AUTOMATED CALCULATION OF REACTION KINETICS

VIA TRANSITION STATE THEORY

A Dissertation Presented

By

Pierre Lennox Bhoorasingh

to

The Department of Chemical Engineering

In partial fulfillment of the requirements

for the degree of

Doctor of Philosophy

in the field of

Chemical Engineering

Northeastern University

Boston, Massachusetts

August 2016

Dedication

I dedicate this thesis to AMT.

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Acknowledgments

I have been able to complete this thesis work due to the help I have received from those

who have found time in their busy schedules. This is my attempt to express my profound

gratitude to those who have helped me during my thesis work.

Thanks to my advisor, Prof. Richard West, for the guidance over the 5 years. You also

gave me the freedom to explore and that has only enhanced my thesis work, and it has been

a pleasure to be your first graduate student.

I would also like to thank my thesis committee members, Dr. David Budil, Dr. Hicham

Fenniri, Dr. C. Franklin Goldsmith, and Dr. Reza Sheikhi. They made the time to have

engaging discussions that impacted this thesis, and were also very generous with their

professional advice.

Thanks to the Computational Modeling group. Fariba Seyedzadeh Khanshan and Be-

linda Slakman, you were always helpful in our discussions and made the laboratory a fun

working environment. I’d also like to thank Jason Cain for being a super helpful under-

graduate who assumed nothing in pursuit of the right approach. I want to also thank Sean

Troiano, Victor Lambert, Jacob Barlow, and Elliot Nash for their contributions to laboratory

discussions.

Thanks to past and present RMG developers, who do a great job working on a complex

open-source software. I would like to thank Joshua Allen and Amrit Jalan for their scientific

perspectives in the early stages of this thesis work. I’d also like to thank Shamel Merchant

and Enoch Dames for their help with CanTherm.

I would like to thank Greg Landrum and the RDKit developers, for this thesis would be

much more difficult without their work.

Thanks to Pat Rowe, Jessica Smith-Japhet, and Brandon Mennillo for their assistance

over the years. I would like to express my gratitude to the Research Computing team at

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Northeastern University, and in particular Dr. Nilay Roy, for their work on the Discovery

cluster. I would also like to thank Bill Sheehan for his help with the now retired Venture

and Opportunity clusters.

I’d like to thank the Combustion Energy Frontier Research Center, especially Prof.

Chung Law and Lilian Tsang, for organizing and hosting the Combustion Summer School,

which I had the opportunity to attend twice (2012 and 2014).

I must thank Prof. David Beck and the organizers of the 2015 Data Science Work-

shop for hosting an enjoyable and intense discussion group on the role of data science in

academia. I would also like to thank Michael Li and the team at the Data Incubator for

running an informative and rigorous data science bootcamp that I had the opportunity to

attend in the Spring of 2016.

Thank you to my classmates, Avinash, Dan, Dinara, Emily, and Nil. Your support has

been important through the years. I want to also thank the friends I made in the Chemical

Engineering Department.

Finally, thanks to my family, for their unending support as I take another step in life.

Abstract

Modeling complex chemical systems often requires knowledge of the elementary reac-

tions involved, such as in combustion kinetics where models routinely contain thousands of

reactions. Automated tools have been developed to construct such models, as manual meth-

ods have proven to be tedious and susceptible to human error. A large number of kinetic

parameters are required to complete the construction of detailed kinetic models, but the

available data are quite sparse. As a result, estimation methods use existing data to predict

the many unknown kinetics, but the accuracy of these kinetics suffers due to insufficient

data to make good kinetic predictions.

Theoretical calculations can be used to improve the kinetics in models, but these cal-

culations require a transition state geometry estimate that is typically provided manually.

Manual geometry estimation is slow and infeasible for automated construction of reaction

mechanisms, so this thesis describes an automated method to estimate transition state ge-

ometries and calculate reaction kinetics. The three dimensional chemical structure for un-

reactive atoms at the transition state can be predicted with existing computational methods,

but the geometry of the reaction center is unknown. The unknown section of the transition

state must be predicted to create the transition state geometry.

The reaction center distances are predicted using data from analogous transition state

structures, and the transition state geometry prediction is constructed using an existing tech-

nique known as distance geometry. The transition state geometry prediction is optimized

using a commercially available computational chemistry software package in order to cal-

culate molecular properties of the transition state, such as bond vibrational frequencies.

The molecular properties of reactants and products are also required to calculate reaction

kinetics, and these are determined using an existing automated method. Molecular prop-

erties of the reactants, products, and transition state are used to calculate the kinetics of a

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reaction via classical transition state theory.

The work in this thesis was initially developed for hydrogen abstraction reactions, and

has been extended to β-scission and intra-hydrogen migration reactions. The automatically

determined kinetics and state-of-the-art estimation methods were compared to high accu-

racy theoretical calculations, and the automated calculations were shown to outperform

the estimation methods. This enables improved mechanism generation, where high-fidelity

complex chemical models can be constructed with minimal human intervention.

Contents

1 Introduction 1

1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

1.1.1 Automatic mechanism generation . . . . . . . . . . . . . . . . . . 2

1.1.2 Kinetic and thermodynamic parameter estimation . . . . . . . . . . 4

1.1.3 Theoretical rate calculation . . . . . . . . . . . . . . . . . . . . . . 5

1.1.4 Statistical mechanics and quantum chemistry . . . . . . . . . . . . 8

1.1.5 Stable geometry and transition state searches . . . . . . . . . . . . 10

1.1.6 Automated transition state searches . . . . . . . . . . . . . . . . . 11

1.1.7 Kinetic Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

1.2 Thesis overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2 Using double-ended methods to automate transition state searches 15

2.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

2.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.1 Generating 3-dimensional geometries for double-ended search meth-

ods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.2 Locating transition states with the automatic double-ended search . 22

2.2.3 Electronic Structure calculations . . . . . . . . . . . . . . . . . . . 23

2.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.5 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26

2.5.1 Semi-empirical methods are insufficient for transition state searches 26

2.5.2 Consider more robust double-ended search methods . . . . . . . . 27

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3 Automatic transition state geometry estimation using group contributions 28

3.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

3.2.1 Geometry estimation and optimization . . . . . . . . . . . . . . . . 31

3.2.2 Method evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.1 Transition state geometries were successfully estimated using the

distance estimates . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

3.3.2 Increasing training data improves the group value predictions . . . 38

3.3.3 Geometry estimation needs improvement to make best use of pre-

dicted values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

3.3.4 Algorithm optimization . . . . . . . . . . . . . . . . . . . . . . . . 43

3.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

3.5 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

3.5.1 Conformer recognition . . . . . . . . . . . . . . . . . . . . . . . . 44

4 Improving the group contribution transition state search method 45

4.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

4.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

4.2.1 Modifying the transition state geometry prediction . . . . . . . . . 46

4.2.2 Modifying the transition state optimization sequence . . . . . . . . 49

4.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.3.1 Tree structure and data diversity affect prediction accuracy . . . . . 49

4.3.2 Manipulating distance limits and force constants can improve UFF

optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.3.3 Replacing the UFF optimization with more robust calculations may

improve transition state prediction . . . . . . . . . . . . . . . . . . 54

4.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

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4.5 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.5.1 Efficient calculation of the molecular group contributions . . . . . . 57

4.5.2 UFF optimization with constrained optimization . . . . . . . . . . 58

5 Method extension to new reaction families and automated kinetic parameter

calculation 59

5.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

5.2 Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

5.2.1 Computational chemistry . . . . . . . . . . . . . . . . . . . . . . . 61

5.2.2 Automated geometry searches . . . . . . . . . . . . . . . . . . . . 61

5.2.3 Kinetic calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 63

5.2.4 Comparison of Automated TST calculations and Rate Rules . . . . 63

5.2.5 Comparison to benchmark calculations . . . . . . . . . . . . . . . 64

5.3 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64

5.3.1 Comparison of automated TST calculations and rate rules . . . . . 65

5.3.2 Comparing predictions to benchmark calculations . . . . . . . . . . 65

5.3.3 Sources of error in the automated calculations . . . . . . . . . . . . 66

5.4 Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

5.6 Recommendations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73

5.6.1 Improve symmetry number calculation . . . . . . . . . . . . . . . 73

5.6.2 Automate hindered rotor calculations . . . . . . . . . . . . . . . . 73

6 Summary 75

Appendices 90

Appendix A Double-ended method 91

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Appendix B Group contribution method 100

B.1 Group Training Regression Details . . . . . . . . . . . . . . . . . . . . . . 100

B.2 Predicted vs Optimized distances . . . . . . . . . . . . . . . . . . . . . . . 102

B.3 Group Naming Convention . . . . . . . . . . . . . . . . . . . . . . . . . . 103

B.4 Group values for original tree . . . . . . . . . . . . . . . . . . . . . . . . . 104

B.5 Group values for new tree . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

B.6 List of test reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118

B.7 Effect of increasing force constants and reducing the difference between

upper and lower limits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

Appendix C Kinetic calculations 150

C.1 Molecular group trees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

C.1.1 Hydrogen Abstraction . . . . . . . . . . . . . . . . . . . . . . . . 150

C.1.2 Intra-hydrogen migration . . . . . . . . . . . . . . . . . . . . . . . 160

C.1.3 β-scission . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

List of Figures

1.1 Beta-scission reaction template from RMG. . . . . . . . . . . . . . . . . . 3

1.2 Potential energy profile for a typical reaction. . . . . . . . . . . . . . . . . 6

2.1 The molecular bounds matrix. (A) Bonded atom limits are set by bond

length rules, while connectivity limits non-bonded atoms in the same molecule.

Van der Waals radii set the lower limits for atoms on separate molecules,

while there are no upper limits (set to 1000 A). (B) By editing these dis-

tance limits, we can position molecules relative to one another, as well as

stretch or shrink bond distances. . . . . . . . . . . . . . . . . . . . . . . . 19

2.2 Potential energy surface showing minimum energy pathway (dotted line)

from reactants (R) to products (P). A double-ended search between 1 and 2

will start closer to the TS (grey circle) than a search between R and P. . . . 20

2.3 Definition of the 3 key distances for editing the transition state geometries.

H represents the abstracted hydrogen, X the atom bonded to the hydrogen,

and Y the radical abstracting the hydrogen. . . . . . . . . . . . . . . . . . 21

2.4 Automatic double-ended enabled transition state search procedure. . . . . . 23

2.5 Points of failure along the automatic double-ended algorithm with SAD-

DLE/PM7 calculations. The arrow widths are in proportion with the num-

ber of associated reactions. 194 succeeded with 128 reactions failing at the

reaction path validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24

2.6 dXH transition state distances in Angstrom calculated with M06-2X/6-

31+G(d,p). Abstracting radicals (Y) are on the left, and the hydrogen and

the carbon it is abstracted from (XH) are on top. Similar trends were ob-

served for dHY, and dXY. . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

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3.1 Manipulating the molecular bounds matrix to create transition state geom-

etry estimates. (A) The matrix generated for a pair of stable species. (B)

Editing the matrix with the group contribution predictions for transition

state distances. (C) Conflicting lower limit distances are corrected, creat-

ing a valid transition state distance bounds matrix. . . . . . . . . . . . . . 34

3.2 The automated transition state search algorithm. . . . . . . . . . . . . . . . 36

3.3 Distances from 907 validated transition states found at B3LYP/6-31+G(d,p)

were compared to predictions derived from molecular group values. The

solid line represents parity with the optimized distances, and the dashed

lines represent the root mean squared error of the estimates from parity.

The predictions improved as the training set used to calculate the group

values was expanded. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

3.4 422 transition states found in one trial of the algorithm were unsuccessful

in another. Comparing optimized distances against the failed estimation at-

tempt showed: 1. poorly estimated distances that were improved when the

training set was expanded 2. the conversion from prediction to geometry

estimate introduced additional error. . . . . . . . . . . . . . . . . . . . . . 41

3.5 Probability of a failed TS search as a function of RMS error in reactive

distances of starting geometry. For each point the vertical bar show the

Clopper–Pearson [122] 95% confidence interval of the lower bound and

the horizontal bar shows the range of RMS errors used to calculate it. . . . 42

4.1 The RMS error for the distance estimates compared to the optimized tran-

sition state distances. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.2 Probability distribution for the root-mean-squared error of the reaction cen-

ter distances when training the groups with 44 transition state distances, for

the Original and New tree structures. . . . . . . . . . . . . . . . . . . . . . 52

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4.3 Decreasing the distance and increasing the force constants for the reaction

center each minimized error in the dXH distance introduced during the con-

struction of the 3-dimensional transition state estimate. The error reduction

is additive as seen when combining the modifications. . . . . . . . . . . . . 53

4.4 Mean and standard deviation of the absolute error in dXH distances from

the final optimized transition state at each stage of the transition state pre-

diction process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.5 Mean and standard deviation of the absolute error in dHY distances from

the final optimized transition state at each stage of the transition state pre-

diction process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

4.6 Mean and standard deviation of the absolute error in dXY distances from

the final optimized transition state at each stage of the transition state pre-

diction process. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

5.1 Automated transition state search algorithm as described in ref. 136. The

steps with bold borders, adapted from the AARON software [81], are devi-

ations from the original algorithm. . . . . . . . . . . . . . . . . . . . . . . 62

5.2 The automated kinetic calculations involve an automated transition state

search (Figure 5.1), automated search for reactant and product geometries

[8], and automatically calculating kinetics using CanTherm [84]. . . . . . . 63

5.3 Rate rule estimates (y-axis) plotted against automated algorithm TST cal-

culations (x-axis) at 1000 K. . . . . . . . . . . . . . . . . . . . . . . . . . 66

5.4 Comparison of kinetic estimates for hydrogen abstraction reactions. . . . . 67

5.5 Comparison of kinetic estimates for intramolecular hydrogen migration re-

actions R3 (a) and R4 (b). . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5.6 Comparison of kinetic estimates for β-scission reactions R5 (a) and R6 (b). 69

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5.7 Magnitude of the sources of error in each automated algorithm compared

to its respective benchmark calculation. The summation of all errors are

represented by the algorithm calculation. . . . . . . . . . . . . . . . . . . . 70

B.1 Comparison of distances from validated transition states to predictions from

molecular group values calculated from different sized data sets. The solid

line represents parity, the dashed lines represent the root mean squared er-

ror of the estimates from parity. The predictions derived from the original

and new trees are represented by the black and red circles respectively. . . . 102

B.2 Decreasing the distance and increasing the force constants for the reaction

center each minimized error in the dHY distance introduced during the con-

struction of the 3-dimensional transition state estimate. The error reduction

is additive as seen when combining the modifications. . . . . . . . . . . . . 148

B.3 Decreasing the distance and increasing the force constants for the reaction

center each minimized error in the dXY distance introduced during the con-

struction of the 3-dimensional transition state estimate. The error reduction

is additive as seen when combining the modifications. . . . . . . . . . . . . 149

List of Tables

3.1 Part of the hierarchical molecular group tree for transition state distances

trained using 1071 transition state distances calculated using B3LYP/6-

31+G(d,p). The full tree is provided in the appendices. . . . . . . . . . . . 35

3.2 Training set information. As the training set was expanded, the RMS error

from the validated transition state distances decreases. . . . . . . . . . . . . 38

4.1 Training set information. As the training set was expanded, the RMS er-

ror from the validated transition state distances decreases. The new tree

structure performed better when training data was sparse. . . . . . . . . . . 51

5.1 Number of reactions for each family contained in the combustion model,

and success of the AutoTST algorithm. . . . . . . . . . . . . . . . . . . . . 65

5.2 Reactions compared to benchmark calculations. . . . . . . . . . . . . . . . 65

5.3 Difference in the activation energy (kJ/mol) compared to the benchmark

calculations. Kinetics fitted to Arrhenius form between 600K and 2000K. . 68

5.4 Difference in the log10 of the A factor compared to the benchmark calcula-

tions. Kinetics fitted to Arrhenius form between 600K and 2000K. R3 and

R4 are in [s−1] and the rest are in [cm3/(mols)] . . . . . . . . . . . . . . . 69

A.1 Transition states determined at M06-2X/6-31+G(d,p) showed trends in the

distances (in Angstroms) with changes to molecular groups. The distances

dXH, dHY, and dXY are defined in Figure 2.3. . . . . . . . . . . . . . . . 91

A.2 334 hydrogen abstraction reactions used to test automated transition state

algorithms. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91

B.1 Original tree structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

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B.2 Modified tree structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110

B.3 1393 hydrogen abstraction reactions used to test the group estimates cou-

pled with the automated transition state algorithm. The reactants and prod-

ucts are provided as SMILES strings. Transition states that were found and

validated are available in CML format. . . . . . . . . . . . . . . . . . . . . 118

C.1 HAbs tree structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

C.2 intraH tree structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

C.3 β-scission tree structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

1. Introduction

Detailed kinetic modeling allows researchers to gain a deeper understanding of the

chemistry contributing to phenomena observed in complex chemical systems [1]. Such

complex systems include the combustion of novel renewable fuels [2], and the formation

of silicon nanoparticles [3]. Detailed kinetic, or microkinetic, models aim to capture all the

relevant chemistry for a system of interest, including thermodynamic parameters for each

species, the elementary reactions involving these species, and the kinetic parameters for

each reaction contained in the model. Adding these necessary details often leads to models

that are quite large, such as the combustion model developed for 2-methylalkanes that

contained approximately 7200 species and 31400 reactions [4]. Lu and Law also showed

that models have only increased in size over time, as new important reaction pathways are

discovered and included in models [5]. The current size and complexity of detailed models

mean it is an inefficient and error prone process to continue constructing these models by

hand.

Automated software, such as Reaction Mechanism Generator (RMG) [6], have been

developed to address the difficulties of large model construction, but the models require

many thousands of parameters, most of which are unknown and must be estimated. Esti-

mation methods are usually derived from group additivity and are attractive due to being

computationally efficient, but the estimates used can be quite inaccurate. This is not only

detrimental to the model accuracy, but also to the reactions considered during the model

construction due to the rate-based approach employed by RMG in building a tractable

model, where reaction pathways with the highest flux are explored and low flux pathways

are ignored [7]. An alternate method to determine thermodynamic parameters was devel-

oped using quantum chemical calculations, and this method has been implemented in RMG

to good effect [8]. An alternative approach is also desired for kinetic parameters to address

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the widespread uncertainties of models.

Automating kinetic calculations requires the automation of several steps. The reactant

species geometries must be estimated automatically, but this has been previously achieved

in the automated thermodynamic parameter calculator. A transition state geometry esti-

mate is also required, so an estimation method must be developed since existing conformer

generation tools are not capable of predicting transition states. Transition state validation

methods rely on visual inspection, so an alternate automated approach needs to be de-

veloped. Finally, the automated transition state search method must be integrated with a

kinetic calculation software to provide the kinetic parameters via transition state theory

calculations.

1.1 Background

1.1.1 Automatic mechanism generation

One of the earliest reaction network generators was developed in 1979 by Ugi et al. to

take advantage of ”the inherent capabilities of modern computers” in determining chemi-

cal synthesis pathways [9]. Molecules were represented by bond-electron matrices, which

stored bond and free valence electron information for each atom in a molecule, and a trans-

formation matrix would represent a reaction type that would convert reactant molecule

matrices to product matrices. Iteratively applying the transformation matrices would allow

the algorithm to postulate all possible reactions.

More modern and efficient mechanism generators have been developed [6, 10–17], and

these benefit from the evolution of new methods and advances in computational power.

These modern mechanism generators represent molecules as chemical graphs with atoms

represented as nodes and bonds as edges. Graphs theory [18] can efficiently compare these

chemical graphs [19], to determine if a newly made molecule already exists in the model

due to an alternate reaction pathway. Reaction templates are used to convert chemical

graphs from one form to another, and each type of reaction (a reaction family) has its own

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reaction template [18].

2R 1R 3R 1R 3R+ 2R

Figure 1.1: Beta-scission reaction template from RMG.

Mechanism generators restrict model size in order to exclude reactions of little impor-

tance at the conditions of interest, and several model size restriction strategies exist. The

REACTION software allows the user to specify which reaction families to apply for each

stage of the model generation [13]. MAMOX generates a detailed primary mechanism

which is then lumped to reduce the model size [12]. These steps are iterated to produce

a series of highly lumped mechanisms [1]. The approach in EXGAS uses a base mecha-

nism for small molecule chemistry, with the rest of the mechanism consisting of a detailed

primary mechanism and a lumped secondary mechanism [14]. Reaction Mechanism Gen-

erator (RMG) restricts model size using the rate-based screening algorithm of Susnow et al.

[7]. A species is only included in the model if the flux to the species surpasses a cutoff cri-

teria.

Other mechanism generators differ in how molecules are represented. Rule Input Net-

work Generator (RING) allow users to specify constraints on molecules at the input, such

as the maximum number of heavy atoms [16]. GENESYS treats stereo-isomers as unique

species [17], allowing model construction for pharmaceuticals and other systems.

Detailed kinetic models also require thermodynamic and kinetic parameters to com-

pletely describe a system [20]. These parameters are ideally taken from sources where

they were either experimentally measured or theoretically calculated, but well determined

parameters are sparse when compared to the number of parameters required to complete a

model. When a needed parameter is unknown, estimation methods are used to supplement

the available data.

A sensitivity analysis on a microkinetic model will identify the important parameters,

and these should be targeted for improvement if they were estimated. Typically theoreti-

cal approaches are applied, such as the calculation of reaction kinetics via transition state

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theory.

