of the radical has a larger effect on the rates

than the polarity of the solvents in this reaction family.

3.1.3.3 Beta scission

β-scission of tert-butoxyl radicals using electron spin resonance to measure rates was in-

vestigated by Weber and Fischer [124]. They found that at 300 K, the solvation rates were

at least ten times larger than the gas phase rates. This result was explained by a transition

state effect, where the transition state is more polar than the radical and is thus more sta-

bilized by interactions with polar and polarizable solvents. Furthermore, the β-scission of

cumyloxyl radicals using laser flash photolysis also showed a rate increase with increas-

ing solvent polarity [125]. The same effect was found for alkyloxyl radicals [126]. Bietti

43

Figure 3.6: β-scission rates correlate with Dimroth-Reichardt parameter ET . Reproducedfrom [123]

et al. also confirmed this effect and found that the solvent Dimroth-Reichardt parameter

(ET ) correlated well with the increase in rate [127], confirming earlier results by the Ingold

group [123], see Figure 3.6. The ET parameter represents the charge-transfer absorption of

the solvent in pyridinium N-phenolbetaine and serves as a different measure of solvent po-

larity than the dielectric constant [128]. For example, methyl formamide has an extremely

high dielectric constant but is of similar polarity to methanol as characterized by its ET

value. It appears from these studies that the rates of β-scission reactions can be general-

ized to increase with some measure of solvent polarity such as ET . However, since only

reactions of cumyloxyl and alkyloxyl radicals have been investigated, and mostly in water,

acetonitrile or mixtures of the two, it is difficult to infer kinetic solvent effects for the entire

reaction family.

3.1.3.4 Diels-Alder

Like the other reaction families discussed, the rates of Diels-Alder reactions in so-

lution, in general, depend on both solute and solvent properties [130]. Breslow et al. [131]

described a large increase in rate of Diels-Alder reactions in water and in stereoselectivity

between endo and exo products. They explain the acceleration in terms of the reactant struc-

tures; the diene and dienophile engage in hydrophobic stacking. Experimental studies with

44

Figure 3.7: Example of Diels-Alder reaction of cyclopentadiene and (-)-menthyl acrylateand possible product isomers. Figure reproduced from [129]

methanol show that it is indeed this hydrophobic effect rather than a polarity effect which

increases the rate in water, as the rates of some reactions actually decrease in methanol,

which is unexpected.

Later, Ruiz-Lopez et al. [129] studied Diels-Alder reactions of cyclopentadiene and

methyl acrylate using ab initio calculations. They found that because the solvent’s electric

field changes the shape of the potential energy surface, a direct change in the overall reac-

tion mechanism is seen with solvation. It is argued that only adding the solvation energy to

the gas-phase energy is not sufficient to determine the reaction path in solution. However,

they also maintain that continuum theory models are sufficient for capturing some specific

interactions with solvents, such as hydrogen-bonding, since overall electrostatic effects

will implicitly include these properties. Another simulation study on the reaction of methyl

acrylate with cyclopentadiene was done by Sheehan and Sharratt using molecular dynam-

ics [132]. The reaction was studied in both methanol and n-hexane. The result showed that

the endo/exo selectivity of the reaction products is related to the difference in the solvated

transition states’ free energies. Further, the rates and selectivity were affected by properties

of the solvent such as their polarity and H-bonding ability. In methanol, the product was

energetically favored as compared to the energy in n-hexane; this was explained by the

similarity in polarity between the product and methanol.

Soto-Delgado et al. studied the reaction of cyclopentadiene and methyl vinyl ke-

tone in both water and methanol, using a combined QM/MM-MD approach [133]. The

45

activation free-energy barrier in methanol is 2.1 kcal/mol higher than that in water, which

is within 0.1 kcal/mol from the experimental difference (a rate deceleration of 2 orders

of magnitude. Again, the ability of hydrogen bonding between solvent and transition

state, which is stronger and longer-lived in water than in methanol, contributes to this

effect. Kiselev et al. compared reaction rates of 9-(hydroxymethyl)anthracene and 9,10-

bis(hydroxymethyl)anthracene with maleic anhydride, N-ethylmaleimide and N- phenyl-

maleimide, in organic and water-1,4-dioxane cosolvents [134]. It was found that even

those reactants which do not hydrogen-bond with water experienced acceleration of rate in

water, depending on the structure of the diene. The organic cosolvents reduced the reaction

rate, also depending on the polarity of the reactants.

These studies illustrate the importance of both polarity of reactants and hydrogen

bonding ability in kinetic solvent effects of Diels-Alder reactions, and verify that contin-

uum models and other computational methods can capture both of these effects reasonably.

Despite the success of these models, experimental studies were necessary to show the hy-

drophobic effect that is crucial in some cases. Additionally, merely adding solvation en-

ergies to those obtained in the gas-phase is not sufficient enough when the transition state

geometries or shape of the potential energy surface change significantly in a solvent.

3.1.3.5 Acetylation

Figure 3.8: Acetylation mechanism, reproduced from [135]

Xu et al. [136] theoretically investigated the catalyst-assisted acetylation of tert-butanol

with acetic anhydride in the gas phase and in three solvents. The geometry optimization

46

and reaction energies were found with B3LYP/6-311++G(d,p) and B3LYP/6-31G(d), while

solvation energies were found using PCM. They found that the reaction proceeds via a

mechanism characterized by nucleophilic attack of the catalysis, and that this mechanism

does not change, nor does the rate-limiting step, with solvent. Because polar solvents

solvate the reactants better than the transition states or reaction intermediates, the reaction

is less favorable in these solvents. Consequently, the reaction proceeds less favorably in

going from gas, to carbon tetrachloride, to chloroform, and finally to dichloromethane, the

most polar solvent of the group. These results are also supported by early experimental

studies [137].

3.1.3.6 Epoxidation

The epoxidation of olefins by hydrogen peroxide was studied both experimentally and with

DFT by Berksessel and co-workers [89, 138, 139]. They find that for these reactions,

using fluorinated alcohols such as HFIP accelerates the rate in relation to 1,4-dioxane [138,

139]. From 0-4 molecules of HFIP were studied with the reactants quantum mechanically

in the gas-phase, and then the whole system was treated with PCM [89]. Acetone was

chosen as a model solvent for HFIP, because of its similar dielectric constant, with some

additional considerations for cavitation. The activation enthalpies were shown to decrease

with increasing number of HFIP molecules, while increasing contribution of entropy lead to

the Gibbs free energy of activation reaching saturation with three or four HFIP molecules.

The same theoretical study was done using methanol as a solvent, but increasing the number

of methanol molecules had no influence. However, the activation barrier was reduced more

with methanol than with HFIP. This result shows that methanol acts only as a polar solvent

for the reaction, and explicit hydrogen-bonding with methanol does not affect the reaction

rate, as it does with HFIP. While prior theoretical study by the Shaik group showed that

fluorinated alcohols increased the epoxidation reaction rate [140], the studies by Berkessel

explicitly showed the effect of multiple aggregates of the solvent molecules.

47

(a) (b)

Figure 3.9: Plots for epoxidation rate of β-caryophyllene versus differing solvent parame-ters, reproduced from [141]

Later, Steenackers et al. experimentally studied the epoxidation of β -caryophyllene

to caryopyllene oxide in aqueous H2O2, alcohols, nitrogen containing solvents, and furans,

11 in total [141]. In all cases, the rate correlated extremely well with Abraham’s hydro-

gen bonding parameters (R2 = 0.97), and interestingly, not well at all with the dielectric

constant (R2 = 0.17), as shown in Figure 3.9 reproduced from the paper. They further char-

acterized solvent effect using ωB97XD/g-311++G(df,pd) and IEPCM. This computational

study confirmed previous studies that the solvent stabilizes the O-O bond in H2O2 in the

transition state structure via hydrogen bonding.

3.1.3.7 Hydrolysis

Almerindo and Pliego studied the hydroylsis of formamide with ab initio calculations and

PCM [142]. 1-4 explicit water molecules were considered. Two mechanisms, stepwise and

concerted, were investigated; see Figure 3.10. For the stepwise mechanism, the activation

barrier increased by 4.6 kcal/mol with one water molecule and 11.0 kcal/mol with two water

molecules. Adding water molecules beyond two made the system entropically unfavorable.

For the concerted mechanism, the solvation only increased the barrier by 6.4 kcal/mol with

two water molecules, indicating that the transition state is more stabilized by the solvent

48

Figure 3.10: The possible mechanisms in the hydrolysis of formamide. Figure reproducedfrom [142]

than in the stepwise mechanism. Additionally, the level of theory used for the calculations

had a large effect on the barriers. The discrepancy caused by the level of theory was larger

than the difference between using geometries optimized in the liquid-phase, rather than

geometries optimized in the gas phase and then modeled with PCM.

3.1.3.8 O-neophyl rearrangement

The O-neophyl rearrangement of two 1,1, diphenylethoxyl radicals was investigated with

laser flash photolysis in five solvents by Bietti and Salamone [143]. For both radicals, the

rate constant decreased with increasing solvent polarity. There was a linear correlation

found between the logarithm of the rearrangement rate constant and the Dimroth-Reichardt

parameter E NT . Because E N

T represents the solvent anion’s solvating ability, the trend was

explained in terms of the “decrease in the extent of negative charge on the oxygen atom on

going from the starting radical to the transition state.” [143]

49

3.2 Methods

As the numerous studies in the Background showed, chemical reactivity can change

drastically in different solvents. While some rates change systematically with solvent po-

larity, it is not always clear what properties of the solvent and reactant structure will have

an effect on the rates. Experimental data are only available for certain radical reactions

in some reaction families, most extensively hydrogen-abstraction. Again, because RMG

contains information and estimation methods for gas-phase kinetics, it is desirable to de-

vise a method to correct these rates in the liquid-phase, which is done in this dissertation.

For diffusion effects, simple correlations are available for correcting reaction rates, and are

utilized here; however, correcting intrinsic kinetics is more complicated. Using quantum

chemistry provides a powerful tool for determining reactant and transition state energies.

These quantum calculations are expensive, so in this work, we take the approach of study-

ing a subset of reactions and generalizing the results.

3.2.1 Diffusion

Diffusion corrections to reaction rate are needed because reactions are physically

impeded by the presence of solvent. To implement this phenomenon into RMG-Py, simple

correlations based on the hard-sphere approximation were used to minimize computational

cost and complexity. The correction is only made in the bimolecular direction; no cor-

rection is needed for unimolecular reactions. For reactions which are bimolecular in both

directions, the diffusion correction is calculated based upon the direction where it will have

the greater effect. In all cases, since the equilibrium constant does not change as a re-

sult of diffusion, it is used to modify the reverse rate of reaction proportionally [50]. This

modification is implemented by calculating an effective rate constant [144]:

keff =4π(r1 + r2)(D1 +D2)kint

4π(r1 + r2)(D1 +D2) + kint

50

where r1 and r2 are the radii of the reacting species, D1 and D2 are their diffusivities, and

kint is the intrinsic reaction rate in the gas phase. The radii are calculated by assuming the

molecules are spherical and using the McGowan volume, which gives a contribution to the

volume for each atom and a subtraction for each bond [145]. The Stokes-Einstein equation

is used to calculate the diffusivities:

D =kBT

6πηr

and the viscosity η, dependent on temperature, can be calculated with the following:

η = A+B

T+ C log T +DTE

where A,B,C,D and E are fitted parameters tabulated for many solvents [146]. This

temperature dependence is an improvement over the implementation in RMG-Java, where

solvent viscosity is assumed to be its value at 298 K. The solvent database, which contains

the solvent descriptors described in Chapter 2, also include the A−E parameters for each

solvent.