1.1.2 Kinetic and thermodynamic parameter estimation

Estimation methods are used to address the shortage of thermodynamic and kinetic

parameters. Thermodynamic parameters are typically estimated using Benson’s group ad-

ditivity, where the contribution of molecular groups contained in a molecule are summed to

provide an estimate of the thermodynamics of the molecule [21]. The value of the molec-

ular group contributions are determined from molecules with well known thermodynamic

values, and the method has been shown to work for a variety of systems [22–25].

The accuracy of Benson’s method depends on the data used to determine the molecular

group values, and the ability to account for the important factors affecting the thermody-

namics of a molecule. Difficulties in accounting for the effects of radicals and fused-rings

on thermodynamic parameters has motivated work on supplementary estimation methods.

The Hydrogen Bond Increment method has improved radical species thermodynamic esti-

mation by using summing the thermodynamics of a closed-shell molecule and the contribu-

tion of removing a H atom to form the radical [26]. The contribution of the loss of a H atom

is calculated using known thermodynamic parameters for other closed-shell molecules and

its associated radical. Fused-ring thermodynamics have been addressed in RMG by au-

tomating thermodynamic parameter calculations from first principles [8].

Kinetic estimation methods have also been developed that can make predictions in good

agreement with experimental data. The Evans-Polanyi relationship is the classic method for

estimating kinetic parameters, relating the activation energy of a reaction to the enthalpy

of reaction [27]. This methods can be automated and is also computationally efficient

[28], but the relationship is not always appropriate for some systems such as the hydrogen

abstraction from polynuclear aromatics by methyl radicals [29]. In recent years, the most

commonly applied kinetic estimation methods rely on transition state theory calculations

on select reactions in order to develop rate rules to be used for similar reactions [30–35].

5

The considerable time, effort, and expertise required to develop rate rules has motivated

alternative high throughput means to determine chemical kinetic parameters [20].

The Evans-Polanyi relationship

k(T ) = A exp

(−(E0 + α∆H◦)

RT

)(1.1)

is a simple approach to estimating reaction kinetics [27], requiring just the change in en-

thalpy of the specific reaction (∆H◦), and three parameters for the reaction family (A, E0,

α).

1.1.3 Theoretical rate calculation

The central aim of theoretical kinetics is to understand why reactions are fast or slow,

but we have progressed to understanding the temperature dependence of a reaction, and can

even calculate reaction rates. One of the earliest approaches to determining reaction rates

was collision theory, which started with the basic knowledge that a reaction can only occur

if the reactants collide. Each reactant is treated as a hard sphere, where they maintain their

shape during a collision, and there is no interaction between spheres until they collide [36].

A reaction occurs when the valence electrons are disturbed, which requires energy. This

energy can only be overcome (an energy barrier) by collisions that have sufficient energy

at the moment of impact.

k = Ze−∆GRT (1.2)

The form of the kinetic temperature dependence is captured by collision theory, but it

produced large overpredictions compared to observed reaction rates [37]. One approach to

refine collision theory introduced a steric factor to represent the fraction of collisions that

led to successful reactions (Equation 1.3) [38], but this arbitrary approach still could not

6

account for the discrepancies found for some reactions.

k = Zρe−∆GRT (1.3)

V

rAB

rBC

X‡

X‡

Reaction coordinate

En

erg

y

Reactants

Products

Reactants Products

Figure 1.2: Potential energy profile for a typical reaction.

The activated complex theory, more commonly known as transition state theory, as-

sumes a reaction proceeds from reactants to products via an activated complex [39]. If the

change in molecular structure during the reaction (the reaction coordinate) is plotted against

its potential energy, the reactants and products lie in energy minima and the transition state

is located at the highest point along the reaction coordinate (Figure 1.2). The transition

state is unstable with respect to the reaction coordinate, but it lies in an energy minimum

with respect to all other coordinate axes. Transition state theory assumes the reactants and

transition state are in quasi-equilibrium, and the rate limiting step is the decomposition

of the transition state to products. Based on these assumptions, the Eyring equation de-

scribes the relationship between the rate of an elementary reaction and the thermodynamic

properties of the equilibrium between the reactants and transition state.

7

k(T ) =kBT

hexp(−∆G‡

RT) (1.4)

kB is the Boltzmann constant, h is Planck’s constant, R is the molar gas constant, and

∆G‡ is the change in Gibbs free energy between the reactants and transition state. Equation

1.5 shows the elementary reaction rate expressed in terms of the partition functions of the

reactants and transition state based on the same transition state theory assumptions.

k(T ) =kBT

h

Q‡∏ni Qi

exp(−∆E‡0kBT

) (1.5)

The above equation accounts for all cases where the reactants collide and form an ac-

tivated complex, but does not account for the effects of quantum tunneling. Tunneling is

a phenomenon of quantum mechanics that describes the finite possibility that a particle

will tunnel through a barrier that it cannot overcome in a classical sense, so some reactants

will form products even though they have less energy than the barrier height [40]. In reac-

tion kinetics, this effect is small at high temperatures, but increases in importance at lower

temperatures. This is represented by κ in the classical transition state theory equation.

k(T ) = κkBT

h

Q‡∏ni Qi

exp(−∆E‡0kBT

) (1.6)

Good reaction rate predictions can be made using classical transition state theory, but

further refinement is sometimes necessary. Variational transition state theory is one such

refinement, where the dividing surface between reactants and products is varied such as to

minimize the reaction rate [41].

A reaction rate determined using classical transition state theory only considers the

8

lowest energy conformer for the reactants, products, and transition state. This approach

is appropriate since the lowest energy conformer is usually the dominant conformer in the

species population. This breaks down when reacting species have multiple conformers

of similar energy to the lowest energy conformer [42–44], so the multi-structural varia-

tional transition state theory method was developed for such cases [45, 46]. The multi-path

variational transition state theory method was developed to account for complex reacting

molecules with multiple reactants and multiple transition states [47].

1.1.4 Statistical mechanics and quantum chemistry

The kinetics of a reaction can be determined via transition state theory if the total par-

tition function of the reacting molecules and the transition state are known. The rigid-rotor

harmonic-oscillator approximation is often used to calculate the total partition function,

Qtot.

Qtot = QtransQrotQvibQelec (1.7)

Qtrans = V

(2πMkBT

h2

) 32

(1.8)

Qrot =

√π

σexternal

(8πImkBT

h2

) 32

; Im = IxIyIz (1.9)

Qvib =∏i

(1− e−hvikBT )−1 (1.10)

Qtrans,Qrot,Qvib, andQelec represent the translational, rotational, vibrational, and elec-

tronic partition functions of the molecule. Aside from temperature (T ), Boltzmann’s con-

stant (kB), and Planck’s constant (h), the total partition function is related to properties

specific to the molecule. The electronic partition function is taken to be the electronic spin

multiplicity of the molecule, as only the lowest electronic energy state is accessible. The

translational partition function is related to the unit volume, V , and the molecular weight

9

of the molecule, M . The rotational partition function is related to the external symmetry,

σexternal, and the moments of inertia, Ix, Iy, and Iz. The vibrational partition function is

related to the vibrational frequencies of every bond in the molecule, vi.

The rigid-rotor harmonic-oscillator approximation is not always appropriate as it does

not account for anharmonicity, but can be corrected using the 1-D hindered rotor approxi-

mation [48]. Alternatively, the vibrational and rotational partition functions can be treated

as a coupled conformer partition function, as in the case of the multi-structural anharmonic-

ity method [43, 44].

Molecular properties can be theoretically calculated by solving the electronic Schrodinger

equation, HΨ = EΨ, where H is the Hamiltonian, E is the electronic energy, and Ψ is

the wavefunction. Approximations of the Schrodinger equation are used in computational

chemistry software for practical reasons to determine the molecular properties. Several

approximations can be made, and typically each approximation offers significant savings

and computational time, but this comes at the risk of decreased accuracy. Semi-empirical

methods, such as Parameterized Model number 3 (PM3) [49], were developed using ex-

perimental data to parameterize the Schrodinger equation solution, making these method

computationally efficient but are only accurate for molecules similar to those used to pa-

rameterize the solution. Hartree-Fock (HF) methods assume the wavefunction can be ap-

proximated by a single expression known as a Slater determinant, and this method is often

used to get a fast and good approximation before more robust methods are applied [50].

Moller-Plesset methods, such as MP2 and MP4 [51, 52], uses perturbation theory to im-

prove on HF. Density functional theory uses an approximate electron density functional to

find the solution, instead of solving the wavefunction. Coupled cluster theory is a further

improvement to solving the wavefunction can produce some of the most accurate calcula-

tions but at a significant computational cost [53]. Basis sets contain basis functions which

describes molecular orbitals, and these are used in conjunction with the above described

electronic structure methods.

10

These calculations can only be used to determine the molecular properties if the cor-

rect transition state, reactant, and product geometries are known. This requires the use of

algorithms that search the potential energy surface for the lowest energy conformer of each

reactant and product, and other methods that search for the transition state which rests at

the first-order saddle point between the reactants and products.

1.1.5 Stable geometry and transition state searches

Partition function calculation requires molecular properties such as vibrational frequen-

cies and moments of inertia, all of which can be theoretically calculated if the correct

structures are known. Search algorithms have been developed that require a geometry

prediction, after which the method will automatically search for either a local minimum

representing a stable species, or a saddle point for the transition state.

Stable species searches determine if the structure lies in a local minimum. The search

method perturbs the supplied geometry so that the energy of the molecule is decreased,

and the search is terminated when any further change in geometry will result in an increase

in energy [54–59]. This method has also been called a surface-walking method since the

geometry is being slowly perturbed toward its final configuration.

Transition state geometry searches use similar surface-walking algorithms, except that

the geometry now lies at a first-order saddle point on the potential energy surface [60, 61].

The location of the transition state means a estimate quite similar to the real geometry is

required for the search to be successful. It is sometimes difficult to determine the transition

state geometry, so double-ended algorithms have been developed that use structures of the

reactants and products to make the transition state structure prediction. A user starts by

manually providing a transition state structure estimate to initiate the surface-walking tran-

sition state search. If successful, a reaction path analysis calculation, such as an intrinsic

reaction coordinate (IRC) calculation, is necessary to confirm the transition state. If unsuc-

cessful, the user would then use a double-ended search algorithm, where the user would

11

provide the reactant and product structures.

Double-ended search algorithms typically rely on two strategies: interpolation and path

analysis. The earlier linear and quasi-synchronous transit methods compare the provided

reactant and product structures and interpolate their atom positions to create the transition

state prediction [62, 63]. More advanced methods have improved on interpolation methods,

where several geometries, or images, are interpolated between the reactants and products

[64]. Elastic band methods, such as the nudged (NEB) and double-nudged elastic band

(DNEB) methods [65–68], determine the gradients of the images on the potential energy

surface, and determines spring constants between every image and its two neighbors. These

calculations determine how to move each image so that the spring constants are minimized.

String methods attempt the build the minimum energy pathway by partially modifying

the reactant geometry to move it toward the product [69]. The new reactant is partially

optimized to find the minimum energy pathway, then the product is interpolated toward the

new reactant structure. These steps are iterated until the transition state structure can be

postulated [69]. The various string methods differ subtly in their treatment of the string

as it is formed. The freezing sting method maintains the partially optimizes structures

[70], while the growing string method allows the entire string to be reevaluated during the

calculation [71, 72]. The DNEB and growing string methods are the most widely used

of the more advanced methods, but there is no definitive advantage of using one over the

other [73]. The advanced methods have a higher associated computational cost due to the

increased number of calculations required, but do not require a reaction path analysis to

validate the transition state step since the calculation discovers the reaction path.

1.1.6 Automated transition state searches

Semi-automated search methods have been developed to locate transition state struc-

tures on a potential energy surface. Surface-walking algorithms require a user to provide a

good transition state estimate to initiate the search for a first order saddle point, the location

12

of a transition state. The small margin of error required for the transition state estimate led

to the development of double-ended search algorithms, starting with the linear and quasi

synchronous transit methods to the more robust elastic band and string methods. These

still require starting structures from the user, but structures of the reactant and product

species often in their reactive form. High-throughput kinetic calculation methods require

fully automated approaches to find and validate transition state geometries. A variety of ap-

proaches have been developed, with some building on the semi-automated transition state

approaches.

Maeda and Morokuma used an artificial force to push reacting molecules together, to

probe the potential energy surface around atoms, predicting reactions and finding their tran-

sition states [74, 75]. This artificial force induced reaction (AFIR) method has the potential

to discover new reaction pathways, but also requires many random starting orientations

which leads to a high computational cost.

Zimmerman used the growing string double-ended search method [71] to find possi-

ble transition states [76], and while there is a high computational cost in the transition

state search, the string method negates the need for a transition state validations step. This

method has been extended to the construction of detailed mechanisms for systems contain-

ing approximately 100 reactions, where the user limits path exploration with restrictions

such as barrier height limits [77]. A similar method was also developed using the freezing

string double-ended method [78]. The approach is limited by access to software with the

more advanced string methods. The method has been further developed to create a single-

ended transition state search, which uses driving coordinates from reactants to find several

products, from which the transition states can be found using the growing string method

[79].

A rule-based approach was developed by Zador and Najm that starts with a reactant

structure and directs atoms toward a product, using gradient and energy calculations at

each step to determine the location of the transition state [80]. The method can reliably

13

determine transition states if the reaction type is known but is not computationally efficient

due to the number of gradient and energy calculations. It is best suited to smaller reaction

systems, such as the exploration of a pressure dependent reaction network.

The Automated Alkylation Reaction Optimizer for N-oxides (AARON) code was de-

veloped to automate the screening of potential organocatalysts [81]. A catalyst structure is

provided by the user and mapped onto a parent catalyst structure for which the transition

state geometry is already known, then a series of partially constrained semi-empirical and

DFT optimization steps allow the new transition state to be found. This approach is limited

to catalysts systems and is not fully automated as it requires the user to provide all catalyst

structures and a starting known transition state geometry.

The methods described above apply different strategies to explore the potential energy

surface, and have been successful at finding transition states for tested applications. AFIR,

KinBot, and the double-ended enabled approach of Zimmerman are fully automated but

their use is restricted to smaller systems due to the computational cost. They are also better

suited at finding various transition states for a given set of reactants. These methods are not

ideal for automated mechanism generation, where a method is required to efficiently find

transition states for various reactions belonging to the same reaction family.

1.1.7 Kinetic Programs

Automated methods to determine reactant, product, and transition state structures have

been previously discussed. These structures can be used to theoretically calculate molec-

ular properties, such as bond vibrational frequencies and molecular moments of inertia.

Reaction kinetics can be calculated via transition state theory using the calculated molecu-

lar properties if the reactants and transition state.

Kinetic programs have been developed to automatically apply transition state theory if

provided the relevant molecular properties. They accept output files, containing the neces-

sary molecular properties, from various quantum chemistry packages.

14

The POLYRATE kinetic program was developed to apply variational transition state

theory and semi-classical tunneling methods [82]. Other kinetic programs have been de-

veloped to be more flexible, employing classical transition state theory and allowing the

user to selectively apply corrections, such as 1-D hindered rotor approximation. The pro-

grams may differ in the application of features, such as in the way corrections are applied.

For example, Variflex [83] and CanTherm [84] calculate the reduced moment of inertia

based on the axis of rotation and the identity of all the atoms on each side of the rotated

bond for the most stable species. MultiWell [85] treats the moment of inertia as a function

of the dihedral angle for an internal rotation, which is fitted with several cosine terms. De-

spite the differences, the reaction rates from these kinetic programs were shown to be in

close agreement, as shown for reactions important in the combustion of alcohols [86].

1.2 Thesis overview

This thesis describes methods to automate kinetic calculations by applying transition

state theory. The methods have been developed for the purposes of improving the kinetics

used in the construction of detailed chemical mechanisms, but the algorithm is not limited

to this application.

An algorithm to calculate reaction kinetics needs to find and validate stable species and

transition state structures. Automated methods exist to determine stable species structures

and have been discussed above. Chapter 2 describes efforts use double-ended search al-

gorithms to fully automate transition state structures. Chapter 3 details a group-additive

method that bypasses double-ended search methods to predict transition state geometries,

developed based on insights gleaned in Chapter 2. Chapter 4 discusses optimization of

the group-additive transition state prediction method. Chapter 5 describes the integration

of the automated transition state geometry search method with other software packages to

calculate reaction kinetics, and the comparison of those kinetics with the state-of-the-art

prediction methods.

2. Using double-ended methods to automate transition state searches

2.1 Background

Industrial and environmental applications, such as combustion for energy production,

require detailed kinetic models to sufficiently describe the reaction mechanisms of inter-

est. As these models can contain thousands of reactions [87], manual generation of these

mechanisms is an error-prone and laborious process. Automatic network generators, such

as Reaction Mechanism Generator (RMG) [88], represents molecules as chemical graphs

[18] to apply reaction rules to find all possible reaction pathways. As new species are

added to the model, the number of possible pathways grows exponentially [5]. RMG uses

a rate-based approach to screen reactions in order to build a tractable model, running a

series of simulations as it builds the model and exploring the reaction pathways that have

the highest flux [89]. This rate-based sorting places further importance on the accuracy of

thermodynamic and kinetic parameter estimates: an important pathway could be omitted

from a model if its rate is estimated too inaccurately. Experimentally determined or theo-

retically calculated parameters are preferred for their accuracy, but too few are known to

describe an entire model. Unknown kinetic parameters must be estimated, typically using

a functional-group database trained from other reactions of the same family [31, 90].

The group-based rate estimates can often be inaccurate, especially when derived us-

ing insufficient data. Theoretical calculations can improve the accuracy of these reaction

rates when experimental measurements are not feasible. Theoretical calculations require

properties of the reactants, products, and transition state [91], which can be determined

using ab initio calculations if each 3-dimensional structure is known. Efficient algorithms

have been developed to find the geometries of the reactant and product species [55, 57],

and these are used in the automated calculation of thermodynamic parameters for use in

mechanism generation [8]. Transition state geometries can be found using surface-walking

15

16

algorithms [60, 61], but require very good initial guess structures to be successful. Estimat-

ing the geometry becomes increasingly difficult for more complex chemical systems, and

an inaccurate estimate can lead to either the wrong saddle point or no saddle point being

located.

Double-ended search algorithms have been developed in an attempt to simplify the tran-

sition state search. These methods use geometries of the reactant and product structures as

inputs to create a TS estimate. A common difficulty in manually initiating these algorithms

is the requirement to consistently order the atoms on both reactants and products. Also,

the reactants and products need to be positioned such that active atoms in the reaction

are approaching their transition points (where bonds are formed or broken). Interpolation

methods were first developed where an intermediate guess structure is produced from the

provided reactant and product geometries [62, 63, 92]. These methods are simple to imple-

ment but are not reliably successful in determining the transition state as the PES is often

complex. Path optimization strategies improve on interpolation methods to determine the

reaction path [66, 68, 70, 72, 93]. Several strategies have been developed, but these meth-

ods are not as simple to implement as they contain parameters that need to be optimized for

efficient use [93]. The various strategies adopted have improved on simple interpolation

methods, but no definite advantage has yet been found for any strategy [73].

Other methods have been developed to locate transition states by exploring the potential

energy surface (PES) starting from the reactant valley. PES scanning perturbs the reactant

geometry, calculating points along the PES [94]. Isopotential searching methods explore

the PES at a given energy looking for exits (transition state) from the reactant valley [95].

Artificial Force Induced Reaction (AFIR) uses a bias potential approach, modifying the

PES to push reacting molecules together when performing a geometry optimization [74].

These methods are useful when searching for previously unknown pathways, but require a

large number of calculations and sometimes many repetitions. This makes them unsuited

for automatic mechanism generation where the reaction pathways are known, and thou-

17

sands of reactions must be evaluated.

This chapter describes an algorithm that automates the prediction of the reactant and

product geometries required for double-ended search algorithms. Reactions from RMG

were used to test the algorithm, and the chemical graphs of the reactants and products

from RMG were converted to 3-dimensional structures using distance geometry [96]. The

geometries were used to start quasi-synchronous transit [62, 63] and SADDLE [92] double-

ended searches. These methods were chosen for their ease of accessibility and as they are

simple methods to implement. Semi-empirical electronic structure methods were used to

conduct the double-ended transition state searches in an effort to reduce computational

cost, and the SADDLE method proved more successful. Transition states found with the

SADDLE method were then used for more robust transition state searches using density

functional theory. The algorithm has been tested on hydrogen abstraction reactions from

RMG, with more than 50% of the transition states found.

2.2 Methods

2.2.1 Generating 3-dimensional geometries for double-ended search methods

Molecules in RMG are represented as 2-dimensional graphs. These can be converted

into 3-dimensional structures using distance geometry via RDKit [8, 97]. RDKit creates

stable 3-dimensional structures, but double-ended search methods require reacting atoms

to be positioned within range of each other, where their bonds are broken or formed. This

requires modification to the automated geometry prediction implemented in RMG [8].

Distance geometry

The open-source cheminformatics toolkit RDKit [97] was chosen for its speed and

accuracy as a conformer generation tool [98]. The distance geometry approach used in

RDKit is described by Blaney and Dixon [96]. This approach uses a molecular bounds

matrix containing upper and lower bounds on distances separating each atom pair.

18

RDKit predicts molecular geometries using distance geometry. A molecular bounds

matrix is created when a molecule is passed to RDKit. The molecular bounds matrix is

a construct containing two distances per atom pair, representing upper and lower limits

for the distance between the atoms (Figure 2.1). These are set using atom types and the

hybridization of the atom pairs. For bonded atoms, the limits are set based on typical bond

distances for stable molecules; e.g. H—H bond is limits are set to 0.71 to 0.72 A. Distance

limits are calculated based on trigonometry and typical bond angles for non-bonded atom

pairs in the same molecule. For atom pairs where the atoms are on separate molecules,

lower limits are set as the sum of the atomic van der Waals radii, and the upper limits are

set to 1000 A(intended to be infinitely large).