All changes to the source code were made in RMG-Py’s solvation module, used to

store the solvent properties when loaded, and a newly created diffusionlimited module that

has functions based on the empirical correlations. Additionally, the reaction module was

modified in order to correct the gas-phase rate when solvation is turned on as specified by

the user in the RMG input file.

3.2.2 Intrinsic kinetics

Group-based estimation techniques have proved effective for predicting parame-

ters for mechanism generation, including thermodynamic parameters [27], kinetics [30],

and most recently, transition state geometries [39]. In this dissertation, I show that such

an approach is also possible for predicting the difference in a reaction’s activation energy

51

between the gas-phase and liquid-phase (∆EA). First, the effect on ∆EA of changing re-

actant functional groups was tested in small sets of hydrogen abstraction reactions. The

required reactant and transition state geometries and energies were calculated with density

functional theory (DFT) and a continuum solvation method, which have previously been

used to determine kinetic solvent effects [89, 136, 141]. All calculations were completed

using the Gaussian ‘09 computational chemistry package [95] carried out on Northeast-

ern University’s Discovery cluster, a high performance computing cluster. Based on the

observations from these calculations, a group estimation method was developed to predict

∆EA for different classes of solvents, described in the following sections. The method was

applied to a published n-dodecane/methyl oleate oxidation model previously built using

RMG, serving to represent a middle-distillate fuel with a fatty acid methyl ester (FAME)

additive, both which are components of biofuels [4]. I then observed the effect of including

kinetic solvent effects on predicted fuel induction period (IP).

3.2.2.1 Quantum chemistry protocol

For the quantum chemistry calculations, 53 hydrogen abstraction reactions were

chosen to best observe effects of functional groups on reaction barriers (Table 3.1, rep-

resented by SMILES). These reactions included carbon, hydrogen, oxygen and nitrogen

atoms, and probed the effect of alcohol groups versus alkanes, different abstraction sites

within the same molecule, unsaturated versus saturated rings, and carbon chain length. For

this set of reactions, gas-phase reactant geometries and transition state geometries were

optimized using M06-2X [147, 148]/MG3S [149–154]. The transition states were verified

with an intrinsic reaction coordinate calculation. Once a correct transition state was found,

single point energies were calculated in eight different solvents, for both the reactants and

transition states, using SMD [94]. These eight solvents, given in Table 3.2, cover a wide

range of dielectric constants and at least one falls under each of six categories of solvent

as defined by Schmid [155]: 1) nonpolar, 2) aliphatic, 3) protic/protogenetic in which one

52

Reaction # heavy atoms1 [CH3] + C←→ C + [CH3] 42 [OH] + C←→ O + [CH3] 43 O[O] + C←→ OO + [CH3] 64 [CH3] + CC←→ C + C[CH2] 65 [CH3] + CO←→ C + C[O] 66 [CH3] + CO←→ C + [CH2]O 67 [OH] + CC←→ O + C[CH2] 68 [OH] + CO←→ O + C[O] 69 [OH] + CO←→ O + [CH2]O 610 O[O] + CC←→ OO + C[CH2] 811 O[O] + CO←→ OO + C[O] 812 O[O] + CO←→ OO + [CH2]O 813 [CH3] + CCC←→ C + CC[CH2] 814 [CH3] + CCC←→ C + C[CH]C 815 [CH3] + CCO←→ C + CC[O] 816 [CH3] + CCO←→ C + C[CH]O 817 [CH3] + CCO←→ C + [CH2]CO 818 [OH] + CCC←→ O + CC[CH2] 819 [OH] + CCO←→ O + CC[O] 820 [OH] + CCO←→ O + C[CH]O 821 [OH] + CCO←→ O + [CH2]CO 822 O[O] + CCO←→ OO + CC[O] 1023 O[O] + CCO←→ OO + C[CH]O 1024 O[O] + CCO←→ OO + [CH2]CO 1025 [CH3] + CCCO←→ C + CCC[O] 1026 [CH3] + CCCO←→ C + CC[CH]O 1027 [CH3] + CCCO←→ C + C[CH]CO 1028 [CH3] + CCCO←→ C + [CH2]CCO 1029 [OH] + CCCO←→ O + CCC[O] 1030 [OH] + CCCO←→ O + CC[CH]O 1031 [OH] + CCCO←→ O + C[CH]CO 1032 [OH] + CCCO←→ O + [CH2]CCO 1033 O[O] + CCCO←→ OO + CCC[O] 1234 O[O] + CCCO←→ OO + CC[CH]O 1235 O[O] + CCCO←→ OO + C[CH]CO 1236 O[O] + CCCO←→ OO + [CH2]CCO 1237 [CH3] + O1C=CC=C1←→ C + O1C=[C]C=C1 1238 [CH3] + O1C=CC=C1←→ C + O1[C]=CC=C1 1239 [CH3] + [NH]1C=CC=C1←→ C + [NH]1C=[C]C=C1 1240 [CH3] + [NH]1C=CC=C1←→ C + [NH]1[C]=CC=C1 1241 [CH3] + [NH]1C=CC=C1←→ C + [N]1C=CC=C1 1242 [OH] + C1C=COC=1←→ O + C1C=[C]OC=1 1243 [OH] + C1C=COC=1←→ O + C1[C]=COC=1 1244 [OH] + [NH]1C=CC=C1←→ O + [NH]1C=[C]C=C1 1245 [OH] + [NH]1C=CC=C1←→ O + [NH]1[C]=CC=C1 1246 [CH3] + C1=CC=CC=C1←→ C + C1=[C]C=CC=C1 1447 [CH3] + C1=CC=NC=C1←→ C + C1=C[C]=NC=C1 1448 [CH3] + C1=CC=NC=C1←→ C + C1=[C]C=NC=C1 1449 [CH3] + C1=CC=NC=C1←→ C + [C]1=CC=NC=C1 1450 [CH3] + C1CCCCC1←→ C + C1[CH]CCCC1 1451 [OH] + C1=CC=NC=C1←→ O + C1=C[C]=NC=C1 1452 [OH] + C1=CC=NC=C1←→ O + C1=[C]C=NC=C1 1453 [OH] + C1=CC=NC=C1←→ O + [C]1=CC=NC=C1 14

Table 3.1: Training reactions used to deduce kinetic solvent effects

53

hydrogen atom is bonded to oxygen, 4) halogenated, 5) amines, and 6) select “normal”

solvents which are non-protonic, do not contain chlorine, and are aliphatic with a single,

dominant bond dipole. The SMD calculations and gas-phase energy calculations then made

it possible to calculate ∆EA for each reaction in each solvent.

Solvent εOctane 1.9Benzene 2.3Tetrahydofuran 7.4Dichloromethane 8.9Pyridine 13.0Acetonitrile 35.7Dimethylsulfoxide 46.8Water 78.4

Table 3.2: Solvents used for single-point energy calculations on training reactions

3.2.2.2 Molecular structure group training

Based upon the observations from the training set of reactions, two hierarchical,

molecular group trees (one for each reactant) were manually constructed based on the fea-

tures considered most important to predicting ∆EA. I chose these features based on both

chemical intuition and the data, and a similar procedure for constructing similar group trees

has been described [39]. Using regression, group contributions to ∆EA were calculated for

each leaf in the trees to best fit the data for the ∆EA of the 53 training reactions. The

top level of the tree contains a base value for ∆EA, and the total ∆EA is calculated by

adding this base value to the values for the leaf in each tree which which best matches the

reacting groups in the reaction of interest. This calculation method is similar to the current

procedure for gas-phase thermodynamics, solvation thermodynamics, and transition state

geometry data estimation in RMG (and hierarchical trees are also used for the rule-based

estimation of gas-phase kinetics). Methods for calculating ∆EA based on this group con-

tribution method were added to the solvation module of RMG, drawing from the newly

added databases of solvation kinetics group values in RMG-database.

54

Though the trees for each solvent have the same structure, a different contribution to

∆EA is used according to the calculations in that solvent. Twenty-six solvents are currently

available to use for thermodynamic corrections in RMG, and these may be expanded in the

future. These solvents can be generalized to different categories, as mentioned above. The

eight solvents for which SMD calculations have been done will be used to construct these

categories; ∆EA for solvents outside of these eight will be calculated using the appropriate

category.

3.2.3 Fuel oxidation model modification

The published n-dodecane/methyl oleate model, generated with RMG by Ben Amara

et al., includes a Chemkin file and a dictionary which gives the SMILES strings for each

named species in the mechanism [4]. Using this information, I parsed the Chemkin file

using methods in RMG to generate a reaction in RMG format, corresponding to each hy-

drogen abstraction reaction in the mechanism. Once the reacting groups were determined

by this script, the tree was traversed to find the contributions to ∆EA which are most ap-

plicable to the reaction. The contributions from the n-octane solvent tree were used, as

it is the solvent which is most chemically similar to n-dodecane. The script then rewrote

the Chemkin file, updating the EA of each hydrogen abstraction reaction. The updated

Chemkin file is included in Appendix A.3, and the script used to generate it can be found

in Appendix A.2.

3.2.4 Reactor simulations

To examine the effect of changing the reaction barriers in the fuel oxidation method,

I simulated a reactor using both the previous (gas-phase kinetics) and updated (liquid-phase

kinetics) models. An ideal gas reactor model was used, with the density set to the liquid fuel

density of n-dodecane, to approximate a liquid-phase reactor. Oxygen was continuously

replenished throughout the course of the simulation to emulate a constant partial pressure

55

of oxygen. Other conditions were set to be the same as the conditions set in the modeling

study conducted by Ben Amara et al. [4]. Different methyl oleate concentrations (0%-30%

by volume) were used. The induction period, which is defined as the time at which the fuel

is 5% converted, was compared for both models as well as to prior experimental data. The

script used to simulate the reactor is included in Appendix A.4.

3.3 Results

Some of the trends observed for change in ∆EA with molecular structure groups

are outlined below. The trends were used to generate the group tree for correcting the gas

phase kinetics in different solvents. Finally, the data for n-octane was used to modify the

EA in a fuel oxidation model; the updated reactor simulations are shown below.

3.3.1 Solvation kinetics trends

Several solvation kinetics trends, based on solvent and molecular structure, were

deduced from the training data. One such relationship is displayed in Figure 3.11. Here,

when ·OH abstracts a hydrogen from different sites of propanol, the kinetic solvent effect

increases as the abstraction site gets closer to the alcohol group.

Examples of other such trends will be briefly listed. Solvent effect on hydrogen

abstraction from alkanes is the same with increasing carbon chain length, with the only

difference being for methane; hydrogen abstraction from saturated rings and unsaturated

rings have a slight difference, with larger differences occurring for high dielectric solvents;

and hydrogen abstraction by ·OOH trends differently than abstraction ·OH and ·CH3, with

the latter two behaving similarly [156]. The intuition gathered from these trends was used

to construct the molecular structure group tree for ∆EA.

56

Figure 3.11: Difference in energy between gas-phase and liquid-phase, between reac-tants and transition state (∆EA), for the reaction XH + ·OH←→ ·X + H2O, where XH ispropanol and each symbol represents a different abstraction site (indicated by moleculeson the right with the abstraction site circled in purple). Kinetic solvent effect increases asdistance of abstraction site to alcohol group decreases.

3.3.1.1 Group tree

From the intuition gained from the trends discovered in the section above, along

with general principles included in the existing thermodynamics and kinetics databases in

RMG, a molecular structure group tree was constructed for the determination of solvation

kinetic corrections for hydrogen abstraction reactions. Importantly, the structure of this tree

determines what estimates will be used for ∆EA when an exact value is unavailable. The

first few levels of the tree are displayed in Figure 3.12; the full tree has 1-2 more layers of

complexity.

Similar studies were conducted for intra-hydrogen migration reactions, although the

solvation corrections were not applied to the n-dodecane/methyl oleate oxidation model.

57

(a) Molecular structure group tree for the molecule being abstracted from (XH)

(b) Molecular structure group tree for abstractingspecies (Y·)

Figure 3.12: Illustration of the first few levels of group trees for hydrogen abstraction. Thefull tree contains 2 more levels of complexity. Reacting atoms are colored in blue. R’ refersto a functional group that is not a hydrogen.

58

Both hydrogen abstraction and intra-hydrogen migration group trees were also further

trained with a larger set of reactions (see Recommendations section). The full tree along

with group values for ∆EA, for hydrogen abstraction in n-octane, is included in Appendix

A.1; this tree was trained using the large set of reactions.

3.3.2 New reactor simulations

Figures 3.13, 3.14, 3.15, and 3.16 compare the results of reactor simulations us-

ing the original, gas-phase kinetic model for n-dodecane/methyl oleate oxidation, the up-

dated model with kinetic solvent effects, and experiments. For the simulation with pure

n-dodecane (0% methyl oleate), addition of solvation kinetic effects appears to increase the

induction period of the fuel. This increase is in the direction of most, though not all, of the

experimental data points. The amount that the modified model increases the induction pe-

riod, on a logarithmic basis, is dependent on the amount of methyl oleate in the fuel blend.

Additionally, the model which is least consistent with the experimental data is the one built

for 30% methyl oleate content. These results may suggest more training data are needed

for the solvation kinetic groups which contain or are proximal to oxygen atoms. While not

relevant in this example, as n-dodecane is a non-hydrogen bonding solvent, oxygen as a re-

acting atom will matter even more in such cases as the transition state would be stabilized

by a hydrogen bonding solvent relative to the reactants.

3.4 Summary

In this chapter, modifications to the RMG-Py software were implemented for liquid-

phase mechanism generation, specifically for reaction kinetics. Based on well known corre-

lations, reaction rates were modified to account for diffusion effects, with an improvement

over the implementation in RMG-Java: the addition of temperature-dependence in the sol-

vent viscosity. Additionally, a large part of this chapter was devoted to demonstrating the

applicability of a group contribution method for estimating kinetic solvent effects. Several

59

2.20 2.25 2.30 2.35 2.40 2.45 2.501000T

(K−1 )

10-1

100

101

102

Indu

ctio

n P

erio

d (h

ours

)

ExperimentsBen Amara 2013 modelModified model

Figure 3.13: Comparison of experiments, original model and updated model with kineticsolvent effects for 0% methyl oleate.

2.2 2.3 2.4 2.51000

T (K 1)

10 1

100

101

102

Indu

ctio

n P

erio

d (h

ours

)

ExperimentsBen Amara 2013 modelModified model

Figure 3.14: Comparison of experiments, original model and updated model with kineticsolvent effects for 5% methyl oleate.

experimental and theoretical methods for measuring liquid phase rate constants were re-

viewed; however, given RMG’s extensive database of gas-phase rates, it was preferable to

design a method that modified these rates systematically to account for a solvent. A train-

ing set of hydrogen abstraction reactions, and later intra-hydrogen migration reactions, was

used to deduce trends based upon molecular structure on the change in energy between gas-

phase and different solvents, for both reactants and transition states. The calculations were

completed using M06-2X/MG3S. Based upon the trends, a group contribution method was

devised, and used to modify rates of a fuel oxidation model built using RMG-Java. Reac-

tor simulations using the updated model showed that correcting rates changes the induction

60

2.2 2.3 2.4 2.51000

T (K 1)

10 1

100

101

102

Indu

ctio

n P

erio

d (h

ours

)

ExperimentsBen Amara 2013 modelModified model

Figure 3.15: Comparison of experiments, original model and updated model with kineticsolvent effects for 10% methyl oleate.

2.2 2.3 2.4 2.51000

T (K 1)

10 1

100

101

102

Indu

ctio

n P

erio

d (h

ours

)

ExperimentsBen Amara 2013 modelModified model

Figure 3.16: Comparison of experiments, original model and updated model with kineticsolvent effects for 30% methyl oleate.

period measurement, generally towards the direction of experimental induction period. The

more methyl oleate in the fuel blend, the worse the agreement of the updated model with

the experimental values. This reflects a need for more training reactions including methyl

esters, and oxygen-containing species in general.

61

3.5 Recommendations

Several recommendations to improve solvation kinetics in RMG-Py are outlined

below. Among these are better automation, benchmarking, and integration with estimation

methods to ensure thermodynamic consistency.

3.5.1 On-the-fly estimation of solvation kinetics

In the future, the algorithm described in this chapter can be integrated into the RMG

software such that the mechanism including the kinetic solvent effect can be generated on

the fly, instead of as a post-processing step to modify a Chemkin file. On-the-fly genera-

tion of solvation kinetics ensures that important reactions are included in the model, since

a post-processing step is done on reactions whose inclusion in the mechanism was based

on their gas-phase rates. This framework has already been partially set up, as the post-

processing step is completed using methods I added to RMG. When the solvation database

is loaded, the solvation kinetics correction database is loaded in addition to the thermody-

namic database files. A method to calculate the barrier correction using group contributions

was added to the solvation module. The missing step is correcting the intrinsic reaction rate

during model generation, as we similarly do to account for diffusion. Because these steps

are similar, it may make sense to do them in the same place in the source code. Some

placeholder code is included in the diffusionLimited module for this purpose, in a new

class called LiquidKinetics. Complete interfacing with the kinetics and solvation databases

is currently incomplete. Importantly, this on-the-fly step should not be integrated into RMG

until further benchmarking and consistency checks are done, explained below.

62

3.5.2 Benchmarking the estimates

To minimize computational cost, the training reactions used to train group additivity

values for ∆EA involved small molecules, but the reactions in real detailed kinetic mod-

els for fuel oxidation will contain many more atoms. Thus, it is important to understand

whether our training reaction set can accurately capture the kinetic solvent effect on the

actual reactions. It is hypothesized that the chemistry of the reacting site is most important

to ∆EA, and that effects beyond the next-nearest neighbor are negligible. To test this, the

∆EA for some hydrogen abstraction and intra-hydrogen migration reactions from the n-

dodecane/methyl oleate model should be calculated using M062X/MG3S and SMD using

the same protocol as above. These ∆EA can then be compared to the ∆EA that would have

been estimated for the same reaction using the automated method. This is work currently

in progress at the time of writing.

3.5.3 Check thermodynamic consistency with LSERs

One way of checking the consistency of both the SMD calculations, and the linear

solvation energy relationships (LSERs) discussed in Chapter 2, is to compare the equilib-

rium constant obtained by using both of these methods. Using LSERs, the equilibrium

constant of reaction, Keq, can be obtained with:

Keq = exp−∆G

RT

∆G = ∆Ggas + ∆Gsolv

where ∆Gsolv was calculated via the partition coefficient obtained from the Abraham corre-

lations. Another Keq can be calculated using ∆G for the reaction’s reactants and transition

state, which are calculated using the DFT and SMD method outlined in this chapter. Since

data from both of these methods would be used alongside each other in mechanism gener-

63

ation codes such as RMG, it is important the values obtained from each method reasonably

match.

3.5.4 Data-driven approaches

The algorithm for predicting intrinsic kinetic solvent effects has two main draw-

backs: small amounts of training data, and a human-constructed tree structure. Manually

setting up transition state calculations is tedious, thus the first iteration of this algorithm

only contained 53 hydrogen abstraction reactions as training data, with the starting transi-

tion state geometry guess and input files all set up by hand. Using larger amounts of data

which had been previously calculated automatically, and the effect of more data points on

the estimation of solvation kinetics, can be explored.

Furthermore, the molecular structure trees in RMG are all constructed with the fea-

tures ordered in the way the scientist believes to be the most important. For example, many

of the trees in RMG for calculating thermodynamic or kinetic parameters consider the ele-

ment of the central reacting atom to be more important than its bonding configuration, and

the number of its radical electrons to be more important than its element. While a chemist’s

intuition should not be ignored, a data driven approach may improve the accuracy of the

estimation method. To explore this concept, automated decision trees can be constructed

for solvation kinetics using the Python package, scikit-learn [157].

3.5.4.1 Automated transition state theory to generate large training sets

To generate the large solvation kinetics training set, we needed a large set of gas-

phase transition states, as this calculation set-up is the bottleneck of calculating ∆EA. The

set of transition states was created using an automated algorithm, based on a group contri-

bution approach to predicting transition state geometries [39]. Outside of this algorithm,

Python scripts were written to streamline the process of 1) obtaining the gas-phase tran-

sition state geometry and energy from the database of transition states, 2) calculating the

64

Figure 3.17: Algorithm for obtaining solvation energy estimation values from a large tran-sition state dataset. Utilizes software (from top to bottom): AutoTST [39], Gaussian 09[95], cclib [158], and RMG-Py [7, 8], with helper scripts written as part of this work.

single-point energy of the transition state and reactant(s) in the solvent of interest, 3) cal-

culating ∆EA for this reaction, and 4) using the values to train group values for the ∆EA

estimation algorithm. A schematic for this process is shown in Figure 3.17.

3.5.4.2 Automatic generation of decision trees with scikit-learn

Scikit-learn is an open source Python package used for machine learning [157]. It

has been used for automatically constructing decision trees in several chemical and bio-

logical applications [159–161]. Rather than using a chemist’s intuition about how to order

the decision tree, scikit-learn will utilize a user-defined metric (such as RMS error on a

training set, for example), for determining how the tree should be constructed. Using a

package such as scikit-learn opens up several other possibilities. The decision tree model

can be robustly cross-validated on the training set and model hyperparameters can be tuned

using built in modules. Also, ensemble methods such as random forests, which use several

decision trees to estimate the quantity of interest, can improve the accuracy of the model.

Several feature selection, parameter tuning and model combinations can be tested using

pipelines in scikit-learn, with much less code than building these trees manually. Some ex-

ample experimental code for building decision trees for estimating solvation kinetic effect

65

is included in Appendix A.5.

66

4 AUTOMATED SILICON HYDRIDE MECHANISM GENERATION

Chemical vapor deposition (CVD) is a candidate domain for studying detailed

chemical kinetics. The gas-phase chemistry of the precursors to CVD directly affects

the yield and quality of the solid materials produced, and is thus an important facet of

the process for industrial scientists, such as those fabricating microelectronics, to under-

stand. Complete, detailed models of the reactions of these precursor gases, mainly silicon

hydrides such as silane (SiH4), can provide necessary insights to the semiconductor indus-

try. Detailed kinetic models also allow performance predictions to be made at different

operating conditions than what has been studied experimentally. However, building these

large mechanisms by hand is tedious, and automatic mechanism generators can be used to

build the models faster and minimize errors. Using automatic mechanism generation en-

sures that all important reaction pathways, including those involving radical species, will

be considered in modeling and prediction of the CVD process. Furthermore, a framework

for studying gas-phase silicon hydrides provides the first step in studying surface reactions

involved in CVD.