RDKit positions atoms in 3-dimensional space using the distance constraints of the

bounds matrix by the process of ”embedding” [99]. The atoms are positioned in a ran-

dom arrangement that satisfies the matrix. The embedded geometry can then optimized

using universal force fields (UFF) [100], to give a refined geometry. The magnitude of the

spring constants for each atom pair used in the UFF optimization are determined using the

distance limits in the molecular bounds matrix. Repeated embeddings ensure a variety of

conformers are considered, and the minimum energy conformer estimate is selected.

Methods to generate the bounds matrix, then embed and optimize molecules based on a

bounds matrix, are all available in the open source cheminformatics software RDKit [97].

Positioning reactive atoms

Reactant and product positioning is important in the success of double-ended search

algorithms [101]. The gray area in Figure 2.2 represents a range of geometries close to

the TS that would lead to a successful surface-walking TS search. The dashed lines rep-

resent what a simple interpolation strategy may generate. Double-ended search methods

are always more successful if the reactants and products are placed closer to the transition

state (1 and 2) than using the minimum energy structures (R and P). We therefore need a

19

0.0 1.12 1.12 1.12 1.12 1000 1000 10001.10 0.0 1.86 1.86 1.86 1000 1000 10001.10 1.78 0.0 1.86 1.86 1000 1000 10001.10 1.78 1.78 0.0 1.86 1000 1000 10001.10 1.78 1.78 1.78 0.0 1000 1000 10003.65 2.9 2.9 2.9 2.9 0.0 1.33 1.043.65 2.9 2.9 2.9 2.9 1.31 0.0 1.973.15 2.4 2.4 2.4 2.4 1.02 1.89 0.0

0.0 1.12 1.12 1.12 1.12 2.60 1000 10001.10 0.0 1.86 1.86 1.86 1000 1000 10001.10 1.78 0.0 1.86 1.86 2.10 1000 10001.10 1.78 1.78 0.0 1.86 1000 1000 10001.10 1.78 1.78 1.78 0.0 1000 1000 10003.65 2.9 2.9 2.9 2.9 0.0 1.33 1.042.50 2.9 2.00 2.9 2.9 1.31 0.0 1.973.15 2.4 2.4 2.4 2.4 1.02 1.89 0.0

CHHHHOOH

C H H H H O O H

CHHHHOOH

C H H H H O O H

2.55

2.05

A

B

Figure 2.1: The molecular bounds matrix. (A) Bonded atom limits are set by bondlength rules, while connectivity limits non-bonded atoms in the samemolecule. Van der Waals radii set the lower limits for atoms on separatemolecules, while there are no upper limits (set to 1000 A). (B) By editingthese distance limits, we can position molecules relative to one another, aswell as stretch or shrink bond distances.

bounds matrix that predicts geometries closer to the transition state. This can be achieved

by positioning reactive atoms almost close enough that bonds are formed and/or broken.

For hydrogen abstraction reactions, 3 distances (Figure 2.3) were considered for modi-

fication to create the necessary starting geometries for double-ended methods: the distance

between the abstracted hydrogen atom and the heavy atom it is bonded to (dXH), the dis-

tance between the abstracted hydrogen and the abstracting radical (dHY), and the distance

between the heavy atom and the abstracting radical (dXY). These key distances undergo

significant change when the reaction proceeds from reactant to product as they occur where

bonds are broken and formed. The algorithm sets distance limits of 2.0 – 2.1A for dHY, and

2.5 – 2.6A for dXY. These distances were the most successful when tested on a test set of

50 hydrogen abstraction reactions (provided in Appendix A) involving various molecular

20

R

P2

1

Figure 2.2: Potential energy surface showing minimum energy pathway (dotted line)from reactants (R) to products (P). A double-ended search between 1 and2 will start closer to the TS (grey circle) than a search between R and P.

types. The same distance limits were used for the product geometries, but the X and Y

atoms for the reactants are now the respective Y and X atoms for the products. Embedding

and optimizing the reactants and products with their respective bounds matrices produced

starting geometries required for the QST2 method.

Transition state validation

An algorithm was created to control the transition state refinement and validation. The

algorithm interfaces with computational chemistry software to perform the transition state

optimization using electronic structure methods such as density functional theory. The

21

YX H

dXH dHY

dXY

Figure 2.3: Definition of the 3 key distances for editing the transition state geometries.H represents the abstracted hydrogen, X the atom bonded to the hydro-gen, and Y the radical abstracting the hydrogen.

calculation is checked for an absence of errors, and the presence of a single imaginary

frequency. The optimized geometry is then used for an intrinsic reaction coordinate calcu-

lation (IRC) [102].

The IRC result should connect the original reactants and products for a successful tran-

sition state. The result is typically inspected visually for comparison, but this is not possible

for an automatic procedure. In our algorithm, the IRC geometries are extracted and con-

verted into chemical graphs using a simplified version of the ConnectTheDots method in

Open Babel [103]. The atoms are sorted along the z-coordinate, with the method starting

with the lowest atom, continuing along the axis, and terminating with the highest. A bond

is made between this first atom, A, and its nearest neighbor, B, if all the following are true:

1. No bond currently exists between A and B

2. the number of other bonds to A and B is less than their respective valencies

3. the distance between A and B is less than the sum of their covalent radii + 0.2A.

The process is repeated with atom A being compared each time to the next-nearest

atom from the previous iteration, until either there are no more atoms to be compared or

the number of bonds on A equals its valency. The method then proceeds on to the next

atom along the z-axis.

With the bonding complete, the chemical graphs of the IRC molecules are compared to

the starting reactants and products using a graph isomorphism algorithm [19]. The transi-

22

tion state search is successful if the chemical graphs are isomorphic.

2.2.2 Locating transition states with the automatic double-ended search

Double-ended searches require that the atoms in the reactants and products must be

provided in corresponding order, e.g. the X atom in the reactant and the Y atom in the

product must be listed in the same place for both geometries. This can sometimes be tedious

for a human starting multiple double-ended searches, but is relatively straightforward in the

context of RMG, which generates the product molecules directly from the reactants.

Semi-empirical methods were used to conduct the double-ended searches to minimize

the computational cost, given the number of reactions being tested and the required number

of gradient calculations per reaction. The resulting transition state estimates were then op-

timized at the same semi-empirical level of theory. The algorithm interfaced with commer-

cially available computational chemistry packages to conduct the transition state searches,

and also validated the outputs to ensure they had converged. All successfully optimized

transition state geometries were validated via intrinsic reaction coordinate (IRC) calcula-

tions [102] to confirm that the saddle points connected with the expected reactants and

products. The successful transition state geometries found using semi-empirical calcula-

tions were used as initial estimates for optimizations using density functional theory. These

geometries were also validated via IRC calculations at the same level of theory as the tran-

sition state search. The overall workflow is shown in Figure 2.4.

334 unique hydrogen abstraction reactions were used to test the algorithm. These re-

actions were collated from hydrogen abstraction reactions in the NIST Chemical Kinetics

Database [104] involving species containing only C, H, and O atoms. They are listed in

Appendix A.

23

Reaction from RMG

Optimize TS geometry

Generate Bounds Matrix

Edit Bounds Matrix close to TS

Embed Matrix in 3D

Double-ended Search

IRCCalculation

Reactants Products

Generate Bounds Matrix

Edit Bounds Matrix close to TS

Embed Matrix in 3D

Figure 2.4: Automatic double-ended enabled transition state search procedure.

2.2.3 Electronic Structure calculations

After the initial embedding in 3D, geometries are refined by constrained optimization

using Universal Force Field (UFF) calculations [100] in RDKit [97]. For the double-ended

searches, Gaussian 09 [105] was used to conduct quasi-synchronous transit (QST2) [63]

searches at the semi-empirical PM6 [49] level of theory, and MOPAC [106] was used to

conduct SADDLE calculations [92] at the semi-empirical PM7 level of theory (a modified

PM6). The resulting transition states were used to start density functional theory calcula-

tions and IRC calculations were performed as noted in the text, using the M06-2X density

functional [107], recently recommended for transition state geometries [108], with the 6-

31+G(d,p) [109, 110] basis set.

24

TS search and refinement

Reaction path analysis

Compare to desired reactants & products

Embed geometry either side of TS

Get bounds matrix

Fail

Succeed

FailFail

H. .OH otherradical

.OH

otherradical

334reactions

4

49 41

8

33

Figure 2.5: Points of failure along the automatic double-ended algorithm with SAD-DLE/PM7 calculations. The arrow widths are in proportion with the num-ber of associated reactions. 194 succeeded with 128 reactions failing at thereaction path validation.

2.3 Results and Discussion

The double-ended algorithm was tested with the set of 334 hydrogen abstraction reac-

tions using Gaussian’s QST2 method at the PM6 level of theory (QST2/PM6) and Mopac’s

SADDLE method at the PM7 level of theory (SADDLE/PM7), with the resulting geome-

tries optimized at the respective levels of theory. 160 of the reactions were successful

with QST2/PM6, and 194 with SADDLE/PM7 (Figure 2.5). The higher failure rate of the

QST2/PM6 approach led to the SADDLE/PM7 approach being used for further calcula-

tions.

For the SADDLE/PM7 calculations, 322 reactions successfully converged to a saddle

point, but 128 of these were invalidated by the reaction path analysis: although a saddle

point was found, it represented a hindered rotor in the reactants, not a formation of prod-

ucts. 90% of these failures comprised reactions with small radicals (H, OH, CH3, and 3O2)

25

A B

1.241 1.237 1.241 1.241 1.214 1.194

1.373 1.376 1.378 1.390 1.365 1.345

1.390 1.395 1.395 1.446 1.419 1.402

O

HO

H3C H2CH3C CH

CH3

OCH

O

HO

H3C

Figure 2.6: dXH transition state distances in Angstrom calculated with M06-2X/6-31+G(d,p). Abstracting radicals (Y) are on the left, and the hydrogen andthe carbon it is abstracted from (XH) are on top. Similar trends wereobserved for dHY, and dXY.

abstracting the hydrogen. The high failure rate of small radical reactions, especially those

involving H radical as the abstracting radical, motivated additional calculations for the H

radical reactions. Transition states for the tested reactions could be found using the M06-

2X/6-31+G(d,p) level of theory, but could not be found with PM6 nor PM7. Thus suggests

the semi-empirical level of theory was insufficient for these transition state searches. The

geometries for H radical abstractions (Y· is H·) were also observed to be dissimilar to the

geometries found automatically: the distance dHY was on average 0.2 A smaller than for

other radicals. This may also have contributed to the failure with small radicals.

The successful transition state geometries were used as initial estimates for M06-2X/6-

31+G(d,p) optimizations. The results were largely successful with less than a 10% failure

rate. This means the transition states found using semi-empirical methods with low com-

putational effort are suitable starting points for more accurate calculations.

The 3 key reaction center distances (dXH, dHY, dXY) were collated from successfully

determined transition states found at M06-2X/6-31+G(d,p). Trends were observed in the

distances at the transition state, demonstrating that modifying a single reacting group had

a quantifiable effect on the reaction center distances (Figure 2.6). The trends shown in

Figure 2.6 suggest the effects of the reacting groups on dXH distances are separable and

consistent. Similar trends were observed for dHY and dXY (see Appendix A).

26

2.4 Conclusion

An algorithm has been developed to automatically determine transition state geometries

for hydrogen abstraction reactions using double-ended search methods. The algorithm uses

distance geometry to provide the starting geometries for double-ended searches. Transi-

tion states were successfully found for over 50% of tested hydrogen abstraction reactions,

using a combination of semi-empirical PM7 calculations and calculations at M06-2X/6-

31+G(d,p). Most failures were saddle points that cannot be found at PM7, and a higher

success rate is expected if DFT electronic structure methods are used when running the

double-ended transition state searches, though this would incur additional computational

expense. Trends were also observed in the reaction center distances, and these suggest

that unknown inter-atomic transition state distances can be estimated via a group-based

approach.

2.5 Recommendations

2.5.1 Semi-empirical methods are insufficient for transition state searches

The automated double-ended search algorithm used semi-empirical methods to con-

duct transition state searches, and the semi-empirical transition states were used to run

more robust density functional theory calculations. The semi-empirical calculations are

computationally inexpensive, but the poor accuracy of the potential energy surface means

many transition states cannot be determined. The computational savings are meaningless

if a large quantity of transition states cannot be found, so more robust electronic structure

methods should be used. Density functional theory provides a good balance between cost

and accuracy, and should be the minimum used for further transition state studies.

27

2.5.2 Consider more robust double-ended search methods

The QST2 and SADDLE methods used in this chapter are interpolation based double-

ended methods, but more robust path optimization methods have been developed. The path

optimization methods discover the reaction path from the same reactant and product ge-

ometries provided to interpolation methods. The path optimization methods determine the

reaction path using differing strategies to determine the reaction path. Path optimization

methods have an increased computational cost due to the number of gradient calculations

required to find the transition state [71]. The additional computational cost of double-ended

methods is somewhat mitigated by not requiring a path analysis calculation once the tran-

sition state is found, since the reaction path is determined during the transition state search.

It should be determined if this increased computational cost makes these calculations feasi-

ble for implementation with automated mechanism generation. Implementing more robust

double-ended approaches may not be feasible for mechanism generators, but could be use-

ful for other applications such as solving a small pressure-dependent reaction network. For

example, other automated transition state searches enabled by double-ended approaches

have been developed to discover new reaction pathways [76, 78].

It has been shown that there is no clear advantage to using a given path optimiza-

tion method [73], where one method may be more successful for some reactions, another

method will be for others. These methods also contain parameters that need to be opti-

mized [93], which further complicates their automated implementation. Several methods

could be implemented, but many of these more robust double-ended methods are imple-

mented in different commercially available software, providing a further barrier to their

widespread implementation.

3. Automatic transition state geometry estimation using group

contributions

3.1 Background

Complex chemical systems, such as the combustion of novel renewable fuels, can be

better understood with detailed kinetic models. The required detail means a model can

contain thousands of species and reactions [5], making their construction laborious and

prone to human error. Automated mechanism generators have been developed to construct

detailed kinetic models while avoiding the pitfalls of manual construction [1]. Thermody-

namic and kinetic parameters are preferentially sourced from experimental measurements

or high fidelity theoretical calculations to complete a kinetic model, but estimates are also

used as many of the required parameters are unknown [20].

Parameter estimation methods are computationally efficient strategies to provide ther-

modynamic and kinetic values [28]. Most parameter estimation methods are based on Ben-

son’s group additivity [111], in which the thermodynamics of a molecule are estimated by

summing the contributions from the molecular groups present in the molecule, these group

values having first been calculated from molecules with known thermodynamic parameters

[22, 112]. Such group contribution methods have been shown to work well for thermo-

chemistry of hydrocarbon species, and the concept has been extended to kinetic parameter

estimation [113–116]. Group contribution methods become less accurate when parameters

are estimated using groups values that have not been well determined, due to insufficient

training data. For example, group values have been difficult to extend to thermodynamics

of fused rings leading to inaccuracies in their estimates [8].

Such inaccuracies in group-based estimation methods have motivated high-throughput

electronic structure calculations for thermodynamics and kinetics [117, 118]. Such a pro-

28

29

cedure was recently developed to calculate thermodynamic parameters within the frame-

work of the automatic Reaction Mechanism Generator (RMG) [6, 8]. In that procedure,

3-dimensional structures were created via distance geometry [96], with the structures op-

timized using force-fields and semi-empirical electronic structure calculations to provide

molecular parameters, allowing thermodynamic parameters to be calculated. Thermody-

namic error was greatly reduced for fused-ring species compared to estimates derived from

Benson’s group additivity.

In a similar manner, kinetic parameters currently estimated from poorly trained group

values could be improved by applying electronic structure calculations and transition state

theory, but this requires a high-throughput approach for finding transition state geometries.

A transition state geometry estimate, which is typically provided manually, must be quite

similar to the correct transition state geometry for the optimization to converge. Manual

estimation of transition states is not compatible with the context of automated mechanism

generation, which requires thousands or even millions of reaction rates. With continuing

advances in computing power, it has become feasible to automate these searches.

One approach used the growing string double-ended method [71] to search for possible

transition states [76]. While there is an increased computational cost associated with the

transition state search, the use of the string method negates the need for a path analysis

step to validate the transition state. This method has been extended to the construction of

detailed mechanisms, where the user controls the mechanism generation with restrictions

such as barrier height limits [77]. Adoption of this method is limited to those with access

to software with reliable double-ended methods. Zimmerman has further developed these

methods to create a single-ended transition state search [79]. This makes use of driving

coordinates from reactants to find intermediates, from which the transition state can be

found using the growing string method.

Zador and Najm instead use a rule-based approach to direct atoms from a reactant

configuration towards the product, using energy calculations at each step to determine the

30

location of the transition state [80]. This method is best suited to reaction systems with a

small number of atoms, such as the exploration of a pressure dependent reaction network.

The Automated Alkylation Reaction Optimizer for N-oxides (AARON) code automates

transition state searches to screen potential organocatalysts [81]. A catalyst structure is

provided by the user and mapped onto a parent catalyst structure for which the transition

state geometry is already known, then a series of partially constrained semiempirical and

DFT optimizations allow the new transition state to be found.

Maeda and Morokuma used an artificial force to push reacting molecules together, to

probe the potential energy surface around atoms, predicting reactions and finding their

transition states [74, 75]. This Artificial Force Induced Reaction (AFIR) method requires

many random starting orientations.

The methods highlighted above explore the potential energy surface for a given set of

atoms, finding many reaction pathways for a few reactants. These are not well suited to

automated mechanism generation where it is routine to have many reactions of the same

type but with varying reactants. For such applications, this chapter describes an alterna-

tive method to estimate transition state geometries. Trends in reaction center distances at

the transition state were observed in Chapter 2, and have also been observed in previous

studies [31]. These insights inspired the development of molecular group contributions to

predict the inter-atomic distances in the reaction center of transition states, enabling fully

automated prediction of transition state structures.

Estimated 3D geometries are constructed from the predicted distances using distance

geometry. Optimization and validation of the transition state estimates have also been

automated. Hydrogen abstraction reactions from a diisopropyl ketone combustion model

[2], previously developed using RMG, were used to test the method, with transition states

found for over 65% of the 1393 reactions.

31

3.2 Methods

3.2.1 Geometry estimation and optimization

Distance geometry

Further details on the implementation of distance geometry can be found in section

2.2.1.

The open-source cheminformatics toolkit RDKit [97] was chosen for its speed and

accuracy as a conformer generation tool [98]. The distance geometry approach used in

RDKit is described by Blaney and Dixon [96]. This approach uses a molecular bounds

matrix containing upper and lower bounds on distances separating each atom pair.

Distances separating reactive atoms undergo significant change during a reaction, but

the rest of the molecule remains relatively unaffected. As a result, distances between the

reactive atoms are unknown at the transition state, but existing methods can be used to

determine the remaining distances.

For hydrogen abstraction reactions, three atoms lie in the reaction center: the abstracted

hydrogen (H), the atom bonded to the abstracted hydrogen (X), and the radical abstracting

the hydrogen (Y). The three distances separating each reactive atom pair are denoted as

dXH, dHY, and dXY. Estimating these distances allows the entire transition state geometry

to be created using distance geometry. Typically the geometry is specified manually, but

we demonstrate here a group contribution method to estimate the required reaction center

distances.

Molecular group organization

Molecular groups were used to predict distances separating reactive atoms of transition

states. The molecular groups were organized in a hierarchical tree structure, so that distance

predictions were made using the most relevant available data. The tree was limited to

reactions with only atom types (elements) of C, H, and O, but can be expanded to include

32

other atom types by adding the appropriate groups. Two trees were used as hydrogen

abstraction reactions are bimolecular and the reaction center distances are dependent on

both reactants. The head nodes (top groups) for the trees were X H or Xanyrad H and

Y anyrad. The X H or Xanyrad H tree described the reactant where X is a wildcard atom

of any atom type, with zero or more radical electrons, bonded to an H atom (the hydrogen

to be abstracted), and the Y anyrad tree described the abstracting radical of any atom type,

with one or more radical electrons. Child nodes were added to be more detailed than the

parent nodes, for example, a child of the X H or Xanyrad H node is X H(here X is any

element but has no radical electrons), itself having a child H2.

The structure of the molecular group tree was taken from the kinetics database of the

RMG software. This tree structure was developed to make efficient use of sparse data for

estimating kinetic parameters relevant to hydrocarbon combustion. The development of this

tree involved several researchers making independent modifications over a number of years

to provide improved kinetic estimates for specific fuels. Sometimes modifications were

made with the aim of minimizing disruption of the existing tree, rather than of optimizing

the overall tree structure.

The tree structure and associated group values are available in Appendix B.

Group additive distance estimation

Reaction center distances were collated from previously optimized transition state ge-

ometries, creating a training set. Values for molecular groups, organized in a hierarchical

tree, were calculated using values from the training set by linear least squares regression,

using the distances for every reaction in the training set that match the molecular group.

The base value is stored in the top level node, and the value for a descendant is stored as a

correction to the top level node value. This means the value of a given node is calculated

as the sum of the base value and the node’s correction.

The linear least squares regression calculates group values by finding the best fit to

33

the available training data. For each set of distances in the training set, the reactants are

matched to groups in the group tree. All groups that match the X H or Xanyrad H reactant

are paired with the groups that match the Y anyrad reactant, and the sum of each pair and

a base value is set equal to the training distances. This creates a system of equations where

the variables are the group values and the known values are the training data. The regression

is conducted using the linear algebra package in numpy, finding the group values that best

fit the data [119]. A detailed description of the least squares regression is available in the

appendices.