In this section of the dissertation, Reaction Mechanism Generator (RMG), an au-

tomatic mechanism generator discussed in the prior sections, was used to build detailed

kinetic models for silicon hydrides used for CVD. A new element, silicon, was added to

the RMG framework. Specifically, data for silicon hydrides were added to RMG’s database

of thermodynamic and kinetic parameters. Radical reaction types, which already existed in

RMG but lacked data for silicon, and new reaction types specifically important for silicon

hydride chemistry, can both be proposed with the updated RMG.

67

Using the new data in RMG, a model for SiH4 thermal decomposition was built.

The resulting model was used to simulate a flow reactor, and these simulations were com-

pared to SiH4 flow tube experimental data obtained from Onischuk et al. [162], including

data for SiH4 and Si2H6 concentration profiles with time, and at different temperatures,

residence times, and initial concentrations of SiH4. Studying SiH4 can serve as a proof-of-

concept that can be extended to other novel gas precursors.

4.1 Background

SiH4 CVD has been well studied experimentally and theoretically [163–170], among

others, for the past 5 decades. Several representative studies will be discussed in the fol-

lowing sections.

4.1.1 Experimental work on SiH4 chemistry

Several decades ago, Purnell and Walsh experimentally studied SiH4 pyrolysis be-

tween 375 and 430◦ C. They found the overall rate of SiH4 −→ SiH2 + H2 to be of order

1.5, and propose different chemical mechanisms to account for this order. The authors

rule out heterogenous steps under these conditions, because the vessel’s A/V ratio did not

strongly change the reaction rate. Thus, they conclude that the mechanism must include

a unimolecular, first order decomposition which is pressure dependent along with chain

reactions. However, the choice of whether SiH4 first decomposes to SiH3 or SiH2 required

further information of bond dissociation energies [163].

Newman et al. studied silane decomposition in a shock tube, supplemented by

RRKM rate calculations. They found that rate of silane decomposition is independent of

initial silane concentration, and also that hydrogen atom production is not important in the

process, providing evidence that SiH4 decomposition to SiH2 is the most important initial

step. However, because they did not see disilane, Si2H6, as a product, they hypothesize the

SiH2 must be consumed by some other means rather than producing hydrogen atoms [171].

68

Michael Coltrin and co-workers at Sandia National Laboratories have done exten-

sive work on silane CVD in a rotating disk reactor, which eliminates temperature and con-

centration gradients allowing CVD to be more uniform [165, 167]. Based on laser fluo-

rescence measurements, two reactions are proposed that produce Si atoms, which involve

disilylene (H3SiSiH). These reactions are in contrast to what was previously thought to be

the route to Si atoms, SiH2 −→ Si + H2 [167].

Frenklach et al. studied silane and disilane pyrolysis in a shock tube, diluted with

both argon and hydrogen, at high temperatures (900-2000 K). The results of these ex-

periments were used to build a detailed kinetic model for both gas-phase and gas-surface

reactions. Comparison to the experiment showed that the refractive index of the silicon

material used greatly affects model predictions [168].

Onischuk et al. investigated silane pyrolysis in a flow reactor between 800-1000

K. For the gas phase, the effects of initial silane concentration on silane decomposition

and disilane evolution were elucidated; specifically, these rates increased with increasing

silane concentration. At different residence times, the effect of temperature on final silane

concentration was probed. The solid phase was also investigated; the concentration of

particles as well as hydrogen content in the solid product was measured. Based on the

experimental results, the chemical mechanism was described as an initial decomposition of

silane into SiH2 and H2, followed by subsequent silylene insertions to create higher silanes

and substituted silylenes [162]. The Onischuk et al. experiments are used as a basis of

comparison in this chapter of the dissertation.

4.1.2 Detailed mechanisms for SiH4 CVD

Mechanisms for SiH4 thermal decomposition have been developed using the above

experimental data as well as theoretical calculations, by hand and automatically. Yuuki et

al. developed a model for SiH4 and Si2H6 from the experimental observations of Purnell

and Walsh and Newman et al. [163, 164, 171]. The model includes 10 species and 11

69

reactions, and it achieves good agreement with two experiments [163, 172].

Coltrin et al. developed a mathematic model for their rotating disk reactor, which

includes a 26 reaction gas-phase chemical mechanism [165]. Several rate constants were

taken from the RRKM calculations of Becerra and Walsh [173].

Giunta et al. built a gas-phase silane decomposition mechanism from prior exper-

imental works on SiH4/NO CVD[174] and CVD from Mg2Si [175], which includes 18

gas-phase reactions. They hypothesize that film growth is mainly due to disilene species.

The model generally modeled CVD from silane well, compared to experiment, while ex-

perimental comparison to disilane CVD only agrees qualitatively at best. Authors cite low

reliability of rate constants as well as the absence of heterogeneous chemistry from the

model as reasons why Si2H6 experiments do not match well [166].

The largest manual reaction mechanism for the pyrolysis of silane to form silicon

nanoparticles, which was built by Swihart and Girshick, contains 220 chemical species and

2600 chemical reactions. To build the mechanism, a group additivity method was devel-

oped to estimate the thermochemistry of several silicon hydrides in the model. Reactivity

rules were also developed to generate reactions in the mechanism, including templates for

silylene (SiH2) insertion into Si-H and H-H bonds (and its reverse, SiH2 elimination); sily-

lene to silene isomerization; and ring opening and closing isomerizations [5]. Later, this

work was continued in collaboration with the the Broadbelt group at Northwestern Univer-

sity, which has extensively modeled the pyrolysis of silane, particularly for the application

of silicon nanoparticle formation. The group additivity thermochemistry method was im-

proved, using the G3//B3LYP level of theory [70, 176]. Wong et al. [6] used automatic

mechanism generation to build a model for silicon nanoparticle formation from SiH4 de-

composition. In that study, automatic mechanism generation software developed by the

Broadbelt group, which uses a rate-based termination criteria to limit model size, was em-

ployed. Reaction types were the same as in the previous study by Swihart and Girshick

[5]. The study included a comprehensive analysis of the different factors contributing to

70

silicon particle clustering. However, radical pathways were not included in the built mod-

els. Adamczyk and co-workers further developed group additive rate rules for the reaction

families involved, derived from quantum chemistry calculations at G3//B3LYP [177–180].

4.1.3 Importance of radical chemistry in silicon hydride thermal decomposition

In their early study, Purnell and Walsh suggested that decomposition of SiH4 to

SiH3 and H plays a role in silane pyrolysis despite not being the most dominant path-

way [163]. An earlier study by Emeleus and Reid [181] suggested the role of SiH3 be-

comes more important when Si2H6 and Si3H8 are used as the silicon hydride precursor to

CVD. The involvement of radicals may also be more important at certain CVD conditions

[182, 183], for example, in low temperature CVD in silane plasma [184]. SiH3 was found

to be the dominant radical species at steady state in silane plasmas in a study by Robertson

et al. [185]. Watanabe et al. later demonstrated that the concentration profiles of Si, SiH

and SiH2 radicals greatly affect particle growth in these systems [186]. Given that these

studies all theorize the role of radical reaction pathways in silicon hydride thermal decom-

position, methods for building detailed kinetic models should have the ability to include

these pathways if they are important.

4.2 Methods

To enable RMG to generate detailed kinetic models for silicon hydrides, small up-

dates to the RMG source code were made, and its database was updated. Once these

updates were performed, RMG was used to build detailed kinetic models for silane thermal

decomposition. The models output by RMG were used to simulate a reactor for comparison

to the experiments of Onischuk et al. [162].

71

4.2.1 RMG source code

Although silicon atom types already existed in RMG, the functionalities for in-

crementing and decrementing bond orders, breaking and forming bonds, and adding and

removing lone pairs and radical electrons were fully implemented in this work. These

updates were made in the molecule module of RMG.

Additionally, several thermodynamic and kinetics calculations were completed us-

ing quantum chemistry and CanTherm, which parses quantum chemistry output files to

perform thermodynamic and kinetics calculations, and is a subprogram of RMG [33]. In

this work, CanTherm uses the rigid rotor harmonic oscillator approximation to calculate

thermodynamic properties and canonical transition state theory with Eckart tunneling to

calculate kinetic parameters. In order to perform these calculations, CanTherm must apply

atom, bond and spin-orbit coupling energy corrections to adjust the energies calculated for

a particular level of theory and quantum chemistry program. These corrections must be

manually entered into the RMG source code for silicon atom types and silicon containing

bonds. Thus, the necessary parameters were entered for the levels of theory used in the

calculations, either from published data [70, 187, 188] or additional calculations of atomic

energies using Gaussian 09 [95].

4.2.2 Updating RMG’s database

RMG’s database was updated with both kinetics and thermodynamics data for sil-

icon hydrides. Published reaction rates have been added to reaction libraries, which are

preferentially used during RMG simulations if they match a generated reaction. Additional

rates were calculated using transition state theory. Some published and calculated rates

have been added to the training data for four reaction families, to be described below, and

will be used to estimate reaction rates in these families where the exact rates are unavail-

able. Published, calculated, and group additive thermodynamic data for silicon hydrides

have also been added to RMG’s database.

72

4.2.2.1 Kinetics data

In this work, two reaction rate libraries were added to RMG’s database. The li-

braries are based on one experimental study of SiH4 CVD [166] and one theoretical study

involving pressure-dependent rate calculations for mainly Si2 species [170]. If specified

in the input file of an RMG job, the rates from these libraries will be used if an RMG-

generated reaction matches a reaction in the library.

Additionally, two new reaction families were added to RMG’s database: 1. sily-

lene insertion, in which a silicon atom with a lone pair can insert into a silicon-hydrogen

or hydrogen-hydrogen bond; and 2. silylene-to-silene isomerization, in which a hydrogen

atom migrates from an sp3 bonded silicon atom to a silicon atom with a lone pair, and a

double bond is formed. These families are based on the reaction types used in a previous

work on model generation [6]. The kinetics data in these reaction families come from rates

calculated by Adamczyk et al. [177–179] using G3//B3LYP.

The third reaction family considered in previous mechanism generation for silicon

hydrides were ring closing reactions (and its reverse, ring opening), in which a silylene

molecule with at least three silicon atoms isomerizes to form a ring structure. Two of these

reactions (for Si3H6 and Si4H8) were added into a reaction library. Because the current work

does not consider larger molecules, an RMG reaction family for arbitrarily large rings was

not created.

In addition, the training reaction databases of two existing reaction families in

RMG, hydrogen abstraction and radical recombination, were updated with silicon hydride-

containing reactions and kinetic parameters [183, 189], found in the NIST kinetics database

[190]. For hydrogen abstraction reactions, ten additional rates were calculated. The reac-

tant and transition state geometries were optimized using M06-2X [147, 148] / 6-311+G(3d2f)

[150–152, 191, 192] , with a clear saddle point found for each reaction. The CanTherm

package, which applies conventional transition state theory, was used to determine the

Arrhenius kinetic parameters [33]. More detailed information about CanTherm can be

73

found in Chapter 1. Reliability of these new, calculated rates were tested by comparing to

available published experimental and theoretical rate calculations for hydrogen abstraction

reactions of silicon hydrides [182, 189, 193–197].

Reaction family Template

Hydrogen abstraction R1 H + R2 R1 R2 H+

Radical recombination R1 + R2 R1 R2

Silylene insertion R1 Si H R2 H+ SiH2R1R2

Silylene-to-silene isomerization Si Si HHR1

R2Si SiH2

R1R2

Table 4.1: Reaction families used to generate mechanisms for silicon hydrides in RMG

The templates for these four reaction families, which are used to generate the SiH4

thermal decomposition models, are given in Table 4.1. Since these general reactions are

reversible, reactions based on the reverse templates (i.e. silylene elimination) are also in-

cluded in the model.

Further information about how RMG prioritizes reaction rates from libraries and

families can be found in Chapter 1.

4.2.2.2 Thermodynamics data

Group additivity values for the thermodynamics of silicon hydride species (silanes,

silenes, and silylenes) were previously calculated by Swihart and Girshick [5]. The group

values were later improved upon by Wong et al. by fitting to G3//B3LYP calculations [70].

In this work, the Wong et al. values were added to RMG’s database for use in the existing

group additivity scheme for calculating thermodynamic parameters in RMG.

For radical species, group additivity values have not previously been determined.

We used G3//B3LYP quantum chemistry calculations to generate hydrogen bond increment

(HBI) values for silicon hydride radicals. HBI is a method, described in more detail in

Chapter 1, used to calculate the thermodynamic parameters of a radical species R∗ from

74

its parent molecule RH, which is the chemical species created by saturating the radical

with hydrogen atoms [28]. Both the G3//B3LYP calculations for the closed-shell species

and group additivity values using HBI for radical species were benchmarked against higher

level calculations by Katzer et al. [198]

4.2.3 RMG model generation

The conditions for the RMG simulation were chosen to closely mirror those of the

experimental conditions in the flow tube experiment [162], with the base case conditions of

T = 913 K, P = 39 kPa, and y0(SiH4) = 0.00016 in an argon bath gas. Temperature, pressure,

and initial SiH4 mole fraction were varied around these values to generate a comprehensive

mechanism that could be used for reactor simulations at a variety of conditions. Pressure

dependence was included in some of the built models to test its effects on the model ac-

curacy. The pressure dependence scheme in RMG has been described in Chapter 1 and

previously [25].

4.2.4 Reactor modeling

Once the models were built in RMG, they were tested for validity by comparison

to experimental results using a constant pressure reaction model in Cantera, which inte-

grates with Python [199]. The Python script used to simulate the reactor and generate the

comparison plots are provided in Appendix B.4. We simulated the same conditions for

temperature, pressure, initial SiH4 mole fraction, and residence time given in the experi-

ment by Onischuk et al. [162] The rate constants and thermodynamic parameters used in

the simulation come from the RMG-generated mechanism; the RMG simulation provides a

Chemkin file as output, which can be easily converted to a Cantera input file with a script.

Different simulations as well as sensitivity analyses were performed to understand the ef-

fects of temperature, pressure, initial SiH4 mole fraction, residence time, and model size

on the SiH4 concentration profile.

75

4.3 Results

The thermodynamic and kinetic data calculated were compared to published data

in order to validate their use in RMG’s database. After updating the database, the RMG

generated models were used in simulations and compared with experimental results. The

effects of changing various process conditions were considered.

4.3.1 Kinetics of hydrogen abstraction reactions

# Reaction log A Ea log k300K log k1000K Source

1 SiH4 + H −→ SiH3 + H2 14.8 10.7 13.1 14.2 This work13.9 11.7 11.9 Ref. 196

11.2 13.6 Ref. 18913.2 Ref. 197 (QI)13.1 Ref. 197 (VTST)13.2 Ref. 195

11.3 Ref. 194

2 SiH3 + H2 −→ SiH4 + H 13.4 72.3 1.03 9.51 This work12.4 61.6 1.65 Ref. 196

3 Si2H6 + H −→ Si2H5 + H2 15.9 3.55 15.5 15.7 This work13.8 11.1 11.9 Ref. 193

11.9 14.0 Ref. 189

4 Si2H5 + H2 −→ Si2H6 + H 14.2 77.0 1.01 10.1 This work

5 Si2H6 + SiH3 −→ Si2H5 + SiH4 15.1 12.7 13.2 14.3 This work9.6 Ref. 182

6 Si2H5 + SiH4 −→ Si2H6 + SiH3 14.8 24.6 10.9 13.4 This work

7 Si2H5 + H −→ SiH3SiH + H2 14.5 4.55 13.9 14.2 This work

8 SiH3SiH + H2 −→ Si2H5 + H 14.1 88.1 -0.97 9.45 This work

9 Si2H4 + H −→ Si2H3 + H2 14.7 7.95 13.5 14.3 This work

10 Si2H3 + H2 −→ Si2H4 + H 13.6 126 -8.11 6.93 This work

Table 4.2: Hydrogen abstraction rates calculated from M062X/6-311+(3d2f) and transitionstate theory using Cantherm. Rates were compared with those obtained from literature,where available. Units in kJ, mol, cm3, s. Logarithms are base 10.

76

We calculated ten hydrogen abstraction reaction rates for use in RMG’s database,

but only four prior published rates were available for comparison. The rate coefficients

at 300 K and 1000 K and Arrhenius parameters are displayed in Table 4.2, along with

published data where available (Reactions 1, 2, 3 and 5). The calculated geometries of the

transition states of these ten reactions are included in Appendix B.1. There are only five

transition state geometries given, since the reverse reactions will have the same transition

states.

In all cases, the rate coefficients at 1000 K are within 1–2 orders of magnitude

of the published data. However, at 300 K, the discrepancy is much greater for Reactions

3 and 5. Because we are considering temperatures between 800 K and 1000 K for this

study, the differences at low temperatures are not particularly concerning. For reactions

such as Reaction 1, where many experimental and theoretical data are available and are in

agreement with one another, it is practical to use this agreed-upon rate in RMG’s database

instead of the less accurate rate calculated here. However, the comparison of these four

calculated rates to the literature data shows that for reactions where data are unavailable or

scarce, such as Reaction 4, these DFT estimates are reasonable enough for the purposes of

automatic mechanism generation, particularly at CVD relevant temperatures. If the RMG

generated model were to be simulated at process conditions at which radical chemistry

becomes more important (see further results), or different silicon precursors are used, more

accurate calculations should be done.

4.3.2 Calculated thermodynamic data

All geometry optimization results from G3//B3LYP calculations on silicon hydrides

species are provided in Appendix B.2. The parity plot shown in Figure 4.1 reveals that cal-

culations of ∆fH◦298 using G3//B3LYP for both closed-shell and radical species compare

well with the high level calculations of Katzer et al. [198]. Most discrepancies are less

than 5 kcal/mol. Larger differences between the two methods are seen for some Si3 and

77

Figure 4.1: G3//B3LYP calculations of ∆fH◦298 (this work) compared to high level calcu-

lations by Katzer et al. [198], for silicon hydride species with up to three silicon atoms.Structures shown for species with more than 5 kcal/mol discrepancy.

multiradical species. Katzer et al. report that for proper treatment of these species, which

have both multiple radicals and divalent silicon atoms, a multiconfiguration reference wave

function with a post-self-consistent field calculation method must be used [198]. Therefore,

we know that our treatment with G3//B3LYP will not be exact. However, G3//B3LYP pro-

vides a reasonable and computationally less expensive estimation of the thermochemistry

for most species, which justifies our use of it for other calculations in this work.

Hydrogen bond increment (HBI) values derived from the G3//B3LYP calculations

of radical species and their parent molecules are given in Table 4.3. ∆fH◦298 for 16 silicon

hydride radicals were then calculated via group additivity and compared to the Katzer et

al. values [198], illustrated in Figure 4.2. In this particular comparison, the group addi-

tivity values of Wong et al. [70] were used to calculate the thermodynamics for the parent

molecules, for the sake of consistency across species, but during an actual RMG simulation,

exact species thermodynamics would be used for the parent molecules if available in the

database. Because of this, Figure 4.2 is a reflection of both the accuracy of Wong’s group

78

Radical species Parent moleculeHBI(∆fH

◦298)

(kcal/mol)HBI(S◦298)

(cal/mol/K)

SiH3Si HSi SiH3 74.0 -3.47SiH SiH2 75.3 -4.92

HSi SiH2 HSi SiH3 75.8 -0.571H2Si SiH H2Si SiH2 83.1 3.01

SiH3

HSi

H3Si SiH3

H2Si

H3Si86.0 1.76

H2Si SiH3 H3Si SiH3 88.5 0.812SiH3 SiH4 91.3 0.192

Si SiH2 146 -12.9

H2Si Si H2Si SiH2 154 -0.446

SiH3

SiH3Si SiH3

H2Si

H3Si168 3.00

HSi SiH3 H3Si SiH3 174 0.443

SiH2 SiH4 181 -1.03

Table 4.3: Hydrogen bond increment (HBI) corrections calculated with G3//B3LYP. Thesecorrections account for the effect of losing 1 or 2 hydrogen atoms on the enthalpy andentropy.

79

Figure 4.2: Group additivity calculations of ∆fH◦298 from RMG-Py, derived from Wong

et al. GAV [70] and HBI corrections (this work), compared to high level calculations byKatzer et al. [198], for 16 silicon hydride radical species. Structures shown for specieswith more than 5 kcal/mol discrepancy.

additivity values and our calculated HBI values. While most values compare reasonably

well, there are again significant differences for three multiradical species which contain

either double bonds or divalent silicons, for the reasons discussed above. It may be prefer-

able, therefore, to calculate the thermodynamics of these multiradical species at a higher

level and to put them in a thermodynamic library in RMG, which are used preferentially

over group additivity estimates.

4.3.3 RMG generated mechanisms

Two RMG mechanisms were used for most of the reactor simulations, the difference

being inclusion of pressure dependent rate parameters. Tolerance was adjusted to make

the size of the models roughly equal and to ensure that radical chemistry was included in

both models. The mechanism including pressure dependence contains 63 silicon hydride

species and 1298 reactions and the mechanism without pressure dependence contains 57

80

species and 578 reactions. A third (pressure-dependent) mechanism was also generated to

incorporate important species and reactions at a variety of initial SiH4 concentrations for

comparison to experiment. This mechanism was larger, with 83 species and 2708 reactions.

The largest RMG-generated mechanism (Chemkin file, species dictionary, and converted

Cantera input file) is provided in Appendix B.3.

4.3.3.1 Effect of pressure dependence

A constant-pressure reactor model was simulated with both the pressure dependent

and non-pressure dependent RMG mechanisms. The result, shown in comparison to the

prior experimental results, is displayed in Figure 4.3(a). Since the RMG model containing

pressure dependence is shown to replicate more accurately the experimental result, pressure

dependence was used for the remaining analysis. This result is expected, as including

pressure dependent networks in the model is important at the low pressures typically used

for SiH4 CVD.