The reaction CH4 + C2H5 is used as an example. Table 3.1 shows the sections of

the molecular group tree relevant to this reaction. The most specific group that matches

each reactant is found by descending the tree. CH4 matches the C methane group in the

X H or Xanyrad H tree, while C2H5 matches the C rad/H2/Cs\H3 group in the Y anyrad

tree. An explanation of the naming convention, and complete tree definitions, are provided

in the appendices. The distance estimates are calculated by summing the top node value

and the group correction for each reactant, predicting respective values for dXH, dHY, and

dXY as 1.388A, 1.331A, and 2.721A.

Transition state geometry estimation

With the distances between atoms at the reaction center estimated using molecular

group values as described in the previous section, transition state geometry estimates can

be created via distance geometry (Figure 3.1). For a pair of reactants, a bounds matrix

is first generated in RDKit for the stable species, comprising upper and lower limits on

the distances between each pair of atoms. For the distances dXH, dXY, and dHY, the val-

ues in the bounds matrix are updated to be the distance prediction as described earlier, ±

0.05A. Some combinations of upper limits from these edits may conflict with previously

set lower limits, particularly lower limits between a reactive atom (X, H, or Y) and some

non-reacting atoms, forming an inconsistent bounds matrix. In these cases the conflicting

34

C H H H H C C H H H H HC 0.00 1.12 1.12 1.12 1.12 1000 1000 1000 1000 1000 1000 1000H 1.10 0.00 1.86 1.86 1.86 1000 1000 1000 1000 1000 1000 1000H 1.10 1.78 0.00 1.86 1.86 1000 1000 1000 1000 1000 1000 1000H 1.10 1.78 1.78 0.00 1.86 1000 1000 1000 1000 1000 1000 1000H 1.10 1.78 1.78 1.78 0.00 1000 1000 1000 1000 1000 1000 1000C 3.90 3.15 3.15 3.15 3.15 0.00 1.52 1.12 1.12 1.12 2.20 2.20C 3.90 3.15 3.15 3.15 3.15 1.50 0.00 2.20 2.20 2.20 1.12 1.12H 3.15 2.40 2.40 2.40 2.40 1.10 2.12 0.00 1.86 1.86 3.08 3.08H 3.15 2.40 2.40 2.40 2.40 1.10 2.12 1.78 0.00 1.86 3.08 3.08H 3.15 2.40 2.40 2.40 2.40 1.10 2.12 1.78 1.78 0.00 3.08 3.08H 3.15 2.40 2.40 2.40 2.40 2.12 1.10 2.26 2.26 2.26 0.00 1.86H 3.15 2.40 2.40 2.40 2.40 2.12 1.10 2.26 2.26 2.26 1.78 0.00

A

B

C

1.33Å

< 3.15Å

C H H H H C C H H H H HC 0.00 1.40 1.12 1.12 1.12 1000 2.73 1000 1000 1000 1000 1000H 1.38 0.00 1.86 1.86 1.86 1000 1.34 1000 1000 1000 1000 1000H 1.10 1.78 0.00 1.86 1.86 1000 1000 1000 1000 1000 1000 1000H 1.10 1.78 1.78 0.00 1.86 1000 1000 1000 1000 1000 1000 1000H 1.10 1.78 1.78 1.78 0.00 1000 1000 1000 1000 1000 1000 1000C 3.90 3.15 3.15 3.15 3.15 0.00 1.52 1.12 1.12 1.12 2.20 2.20C 2.71 1.32 3.15 3.15 3.15 1.50 0.00 2.20 2.20 2.20 1.12 1.12H 3.15 2.40 2.40 2.40 2.40 1.10 2.12 0.00 1.86 1.86 3.08 3.08H 3.15 2.40 2.40 2.40 2.40 1.10 2.12 1.78 0.00 1.86 3.08 3.08H 3.15 2.40 2.40 2.40 2.40 1.10 2.12 1.78 1.78 0.00 3.08 3.08H 3.15 2.40 2.40 2.40 2.40 2.12 1.10 2.26 2.26 2.26 0.00 1.86H 3.15 2.40 2.40 2.40 2.40 2.12 1.10 2.26 2.26 2.26 1.78 0.00

C H H H H C C H H H H HC 0.00 1.40 1.12 1.12 1.12 1000 2.73 1000 1000 1000 1000 1000H 1.38 0.00 1.86 1.86 1.86 1000 1.34 1000 1000 1000 1000 1000H 1.10 1.78 0.00 1.86 1.86 1000 1000 1000 1000 1000 1000 1000H 1.10 1.78 1.78 0.00 1.86 1000 1000 1000 1000 1000 1000 1000H 1.10 1.78 1.78 1.78 0.00 1000 1000 1000 1000 1000 1000 1000C 3.90 2.76 3.15 3.15 3.15 0.00 1.52 1.12 1.12 1.12 2.20 2.20C 2.71 1.32 3.10 3.10 3.10 1.50 0.00 2.20 2.20 2.20 1.12 1.12H 3.15 2.40 2.40 2.40 2.40 1.10 2.12 0.00 1.86 1.86 3.08 3.08H 3.15 2.40 2.40 2.40 2.40 1.10 2.12 1.78 0.00 1.86 3.08 3.08H 3.15 2.40 2.40 2.40 2.40 1.10 2.12 1.78 1.78 0.00 3.08 3.08H 3.15 2.40 2.40 2.40 2.40 2.12 1.10 2.26 2.26 2.26 0.00 1.86H 3.15 2.40 2.40 2.40 2.40 2.12 1.10 2.26 2.26 2.26 1.78 0.00

1.33Å

3.15Å

Figure 3.1: Manipulating the molecular bounds matrix to create transition state ge-ometry estimates. (A) The matrix generated for a pair of stable species.(B) Editing the matrix with the group contribution predictions for tran-sition state distances. (C) Conflicting lower limit distances are corrected,creating a valid transition state distance bounds matrix.

35

Table 3.1: Part of the hierarchical molecular group tree for transition state distancestrained using 1071 transition state distances calculated using B3LYP/6-31+G(d,p). The full tree is provided in the appendices.

Group dXH dHY dXYBase 1.336010 1.336330 2.667560L1: X H or Xanyrad H

L2: X H –0.002556 0.002864 0.000227L3: H2 –0.327434 –0.045046 –0.369886...L3: Cs H 0.007461 0.023642 0.032296L4: C methane 0.076680 –0.051468 0.028801L4: C pri 0.025511 –0.002230 0.025031L5: etc.

L4: C sec –0.026003 0.069757 0.044341L4: C ter –0.025676 0.062321 0.034956L5: etc.

L2: Xrad H 0.094987 –0.106435 –0.008430etc.

L1: Y anyrad...L2: Y rad 0.002857 –0.002500 0.000277L3: H rad –0.044160 –0.330263 –0.371926...L3: Cs rad 0.024200 0.007289 0.032625L4: C methyl –0.050813 0.075919 0.028607L4: C pri rad –0.001792 0.025273 0.025176L5: C rad/H2/Cs –0.032772 0.051719 0.021617L6: C rad/H2/Cs\H3 -0.024753 0.045959 0.024509L6: C rad/H2/Cs\Cs2\O –0.125966 0.025305 –0.097425

etc.

lower limits are reduced to be in agreement with the previous edits. Finally, a triangle

inequality algorithm is used to smooth the bounds matrix.

Transition state estimates are created by randomly “embedding” the atoms in 3D space

such that they satisfy the bounds matrix. Repeating this process allows multiple conform-

ers to be created. The conformer geometries are then optimized using a UFF force field

calculation constrained by the bounds matrix. The lowest energy conformer according to

the UFF calculation is selected as the transition state estimate. While the accuracy of the

force field energy calculation is low, it is sufficient for conformer selection.

36

Figure 3.2: The automated transition state search algorithm.

Transition state validation

An algorithm was created to control the transition state refinement and validation. The

geometry estimate resulting from the constrained force field optimization, is used as the

initial guess for a transition state optimization using electronic structure methods such as

density functional theory. The calculation is checked for an absence of errors, and the

presence of a single imaginary frequency. The optimized geometry is then used for an

intrinsic reaction coordinate calculation (IRC) [102]. Full details of the transition state

validation steps are provided in section 2.2.1. The full automated algorithm is outlined in

Figure 3.2.

Training the molecular group values

Molecular group values were trained with known values taken from transition state

geometries that were optimized and validated with the B3LYP electronic structure method

and a 6-31+G(d,p) basis set. All data added to a training set came from transition states

37

found and validated using the same electronic structure method and basis set. Transition

states found and validated with the automated algorithm were also added to the training set

at the end of each test of the automated algorithm. Before each run of the algorithm, the

molecular group values were retrained using the training set expanded from the previous

run.

3.2.2 Method evaluation

H abstraction reactions from a DIPK combustion model.

1,393 hydrogen abstraction reactions from a diisopropyl ketone (DIPK) combustion

model (total of 4,027 reactions) [2] were used to test the automated algorithm. Reactions

were passed to the transition state search algorithm, which created transition state estimates,

then optimized and validated them.

First, a preliminary training set was created from 44 unique hydrogen abstraction tran-

sition states, and was used to train the molecular group tree. As few groups were trained,

we found the distance estimates to be insufficient for reliably predicting transition states.

As a result, the training set was expanded to contain data from a total of 230 transition

states. This expansion of the training set was done with geometries found both manually

and using the automated algorithm. The reactions from the DIPK model were then passed

to the automated algorithm, with data from the successfully found transition states added

to the training set. The groups were retrained, and the method was tested again on the same

reactions from the DIPK model. This led to the expansion of the training set from data for

230 transition states to 827 and then 1,071 transition states. Characteristics of the group

contribution method were investigated using 4 training sets (Table 3.2).

Computational Chemistry

Estimated geometries were refined in RDKit using universal force fields (UFF) [100].

Geometry optimization and path analysis calculations were run using B3LYP [120, 121]

38

Table 3.2: Training set information. As the training set was expanded, the RMS errorfrom the validated transition state distances decreases.

Training Transition Geometries RMSset States in found Error

name training set A44TS 44 not run 0.181230TS 230 658 0.102827TS 827 734 0.0401071TS 1071 not run 0.036

with the 6-31+G(d,p) [109, 110] basis set in the Gaussian 09 [105] quantum chemistry

package.

3.3 Results and Discussion

3.3.1 Transition state geometries were successfully estimated using the distance es-

timates

The algorithm was tested on the DIPK reactions with the groups trained with the train-

ing set named ‘230TS’, and found 658 of the 1,393 transition state geometries. 597 of the

resulting geometries were not already in 230TS, making a set 827TS when added to the

training set. The set 827TS was used to retrain the group values, with the algorithm again

tested on the DIPK reactions, where 734 transition states were found, of which were 244

unique to the training data. The additional 244 transition states allowed the creation of the

1071TS set. Over the 2 test runs, 907 transition states of the 1,393 reactions were found

and validated, expanding the training data from 230 to 1,071 transition states.

3.3.2 Increasing training data improves the group value predictions

The reaction center distances from the 907 transition states found using the algorithm

were compared to distances estimated by molecular group values at differing training set

sizes (Figure 3.3). The root-mean-squared (RMS) error for each of the 3 distances de-

creased when the training set containing transition state data was increased from 44 up

39

to 1,071 entries. There was little improvement in the estimated values when the training

set expanded from 827 geometries to 1,071 in comparison to the earlier expansions of the

training set.

The observed improvement in the distance predictions as the groups were trained with

more data was consistent with our hypothesis. With a larger training set, some untrained

groups now have data and some trained groups have more data, improving their accu-

racy. If the group was newly trained, the algorithm would use more relevant and specific

group values, improving the predicted distances. This was observed in the improvement in

the distance predictions moving from 44TS to 230TS. With new training data, previously

trained groups improve as more data are used to train the group values, as seen when com-

paring the groups trained using 230TS and 827TS. Little improvement in the RMS error

for predictions made with 827TS and 1071TS shows that the 827TS groups were relatively

well trained so the extra data from 244 transition state geometries had little effect on group

value predictions.

The observations show certain data are more desirable when expanding a training set

for molecular group values. For example, if the reactions of interest are hydrogen abstrac-

tions from the OH group of an alcohol, the training set should contain such reactions with

different types of radicals abstracting the hydrogen. If the training set contains data from a

large number of transition states for hydrogen abstractions from alkanes by an alkyl radi-

cal, little will be gained by adding a transition state for ethyl abstracting a hydrogen from

methane. Both the reactions of interest and the available data should be considered when

adding new data to a training set.

3.3.3 Geometry estimation needs improvement to make best use of predicted values

As described earlier, two attempts were made to find all the TSs in the DIPK model:

first with the original group tree trained with the 230TS training set, and secondly trained

with the 827TS training set. Of the 907 geometries found over these two iterations, 422

40

dXH dHY dXYPr

edic

ted

Dis

tanc

e(A

)

44T

S23

0TS

827T

S10

71T

S

Optimized Distance (A)

Figure 3.3: Distances from 907 validated transition states found at B3LYP/6-31+G(d,p) were compared to predictions derived from molecular groupvalues. The solid line represents parity with the optimized distances, andthe dashed lines represent the root mean squared error of the estimatesfrom parity. The predictions improved as the training set used to calcu-late the group values was expanded.

41

were found during one iteration but not the other. This allowed comparison of estimates that

were unsuccessful, against the true optimized values from the successful attempts (Figure

3.4). One cluster of failures, with RMS errors greater than 0.15 A, came from the 230TS

iteration, and were mostly successful at the 827TS iteration. For distance estimates with

RMS errors below 0.05 A, the conversion from a predicted value into a UFF-optimized 3D

geometry using the current algorithm resulted in additional error being introduced into the

distances, possibly causing the failure. This suggests that while the group additive method

can make accurate distance predictions, further optimization of the algorithm for converting

these distances into 3D geometries is necessary.

0102030405060708090

100

0.01 0.06 0.11 0.16 0.21 0.26

# of

Fai

led

Geo

met

ries

RMS Error (Å)

Group Additive PredictionUFF Optimized Distances

Figure 3.4: 422 transition states found in one trial of the algorithm were unsuccessfulin another. Comparing optimized distances against the failed estimationattempt showed: 1. poorly estimated distances that were improved whenthe training set was expanded 2. the conversion from prediction to geom-etry estimate introduced additional error.

Figure 3.5 shows the probability of a failed transition state search increases with in-

creasing root mean squared (RMS) error in the three reacting distances of the starting ge-

ometry. The lower bound probabilities are calculated from trials from the 230TS training

set. It is a lower bound of P (failure) because only the 249 failures that later succeeded

with the 827TS training set were included; for the 486 reactions that continued to fail, the

true distances are not known and the RMS error could not be calculated. Because few of

our starting geometries were worse than 0.2 A we do not have many trials in this region and

42

our estimate of the failure probability is quite uncertain, hence the wide Clopper–Pearson

[122] 95% confidence interval of P (failure) (the vertical bars in figure 3.5). To estimate

the upper bound of the failure probabilities, we distributed the 486 additional failures us-

ing a variety of assumptions, each giving a different estimate of the P (failure) curve; the

upper bound in the figure encompasses all these curves.

Although uncertain, the shapes of these bounds are informative, and they support the

need for good starting geometries for a transition state search: embedded geometries with

an RMS error greater than 0.15 A have a high failure rate. Other reaction families, opti-

mization algorithms, and software packages may behave differently.

Upper boundLower bound

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 0.1 0.2 0.3 0.4 0.5

Prob

aliti

y of

failu

re

RMS error in starting geometry distances (Å)

Figure 3.5: Probability of a failed TS search as a function of RMS error in reactivedistances of starting geometry. For each point the vertical bar show theClopper–Pearson [122] 95% confidence interval of the lower bound andthe horizontal bar shows the range of RMS errors used to calculate it.

43

3.3.4 Algorithm optimization

The automated algorithm takes advantage of the molecular group estimates to predict,

optimize, and validate transition state geometries, but it does not make best use of the

group-based distance estimates, and could be improved in future work. In the algorithm

tested here, after the atoms are positioned in the 3D space, a constrained UFF refinement

step is done in RDKit before the transition state search at DFT. This is designed to improve

the geometry of the non-reacting atoms, but the refinement can alter the reaction center

distances, dragging them away from their well-predicted values. This could be addressed

by tightening the constraint spring constants before the UFF refinement or replacing the

refinement step with a DFT optimization with the reaction center distances frozen as is

done in the AARON code [81].

The difference between the upper and lower bounds for the reaction center distance

estimates is currently set to 0.1A, which can be as much as 10% of some distances. This

range should be related to the uncertainty calculated when determining the group values by

linear regression, allowing well known values to have tight restrictions.

3.4 Conclusion

Automated transition state searches have previously been described as an important

challenge for studying complex chemical systems, helping to move mechanism genera-

tion closer to being predictive. A group contribution method has been developed to take

advantage of available chemical data to make predictions of transition state geometries.

The group contribution method performs best with well trained groups, as seen when pre-

dictions improved by adding more training data. The group contributions were used in

a novel, fully automated algorithm to create a transition state estimate using distance ge-

ometry methods, with the estimate then optimized and validated to find the true transition

state structure. The validation step makes it a self-improving machine learning algorithm,

44

as new transition state data are used to improve group values. That a simple sum of con-

tributions from the abstracting and donating groups can so fully determine the transition

state geometry offers new physical insight into these reactions. Although the algorithm

for generating 3D geometries from distances is a first generation and could be improved,

the simple method for predicting the inter-atomic distances is already remarkably accurate

with typical root-mean-squared errors of 0.04 A.

3.5 Recommendations

3.5.1 Conformer recognition

The lowest energy conformers are used when calculating thermodynamic and kinetic

parameters using quantum mechanics in its simplest form. Cases have been shown that

ignoring other conformers can introduce error in the parameters calculated [43–46]. Many

conformational isomers can be generated using the algorithm described above by repeated

embedding using a single molecular bounds matrix. It would be beneficial to develop

an algorithm to identify conformational isomers that are unique so they can be used in

statistical treatments that account for multiple conformers.

Each transition state conformer would need to be optimized and validated as described

above, adding computation time to the process. The gains in kinetic accuracy need to be

considered if this approach is implemented.

4. Improving the group contribution transition state search method

4.1 Background

Detailed mechanisms help understand complex chemical systems. Such detailed mech-

anisms can contain over 10,000 unique reactions, making their manual construction a falli-

ble and laborious process. Automated mechanism generation can resolve these difficulties,

where published sources are preferentially used to predict reaction rates, with estimation

methods deputizing when data are unavailable. Reaction rate estimates can be quite approx-

imate, but they can be improved using theoretical calculations via transition state theory.

Theoretical calculations are also laborious so a high throughput kinetic calculation method

is required for transition state theory to be used with automated mechanism generators, and

this requires an automated method to predict and find transition state structures. Chapter 3

describes the automated geometry search method.

Several steps are involved in the automatic transition state search method, starting with

the estimation of distances in the reaction center of the transition state using a molecular

group contribution method. The predicted transition state distances are used to create a

3-dimensional transition state estimate by applying distance geometry. The transition state

estimate is used to start a transition state search in order to find the true transition state

structure. Each transition state is validated using a reaction path analysis calculation.

Options exist for some of the steps involved in automating the transition state search,

and it is important to explore these options as they may improve the automated search

method. It was shown in Chapter 3 that increasing training data improves the accuracy

of the molecular group values, but additional data can only improve group values that are

poorly determined. This chapter discusses modifications to the algorithm and their effects

on transition state prediction accuracy. The modifications discussed are changes to the

group contribution prediction method and additions to the sequence of optimization steps

45

46

performed on the geometry estimate during the transition state search.

4.2 Methods

4.2.1 Modifying the transition state geometry prediction

Reshaping the molecular group tree

The automated algorithm uses molecular groups to predict distances separating reactive

atoms of transition states. The molecular groups were organized in a hierarchical tree

structure, so that distance predictions were made using the most relevant available data.

Details about the group tree structure were previously discussed in Section 3.2.1.

The structure of the molecular group tree used in Chapter 3 was taken from the kinetics

database of the RMG software. The development of this tree involved several researchers

making independent modifications over a number of years to provide improved kinetic es-

timates for specific fuels. Sometimes modifications were made with the aim of minimizing

disruption of the existing tree, rather than of optimizing the overall tree structure. The un-

coordinated nature of the modifications led to a tree structure that is hierarchical, but lacks

obvious logic in its structure, and was not optimized for best results for transition state

distances. For example, the O H group has descendants that are peroxides except for the

peroxyradical group (Orad O H), which is instead a sibling group.

A new tree structure was developed for comparison to the RMG designed structure, and

to better understand the effect of the tree structure on the predictions of the transition state

reaction center distances. The same top nodes were used for the new tree as they described

all possible reacting molecules for the hydrogen abstraction family. Each descendant gen-

eration in the molecular group tree had a single characteristic defined that was not in the

ancestor generations. Characteristics were also defined earlier (higher in the tree) when

they were thought to have a greater impact on the reaction center distances than other un-

defined characteristics. For example, the children of the head nodes specified the elements

47

of the wildcard atoms (X and Y), but no bonding or radical electrons were specified be-

cause, while important, they are less critical than the wildcard atom types. This meant that

child nodes to X H or Xanyrad H were H2, C H, and O H (the X is defined as H, C, or O),

while the children of Y anyrad were Hrad, Orad, and Crad. The following two generations

defined the radicals and bonding. For the X branch of the tree the bonding was defined first,

then the radicals; on the Y branch the radicals were defined first, then the bonding. This

convention was continued until the bonding on the nearest neighbor atoms were defined

(the R groups in R X H and R Y rad).

The tree structure from Chapter 3 is referred to as the ”original tree” and the structure

described in this section is referred to as the ”new tree”. Both the original and new tree

structures are provided in Appendix B.

Tree structure comparison

The original molecular group tree structure was used to automatically find transition

states for hydrogen abstraction reactions in the DIPK combustion model (Chapter 3). The

new group tree was used to estimate the reaction center distances of the transition states

previously found using the original group tree structure. This allowed comparison of the

reaction center distance predictions made with either tree for a given training set, without

repeating all the electronic structure calculations.

Further comparison tested the performance of the molecular group trees for small train-

ing sets. The largest training set from Chapter 3 (1071TS) was randomly sampled to create

many smaller training sets containing data from 44 transition states. With each of the

smaller training sets, group values were trained and distances were predicted then com-

pared to known distances from validated transition states (all contained in 1071TS). This

was done using both the original and new tree structures.

48

Modifying distance limits and the UFF force field optimization

The use of the predicted transition state distances to create 3-dimensional transition

state estimates was fully described in Section 3.2.1. The transition state estimate was cre-

ated based on a molecular bounds matrix, which contains upper and lower distance limits

for each atom pair. For transition state geometries, the distance separating the atoms in the

reaction center of the transition state are unknown. The reaction center distance limits in

the bounds matrix are set as the group contribution distance prediction ± 0.05A, creating a

transition state bounds matrix. The transition state estimate is created by positioning atoms

in 3-dimensional space to satisfy the bounds matrix. The initial 3-dimensional geometry

is then optimized using a universal force field (UFF), where the force constants between

every atom pair is calculated based on the distance bounds matrix (default value of 1,200

kcal/(mol A)).

The group contribution method was developed to provide good reaction center dis-

tances, but setting the distance limits to be the predicted distance ± 0.05A could cause

reaction center distance for two geometries created from the same bounds matrix to dif-

fer by up to 0.1A. The difference between the distance limits were reduced to a total of

0.05A (± 0.025A from the group contribution prediction) to determine the effect of the

distance range.

For the UFF optimization step, the force constants for every atom pair are set based

on the distances in the molecular bounds matrix. This procedure can also modify the re-

action center distances which is undesirable given the accuracy of the predicted distances.

Increased force constants in the reaction center should restrict the reaction center atoms,

so reaction center force constants were tested at 12,000 kcal/(mol A) as well as 100,000

kcal/(mol A). The coupled effects of the distance limit range and force constants were also

tested.

49

4.2.2 Modifying the transition state optimization sequence

The transition state estimate created by positioning molecules in 3-dimensional space

to satisfy distance limits is then is refined via a UFF optimization step. The algorithm uses

the UFF refined transition state estimate to start a surface-walking transition state search.

An alternative approach, inspired by the Automated Alkylation Reaction Optimizer for

N-oxides (AARON) software [81], replaces the UFF optimization step with two partial

refinements. The first freezes the reaction center distances and refines the rest of the geom-

etry, and the second freezes all distances except the reaction center which is refined. The

two refinement steps were run using density functional theory.

Computational Chemistry

Estimated geometries were refined in RDKit using universal force fields (UFF) [100].

Geometry optimization and path analysis calculations were run using M06-2X [107, 123]

with the MG3S [124] basis set in the Gaussian 09 [105] quantum chemistry package.

MG3S is equivalent to 6-311+G(2df,2p) for systems containing H, C, and O atoms [110,

125].

4.3 Results and Discussion

4.3.1 Tree structure and data diversity affect prediction accuracy

The new group tree was trained using the same 4 training sets used in Chaper 3, and

distance predictions were made for comparison to the 907 optimized transition states from

the chapter (Figure 4.1). Predictions made with the new tree structure showed the same

trends previously reported: the error decreased as the training sets were expanded, but

the change from 827TS to 1071TS was minimal. The new tree structure produced better

estimates than the original tree for small data sets, where the data was most erroneous.

The original tree provides marginally better estimates when trained using large data sets.

50

The original tree contained much more detailed groups than the new structure, so the new

tree structure is expected to at least match the accuracy for large data sets if more detailed

groups (more branches in the tree) are added.

0

0.1

0.2

44 230 827 1071

RM

S Er

ror (Å)

TS Geometries in Training Set

Original Tree New Tree

Figure 4.1: The RMS error for the distance estimates compared to the optimizedtransition state distances.

The differences in error observed with the two trees shows the importance of the struc-

ture to the distance predictions. While the new tree structure improves the distance pre-

dictions for smaller training sets, other tree structures might be able to further improve

the predictions. The tree structure may depend on the training data, so to test this 1,000

new training sets containing data from 44 transition states were created by randomly se-

lecting training data from 1071TS. Each of the 1,000 training sets were used to train both

the original and new molecular group trees, and reaction center distances were predicted

51

for comparison with the 907 known transition states previously found. In over 85% of the

1000 cases, the modified tree had a lower RMS error than the original tree. The probability

distribution of the RMS errors (Figure 4.2) show that the predictions are expected to be

more accurate if made using the modified tree instead of the original tree structure, given

the small size of the training set. Even though cases where the original structure outper-

formed the new tree were in the minority, these cases indicate that tree structures cannot be

selected without considering the training data that will be used to train the group values in

the tree.

Table 4.1: Training set information. As the training set was expanded, the RMS er-ror from the validated transition state distances decreases. The new treestructure performed better when training data was sparse.

Training Transition Geometries RMS Error (A)set States in found Original New

name training set tree tree44TS 44 not run 0.181 0.124230TS 230 658 0.102 0.088827TS 827 734 0.040 0.0421071TS 1071 not run 0.036 0.041

The RMS error attained using the 44TS training set was 0.181 A with the original tree

and 0.124 A with the modified tree (Table 4.1). Comparing with the probability distri-

butions in Figure 4.2, which peak around 0.09 A, shows that the probability of randomly

selecting from 1071TS the 44 transition states used in 44TS is very low, i.e. they are

strongly correlated and non-random. This lack of variety in the 44TS set is what leads

to the large RMS errors: some specific groups were well trained, but the overall tree was

poorly trained. This shows that the value of each transition state in a training set decreases

when a similar transition state already exists in that training set, i.e. it is important to have

a variety of structures in the training data, distributed evenly across the tree.

52

0.0

0.2

0.4

0.6

0.04 0.06 0.08 0.10 0.12 0.14

Prob

abili

ty

RMS Error (Å)

P (Original)P (New)

Figure 4.2: Probability distribution for the root-mean-squared error of the reactioncenter distances when training the groups with 44 transition state dis-tances, for the Original and New tree structures.

53

4.3.2 Manipulating distance limits and force constants can improve UFF optimiza-

tion

The molecular group contributions have been shown to make good predictions of the

reaction center distances of transition states given the groups are appropriately trained.

The subsequent steps converting the predicted distances into 3-dimensional structures can

modify the well predicted distances. The force constants applied during the UFF optimiza-

tion and the distance limit ranges were modified to minimize the change in the predicted

distances when producing the 3-dimensional estimate.

Figure 4.3: Decreasing the distance and increasing the force constants for the reac-tion center each minimized error in the dXH distance introduced duringthe construction of the 3-dimensional transition state estimate. The errorreduction is additive as seen when combining the modifications.

Reducing the distance limit range from 0.1A to 0.05A reduced the difference from

the predicted distances in the 3-D structure (Figure 4.3). Further reduction in the distance

limits are expected to help maintain the reaction center distance predictions when creating

the 3-dimensional geometry. Further testing is required as it is possible that a smaller range

54

could prevent successful 3-dimensional geometry construction.

The force constants between reaction center atoms were set to 12,000 kcal/(mol A),

representing approximately an order of magnitude increase. This also reduced the error

introduced in the reaction center when creating the 3-dimensional structure. Applying

the increased force constants with the reduction in the distance limit range led to further

restriction of the reaction center distances.

The strategies discussed show ways to modify the algorithm in order to ensure the

predicted reaction center distances are maintained when constructing the transition state

estimate. This is ideal when the molecular groups used are well trained, but there could be

cases where a relevant group value is unknown or poorly determined. It could be advan-

tageous to allow the reaction center distances to be partially modified when there is low

confidence in the accuracy of the molecular group values used to make the predictions.

4.3.3 Replacing the UFF optimization with more robust calculations may improve

transition state prediction

The transition state estimate is created by positioning atoms in 3-dimensional space in

a manner that satisfies a distance bounds matrix, then refined using a UFF optimization.

An alternative approach would replace the UFF optimization with a series of partial den-

sity functional theory optimizations. The partial optimizations were tested on 50 reactions

and the reaction center distances were compared to the validated transition state distance.

Figures 4.4, 4.5, and 4.6 show the sequence of partial optimizations led to an overall im-

provement in the reaction center distances from the molecular group predictions. There was

an increase in error when converting the molecular group prediction into a 3-dimensional

geometry, and this has been discussed in Section 4.3.2.

The average improvement in the reaction center distances due to the sequence of partial

optimizations is promising, but the standard deviation of the dHY, and dXY distances raises

questions about the consistency of the method. Despite this, the partial optimizations are

55

Figure 4.4: Mean and standard deviation of the absolute error in dXH distances fromthe final optimized transition state at each stage of the transition stateprediction process.

Figure 4.5: Mean and standard deviation of the absolute error in dHY distances fromthe final optimized transition state at each stage of the transition stateprediction process.

56

Figure 4.6: Mean and standard deviation of the absolute error in dXY distances fromthe final optimized transition state at each stage of the transition stateprediction process.

still expected to improve the automated transition state geometry searches, as the remaining

geometry is optimized at the same level of theory used for the transition state search. This

means the transition state geometry estimate provided to the surface walking algorithm is

closer to the true transition state if the partial optimization steps are used instead of the

UFF optimization. The UFF optimization should be used when computational resources

are restricted.

4.4 Conclusion

The group contribution method performs best with well trained groups, but evidence

suggests it can perform reasonably with sparse data if the group tree design is thoughtfully

considered. Aside from tree design, predictions can be improved by adding more training

data, and the value of the new data increases the more unique it is in relation to the existing

training data. Modifications to the reaction center distance limits and force constants can

57

improve the prediction of the transition state structure. The UFF optimization can also be

replaced with partial optimization steps using density functional theory to improve transi-

tion state structure prediction. These approaches provide alternatives to future users of the

automated transition state search method, but further study is required to best apply these

methods.

4.5 Recommendations

4.5.1 Efficient calculation of the molecular group contributions

The molecular group contribution approach classifies transition states as similar based

on the reaction molecular groups. The group contribution is calculated by linear regression

on the reaction center distances of transition states that were classified together. This is a

form of machine-learning and these methods have been hard-coded in the RMG framework,

and requires a developer to update the software when a change is desired. These changes

can be as simple as adding a new molecular group or modifying the structure molecular

group tree, which has been shown in this chapter to affect prediction accuracy. The current

method of optimizing the molecular group prediction method is inefficient and does not

scale well, but can be improved by using the scikit-learn package.

The scikit-learn package was developed to allow simple integration of state-of-the-art

machine-learning algorithms in Python [126]. The package contains the necessary classifi-

cation and regression tools to determine the molecular group contributions as done in this

work, and can also use alternative techniques to improve the group value predictions. The

package includes methods to test and score the models applied to ensure the best combina-

tion of parameters are used. The scikit-learn package contains methods to automatically

determine the best tree structure for the given data, and do not require a developer to modify

the tree structure whenever a new type of molecule is added, since it will add the necessary

group if a new feature is added to the training data. The scikit-learn package has also been

constructed in the most efficient manner, and can be implemented within a few lines of

58

code replacing the few hundred lines hard-coded into the RMG framework.

4.5.2 UFF optimization with constrained optimization

This chapter showed two methods to improve the transition state predictions once cre-

ated using distance geometry. The first applied UFF optimization using higher spring con-

stants for the reaction center distances, and the second bypassed the UFF optimization and

using a series of constrained optimizations to create a good transition state estimate. Their

respective advantages and disadvantages have been discussed previously in this chapter.

Various parameters were used to improve the UFF optimization, and these should be

further explored to ensure the best combination is used. The constrained optimizations can

be applied in addition to the UFF optimization, with the potential of creating a good transi-

tion state estimate at a reduced computational cost. The UFF optimization would provide a

better transition state estimate to the constrained optimizations at a low computational cost,

and the constrained optimizations would require less steps when provided a better starting

point.

5. Method extension to new reaction families and automated kinetic

parameter calculation

5.1 Background

Detailed chemical kinetic modeling of complex systems has been aided by software

for automated reaction mechanism generation [1]. One example of such software, Re-

action Mechanism Generator (RMG) [6], uses a rate-based approach to construct kinetic

models [7]. RMG has been applied to systems such as the pyrolysis and combustion of

isobutanol [127], the fast pyrolysis of bio-oil [128], and the auto-oxidation of a biofuel

surrogate [129]. Mechanism generators require thermodynamic and kinetic parameters to

complete the model construction; these parameters are preferentially sourced from exper-

imental measurements or accurate theoretical calculations, but more commonly estimates

are used as most of the required parameters are unknown [20].

Parameter estimation methods provide thermodynamic and kinetic values in a computa-

tionally efficient manner [28]. Estimation methods are typically based on Benson’s group

additivity method for thermochemistry [21], in which group values are first determined

from molecules with known thermodynamics, then used to estimate the thermodynamics

of other molecules. Benson’s group contributions have been used to make adequate ther-

mochemistry predictions for a variety of systems, including hydrocarbons [22, 112] and

silicon hydrides [23, 24]. Despite these successes, group contribution methods have been

difficult to extend to some cases, such as predicting thermodynamics for polycyclic species,

where the ring strain causes the molecule to be poorly described by the sum of its parts.

The RMG software addresses this deficiency in the group additive approach by perform-

ing semi-empirical or quantum mechanical calculations of thermodynamic parameters for

polycyclic species [8].

59

60

For estimating reaction kinetics, the Evans-Polanyi relationship is a simple approach in

which the change in enthalpy is used to predict the kinetics of the specific reaction [27]. It

is not always appropriate to apply the Evans-Polanyi relationship, such as in the hydrogen

abstraction by methyl radicals from polynuclear aromatics [29]. An alternative approach

extends group contribution methods to predict kinetic parameters [113–116, 130–132].

Group estimation methods can be automated efficiently, making them useful for mecha-

nism generators when specific reaction rates are unavailable [28]. Group-based predictions

can be further improved using reaction rate rules for increasingly specific reacting groups

[32, 35, 133, 134], but appropriate rate rules are rarely available when studying new sys-

tems. In these situations more general (less specific) rules are used, but the accuracy of the

estimates suffers.

Continuing advances in computing power have made it feasible to try to calculate un-

known kinetic parameters via transition state theory (TST) instead of relying on estimates,

motivating the automation of TST calculations. Reactant and product structures can already

be found using the automated software integrated in RMG to calculate species thermo-

chemistry [8]. The artificial force induced reaction (AFIR) method [75, 135], KinBot [80],

and other methods [76, 77, 79, 81, 136] use computational chemistry software to automati-

cally locate the necessary transition state geometries. Kinetic programs such as CanTherm

[84], VariFlex [83], MultiWell [85], and POLYRATE [137] have been developed to cal-

culate reaction kinetics if provided the quantum chemistry outputs. Integrating geometry

search software with kinetic calculators is a promising route to enable high-throughput

kinetics calculations.

The present chapter describes automated algorithms to locate reactants, products, and

transition states based on distance geometry [8, 136] and their integration with the Can-

Therm [84] code to calculate reaction rate expressions. The automated transition state

geometry search method has been described in the previous chapters of this thesis. The

integrated algorithms are referred to as the Automated Transition State Theory (AutoTST)

61

calculator. Kinetics calculated with the integrated algorithm were compared to two sets

of rate rule predictions. The first rate rules were used in the construction of a butanol

combustion model from the Lawrence Livermore National Laboratory (LLNL) [138], and

the second set of rate rule predictions were taken from RMG. Rate rule predictions and

AutoTST calculated reaction rates were compared to benchmark theoretical calculations,

which showed the integrated algorithm improved kinetics when no rate rule exists that is

similar to the reaction in question.

5.2 Methods

5.2.1 Computational chemistry

Geometry optimization and path analysis calculations used the M06-2X DFT functional

[107, 123] with the MG3S basis set [124] (equivalent to 6-311+G(2df,2p) for systems con-

taining C, H, and O) [110, 125] in the Gaussian 09 quantum chemistry package [105]. For

benchmark calculations, electronic energies were computed using the CCSD(T)-F12/RI

method with the cc-VTZ-F12 [139] and cc-VTZ-F12-CABS [140] basis sets in ORCA

[141].

5.2.2 Automated geometry searches

Reactant and product structures were located using the automated algorithm developed

in RMG and described by Magoon and Green [8]. Transition state structures were located

using a group contribution method that predicts transition state reaction center distances

using training data of known transition states, and has been described in the previous chap-

ters of this thesis [136]. The transition state training data used in this study were optimized

and validated at M06-2X with a MG3S basis set, so that predictions were made for the

same electronic structure method used in this study. M06-2X/MG3S provides sufficient

kinetic parameters at a reasonable computational cost, and is widely available in computa-

tional chemistry packages [141–143]. The method, previously demonstrated for hydrogen

62

abstraction reactions, was extended to be applied to intramolecular hydrogen migration and

β-scission reaction families. The modifications to the transition state geometry prediction

algorithm are discussed in the following section.

Modifications to the group contribution transition state search

Figure 5.1: Automated transition state search algorithm as described in ref. 136. Thesteps with bold borders, adapted from the AARON software [81], are de-viations from the original algorithm.

The group contribution method for predicting transition state geometries described in

ref. 136 has been modified to improve its performance (Figure 5.1). The distance geometry

algorithm requires upper and lower limits for the distances between every atom. The differ-

ence between the upper and lower limits for the reaction center distances were previously

set to 0.05A, but this was decreased to 0.025A due to increased confidence in the reac-

tion center predictions. 3-dimensional conformers were constructed to satisfy the distance

limits for every atom pair.

The optimization protocol was also modified, with the transition state geometry pre-

63

diction algorithm no longer using a universal force field optimization, instead adopting a

protocol similar to that used in the AARON code [81]. The geometry estimate undergoes a

constrained optimization to an energy minimum with the reaction center distances frozen,

followed by a transition state (saddle point) search with all distances frozen except the re-

action center. The resulting geometry is then used for a Berny transition state optimization.

5.2.3 Kinetic calculations

The CanTherm software package was used to determine kinetic parameters using clas-

sical transition state theory [84]. Symmetry numbers for the rate calculations were deter-

mined via point group using the SYMMETRY software [144]. SYMMETRY takes as input

the optimized 3-dimensional geometry and a tolerance to allow for small deviations, and

calculates the point group. The point group is used to determine the symmetry number

[145], and a chirality contribution of +R ln 2 is added for point groups that lack a superpos-

able mirror image. Product geometries and energies were also found for these calculations

so the Eckart model could be applied to determine tunneling corrections [146]. Figure 5.2

provides an overview of the automated kinetic calculation method.

Figure 5.2: The automated kinetic calculations involve an automated transition statesearch (Figure 5.1), automated search for reactant and product geometries[8], and automatically calculating kinetics using CanTherm [84].

5.2.4 Comparison of Automated TST calculations and Rate Rules

Rate rule predictions of hydrogen abstraction, intramolecular hydrogen migration, and

β-scission reactions from a butanol combustion model [138] were compared to the Au-

toTST calculations and the automated rate rule implementation in RMG. Kinetics were

compared at 1000K, since the rate rules were determined for a combustion model in that

64

temperature range. High pressure limit reaction rates were used for pressure-dependent

rate predictions in the butanol combustion model.

5.2.5 Comparison to benchmark calculations

In some cases there were large differences between rate rule predictions and AutoTST

calculations. For two of these cases from each reaction family, more accurate theoretical

calculations were applied by accounting for anharmonic rotations and improving barrier

heights using coupled-cluster theory. Other inaccuracies were addressed for cases in which

the automated algorithm did not find the lowest energy conformer or incorrectly deter-

mined the symmetry number. These benchmark calculations were compared to the rate

rule predictions and the AutoTST rates.

The geometries for the benchmark calculations were determined using the same DFT

functional and basis set as the automatically calculated rates, but the benchmark calcula-

tions used an ultrafine grid. For the benchmark calculations, the 1-D hindered rotor ap-

proximation was applied [48]. AutoTST did not always find the lowest energy conformer;

when the hindered rotor scans revealed a lower-energy conformer, this was re-optimized

and adopted for the benchmark calculations. Barrier heights were also improved using

single point coupled-cluster calculations (see the ‘Computational chemistry’ section for

details). Symmetry numbers were manually checked and corrected when the AutoTST

approach was incorrect.

These improvements allowed comparison between AutoTST and the benchmark calcu-

lations to identify the sources of error in the AutoTST calculations.

5.3 Results

The butanol combustion model contained 855 hydrogen abstraction, 78 intramolecular

hydrogen migration, and 131 β-scission reactions. For each reaction family, AutoTST

calculated kinetics for approximately 70% of the reactions (Table 5.1).

65

Table 5.1: Number of reactions for each family contained in the combustion model,and success of the AutoTST algorithm.

Reaction Family Number of Kinetics successfully PercentageReactions calculated calculated

Hydrogen abstraction 855 598 69.9Intramolecular hydrogen migration 78 52 66.7β-scission 184 131 71.2

Total 1117 781 69.9

5.3.1 Comparison of automated TST calculations and rate rules

Kinetic parameters calculated using AutoTST were compared to parameters predicted

using rate rules, applied both manually and automatically. The AutoTST kinetics corre-

sponded with with the rate rule predictions, with most rate rules being within an order of

magnitude (101) of each other (Figure 5.3). Despite the overall trend, a number of reactions

had significant discrepancy between AutoTST rates and the rate rule predictions. Six of the

reactions with significant discrepancies, two from each reaction family, were selected for

benchmark calculations to determine the accuracy of the three prediction sources.