4.3.3.2 Effect of temperature

The full pressure dependent model was further used for reactor simulations at dif-

ferent temperatures. Figure 4.3(b) displays the plot from experiment with the pressure

dependent model simulated at 863 K, 893 K, 913 K (the experimental temperature), and

963 K.

The simulations at 863 K and 963 K show that temperatures within a ± 50 K range

can affect the SiH4 concentration profile enormously. Simulating the reactor at 893 K

provides a close comparison to the experimental data reported at 913 K, illustrating that an

uncertainty of 20 K can fully explain the difference between the model and the experiments.

The main initial decomposition reaction, SiH4 −−⇀↽−− SiH2 + H2, has an activation energy of

about 55 kcal/mol, with many reported theoretical and experimental determinations cov-

ering a range of about ±5 kcal/mol. A 20 K change from 913 K to 893 K corresponds

81

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Time (s)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

ySiH

4

y0,

SiH

4

ExperimentPDepNo PDep

(a)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9Time (s)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

ySiH

4

y0,

SiH

4

Experiment863 K893 K913 K963 K

(b)

Figure 4.3: Simulation results (this work) compared with SiH4 thermal decomposition ex-periment (data points) [162]. (a) Comparison of RMG models with and without pressuredependence to experimental results. Conditions are T= 913 K, P = 39 kPa, and y0,SiH4

=1.6× 10−4 (b) Comparison of RMG model, including pressure dependence, at differenttemperatures, compared to the experimental results at 913 K.

to only a −1.20 kcal/mol change in activation energy for a global reaction rate following

Arrhenius kinetics with a 55 kcal/mol activation energy. In other words, the discrepancy

lies well within the expected uncertainty in the activation energies.

4.3.3.3 Residence time variation with temperature

In the SiH4 experiment, the reactor residence time was varied by changing the volu-

metric flow rate of the feed gas [162]. Our simulations similarly varied the volumetric flow

rate into the reactor. Figure 4.4 compares the SiH4 concentration profile versus temperature

at four different residence times. In the compared experiment, reported inlet volumetric

flow rates and residence times at 843 K were not consistent given a constant volume re-

actor, leading to slight errors in the residence time used in the simulation. The error bars

in the figure represent this discrepancy only, with more information included in Appendix

B.5.

The reactor simulations compare qualitatively well with the experimental data. In

the previous section, it was noted that a 20 K difference in temperature, which is well within

the uncertainty of the reaction rates, would better capture the SiH4 profile. One can imagine

82

800 850 900 950 1000Temperature (K)

0.0

0.2

0.4

0.6

0.8

1.0

ySiH

4

y0,S

iH4 Exp. 0.8 s

Exp. 0.5 sExp. 0.35 sExp. 0.2 sMod. 0.8 sMod. 0.5 sMod. 0.35 sMod. 0.2 s

Figure 4.4: SiH4 concentration vs. temperature at different residence times, from Onischuket al. [162] (points) and from reactor simulations in this work.

that the simulation data in Figure 4.4 would, therefore, become closer to the experimental

results if the curves were shifted by +20 K; the largest discrepancy is about 40 K.

4.3.3.4 Effect of radical reaction families

To investigate the effect of excluding radical reaction families, a new mechanism

was generated with the radical reaction families (hydrogen abstraction, radical recombina-

tion) disabled during the mechanism generation. The results for the mechanisms simulated

at 913 K are displayed in Figure 4.5(a), along with the experimental data. At these condi-

tions, the removal of radical reactions has no noticeable effect on overall SiH4 decompo-

sition rate. Because radical pathways are thought to be relatively more important at lower

temperatures of CVD conditions, RMG mechanisms were generated at 613 K, both with

all reactions included and with radical reaction families removed, and used in simulations.

At this lower temperature and far slower decomposition, as shown in Figure 4.5(b), there is

still hardly a difference between the full mechanism and the mechanisms with radical reac-

tions removed. Comparing the Si fluxes at 6× 104 seconds, which was chosen due to the

slight acceleration of the non-radical pathway at that time, we don’t see a difference in the

significant pathways to SiH4 decomposition, and only negligible participation by radicals.

The flux diagram for the full mechanism is shown in Figure 4.6.

83

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Time (s)

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1.0

ySiH

4

y0,

SiH

4

ExperimentFull mechanismNo radical reactions

(a)

x105

(b)

Figure 4.5: Simulation results for full pressure dependent mechanisms generated by RMG,compared with a mechanism generated without radical reaction families allowed. P = 39kPa, y0,SiH4

= 1.6× 10−4 (a) T = 913 K (b) T = 613 K.

Scale = 1e-10 time = 60158

Si₂H₆

SiH₃SiH

H₄Si₂

SiH₂Si

Si₂

SiH₄

SiH₂

Figure 4.6: Flux diagram for Si at 6× 104 seconds for full, pressure dependent mechanismgenerated by RMG and simulated at 613 K

84

4.3.3.5 SiH4 and Si2H6 concentration profiles

0.00 0.05 0.10 0.15 0.20 0.25Time (s)

0.70

0.75

0.80

0.85

0.90

0.95

1.00y

SiH

4

y0,

SiH

4

y0 = 0.00016y0 = 0.00088y0 = 0.0025y0 = 0.05

0.00 0.05 0.10 0.15 0.20 0.25Time (s)

0.0000.0050.0100.0150.0200.0250.0300.0350.040

ySi2

H6

y0,

SiH

4

y0 = 0.00088y0 = 0.0025y0 = 0.01y0 = 0.05

(a) Experimental results from Onischuk et al. [162]

0.00 0.05 0.10 0.15 0.20 0.25Time (s)

0.70

0.75

0.80

0.85

0.90

0.95

1.00

ySiH

4

y0,

SiH

4

y0 = 0.00016y0 = 0.00088y0 = 0.0025y0 = 0.01y0 = 0.05

0.00 0.05 0.10 0.15 0.20 0.25Time (s)

0.0000.0050.0100.0150.0200.0250.0300.0350.040

ySi2

H6

y0,

SiH

4

(b) Results of reactor simulations using RMG-generated model

0.00 0.05 0.10 0.15 0.20 0.25Time (s)

0.70

0.75

0.80

0.85

0.90

0.95

1.00

ySiH

4

y0,

SiH

4

y0 = 0.00016y0 = 0.00088y0 = 0.0025y0 = 0.01y0 = 0.05

0.00 0.05 0.10 0.15 0.20 0.25Time (s)

0.0000.0050.0100.0150.0200.0250.0300.0350.040

ySi2

H6

y0,

SiH

4

(c) Simulation results after updating three reaction rates.

Figure 4.7: Variation in concentration profiles of SiH4 and Si2H6 with initial SiH4 concen-tration at 873 K.

Figure 4.7 displays the concentration of SiH4 and Si2H6 with time at different ini-

tial SiH4 concentrations at 873 K. These profiles appear not to vary with the initial SiH4

concentration (4.7(b)), although the experimental results show a clear difference (4.7(a)).

In contrast, an early shock tube study reveals that rate of SiH4 decomposition is unaffected

85

by initial SiH4 concentrations [171], although the conditions are different from both this

modeling study and from the Onischuk et al. experiment.

A sensitivity analysis was performed to assess which reactions qualitatively affected

the concentration profiles of SiH4 and Si2H6. Three reactions were identified which, when

the rate constants were modified by no more than two orders of magnitude (102), produced

noticeable changes in these concentration profiles. These reactions are as follows:

SiH2 + SiH2−−⇀↽−− Si2H4

H2 + SiH3SiH −−⇀↽−− Si2H6

H2 + SiH3SiH −−⇀↽−− SiH2 + SiH4

Changing these few rates at the same time can produce concentration profiles that

are close to the experimental results, as shown in Figure 4.7(c). While the authors do not

recommend changing the rates on the basis of the current evidence, the result is shown to

establish that this initial built mechanism is plausible given the uncertainties. For example,

the first altered reaction rate, for SiH2 + SiH2 ←→ Si2H4, was estimated by Giunta et

al. to have the same rate as SiH2 + Si2H6 ←→ Si3H8, which was measured by Jasinski and

Chu[166, 200] (this is the rate used in the RMG mechanism). However, Dollet and de Persis

reported their calculated rate for this reaction to be an order of magnitude different[170].

Therefore, it reasonable to assume considerable uncertainty in this rate. For a final model,

however, modifying rates should be done carefully, with additional evidence and more

knowledge about the fidelity of all rates.

86

4.4 Discussion

Thermodynamic and kinetic data for silicon hydrides were generated to update

RMG’s database, and the computational methods used were benchmarked with available

experimental and high level theoretical data. From both of these studies, it was observed

that where high accuracy data are available, they should be put into a thermodynamic or

kinetic library in RMG for greater model accuracy. However, if data are unavailable, the

calculations provide reasonable enough estimates for initial construction of a model. These

calculations were used in RMG’s database for the hydrogen abstraction reaction family

and to generate hydrogen bond increment values for calculating thermodynamics of radical

species. The additions to RMG’s database allows users to build kinetic models for SiH4

thermal decomposition.

The inclusion of radical reaction families was found to be unimportant to overall

SiH4 decomposition rate at both 613 K and 913 K. Thus, inclusion of these pathways does

not mechanistically change the understanding of thermal decomposition of SiH4, instead

corroborating the prior studies that conclude radical reaction pathways are much slower

compared to the main decomposition pathway to SiH2 and H2 and the subsequent insertion

and elimination reactions that occur. However, the new ability to automatically build more

complex mechanisms for silicon hydrides in general can provide understanding which helps

in selection of process conditions and/or different precursors for CVD which reduce the

amount of radicals formed, thus reducing the risk for unwanted particle formation and

growth in the CVD reactor.

Generation of two detailed kinetic models in RMG, one with pressure dependent

reactions and the other without, showed that the pressure dependent model more accu-

rately compared to experimental data. Furthermore, using the pressure dependent model,

temperature had a large effect on the SiH4 concentration profile with time. A 20 K change

in temperature, which is comparable to a change of only about 1.2 kcal/mol in activation

87

energy at these temperatures, brought the simulation results closer to the experimental SiH4

concentration profile.

Simulations using the RMG generated model were able to reasonably replicate the

effect of residence time on the SiH4 concentration profile at different temperatures. If

uncertainty in temperature by about 20 K is taken into account, the simulations using the

RMG generated model more closely match the experiment.

Comparing the SiH4 and Si2H6 profiles obtained by varying initial SiH4 concen-

tration, the model does not match well with the experimental data. Specifically, the sim-

ulations show no change in these profiles at different initial concentrations, whereas the

experiment shows a clear dependence.

The qualitative trends seen in the experimental results can be obtained by chang-

ing three reaction rates by amounts likely within the uncertainty of these rates; however,

this approach to modifying rates is not advised, as the causes of the discrepancy may lie

elsewhere. Instead, it’s recommended to calculate carefully those reaction rates which can

feasibly be calculated. A global sensitivity analysis could provide additional information

about which rates significantly affect the SiH4 and Si2H6 concentration profiles. Addi-

tionally, given that these results in this dissertation are more in line with the Newman et

al. experiment at different conditions, the effect of SiH4 initial concentration still remains

unclear. Further investigation by detailed measurements and calculations of these important

rates could improve the accuracy of RMG’s database for silicon hydrides.