5.3.2 Comparing predictions to benchmark calculations

Table 5.2: Reactions compared to benchmark calculations.

Label Family Reaction

R1 H abstraction C2H5OO· + C2H6 −−⇀↽−− C2H5OOH + .CH2CH3R2 H abstraction .OOH + CH3C(−−O)C2H5 −−⇀↽−− H2O2 +

.CH2C(−−O)C2H5R3 Intramolecular H migration O−−CHCH2OO· −−⇀↽−− O−−C·CH2OOHR4 Intramolecular H migration CH3C(CH3)(C−−O)OO· −−⇀↽−− CH3C(CH3)(.C−−O)OOHR5 β-scission CO2 +

.CH3 −−⇀↽−− CH3C(−−O)O·

R6 β-scission CH2C(CH3)CH−−O + HO2· −−⇀↽−− .CH2C(CH3)(CH−−O)OOH

Six reactions were selected for comparison to benchmark calculations, with two se-

lected from each reaction family (Table 5.2). The reactions were selected if there was a

102 discrepancy between the automatically calculated rate and both rate rule predictions at

1000K. For reaction 5, the rate from the LLNL model was provided in the reverse direc-

66

₁₀5

₁₀6

₁₀7

₁₀8

₁₀9

₁₀10

₁₀11

₁₀12

₁₀13

₁₀14

₁₀5 ₁₀6 ₁₀7 ₁₀8 ₁₀9 ₁₀10 ₁₀11 ₁₀12 ₁₀13 ₁₀14

k(T=

1000

K) [

cm³/m

ol/s

] by

LLNL

or R

MG

k(T=1000 K) [cm³/mol/s] by AutoTST

Hydrogen Abstraction

LLNLRMG-PyParity1 Order of Magnitude

Figure 5.3: Rate rule estimates (y-axis) plotted against automated algorithm TST cal-culations (x-axis) at 1000 K.

tion, so the rate shown was calculated using the provided rate and thermodynamics from

the model. The rate rule predictions better replicated the benchmark calculations than Au-

toTST for reaction 1 (Figure 5.4a), but the AutoTST calculations showed better agreement

than the rate rules for reactions 2 through 6 (Figures 5.4b, 5.5, and 5.6). This is addressed

in the discussion section.

5.3.3 Sources of error in the automated calculations

Discrepancies between the AutoTST calculations and the benchmark calculations pre-

sented an opportunity to identify sources of error in the AutoTST method. Geometries

were determined using the same DFT electronic structure method, but in some cases the

automated geometry search methods had not found the lowest energy conformer, and the

automated method to determine symmetry was not always correct. Other differences were

the use of couple-cluster calculations to improve barrier height calculation, and addressing

67

-6

-3

0

3

6

9

12

0 1 2 3

log₁₀(k

/ (c

m³/m

ol/s

))

1000K / T

BenchmarkAlgorithmLLNLRMG-Py

(a)

-6

-3

0

3

6

9

12

0 1 2 3

log₁₀(k

/ (c

m³/m

ol/s

))

1000K / T

(b)

Figure 5.4: Comparison of kinetic estimates for hydrogen abstraction reactions.

anharmonic rotations using the 1-D hindered rotor treatment, all done for the benchmark

calculations. Each correction was individually removed from the benchmark calculations

and replaced with the equivalent used for the automated calculations.

Table 5.3 displays the difference in activation energy due to each source of error and

the benchmark calculation, and Table 5.4 shows the changes to the A factor due to the

same effects. Figure 5.7 shows the magnitude of this difference for the rate coefficient at

1000 K. The major source of error for AutoTST calculations was the lack of treatment of

anharmonic rotors, but this was not consistent for all reactions since some contained few

rotors (e.g. R5). Symmetry was also a major source of error when the automated method

incorrectly determined symmetry numbers. This was not consistent for all tested reactions

as the automated method correctly determined symmetry for some cases. As expected, the

activation energy is unaffected by correcting the symmetry number (Table 5.3). AutoTST

was not always successful in finding the lowest energy conformer for all structures, which

contributed to errors of varying degrees. The intramolecular hydrogen migration reactions

were most affected by these, where a single wrong conformer would contribute signifi-

cantly to an error in the barrier height. Correcting the DFT energy had little effect on the

68

-6

-3

0

3

6

9

12

0 1 2 3

log₁₀(k

/s–1

)

1000K / T

BenchmarkAlgorithmLLNLRMG-Py

(a)

-6

-3

0

3

6

9

12

0 1 2 3

log₁₀(k

/s–1

)

1000K / T

(b)

Figure 5.5: Comparison of kinetic estimates for intramolecular hydrogen migrationreactions R3 (a) and R4 (b).

rate calculations in the combustion temperature range, but at lower temperatures the DFT

energy led to rates that were approximately 101 off of the benchmark calculations.

Table 5.3: Difference in the activation energy (kJ/mol) compared to the benchmarkcalculations. Kinetics fitted to Arrhenius form between 600K and 2000K.

Reaction Benchmark Inaccurate Hindered Incorrect Incorrect OverallEa Energy Rotors Symmetry Conformer Discrepancy

R1 111.98 –5.46 –0.34 0.00 –0.91 –6.01R2 119.38 –9.92 –20.70 0.00 +4.57 –24.53R3 88.54 +6.16 +0.28 0.00 –11.05 –4.06R4 85.19 +7.03 +1.08 0.00 –12.52 –3.35R5 97.24 –7.73 0.00 0.00 –2.52 –7.68R6 84.89 –6.74 –8.35 0.00 +0.01 +1.91

5.4 Discussion

AutoTST found transition states and calculated kinetics for 70% of the 1117 reactions

tested. The percentage successfully calculated was consistent across all reaction families,

so the AutoTST success rate is independent of the reaction type.

69

-6

-3

0

3

6

9

12

0 1 2 3

log₁₀(k

/ (c

m³/m

ol/s

))

1000K / T

BenchmarkAlgorithmLLNLRMG-Py

(a)

-6

-3

0

3

6

9

12

0 1 2 3

log₁₀(k

/ (c

m³/m

ol/s

))

1000K / T

(b)

Figure 5.6: Comparison of kinetic estimates for β-scission reactions R5 (a) and R6 (b).

Table 5.4: Difference in the log10 of the A factor compared to the benchmark calcula-tions. Kinetics fitted to Arrhenius form between 600K and 2000K. R3 andR4 are in [s−1] and the rest are in [cm3/(mols)]

Reaction Benchmark Inaccurate Hindered Incorrect Incorrect Overalllog10A Energy Rotors Symmetry Conformer Discrepancy

R1 13.96 0.020 –0.772 –1.079 0.000 –2.337R2 13.27 0.010 –2.659 0.000 -0.016 –1.854R3 12.00 –0.001 0.416 0.000 0.004 0.620R4 11.64 –0.002 1.253 0.000 0.004 1.369R5 12.83 0.000 0.000 –1.079 0.000 –1.169R6 11.53 0.000 –0.483 0.000 0.000 0.141

Reaction rate rules, when used appropriately, can provide good rate predictions. The

strong correlation between the rate rules and AutoTST calculations is evidence for contin-

ued use of rate rules. Rate rule use is computationally efficient, so should be applied for

reactions where the structure of the reacting molecular groups similar to that of the rate

rule. When such rate rules are unavailable, AutoTST now provides an alternate method to

determine kinetics.

The comparison of the 6 reactions with large discrepancies between rate rule predictions

and AutoTST show the automated method performs well for all tested reaction families.

70

-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

R1

R2

R3

R4

R5

R6

Δlog(k(T=1000K))

DFT EnergyNo Hindered Rotor CorrectionAutomated SymmetryAutomated ConformerFully Automated Algorithmdummy

Figure 5.7: Magnitude of the sources of error in each automated algorithm comparedto its respective benchmark calculation. The summation of all errors arerepresented by the algorithm calculation.

71

This is particularly true when considering the performance of the kinetics across a wide

temperature range, where the kinetics calculated with AutoTST trend well with the high

accuracy calculations, but the rate rules perform best in the temperature range for which

they were developed.

For one case (R1), both rate rule estimates outperformed the AutoTST calculation. The

rate rules used in the model developed for RO2. +C2H6 −−⇀↽−− ROOH+C2H5 [147], and the

RMG rate rule was developed for HO2. + C2H6 −−⇀↽−− H2O2 + C2H5 [148]. The accuracy of

the rate predictions should be expected since the rate rule was developed for reactions quite

similar to R1, and in such cases AutoTST should not be used since the rate rules could

provide a good rate prediction at a far lower computational cost. AutoTST outperformed

the rate rule predictions for all the other reactions.

The RMG rate prediction for R3 was made from a generalized rate rule, so the kinetic

data used to make the prediction was very unlike the reaction leading to the large discrep-

ancy in the reaction rate. The value used in the LLNL model was not an estimate but a

theoretically calculated value for the specific rate [149]. Comparison to the benchmark

calculations shows it is sufficiently accurate to describe this reaction. In other such cases,

when specific reaction rates are available, the available data should be relied on, bypassing

AutoTST.

Not treating anharmonic rotations, determining symmetry incorrectly, and not finding

the lowest energy conformer were the major sources of error for AutoTST. Improving bar-

rier heights with coupled-cluster calculations showed that using DFT energies also con-

tributed to errors, but was less significant. While all need to be addressed, automating

hindered rotors and providing a more robust symmetry determining algorithm should be

targeted. Automating hindered rotor calculations will also help identify the lowest energy

conformer.

72

5.5 Conclusion

AutoTST has calculated kinetics for approximately 70% of all tested reactions. The

method is extensible, and has now been applied to hydrogen abstraction, intramolecular

hydrogen migration and β-scission reactions. The successful extension of AutoTST moti-

vates further work to include other reaction families with a reaction barrier.

Good kinetic estimates can be calculated using the automated algorithm, and the proto-

col should be used for mechanism generation. It has also been shown to outperform other

kinetic estimation methods when specific rate rules are unavailable for a reaction. The cur-

rent estimation methods should not be abandoned, as they can still provide good kinetic

predictions if used appropriately (R1) and in a computationally efficient manner. AutoTST

should be used to target reactions where the kinetics are estimated with more generalized

rate rules.

The current major sources of error in the automated kinetics are improperly determin-

ing symmetry, and not accounting for internal rotor contributions. Based on these errors,

the automated algorithm can be further improved to provide even better parameters. Im-

proved automated methods for determining symmetry numbers would reduce the uncer-

tainty in AutoTST calculations. Internal rotor contributions could be included in the calcu-

lations by automating hindered rotor calculations. The hindered rotor calculations would

also help identify an existing lower energy conformer, correcting cases where the lowest

energy conformer was not automatically found. The additional computational cost of au-

tomating coupled-cluster calculations to improve barrier heights would have to be balanced

against available computational resources, as using the DFT energy was not a major source

of discrepancy. Despite these sources of error, the method can provide improved kinetic

parameters for many reactions in microkinetic models, reducing the uncertainty of these

models.

73

5.6 Recommendations

5.6.1 Improve symmetry number calculation

Symmetry numbers for the rate calculations were determined using the SYMMETRY

software [144], developed in 2003. The software takes optimized geometries and tries to

determine their respective point groups. A tolerance is also used to allow small deviations

from the exact symmetry. The symmetry number can then be determined from the point

group. The calculations in this chapter show that the automated symmetry calculations are

imperfect, and can have a large effect on the calculated reaction kinetics when they are

incorrect.

It is often difficult to correctly determine symmetry numbers manually, and it has been

shown to be the source of discrepancies between kinetics calculated by different experi-

enced research groups [150]. Efforts have been made to standardize the application of

symmetry numbers in transition state theory [151], and recently a new automated approach

has been developed to determine symmetry numbers from an augmented chemical graph

[152].

These methods could potentially resolve issues with symmetry numbers, or at least

reduce the error associated with symmetry number calculation in the automated method

described in this chapter. This should provide an overall improvement in the performance

of the automated transition state theory method.

5.6.2 Automate hindered rotor calculations

Hindered rotor calculations help account for anharmonic effects that are neglected when

applying classical transition state theory. Comparison of the benchmark calculations with

the automated kinetics in this chapter showed the importance of accounting for hindered ro-

tors when dealing with larger molecules. These calculations, like transition state searches,

are computationally and labor intensive. Automating these calculations would be beneficial

74

as they would remove the need to manually set up these calculations, allowing the compu-

tationally intensive calculations to be moved to distributed computing resources for more

efficient calculations.

The 1-D hindered rotor approximation is simplest method to account for hindered rotors

[48]. This method was used for the benchmark calculations described in this chapter. An

automated approach would need to reliably determine the rotors, but this can be achieved

by using the chemical graph used to construct the 3-dimensional transition state estimate.

The computational cost added to the kinetic calculations would vary depending on the size

of the reacting molecules.

Automating 1-D hindered rotor calculations will have an added benefit of identifying

if the conformer used is not the lowest energy conformer. The calculation explores all

rotations in a conformer and will identify if another conformation has a lower energy. The

lower energy conformer can be extracted and used in the subsequent kinetic calculation.

Accounting for hindered rotors will also benefit automated thermodynamic calcula-

tions, further improving mechanism generation and allowing its expansion to new chemical

systems.

6. Summary

This thesis describes an automated method to calculate chemical kinetic parameters

using ab initio quantum chemistry methods. The method is referred to as AutoTST, and

requires a 2-dimensional representation of each reaction, making it ideal high-throughput

kinetics.

AutoTST uses distance geometry to to convert the 2-dimensional molecular represen-

tations into 3-dimensional geometries. The distance geometry approach cannot provide a

full description of the transition state geometry, so a machine learning approach is used to

predict the unknown distances of the transition state. The reactant, product, and transition

state geometries are refined using ab initio quantum chemistry programs, so that molecular

properties can be calculated. The kinetic parameters of a reaction are calculated using the

molecular properties via transition state theory.

The transition state geometry prediction method has been shown to have a 70% success

rate, with potential room for improvement. It has been applied to hydrogen abstraction,

intra-hydrogen migration, and β-scission reactions, which shows that the transition state

geometry search is also extensible to any reaction type with an energy barrier. This rep-

resents a significant increase in efficiency, where thousands of reaction kinetic parameters

are required to construct complex chemical reaction networks.

The transition state search method was integrated with two other automated methods

creating the AutoTST method. The first automatically determines geometries for stable

species which are the reactants and products of a reactions. The second applies transition

state theory when provided the optimized reactant, product, and transition state structures

from computational chemistry programs.

Kinetics calculated with AutoTST were compared to rate rule approximations, the best

available existing methods to estimate unknown reaction kinetic parameters. Rate rules

75

76

performed well when used appropriately, but were outperformed by AutoTST when they

were applied beyond their intended scope. Data scarcity means rate rules are often applied

outside their intended use, but now AutoTST offers an alternative approach to determine

chemical kinetic parameters that are unknown.

While AutoTST can be used in its current form to provide kinetics with reasonable ac-

curacy, comparison of its kinetics to high fidelity theoretical calculations showed AutoTST

kinetics contained sources of error that can be addressed. Symmetry numbers for each re-

acting species and the transition state are used to calculation reaction kinetics via transition

state theory, and these numbers are determined automatically in AutoTST. The algorithm

used to determine symmetry numbers is imperfect, and improved methods to determine

symmetry numbers are an active area of research.

Classical transition state theory calculations should be conducted using the lowest en-

ergy conformer. The AutoTST algorithm sometimes used a higher energy conformer,

adding error to the kinetic parameters. The method also did not account for anharmonicity

in the potential energy surface. These sources of error can be addressed by automating

hindered rotor calculations. The 1-dimensional hindered rotor approximation is sufficient

to address anharmonicity and to identify cases where a lower energy conformer exists.

The 1-dimensional hindered rotor approximation method can be automated by using the

geometries found using AutoTST and specifying rotation axes.

This thesis describes the AutoTST method, an automated approach to provide kinetic

calculations for use in mechanism generation. AutoTST can currently provide useful ki-

netics for mechanism generation, allowing rate rules to be applied only when they are

appropriate. This would represent a reduction in the uncertainty of detailed kinetic model.

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Appendices

90

A. Double-ended method

Table A.1: Transition states determined at M06-2X/6-31+G(d,p) showed trends in thedistances (in Angstroms) with changes to molecular groups. The distancesdXH, dHY, and dXY are defined in Figure 2.3.

Reaction dXH dHY dXYCH3CH3 + CH3O↔ CH3CH2 + CH3OH 1.241 1.274 2.509CH3CH3 + CH3CHCH3↔ CH3CH2 + CH3CH2CH3 1.373 1.319 2.689CH3CH3 + CH2OH↔ CH3CH2 + CH3OH 1.390 1.316 2.689CH3CH3 + CH=O↔ CH3CH2 + CH2=O 1.446 1.293 2.720CH3CH2CH3 + CH3O↔ CH3CH2CH2 + CH3OH 1.237 1.275 2.510CH3CH2CH3 + CH3CHCH3↔ CH3CH2CH2 + CH3CH2CH3 1.376 1.319 2.689CH3CH2CH3 + CH2OH↔ CH3CH2CH2 + CH3OH 1.395 1.315 2.701CH3CH(CH3)CH3 + CH3O↔ CH3CH(CH3)CH2 + CH3OH 1.241 1.275 2.509CH3CH(CH3)CH3 + CH3CHCH3 ↔ CH3CH(CH3)CH2 +CH3CH2CH3

1.378 1.317 2.690

CH3CH(CH3)CH3 + CH2OH↔ CH3CH(CH3)CH2 + CH3OH 1.395 1.316 2.707CH3CH2CH3 + CH3O↔ CH3CHCH3 + CH3OH 1.214 1.322 2.531CH3CH2CH3 + CH2OH↔ CH3CHCH3 + CH3OH 1.365 1.340 2.696CH3CH2CH3 + CH=O↔ CH3CHCH3 + CH2=O 1.419 1.315 2.703CH3CH(CH3)CH3 + CH3O↔ CH3C(CH3)CH3 + CH3OH 1.194 1.368 2.559CH3CH(CH3)CH3 + CH2OH↔ CH3C(CH3)CH3 + CH3OH 1.345 1.360 2.695CH3CH(CH3)CH3 + CH=O↔ CH3C(CH3)CH3 + CH2=O 1.402 1.330 2.714

Table A.2: 334 hydrogen abstraction reactions used to test automated transition statealgorithms.

Reactions Success/Failure[CH3] + [H][H]↔ C + [H] SuccessO + [H]↔ [H][H] + [OH] SuccessC#C + [H]↔ [C]#C + [H][H] QST3 neededC[CH2] + [H][H]↔ CC + [H] SuccessC[O] + [H][H]↔ CO + [H] SuccessO[CH2] + [H][H]↔ CO + [H] SuccessO=[CH] + [H][H]↔ C=O + [H] SuccessC=[CH] + [H][H]↔ C=C + [H] Transition state failedO[O] + [H][H]↔ OO + [H] IRC failedO[O] + [H]↔ [H][H] + [O][O] Transition state failedO + [CH3]↔ C + [OH] SuccessCCO + [H]↔ CC[O] + [H][H] SuccessContinued on next page

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Table A.2 – continued from previous pageReactions Success/FailureCCO + [H]↔ C[CH]O + [H][H] Transition state failedCCO + [H]↔ [CH2]CO + [H][H] SuccessC + [CH2]C↔ CC + [CH3] SuccessC + C[O]↔ CO + [CH3] SuccessC + [CH2]O↔ CO + [CH3] SuccessC + [CH]=O↔ C=O + [CH3] SuccessC + [CH]=C↔ C=C + [CH3] QST3 neededC + [O]O↔ OO + [CH3] SuccessC + [O][O]↔ [CH3] + [O]O Transition state failedC#C + [CH3]↔ C + [C]#C Transition state failedCCC + [H]↔ [CH2]CC + [H][H] SuccessC1CC1 + [H]↔ [CH]1CC1 + [H][H] SuccessC1CO1 + [H]↔ [CH]1CO1 + [H][H] IRC failedC=CC + [H]↔ [CH2]C=C + [H][H] SuccessCOC + [H]↔ [CH2]OC + [H][H] SuccessC[CH]C + [H][H]↔ CCC + [H] SuccessCO[O] + [H][H]↔ COO + [H] SuccessC[C]=O + [H][H]↔ CC=O + [H] SuccessO + [C]#C↔ C#C + [OH] SuccessC[O] + O↔ CO + [OH] SuccessO + [CH2]O↔ CO + [OH] IRC failedO + [CH]=O↔ C=O + [OH] IRC failedO + [CH]=C↔ C=C + [OH] SuccessO + [O]O↔ OO + [OH] IRC failedO + [CH2]C↔ CC + [OH] IRC failedO + [O][O]↔ [OH] + [O]O Transition state failedC=CC + [H]↔ [CH]=CC + [H][H] SuccessC=CC + [H]↔ C=[C]C + [H][H] SuccessC=O + C[O]↔ CO + [CH]=O SuccessC=O + [CH]=C↔ C=C + [CH]=O QST3 neededC=O + [O][O]↔ [CH]=O + [O]O IRC failedCCO + [CH3]↔ C + CC[O] SuccessCCO + [CH3]↔ C + C[CH]O SuccessCCO + [OH]↔ C[CH]O + O IRC failedCO + [CH2]O↔ CO + C[O] SuccessCO + [CH]=O↔ C=O + [CH2]O SuccessCO + [CH]=C↔ C=C + C[O] SuccessCO + [CH]=C↔ C=C + [CH2]O SuccessCO + [O][O]↔ [CH2]O + [O]O IRC failedCC(C)O + [H]↔ C[C](C)O + [H][H] IRC failedCC(C)=O + [H]↔ [CH2]C(C)=O + [H][H] SuccessC + CO[O]↔ COO + [CH3] SuccessContinued on next page

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Table A.2 – continued from previous pageReactions Success/FailureCC + C[O]↔ CO + [CH2]C SuccessCC + [CH2]O↔ CO + [CH2]C SuccessCC + [CH]=O↔ C=O + [CH2]C IRC failedCC + [CH]=C↔ C=C + [CH2]C IRC failedCC + [O][O]↔ [CH2]C + [O]O IRC failedC=C + [O][O]↔ [CH]=C + [O]O IRC failedC#C + [CH2]C↔ CC + [C]#C IRC failedCCC + [CH3]↔ C + [CH2]CC SuccessCCC + [OH]↔ C[CH]C + O IRC failedCCC + [OH]↔ O + [CH2]CC IRC failedCC=O + [CH3]↔ C + C[C]=O Transition state failedCC=O + [OH]↔ C[C]=O + O IRC failedCC=O + [OH]↔ O + [CH2]C=O SuccessC1CC1 + [OH]↔ O + [CH]1CC1 SuccessC1CO1 + [CH3]↔ C + [CH]1CO1 SuccessC1CO1 + [OH]↔ O + [CH]1CO1 SuccessCCCC + [H]↔ [CH2]CCC + [H][H] SuccessC=CC=C + [H]↔ [CH]=CC=C + [H][H] SuccessC=CC + [CH3]↔ C + [CH2]C=C SuccessC=CC + [OH]↔ O + [CH2]C=C IRC failedCOC + [CH3]↔ C + [CH2]OC SuccessCOC + [OH]↔ O + [CH2]OC IRC failedC[C](C)C + [H][H]↔ CC(C)C + [H] SuccessC[CH]CC + [H][H]↔ CCCC + [H] SuccessCC(C)C + [H]↔ [CH2]C(C)C + [H][H] SuccessC=C(C)C + [H]↔ [CH2]C(=C)C + [H][H] SuccessC#C + [O][O]↔ [C]#C + [O]O QST3 neededOO + [CH2]O↔ CO + [O]O SuccessOO + [CH]=O↔ C=O + [O]O SuccessOO + [CH]=C↔ C=C + [O]O SuccessCOO + [OH]↔ CO[O] + O Transition state failedOO + [CH2]C↔ CC + [O]O SuccessOO + [O][O]↔ [O]O + [O]O SuccessCCCO + [H]↔ [CH2]CCO + [H][H] SuccessCOC=O + [H]↔ [CH2]OC=O + [H][H] SuccessCOC=O + [H]↔ CO[C]=O + [H][H] SuccessC=CC + [OH]↔ O + [CH]=CC SuccessC=CC + [OH]↔ C=[C]C + O SuccessC[C]=CC + [H][H]↔ CC=CC + [H] Transition state failedCOO + [OH]↔ O + [CH2]OO SuccessC=O + CO[O]↔ COO + [CH]=O SuccessC=O + C[C]=O↔ CC=O + [CH]=O QST3 neededContinued on next page

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Table A.2 – continued from previous pageReactions Success/FailureCO + CO[O]↔ COO + [CH2]O SuccessCO + C[C]=O↔ CC=O + [CH2]O Transition state failedCC(C)=O + [CH3]↔ C + [CH2]C(C)=O SuccessCC(C)=O + [OH]↔ O + [CH2]C(C)=O SuccessCCCCO + [H]↔ [CH2]CCCO + [H][H] SuccessCC + C[CH]C↔ CCC + [CH2]C SuccessCC + CO[O]↔ COO + [CH2]C Transition state failedCCC + [CH2]C↔ CC + [CH2]CC Transition state failedCCC + C[O]↔ CO + C[CH]C Transition state failedCCC + C[O]↔ CO + [CH2]CC SuccessCCC + [CH2]O↔ CO + C[CH]C SuccessCCC + [CH2]O↔ CO + [CH2]CC SuccessCCC + [CH]=O↔ C=O + C[CH]C Transition state failedCCC + [CH]=O↔ C=O + [CH2]CC SuccessCCC + [CH]=C↔ C=C + C[CH]C SuccessCCC + [CH]=C↔ C=C + [CH2]CC SuccessCCC + [O]O↔ C[CH]C + OO SuccessCCC + [O][O]↔ C[CH]C + [O]O IRC failedCCC + [O][O]↔ [CH2]CC + [O]O IRC failedCC=O + [CH2]C↔ CC + C[C]=O SuccessCC=O + [CH]=C↔ C=C + C[C]=O SuccessCC=O + [O][O]↔ C[C]=O + [O]O IRC failedCC(C)C + [CH3]↔ C + C[C](C)C Transition state failedCC(C)C + [CH3]↔ C + [CH2]C(C)C SuccessCC(C)C + [OH]↔ C[C](C)C + O IRC failedCC(C)C + [OH]↔ O + [CH2]C(C)C IRC failedCC(C)(C)O + [H]↔ [CH2]C(C)(C)O + [H][H] SuccessCCC(C)C + [H]↔ [CH2]CC(C)C + [H][H] SuccessCCC(C)C + [H]↔ C[CH]C(C)C + [H][H] SuccessCCC(C)C + [H]↔ CC[C](C)C + [H][H] SuccessCCCC + [CH3]↔ C + C[CH]CC SuccessCCCC + [CH3]↔ C + [CH2]CCC SuccessCCCC + [OH]↔ C[CH]CC + O IRC failedCCCC + [OH]↔ O + [CH2]CCC IRC failedC=CC=C + [CH3]↔ C + [CH]=CC=C IRC failedCCCCC + [H]↔ C[CH]CCC + [H][H] Transition state failedCCCCC + [H]↔ [CH2]CCCC + [H][H] SuccessCCCCC + [H]↔ CC[CH]CC + [H][H] SuccessC=CC + [CH2]C↔ CC + [CH2]C=C SuccessC=CC + C[O]↔ CO + [CH2]C=C SuccessC=CC + [CH2]O↔ CO + [CH2]C=C SuccessC=CC + [CH]=O↔ C=O + [CH2]C=C SuccessContinued on next page

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Table A.2 – continued from previous pageReactions Success/FailureC=CC + [CH]=C↔ C=C + [CH2]C=C Transition state failedC=C(C)C + [CH3]↔ C + [CH2]C(=C)C SuccessC1CCC1 + [OH]↔ O + [CH]1CCC1 IRC failedC1CCCC1 + [H]↔ [CH]1CCCC1 + [H][H] SuccessCC(C)(C)C + [H]↔ [CH2]C(C)(C)C + [H][H] SuccessC=CC + [O][O]↔ [CH2]C=C + [O]O IRC failedOO + [CH2]C=C↔ C=CC + [O]O SuccessCO[O] + [O]O↔ COO + [O][O] SuccessCO[O] + OO↔ COO + [O]O SuccessOO + [CH2]CC↔ CCC + [O]O SuccessC[C]=O + OO↔ CC=O + [O]O SuccessCCC(C)C + [H]↔ [CH2]C(C)CC + [H][H] SuccessC=CCC + [CH3]↔ C + C=C[CH]C SuccessCOC=O + [CH3]↔ C + CO[C]=O SuccessCOC=O + [OH]↔ O + [CH2]OC=O IRC failedCOC=O + [OH]↔ CO[C]=O + O SuccessCOC=O + [CH3]↔ C + [CH2]OC=O SuccessCC=CC + [CH3]↔ C + [CH2]C=CC SuccessCCOCC + [CH3]↔ C + C[CH]OCC Transition state failedCC(C)=O + [CH]=C↔ C=C + [CH2]C(C)=O Successc1ccccc1 + [H]↔ [H][H] + [c]1ccccc1 SuccessCC + [CH2]CCC↔ CCCC + [CH2]C IRC failedCCC + C[CH]C↔ CCC + [CH2]CC IRC failedCCC + CO[O]↔ COO + C[CH]C SuccessCCC + CO[O]↔ COO + [CH2]CC SuccessCCC + C[C]=O↔ CC=O + C[CH]C SuccessCCC + C[C]=O↔ CC=O + [CH2]CC SuccessCC=O + [CH2]C=C↔ C=CC + C[C]=O SuccessCC(C)C + [CH2]C↔ CC + C[C](C)C Transition state failedCC(C)C + [CH2]C↔ CC + [CH2]C(C)C SuccessCC(C)C + C[O]↔ CO + C[C](C)C Transition state failedCC(C)C + C[O]↔ CO + [CH2]C(C)C SuccessCC(C)C + [CH2]O↔ CO + C[C](C)C Transition state failedCC(C)C + [CH2]O↔ CO + [CH2]C(C)C SuccessCC(C)C + [CH]=O↔ C=O + C[C](C)C Transition state failedCC(C)C + [CH]=O↔ C=O + [CH2]C(C)C Transition state failedCC(C)C + [CH]=C↔ C=C + C[C](C)C Transition state failedCC(C)C + [CH]=C↔ C=C + [CH2]C(C)C QST3 neededCC(C)C + [O]O↔ C[C](C)C + OO SuccessCC(C)C + [O][O]↔ C[C](C)C + [O]O Transition state failedCC(C)C + [O][O]↔ [CH2]C(C)C + [O]O Transition state failedCCC(C)C + [OH]↔ C[CH]C(C)C + O IRC failedContinued on next page

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Table A.2 – continued from previous pageReactions Success/FailureCCC(C)C + [OH]↔ CC[C](C)C + O IRC failedCC(C)C=O + [CH3]↔ C + CC(C)[C]=O SuccessCC(=O)C=O + [OH]↔ CC(=O)[C]=O + O IRC failedCCCC + [O]O↔ C[CH]CC + OO SuccessCCCC + [O]O↔ OO + [CH2]CCC SuccessC=CCO + [CH2]C↔ C=C[CH]O + CC IRC failedCOC=O + C[O]↔ CO + CO[C]=O SuccessCCCCC + [OH]↔ C[CH]CCC + O Transition state failedCCCCC + [OH]↔ O + [CH2]CCCC IRC failedCCCCC + [OH]↔ CC[CH]CC + O Transition state failedCCOC=O + [CH3]↔ C + CCO[C]=O SuccessC=CC + C[CH]C↔ CCC + [CH2]C=C SuccessC=CC + CO[O]↔ COO + [CH2]C=C SuccessC=CC + [CH2]CC↔ CCC + [CH2]C=C SuccessC=C(C)C + [O][O]↔ [CH2]C(=C)C + [O]O SuccessCCC=O + [CH2]C↔ CC + CC[C]=O SuccessCCCC=O + [CH3]↔ C + CCC[C]=O SuccessC1CCCC1 + [CH3]↔ C + [CH]1CCCC1 IRC failedC1CCCC1 + [OH]↔ O + [CH]1CCCC1 Transition state failedCC(C)(C)C + [CH3]↔ C + [CH2]C(C)(C)C SuccessCC(C)(C)C + [OH]↔ O + [CH2]C(C)(C)C SuccessO=CC1CC1 + [CH3]↔ C + O=[C]C1CC1 IRC failedCC=CC=O + [CH3]↔ C + CC=C[C]=O SuccessCCO[O] + [O]O↔ CCOO + [O][O] SuccessOO + [CH2]C(C)C↔ CC(C)C + [O]O SuccessCOC(C)=O + [CH3]↔ C + [CH2]OC(C)=O SuccessCOC(C)=O + [CH3]↔ C + [CH2]C(=O)OC SuccessCCC=O + [CH2]C↔ CC + C[CH]C=O SuccessCCC=O + [CH2]C↔ CC + [CH2]CC=O SuccessC=O + CC(C)(C)[O]↔ CC(C)(C)O + [CH]=O SuccessCCOCC + [CH2]C↔ CC + C[CH]OCC SuccessC + [c]1ccccc1↔ [CH3] + c1ccccc1 SuccessCC(C)C + C[CH]C↔ CCC + C[C](C)C SuccessCC(C)C + C[CH]C↔ CCC + [CH2]C(C)C SuccessCC(C)C + CO[O]↔ COO + C[C](C)C Transition state failedCC(C)C + CO[O]↔ COO + [CH2]C(C)C SuccessCC(C)C + [CH2]CC↔ CCC + C[C](C)C Transition state failedCC(C)C + [CH2]CC↔ CCC + [CH2]C(C)C SuccessCC(C)C + C[C]=O↔ CC=O + C[C](C)C SuccessCC(C)C + C[C]=O↔ CC=O + [CH2]C(C)C SuccessCC(C)(C)CO + [OH]↔ CC(C)(C)[CH]O + O IRC failedCC(C)(C)OO + [CH3]↔ C + CC(C)(C)O[O] SuccessContinued on next page

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Table A.2 – continued from previous pageReactions Success/FailureCCC(C)CC + [OH]↔ CC[C](C)CC + O IRC failedC=CC=O + C[CH]C↔ C=C[C]=O + CCC IRC failedOc1ccccc1 + [H]↔ [H][H] + [O]c1ccccc1 SuccessCCOC=O + [CH2]C↔ CC + CCO[C]=O SuccessCCCCCC + [OH]↔ C[CH]CCCC + O Transition state failedCCCCCC + [OH]↔ O + [CH2]CCCCC SuccessCCCCC=O + [CH3]↔ C + CCCC[C]=O SuccessCCCOC=O + [CH3]↔ C + CCCO[C]=O SuccessC1CCCCC1 + [CH3]↔ C + [CH]1CCCCC1 SuccessC1CCCCC1 + [OH]↔ O + [CH]1CCCCC1 Transition state failedC1OCOCO1 + [OH]↔ O + [CH]1OCOCO1 IRC failedC=CC + C[C](C)C↔ CC(C)C + [CH2]C=C Transition state failedC=CC + [CH2]C(C)=O↔ CC(C)=O + [CH2]C=C SuccessC=CC + [CH2]C(C)C↔ CC(C)C + [CH2]C=C SuccessC1CCCC1 + [CH2]C↔ CC + [CH]1CCCC1 SuccessC1CCCC1 + [O]O↔ OO + [CH]1CCCC1 SuccessCC(C)(C)C + [C]#C↔ C#C + [CH2]C(C)(C)C IRC failedCC(C)=C(C)C + [CH3]↔ C + [CH2]C(C)=C(C)C QST3 neededCC(C)CC=O + [CH3]↔ C + CC(C)C[C]=O SuccessCOC(=O)OC + [CH3]↔ C + [CH2]OC(=O)OC SuccessCOC(=O)OC + [OH]↔ O + [CH2]OC(=O)OC SuccessCC(C)OC=O + [CH3]↔ C + CC(C)O[C]=O Transition state failedCC(C)(C)C=O + [CH3]↔ C + CC(C)(C)[C]=O IRC failedO + [c]1ccccc1↔ [OH] + c1ccccc1 SuccessCC(=O)O[O] + [O]O↔ CC(=O)OO + [O][O] SuccessCCC(C)(C)C + [OH]↔ C[CH]C(C)(C)C + O Transition state failedCCC(C)(C)C + [OH]↔ O + [CH2]C(C)(C)CC SuccessCCC(C)(C)C + [OH]↔ O + [CH2]CC(C)(C)C Transition state failedCC(C)C(C)C + [OH]↔ C[C](C)C(C)C + O Transition state failedC=CC=C + [CH]=C=C↔ C=C=C + [CH]=CC=C IRC failedCCCCCC + [OH]↔ CC[CH]CCC + O IRC failedc1ccccc1 + [O][O]↔ [O]O + [c]1ccccc1 Transition state failedCC + [c]1ccccc1↔ [CH2]C + c1ccccc1 Transition state failedCC(C)(C)[O] + CC=O↔ CC(C)(C)O + C[C]=O Transition state failedCC(C)(C)[O] + CC=O↔ CC(C)(C)O + [CH2]C=O SuccessCC(C)C + [CH2]C(C)C↔ CC(C)C + C[C](C)C SuccessCC(C)C=O + C[CH]C↔ CC(C)[C]=O + CCC SuccessCCc1ccccc1 + [H]↔ [CH2]Cc1ccccc1 + [H][H] SuccessOc1ccccc1 + [CH3]↔ C + [O]c1ccccc1 Transition state failedOc1ccccc1 + [OH]↔ O + [O]c1ccccc1 Transition state failedC1CCCCC1 + [O]O↔ OO + [CH]1CCCCC1 SuccessC1=CCCCC1 + [CH2]C↔ CC + [CH]1CC=CCC1 SuccessContinued on next page

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Table A.2 – continued from previous pageReactions Success/FailureC=CC + CC(C)(C)[O]↔ CC(C)(C)O + [CH2]C=C SuccessCCCCCCC + [OH]↔ O + [CH2]CCCCCC IRC failedCCCCCCC + [OH]↔ C[CH]CCCCC + O Transition state failedC1CCCCCC1 + [OH]↔ O + [CH]1CCCCCC1 IRC failedCC(C)(C)C + C[CH]C↔ CCC + [CH2]C(C)(C)C SuccessC1=CCC=C1 + [CH2]C=C↔ C=CC + [CH]1C=CC=C1 Transition state failedC#C[CH2] + C1=CCC=C1↔ C#CC + [CH]1C=CC=C1 SuccessC1=CCCC=C1 + [O][O]↔ [CH]1C=CC=CC1 + [O]O SuccessCOC(=O)OC + C[O]↔ CO + [CH2]OC(=O)OC IRC failedO=CC1CC1 + [CH]1CC1↔ C1CC1 + O=[C]C1CC1 QST3 neededCCCC=O + [CH2]CC↔ CCC + CCC[C]=O SuccessCCCC=O + [CH2]CC↔ CCC + CC[CH]C=O SuccessCCCCCCC + [OH]↔ CC[CH]CCCC + O Transition state failedCCCCCCC + [OH]↔ CCC[CH]CCC + O IRC failedCC(C)C(C)(C)C + [OH]↔ C[C](C)C(C)(C)C + O IRC failedCC(C)C(C)(C)C + [OH]↔ O + [CH2]C(C)C(C)(C)C SuccessCC=CC + C[CH]CC↔ CCCC + C[C]=CC Transition state failedC=C[CH]C + CC=CC↔ C=CCC + [CH2]C=CC SuccessCC1C=CC(=O)C=C1 + [CH3]↔ C + C[C]1C=CC(=O)C=C1 SuccessCC(C)(C)[O] + CC(C)=O↔ CC(C)(C)O + [CH2]C(C)=O SuccessC1CC1 + [c]1ccccc1↔ [CH]1CC1 + c1ccccc1 SuccessCC(C)(C)[O] + CC(C)C↔ CC(C)(C)O + C[C](C)C Transition state failedCC(C)(C)[O] + CC(C)C↔ CC(C)(C)O + [CH2]C(C)C SuccessCOc1ccccc1 + [CH3]↔ C + [CH2]Oc1ccccc1 SuccessCOc1ccccc1 + [OH]↔ O + [CH2]Oc1ccccc1 IRC failedCC(C)(C)[O] + CCCC↔ CC(C)(C)O + C[CH]CC Transition state failedCC(C)(C)[O] + CCCC↔ CC(C)(C)O + [CH2]CCC Transition state failedCCCOC=O + [CH2]CC↔ CCC + CCCO[C]=O SuccessCCCCCCCC + [OH]↔ O + [CH2]CCCCCCC IRC failedC=C(C)C + CC(C)(C)[O]↔ CC(C)(C)O + [CH2]C(=C)C SuccessC1CCCCCCC1 + [OH]↔ O + [CH]1CCCCCCC1 IRC failedC=C=C + [c]1ccccc1↔ [CH]=C=C + c1ccccc1 SuccessCC(C)=C(C)C + C[CH]C↔ CCC + [CH2]C(C)=C(C)C Transition state failedCC(C)(C)C(C)(C)C + [CH3]↔ C + [CH2]C(C)(C)C(C)(C)C SuccessCC(C)(C)C(C)(C)C + [OH]↔ O + [CH2]C(C)(C)C(C)(C)C SuccessC1=CC1 + [c]1ccccc1↔ [CH]1C=C1 + c1ccccc1 IRC failedOOC1CCCC1 + [O][O]↔ [O]O + [O]OC1CCCC1 Transition state failedCC(C)(C)CO[O] + [O]O↔ CC(C)(C)COO + [O][O] SuccessCCCCCCCC + [OH]↔ C[CH]CCCCCC + O IRC failedCCCCCCCC + [OH]↔ CCC[CH]CCCC + O Transition state failedCCCCCCCC + [OH]↔ CC[CH]CCCCC + O IRC failedCC(C)CC(C)(C)C + [OH]↔ C[C](C)CC(C)(C)C + O Transition state failedContinued on next page

99

Table A.2 – continued from previous pageReactions Success/FailureCC(C)CC(C)(C)C + [OH]↔ O + [CH2]C(C)CC(C)(C)C Transition state failedCC(C)(C)[O] + CC=CC↔ CC(C)(C)O + [CH2]C=CC SuccessC1=CC1 + [c]1ccccc1↔ [C]1=CC1 + c1ccccc1 SuccessCC(C)(O)CO[O] + [O]O↔ CC(C)(O)COO + [O][O] IRC failedCCOCC + [CH2]COCC↔ CCOCC + C[CH]OCC Transition state failedCC(C)=O + [c]1ccccc1↔ [CH2]C(C)=O + c1ccccc1 Transition state failedCC(C)C + [c]1ccccc1↔ C[C](C)C + c1ccccc1 SuccessCCc1ccccc1 + [O]O↔ OO + [CH2]Cc1ccccc1 SuccessCCCCC=O + [CH2]CCC↔ CCCC + CCCC[C]=O SuccessCCCCCCCCC + [OH]↔ O + [CH2]CCCCCCCC SuccessCC(C)(C)C + CC(C)(C)[O]↔ CC(C)(C)O + [CH2]C(C)(C)C Transition state failedCC(C)(C)[O] + CC=C(C)C↔ CC(C)(C)O + [CH2]C(C)=CC Transition state failedCC(C)CC=O + [CH2]C(C)C↔ CC(C)C + CC(C)C[C]=O SuccessCC(C)(C)C=O + C[C](C)C↔ CC(C)(C)[C]=O + CC(C)C Transition state failedOOC1CCCCC1 + [O][O]↔ [O]O + [O]OC1CCCCC1 SuccessCC(C)(C)OOC(C)(C)C + [CH3]↔ C + [CH2]C(C)(C)OOC(C)(C)C SuccessC1CCCCC1 + CC(C)(C)[O]↔ CC(C)(C)O + [CH]1CCCCC1 SuccessC1CCCC1 + [c]1ccccc1↔ [CH]1CCCC1 + c1ccccc1 Transition state failedC1=CCC=C1 + [c]1ccccc1↔ [CH]1C=CC=C1 + c1ccccc1 SuccessCC(C)(C)[O] + CC(C)=C(C)C↔ CC(C)(C)O + [CH2]C(C)=C(C)C Transition state failedOOCc1ccccc1 + [O][O]↔ [O]O + [O]OCc1ccccc1 IRC failedCCCCCCCCCC + [OH]↔ O + [CH2]CCCCCCCCC SuccessCCCCCCCCCC + [OH]↔ C[CH]CCCCCCCC + O Transition state failedCCCCCCCCCC + [OH]↔ CC[CH]CCCCCCC + O Transition state failedCCCCCCCCCC + [OH]↔ CCCC[CH]CCCCC + O Transition state failedOc1ccccc1 + [CH]1C=CC=C1↔ C1=CCC=C1 + [O]c1ccccc1 Transition state failedC1CCCCC1 + [c]1ccccc1↔ [CH]1CCCCC1 + c1ccccc1 Transition state failedCC(C)C(C)C(C)C + [c]1ccccc1↔ C[C](C)C(C)C(C)C + c1ccccc1 Transition state failed

B. Group contribution method

B.1 Group Training Regression Details

Consider the trees:XH

X1

X11 X12

X2

X21 X22 X23

and Yrad

Y1

Y11 Y12

Y2

Y21 Y22

and a known transition state that matches nodes X11 and Y22. This example will dealwith a single distance d, but in reality it is done for each of the three distances dXH,dHY, and dXY. The distance d11,22 from the known transition state can be used to train thegroups (X11,Y22) and all combinations of the ancestors of these groups, namely (X11,Y2),(X11,Yrad), (X1,Y22), (X1,Y2), (X1,Yrad), (XH,Y22), (XH,Y2), and (XH,Yrad). If a secondknown transition state matches nodes (X23,Y2) and has distance d23,2 then it provides datafor those groups (X23,Y2) and all the pairs of ancestors: (X23,Yrad), (X2,Y2), (X2,Yrad),(XH,Y2), and (XH,Yrad).