4.5 Summary

A framework for extending the Reaction Mechanism Generator software package

(RMG) to a new class of elements and chemical reactions has been demonstrated, which

allows generation of detailed kinetic models for silicon hydride decomposition. This work

builds on previous efforts to generate these mechanisms automatically, making use of pub-

lished thermodynamic and kinetic data. Additional data were calculated to allow radical

88

reaction pathways to be enabled, including calculations of rates for hydrogen abstraction

reactions of silicon hydrides, and hydrogen bond increment values for radical species. All

thermodynamic calculations were completed at the G3//B3LYP level of theory, while the

reaction rates were calculated using M062X/MG3S and classical transition state theory.

For silane thermal decomposition, simulations using the RMG-generated model reason-

ably compare to experimental results, with inconclusive results on the effect of initial silane

concentration. Inclusion of the enabled radical reaction families, hydrogen abstraction and

radical recombination, made little difference in the reactor simulations. Many other reac-

tion families exist in RMG which can be extended to silicon hydrides, but availability of

experimental or high level theoretical calculations of their reaction rates remains a chal-

lenge. This work represents an important first step in extending RMG to model chemical

vapor deposition by more accurately representing the detailed gas phase chemistry in this

process, and validating the results for silane thermal decomposition.

4.6 Recommendations

Several recommendations for SiH4 model improvement are outlined below. These

mainly involve refinement of the thermodynamics and kinetics parameters used in RMG’s

database for the construction of the model. Additionally, the possibility of including surface

chemistry in RMG is discussed.

4.6.1 Expansion of thermodynamic libraries for radical species

As suggested previously, certain effects caused by multiradical or divalent silicon

species cannot be accounted for using lower-level electronic structure methods [198]. For

species with these particular characteristics, the comparison of the values calculated with

G3//B3LYP as well as the group additivity values using new HBI corrections, and the higher

level calculations of Katzer et al., yielded differences in ∆fH◦298 larger than 5 kcal/mol.

The radical species with these chemical characteristics that appear in the core or edge of the

89

RMG-generated models should be recalculated, using high level methods, such as coupled-

cluster methods. Availability of computational chemistry software that has capability to run

these methods is imperative; ORCA is one such open-source software [201]. Furthermore,

adequate computational resources are necessary to run such high-level calculations. Such

resources are available using the Discovery cluster at Northeastern University, accessible

through the Massachusetts Green High Performance Computing Center (MGHPCC).

4.6.2 Calculation of rates

In this work, ten hydrogen abstraction reaction rates were calculated using DFT and

added to RMG’s database. For silylene insertion, silylene-to-silene isomerization, and ring

opening reactions, rates were sourced from the work of Adamczyk et al [177–180]. All

of these rates from literature were calculated with G3//B3LYP. Both levels of theory used

to calculate rates are known to be approximate, with errors in DFT energies contributing

to discrepancies in barrier heights that have a significant effect on the rate. Furthermore,

the M062X/MG3S calculations used the rigid rotor harmonic oscillator (RRHO) approxi-

mation and did not check whether the reactants, products and transition states found were

the lowest energy conformers. While these effects are generally larger for thermodynamics

calculations since some error cancellation might occur in the calculation of kinetics, the

magnitude of the effect is unknown. Thus, one way of improving RMG-generated models

would be to calculate reaction rates that are either estimated, or used directly from lower-

level calculations, at higher levels of theory. If computational resources are a problem,

the lower levels of theory can be used, but the 1-D hindered rotor approximation can be

incorporated to find the lowest energy conformer and include the effects of hindered rotors

[202].

90

4.6.2.1 Using automatic transition state theory calculations

A recently developed method calculates reaction rates automatically, in a high-

throughput manner, using canonical transition state theory. The method, known as Au-

toTST, uses a machine-learning algorithm to estimate transition state geometries via group

contribution (discussed in Chapter 1) and is integrated with computational chemistry soft-

wares and CanTherm [33, 39, 40]. AutoTST could in theory be applied to the reaction fam-

ilies utilized in this work which have a reaction barrier in order to generate many reaction

rates for these families. However, significant challenges arise when extending AutoTST to

new reaction families. Furthermore, AutoTST currently has some limitations, including in-

accuracies that result from using DFT energies, errors in calculation of symmetry number,

use of the RRHO approximation, and improper determination of lowest-energy conformer

[203]. Use of AutoTST, or any other methods used to calculate reaction rates more care-

fully, should be used in conjunction with sensitivity analyses that identify which reactions

in the mechanism are important.

4.6.3 Sensitivity analysis

One type of sensitivity analysis was employed in this work, where the reaction rates

were individually varied to assess the effect on silane decomposition with differing initial

silane concentration. Once three reactions were identified, they were all modified at the

same time to visualize a more pronounced effect. However, such a sensitivity analysis

was semi-manual and rather unsystematic. Further sensitivity analysis is available using

Cantera, and can be used to see how each parameter in the reactor system affects a system

output variable. In this way, it is possible to rank each reaction rate constant as affecting

concentration of SiH4, Si2H6, or any other species concentration of interest.

91

4.6.4 Surface chemistry

Further extension of RMG to surface chemistry could allow for more rigorous com-

parison to CVD experiments. Many published experiments and mechanisms could not be

used for validation, since the gas and surface phase analysis were coupled, unlike in the

Onischuk et al. paper [162]. A collaborative project between Professor Richard West and

Professor C. Franklin Goldsmith at Brown University involves extending RMG to heteroge-

neous catalysis. The framework used here, which allows for the representation of adsorbed

species and heterogeneous reactions, is extensible to silicon surface chemistry [204].

Another avenue which can aid in developing reaction rules for silicon surface re-

actions is metadynamics. Metadynamics is a method fueled by molecular dynamics and

explores phase space through a bias potential, based on collective variables that describe

the system. Such an approach can map the potential energy surface of a system without

knowing the types of reactions that can occur beforehand [205]. Zheng and Pfaendtner

demonstrated that the approach provides meaningful results for methanol oxidation [206].

Preliminary work in our group, in collaboration with Intel Corporation, also shows that

metadynamics can find simple pathways of SiH4 decomposition on a silicon surface, mod-

eled as a silicon hydride cluster. Clever choice of collective variables may yield addi-

tional reaction pathways involved in silane chemistry, allowing them to be added to RMG’s

database.

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5 CONCLUSION

This dissertation made progress in extending automatic mechanism generation to

two domains not previously or commonly studied in this manner: liquid-phase oxidation

of fuels and gas-phase thermal decomposition of silicon hydrides. These extensions were

made within the framework of the open-source software package, the Reaction Mechanism

Generator (RMG).

5.1 Liquid-phase fuel oxidation

To enable liquid-phase mechanism generation, source code was updated with ex-

isting linear solvation energy relationships and group additivity methods for determining

solute descriptors, in order to calculate solvation thermodynamics. In addition, more ca-

pabilities were added to deal with chemical species with unpaired electrons and lone pairs.

Furthermore, group additivity values for nitrogen and sulfur-containing species, for which

RMG can now generate mechanisms, were added. Addition of a database of known so-

lute descriptors now makes it faster to look up values on the fly rather than using group

additivity every time.

Based on well-known correlations, gas-phase reaction rates in RMG were modified

to account for diffusion effects on bimolecular reactions in the presence of a solvent. In-

trinsic solvent effects were incorporated by development of a group contribution method

to correct gas-phase rates for different solvents systematically, based on molecular struc-

ture of the reaction. This method has been developed for two different reaction families,

intra-hydrogen migration and hydrogen abstraction, for eight different solvents that are

93

categorically different. The corrections have been applied to a detailed kinetic model for

predicting induction period of oxidation of biofuel blends. Used as a training set for the

group contribution method, this work also contributes gas-phase geometries for several

chemical species and transition states calculated at the M062X/MG3S level of theory, and

energies calculated using a continuum solvation model in the eight solvents.

There are several possible avenues for future work on liquid-phase mechanism gen-

eration in RMG-Py. Thermodynamic data can be more accurately represented by perform-

ing high-level quantum chemistry calculations. These may be used to replace some of the

estimation techniques and other assumptions made about species containing lone pairs and

unpaired electrons, or to extend RMG to new applications. Calculations in different sol-

vents, beyond the 26 currently in RMG’s database, can also lead to the development of

new solvent descriptors to be used in the estimation of thermodynamic properties using the

linear solvation energy relationships.

The calculation of kinetic solvent effect could be better automated. At this point, the

easiest feature to implement is the on-the-fly calculation of ∆EA, as most of this code has

been written. This would ensure that important reactions are included in the model, since

a post-processing step only ensures modification of rates of reactions that were included

in the model based on their gas-phase rates. Furthermore, building the decision tree for

determining kinetic solvent effect can also be automated using a software package such as

scikit-learn. Some of this work has already been completed, but the automatically built tree

should be compared to the existing tree for accuracy.

Finally, both the solvation thermodynamics and kinetics estimation methods would

benefit from better benchmarking. Specifically, the values calculated from group contri-

bution should be compared to those calculated exactly from quantum chemistry, using

continuum solvation. If computational power and time is available, benchmarking with

higher-level methods such as coupled cluster methods, and/or more explicit solvent repre-

sentations, could greatly benefit the accuracy of detailed kinetic models and also provide

94

much-needed data to the chemistry community.

5.2 Thermal decomposition of silicon hydrides

The second application of this dissertation, gas-phase silicon hydride decomposi-

tion, demonstrated how to add new classes of elements and chemical reactions to mecha-

nism generation software. While microkinetic models had been developed for some silicon

hydrides previously, this work specifically focused on the ability to include radical reaction

types along with commonly used reaction families. Thermodynamic and kinetic data for

silicon hydrides were added from literature to RMG’s database. The work also contributes

new, calculated data for hydrogen bond increment (HBI) values of silicon hydride species,

as well as hydrogen abstraction reaction rates.

The new additions to RMG were demonstrated by building a model for SiH4 ther-

mal decomposition. Comparison to experimental work shows a qualitative and semi-

quantitative match, within the uncertainty in activation energy of the main SiH4 decom-

position channel. Additionally, this work has added insight on which process conditions,

as well as model generation options, have an effect on the SiH4 decomposition profile,

mainly corroborating early studies.

However, the SiH4 and Si2H6 profiles obtained when initial SiH4 concentration is

varied do not compare well with the experimental data. This motivates further research,

including global sensitivity analysis to see which reactions affect this dependence. If im-

portant reactions are identified, the source of these rates should be investigated and if they

are poorly estimated, should be carefully calculated. To calculate these reactions in a high

throughput way, the automated transition state theory calculator, AutoTST, could be uti-

lized. In its current state, AutoTST has some sources of errors that must be addressed, the

two major errors being in the calculation of symmetry number and improper determination

of lowest energy conformer. Despite these flaws, efforts to extend AutoTST to the silylene

insertion reaction family have been initiated. Alternatively, individual reaction rates could

95

be calculated using quantum chemistry methods at a higher level of theory than DFT.

Another research direction is in extension of RMG further, either to surface chem-

istry, or to new silicon precursors. Enabling surface chemistry is important for comparison

to real chemical vapor deposition experiments. Lastly, extending RMG further to new pre-

cursors (such as those containing germanium or silicon) can shift these generated microki-

netic models from merely confirming prior experiments and modeling, to being predictive.

5.3 Summary

This dissertation reports new thermodynamic and chemical kinetic parameters, as

well as new insights about two systems not previously investigated with automatic mech-

anism generation. Each of these chemistry applications demonstrates how machine learn-

ing can be used to predict parameters during the course of a simulation, where on-the-fly

quantum calculations for every unknown parameter would be computationally infeasible.

Importantly, the work also provides a framework for future developers to add capabilities

for new phases or elements to mechanism generation software.

96

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Appendices

114

A SUPPLEMENTARY INFO FOR SOLVATION KINETICS

A.1 Solvation kinetics molecular structure group trees and values

Table A.1: Group tree for hydrogen abstraction reactions

Group label ∆EA

(kJ/mol)# reactionstrained on

L1: X_H_or_Xrad_H_Xbirad_H_Xtrirad_H 1.925 997L2: Xrad_H -0.033 19L2: Xbirad_H -1.305 2

L3: CH2_triplet_H -1.305 2L3: CH2_singlet_H 0L3: NH_triplet_H 0L3: NH_singlet_H 0

L2: Xtrirad_H 0L3: C_quartet_H 0L3: C_doublet_H 0

L2: X_H 0.003 976L3: O_H 0.579 93

L4: O_sec 0.579 93L5: O/H/NonDeC 0.128 51

L6: O/H/Cs\H3 0.252 4L6: O/H/Cs\Cs|H3 0.083 24L6: O/H/Cs\Cs|Cs/H3 0.53 11

L3: Cs_H -0.259 819L4: C_alkane -1.178 154

L5: C_methane -1.606 9L5: C/H3/Cs\H3 -1.302 18L5: C/H3/Cs\Cs|H3 -1.008 60

L4: C/Hx/O -0.158 92L5: C/H3/O -0.004 45

L6: C/H3/O\H 0.363 32L5: C/H2/Cs/O -0.31 47

L6: C/H2/Cs/O\H -0.249 42L6: C/H2/O/Cs\Cs 0

L7: C/H2/O|H/Cs\Cs 0Continued on next page

115

Table A.1 – continued from previous pageGroup label ∆EA

(kJ/mol)# reactionstrained on

L4: C/Hx/Cs\O -0.879 21L5: C/H3/Cs\O 0

L6: C/H3/Cs\O|H 0L5: C/H2/Cs/Cs\O -0.879 21

L6: C/H2/Cs/Cs\O|H -0.879 21L4: C/H3/Cs\Cs|O 0

L5: C/H3/Cs\Cs|O/H 0L4: C/H2/NonDeC_6ring 1.711 1

L3: Cb_H 0L4: Cb/H/Cb 0

L5: Cb/H/Cb/Cb 0L6: Cb/H/Cb/Cb\O 0L6: Cb/H/Cb/Cb\Nb 0L6: Cb/H/Cb/Cb\Cb|Nb 0L6: Cb/H/Cb/Cb\N_pyrrole 0

L3: Cd/H/Cb 0L4: Cd/H/Cb/O 0L4: Cd/H/Cb/Nb 0L4: Cd/H/Cb/N_pyrrole 0

L3: N3_H 0L4: N3s_H 0

L5: N3s/H/Cb/Cb 0L1: Y_rad_birad_trirad_quadrad 0

L2: Y_1centerquadrad 0L3: C_quintet 0L3: C_triplet 0

L2: Y_1centertrirad 0L3: N_atom_quartet 0L3: N_atom_doublet 0L3: CH_quartet 0L3: CH_doublet 0

L2: Y_1centerbirad -2.192 61L2: Y_rad 0.149 936

L3: Y_2centeradjbirad -2.713 24L3: O_rad 1.971 337

L4: O_pri_rad 0.758 79L4: O_sec_rad 2.355 258

L5: O_rad/NonDeO 2.368 210L3: Cs_rad -0.473 282

L4: C_methyl -2.962 64

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A.2 Script for modifying Chemkin files for solvation kinetics corrections

Included electronically as modifyReactionBarriers.py

A.3 Modified Cantera input file for n-dodecane/ methyl oleate oxidation

Included electronically as liq modified.cti

A.4 Cantera script to simulate liquid fuel oxidation reactor

Included electronically as oxidation.py

A.5 Code for automatic tree building

Included electronically as Building a Tree for Solvation KineticsData using Scikit Learn.ipynb

117

B SUPPLEMENTARY INFO FOR SILICON HYDRIDES

B.1 Geometries of reactants and transition states for hydrogen abstraction reactions

Table B.1: Transition state geometries for silicon hydride hydrogen abstractions. Geome-tries were optimized at M06-2X/6-311+G(3d2f).

Reaction Geometry (xyz)SiH4 + H←→ SiH3 + H2 Si 0.15453 0.00006 -0.00002

H -1.41678 0.00240 0.00055H 0.62492 -0.56812 1.27728H 0.62860 1.38878 -0.14797H 0.62319 -0.82427 -1.12967H -2.62334 0.00039 0.00014

Si2H6 + H←→ Si2H5 + H2 Si 1.08477 -0.21175 0.00000H 1.76873 1.18341 0.00048Si -1.23147 0.06812 0.00000H 1.54266 -0.93570 1.20460H 1.54277 -0.93472 -1.20514H 2.39507 2.29684 0.00003H -1.64097 0.81927 1.20466H -1.91403 -1.24233 -0.00282H -1.64042 0.82406 -1.20185

Continued on next page

118

Table B.1 – continued from previous pageReaction Geometry (xyz)Si2H6 + SiH3 ←→ Si2H5 + SiH4 Si -0.55565 0.74630 -0.57115

H 2.82912 -1.40097 1.04827Si -2.27585 -0.37494 0.52734H -0.67818 0.64407 -2.04227H -0.49801 2.17627 -0.19500Si 2.72787 -0.35594 0.00917H -2.06810 -0.27329 1.98716H -2.25046 -1.80175 0.14252H -3.60717 0.17968 0.19965H 3.22534 -0.86811 -1.28355H 0.98622 0.12059 -0.20376H 3.48999 0.84300 0.41209

Si2H5 + H←→ SiH3SiH + H2 Si 1.09996 -0.23822 -0.10182H 1.92029 1.02459 0.19908Si -1.19412 0.08446 0.01971H 1.64355 -1.36585 0.68301H 2.83364 2.02686 0.17835H -1.63898 0.40468 1.39338H -1.88427 -1.14091 -0.43095H -1.55592 1.20330 -0.87343

Si2H4 + H←→ Si2H3 + H2 Si 0.97302 -0.22919 -0.11437H 1.90926 0.97626 -0.02486Si -1.13964 0.10093 0.07414H 1.55866 -1.43591 0.50100H 2.67744 1.96603 0.49374H -2.07255 -1.04044 0.06669H -1.74016 1.32958 -0.47338

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B.2 Geometries of silicon hydride species

Table B.2: Geometries of silicon hydride species used to calculate thermodynamics proper-ties and HBI values. Geometries were optimized at G3//B3LYP. (S) and (T) indicate singletor triplet electronic state.

SMILES Geometry (xyz)[SiH2](S) Si -1.43587 0.00246 0.06697

H -1.74175 0.47705 -1.35562H -0.04854 0.64701 0.01782

[SiH2](T) Si -1.33315 0.10876 -0.07282H -1.93728 0.40943 -1.40268H 0.04429 0.60833 0.20466

[SiH2]=[Si] Si -3.60702 1.82709 -0.33428Si -1.49125 1.19881 0.33577H -0.81469 -0.11028 0.07296H -0.51770 2.01734 1.12493

[SiH2]=[SiH2] Si -1.53193 -0.02404 -0.20088Si 0.58853 0.34809 0.13524H -2.04746 -1.40486 -0.00758H -2.19289 0.64071 -1.35459H 1.24951 -0.31663 1.28895H 1.10404 1.72891 -0.05809

[SiH2][SiH3] Si 0.64164 0.63190 -0.07677H 2.12401 0.79844 -0.10622H 0.09716 1.50707 0.99666Si -0.01278 -1.58161 0.31378H 0.09701 1.08711 -1.38474H 0.40941 -2.11507 1.64186H 0.40969 -2.53755 -0.75125

[SiH3] Si 0.61349 0.58486 -0.06567H 2.10205 0.54852 -0.07144H 0.09988 1.44264 -1.16912H 0.09996 1.05209 1.25158

Continued on next page

120

Table B.2 – continued from previous pageSMILES Geometry (xyz)[SiH3][Si][SiH3] Si 1.67253 0.27843 0.63961

H 3.14517 0.40071 0.46884Si 0.63136 1.45854 -1.09549H 1.30287 0.82573 1.97628H 1.31054 -1.16767 0.61548Si -1.67483 1.68344 -1.43917H -2.33983 2.35487 -0.28601H -2.33137 0.36094 -1.64601H -1.88650 2.51252 -2.65597

[SiH3][SiH2][SiH3] Si 1.34707 0.41763 0.52351H 2.83377 0.50351 0.50128Si 0.41113 1.59415 -1.28727H 0.86407 0.97917 1.81566H 0.94075 1.03046 -2.56387H 0.84714 3.02022 -1.22248Si -1.94053 1.50667 -1.32139H -2.40856 0.09624 -1.42074H -2.48341 2.26393 -2.48329H -2.50232 2.09543 -0.07399H 0.95938 -1.01934 0.46801

[SiH3][SiH3] Si 1.25034 0.42662 0.50364H 2.73834 0.48621 0.51730Si 0.39108 1.62122 -1.32867H 0.74771 0.99732 1.78408H 0.84025 -1.00347 0.43617H 0.80116 3.05131 -1.26120H -1.09692 1.56161 -1.34235H 0.89373 1.05052 -2.60911

Continued on next page

121

Table B.2 – continued from previous pageSMILES Geometry (xyz)[SiH3][SiH][SiH3] Si 1.61691 0.33637 0.61343

H 3.09531 0.50916 0.63765Si 0.72147 1.40841 -1.26788H 1.04575 0.94103 1.84764H 1.32225 -1.12597 0.63522Si -1.60568 1.62562 -1.43403H 1.32982 0.90996 -2.53930H -2.13957 2.21855 -0.17765H -2.28972 0.31855 -1.65621H -1.94939 2.52478 -2.56959

[SiH4] Si 1.46180 0.40735 0.51255H 2.94718 0.40735 0.51255H 0.96668 -0.24704 -0.72558H 0.96667 1.80680 0.56489H 0.96667 -0.33770 1.69833

[SiH] Si 0.30787 2.67553 0.05506H -0.20525 2.37574 -1.36497

[SiH][SiH2] Si -2.73075 1.30914 0.07907Si -0.47875 1.78249 0.08754H -2.72465 1.27934 -1.44957H 0.33260 1.85245 1.33822H 0.30767 2.46622 -0.98447

[SiH][SiH3](S) Si -2.71696 1.51477 0.05196Si -0.31118 1.56106 0.04435H -2.68937 1.16938 -1.44010H 0.22225 0.23388 -0.39172H 0.30300 1.87871 1.36442H 0.17481 2.58171 -0.93456

[SiH][SiH3](T) Si -2.53013 1.47300 -0.10995Si -0.19734 1.55835 0.01393H -3.23625 1.16324 -1.39379H 0.42084 0.25197 -0.35026H 0.16206 1.88550 1.41850H 0.36336 2.60747 -0.88406

122

B.3 Largest SiH4 decomposition mechanism

Included electronically as chem annotated.inp and species dictionary.txt.

Converted Cantera input file is included as silane.cti.

B.4 Cantera script for simulating reactor

Included electronically as silane decomp.py

B.5 Code for residence time comparison

Included electronically as Residence Times.ipynb