From the two training transition states with distances d11,22 and d23,2 we construct a setof 15 linear equations,

X11 + Y22 + d0 = d11,22 (B.1)X11 + Y2 + d0 = d11,22 (B.2)

X11 + Yrad + d0 = d11,22 (B.3)X1 + Y22 + d0 = d11,22 (B.4)X1 + Y2 + d0 = d11,22 (B.5)

X1 + Yrad + d0 = d11,22 (B.6)XH + Y22 + d0 = d11,22 (B.7)XH + Y2 + d0 = d11,22 (B.8)

XH + Yrad + d0 = d11,22 (B.9)X23 + Y2 + d0 = d23,2 (B.10)

X23 + Yrad + d0 = d23,2 (B.11)X2 + Y2 + d0 = d23,2 (B.12)

X2 + Yrad + d0 = d23,2 (B.13)XH + Y2 + d0 = d23,2 (B.14)

XH + Yrad + d0 = d23,2 (B.15)

where d0 is the base distance common to all transition states, so that the final group values

100

101

contain only deviations from the base value.This set of 15 equations in 9 unknowns is over-specified, for example equations (B.8)

and (B.14) have the same left hand side, and equations (B.9) and (B.15) are also duplicates.Indeed, every known transition state will lead to an expression like (B.9) and (B.15) forXH + Yrad + d0. Although there is not a set of group values (X11, X1, Xrad, Y22, etc.) thatwill precisely solve the above set of linear equations, we can find the values that minimizethe error in the equations in the least-squares sense. This is the form of the linear leastsquares regression used to train the group values.

Writing the above set of equations in matrix form:

0 0 0 1 0 0 0 1 10 0 0 1 0 0 1 0 10 0 0 1 0 1 0 0 10 1 0 0 0 0 0 1 10 1 0 0 0 0 1 0 10 1 0 0 0 1 0 0 11 0 0 0 0 0 0 1 11 0 0 0 0 0 1 0 11 0 0 0 0 1 0 0 10 0 0 0 1 0 1 0 10 0 0 0 1 1 0 0 10 0 1 0 0 0 1 0 10 0 1 0 0 1 0 0 11 0 0 0 0 0 1 0 11 0 0 0 0 1 0 0 1

·

XHX1

X2

X11

X23

YradY2

Y22

d0

=

d11,22d11,22d11,22d11,22d11,22d11,22d11,22d11,22d11,22d23,2d23,2d23,2d23,2d23,2d23,2

(B.16)

we can use the notationX · β = y (B.17)

The least-squares fitted group values in the vector β can be found by

β =(XTX

)−1XTy (B.18)

or using Numpy’s linear algebra library in Python:

beta, residues, rank, s = numpy.linalg.lstsq(X, y)

which computes the vector β that minimizes the Euclidean 2-norm

‖y −Xβ‖2 (B.19)

102

B.2 Predicted vs Optimized distances

dXH dHY dXYPr

edic

ted

Dis

tanc

e(A

)

44T

S23

0TS

827T

S10

71T

S

Optimized Distance (A)

Figure B.1: Comparison of distances from validated transition states to predictionsfrom molecular group values calculated from different sized data sets.The solid line represents parity, the dashed lines represent the root meansquared error of the estimates from parity. The predictions derived fromthe original and new trees are represented by the black and red circlesrespectively.

103

B.3 Group Naming Convention

While much detail is included in molecular group names, a full description of the group

should be checked in the TS groups.py file. Atoms where the element is undefined are

typically assigned as an R atom, unless the atom is reactive where it is assigned as either X

or Y.

Molecular group names assume radical count is zero if undefined. For example, if

radicals are not included in the name, the atom has no radical electrons. So the group X H

describes a molecular group where a hydrogen atom is bonded to an atom X which does

not have any unpaired (radical) electrons.

Atom bonding is described by the letters s, d, dd, t, and b: s mean the atom only has

single bonds, d means the atom has exactly one double bond, dd means the atom has 2

double bonds, t means the atom has a triple bond, and b means the atom is part of an

aromatic ring. Thus Cs signifies Carbon atom with only single bonds (not a caesium atom).

A forward slash denotes atoms bonded to the atom specified before the first forward

slash. For example, C/H3/Cs describes a carbon atom, bonded to 3 hydrogen atoms and to

a carbon with only single bonds.

A backslash has the same meaning as the forward slash, but the atom being considered

is before the first backslash. For example, C/H3/Cs\H2\Cs describes a carbon atom bonded

to 3 hydrogen atoms and to a carbon which has single bonds to 2 hydrogen atoms and a

third carbon (which only has single bonds).

104

B.4 Group values for original tree

Table B.1: Original tree structure, with distance group data in A.

Groups TS count dXH (A) dHY (A) dXY (A)L1: X H or Xanyrad H 2142 1.336010 1.336330 2.667560

L2: X H 2089 -0.002556 0.002864 0.000227

L3: H2 70 -0.327434 -0.045046 -0.369886

L3: Ct H 12 0.426157 -0.214467 0.120589

L4: Ct/H/NonDeC 12 0.426157 -0.214467 0.120589

L3: O H 203 -0.110714 -0.034542 -0.149127

L4: O pri 14 0.075716 -0.199700 -0.158817

L4: O sec 189 -0.122296 -0.024281 -0.148525

L5: O/H/NonDeC 51 -0.061770 -0.091698 -0.156862

L5: O/H/NonDeO 137 -0.143000 -0.000215 -0.144650

L6: H2O2 37 -0.172464 0.030481 -0.143076

L6: ROOH pri 31 -0.164228 0.023011 -0.141922

L6: ROOH sec 1 -0.023183 -0.146971 -0.174787

L6: ROOH ter 1 -0.216642 0.096657 -0.117164

L5: O/H/OneDe 1 -0.241135 -0.138830 -0.383406

L6: O/H/OneDeC 1 -0.241135 -0.138830 -0.383406

L3: Orad O H 22 -0.244636 0.181811 -0.064615

L3: Cd H 319 0.085747 -0.068103 0.017934

L4: Cd pri 210 0.080833 -0.065760 0.015103

L5: Cd/H2/NonDeC 210 0.080833 -0.065760 0.015103

L4: Cd sec 109 0.095340 -0.072680 0.023461

L5: Cd/H/NonDeC 30 0.072086 -0.053192 0.015788

L5: Cd/H/NonDeO

L5: Cd/H/OneDe 79 0.104163 -0.080074 0.026373

L6: Cd/H/Ct 26 0.033884 -0.029006 0.006386

L6: Cd/H/Cb

L6: Cd/H/CO

L6: Cd/H/Cd 53 0.139835 -0.105994 0.036518

L3: Cb H 44 0.124436 -0.092331 0.033127

L3: CO H 153 -0.001372 0.059389 0.057711

L4: CO pri 50 0.000467 0.049726 0.050841

L4: CO sec 103 -0.002287 0.064195 0.061127

L5: CO/H/NonDe 60 -0.009196 0.071787 0.062334

L6: CO/H/Cs 55 -0.009637 0.077298 0.067136

L7: CO/H/Cs\Cs—Cs 6 -0.039990 0.127041 0.088998

L5: CO/H/OneDe 43 0.006808 0.054200 0.059539

L3: Cs H 1266 0.007461 0.023642 0.032296

L4: C methane 69 0.076680 -0.051468 0.028801

L4: C pri 684 0.025511 -0.002230 0.025031

L5: C/H3/Cs 357 0.051887 -0.033063 0.021528

L6: C/H3/Cs\H3 65 0.045880 -0.025075 0.024181

L6: C/H3/Cs\OneNonDe 107 0.053158 -0.037890 0.017928

L7: C/H3/Cs\H2\Cs 59 0.049403 -0.042001 0.010665

L8: C/H3/Cs\H2\Cs—O 1 0.045526 -0.296175 -0.246802

Continued on next page

105

Table B.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L7: C/H3/Cs\H2\O 48 0.057673 -0.032947 0.026660

L6: C/H3/Cs\TwoNonDe 44 0.049381 -0.031488 0.021282

L7: C/H3/Cs\H\Cs\OL7: C/H3/Cs\H\Cs\Cs—O

L5: C/H3/O 53 0.025187 0.000259 0.020403

L5: C/H3/OneDe 274 -0.007707 0.036215 0.030303

L6: C/H3/Ct 36 -0.003456 0.024269 0.023000

L6: C/H3/Cb

L6: C/H3/CO 84 0.012344 0.003831 0.016124

L6: C/H3/Cd 154 -0.019271 0.056043 0.039454

L7: C/H3/Cd\H Cd\H2 46 -0.022590 0.051658 0.031290

L7: C/H3/Cd\H Cd\H\Cs 3 -0.047979 0.075930 0.031408

L7: C/H3/Cd\Cs Cd\H2 3 -0.023917 0.029891 0.010253

L4: C sec 409 -0.026003 0.069757 0.044341

L5: C/H2/NonDeC 73 0.027438 -0.019733 0.010886

L6: C/H2/Cs/Cs\OL6: C/H2/Cs/Cs\Cs—O

L6: C/H2/NonDeC 5ring 5 -0.018316 -0.013568 -0.027701

L7: C/H2/NonDeC 5ring fused6 1

L7: C/H2/NonDeC 5ring fused6 2

L7: C/H2/NonDeC 5ring alpha6ring

L7: C/H2/NonDeC 5ring beta6ring

L6: C/H2/Cs\H3/Cs\H3 53 0.037209 -0.011011 0.029214

L5: C/H2/NonDeO 52 0.011534 0.020231 0.027527

L6: C/H2/CsO 50 0.010769 0.021611 0.027966

L7: C/H2/Cs\Cs2/O

L6: C/H2/O2 2 0.031818 -0.016339 0.015885

L5: C/H2/OneDe 185 -0.037737 0.086334 0.048927

L6: C/H2/OneDeC 184 -0.037603 0.086091 0.048826

L7: C/H2/CtCs

L7: C/H2/CbCs

L7: C/H2/COCs 41 -0.014812 0.053991 0.038405

L8: C/H2/CO\H/Cs\H3 1 -0.050355 0.095460 0.047057

L7: C/H2/CdCs 143 -0.043987 0.095083 0.051745

L8: C/H2/Cd\H Cd\H2/Cs\H3 33 -0.029127 0.076789 0.049531

L6: C/H2/OneDeO 1 -0.059511 0.125879 0.065513

L5: C/H2/TwoDe 99 -0.060370 0.126094 0.067502

L6: C/H2/CtCt

L6: C/H2/CtCb

L6: C/H2/CtCO

L6: C/H2/CbCb

L6: C/H2/CbCO

L6: C/H2/COCO

L6: C/H2/CdCt

L6: C/H2/CdCb

L6: C/H2/CdCO

L6: C/H2/CdCd 99 -0.060370 0.126094 0.067502

L5: C/H2/Cb

Continued on next page

106

Table B.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L4: C ter 104 -0.025676 0.062321 0.034956

L5: C/H/NonDe 16 0.001573 0.003478 0.006838

L6: C/H/Cs3 15 0.006985 0.005657 0.014344

L7: C/H/Cs3 5ring

L8: C/H/Cs3 5ring fused6

L8: C/H/Cs3 5ring adj5

L7: C/H/Cs2/Cs\OL6: C/H/NDMustO 1 -0.128313 -0.048800 -0.173313

L7: C/H/Cs2O 1 -0.128313 -0.048800 -0.173313

L7: C/H/CsO2

L7: C/H/O3

L5: C/H/OneDe 87 -0.029273 0.070037 0.038474

L6: C/H/Cs2 87 -0.029273 0.070037 0.038474

L7: C/H/Cs2Ct

L7: C/H/Cs2Cb

L7: C/H/Cs2CO 87 -0.029273 0.070037 0.038474

L7: C/H/Cs2Cd

L6: C/H/CsO

L6: C/H/OO

L5: C/H/TwoDe 1 -0.119337 0.270561 0.154144

L6: C/H/Cs 1 -0.119337 0.270561 0.154144

L7: C/H/CtCt

L7: C/H/CtCb

L7: C/H/CtCO

L7: C/H/CbCb

L7: C/H/CbCO

L7: C/H/COCO

L7: C/H/CdCt

L7: C/H/CdCb

L7: C/H/CdCO

L7: C/H/CdCd 1 -0.119337 0.270561 0.154144

L6: C/H/TDMustO

L5: C/H/ThreeDe

L5: C/H/Cb

L2: Xrad H 53 0.094987 -0.106435 -0.008430

L3: C rad H 38 0.155959 -0.117206 0.041719

L4: CH3 rad H 38 0.155959 -0.117206 0.041719

L3: OH rad H 15 -0.074639 -0.076468 -0.147944

L2: Xbirad H

L3: CH2 triplet H

L3: CH2 singlet H

L2: Xtrirad H

L3: C quartet H

L3: C doublet H

L1: Y anyrad

L2: Y 1centerquadrad

L3: C quintet

L3: C triplet

Continued on next page

107

Table B.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L3: C singlet

L2: Y 1centertrirad

L3: CH quartet

L3: CH doublet

L2: Y 1centerbirad 53 -0.106387 0.093103 -0.010316

L3: O atom triplet 15 -0.078856 -0.073302 -0.149113

L3: O atom singlet

L3: CH2 triplet 38 -0.116742 0.155689 0.041886

L3: CH2 singlet

L2: Y rad 2089 0.002857 -0.002500 0.000277

L3: H rad 70 -0.044160 -0.330263 -0.371926

L3: Y 2centeradjbirad 22 0.183054 -0.244770 -0.063414

L4: O2b 22 0.183054 -0.244770 -0.063414

L4: C2b

L3: Ct rad 12 -0.215601 0.427396 0.121746

L4: Ct rad/Ct 12 -0.215601 0.427396 0.121746

L3: O rad 203 -0.035877 -0.108766 -0.148471

L4: O pri rad 14 -0.200121 0.080838 -0.153831

L4: O sec rad 189 -0.024990 -0.121335 -0.148115

L5: O rad/NonDeC 51 -0.091751 -0.061514 -0.156592

L6: O rad/Cs\H2\Cs—H—Cs2

L5: O rad/NonDeO 137 0.000232 -0.143066 -0.144048

L6: OOC 100 -0.009950 -0.133086 -0.144316

L5: O rad/OneDe 1 -0.139436 -0.241161 -0.384069

L6: O rad/OneDeC 1 -0.139436 -0.241161 -0.384069

L7: O rad/Cd

L8: O rad/Cd\H Cd\H2

L8: O rad/Cd\H Cd\H\Cs

L8: O rad/Cd\H Cd\Cs2

L8: O rad/Cd\Cs Cd\H2

L8: O rad/Cd\Cs Cd\H\Cs

L8: O rad/Cd\Cs Cd\Cs2

L3: Cd rad 319 -0.068341 0.085680 0.017720

L4: Cd pri rad 210 -0.065901 0.080755 0.014975

L5: Cd Cd\H2 pri rad 37 -0.090673 0.111803 0.024431

L5: Cd Cd\H\Cs pri rad 25 -0.084518 0.116254 0.030054

L6: Cd Cd\H\Cs—H2—Cs pri rad

L5: Cd Cd\Cs2 pri rad

L4: Cd sec rad 109 -0.073073 0.095230 0.023044

L5: Cd rad/NonDeC 30 -0.053245 0.071823 0.015883

L6: Cd Cd\H2 rad/Cs 29 -0.047865 0.071398 0.020717

L6: Cd Cd\H\Cs rad/Cs 1 -0.338387 0.094328 -0.240337

L5: Cd rad/NonDeO

L5: Cd rad/OneDe 79 -0.080561 0.104069 0.025748

L6: Cd rad/Ct 26 -0.028430 0.033281 0.006395

L6: Cd rad/Cb

L6: Cd rad/CO

L6: Cd rad/Cd 53 -0.106627 0.139463 0.035425

Continued on next page

108

Table B.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L3: Cb rad 44 -0.092544 0.124820 0.033389

L3: CO rad 153 0.060690 -0.001930 0.058483

L4: CO pri rad 50 0.051903 -0.000963 0.051657

L4: CO sec rad 103 0.064999 -0.002404 0.061831

L5: CO rad/NonDe 60 0.072193 -0.008661 0.063342

L5: CO rad/OneDe 43 0.055533 0.005830 0.059842

L3: Cs rad 1266 0.024200 0.007289 0.032625

L4: C methyl 69 -0.050813 0.075919 0.028607

L4: C pri rad 684 -0.001792 0.025273 0.025176

L5: C rad/H2/Cs 357 -0.032772 0.051719 0.021617

L6: C rad/H2/Cs\H3 65 -0.024753 0.045959 0.024509

L6: C rad/H2/Cs\Cs2\O 2 -0.125966 0.025305 -0.097425

L6: C rad/H2/Cs\H\Cs\Cs—O 31 -0.033915 0.057010 0.024538

L6: C rad/H2/Cs\H\Cs—Cs\OL6: C rad/H2/Cs\H2\Cs—Cs—O

L6: C rad/H2/Cs\H2\Cs—Cs#O 1 -0.296450 0.035505 -0.257321

L5: C rad/H2/Ct 36 0.026030 -0.004893 0.023289

L5: C rad/H2/Cb

L5: C rad/H2/CO 84 0.004886 0.011458 0.016257

L5: C rad/H2/O 53 0.000911 0.024796 0.020406

L5: C rad/H2/Cd 154 0.056969 -0.019724 0.039836

L6: C rad/H2/Cd\H Cd\H2 118 0.058876 -0.021124 0.040298

L6: C rad/H2/Cd\Cs Cd\H2 3 0.030025 -0.024190 0.010083

L4: C sec rad 409 0.070550 -0.026112 0.044984

L5: C rad/H/NonDeC 73 -0.018369 0.026681 0.011442

L6: C rad/H/NonDeC 5ring fused6 1

L6: C rad/H/NonDeC 5ring fused6 2

L6: C rad/H/Cs\H3/Cs\H3 53 -0.010088 0.036102 0.028957

L6: C rad/H/NonDeC 5ring alpha6ring

L6: C rad/H/NonDeC 5ring beta6ring

L6: C rad/H/Cs\H2\Cs/Cs\H2\OL6: C rad/H/Cs\H\Cs\O/Cs

L6: C rad/H/Cs\H2\Cs—O/Cs

L5: C rad/H/NonDeO 52 0.020310 0.011913 0.027769

L6: C rad/H/CsO 50 0.021612 0.011204 0.028190

L7: C rad/H/Cs\H2\Cs/O

L8: C rad/H/Cs\H2\Cs—H2—Cs/O

L7: C rad/H/Cs\H\Cs2/O

L6: C rad/H/O2 2 -0.016152 0.031780 0.015998

L5: C rad/H/OneDe 185 0.086671 -0.037595 0.049410

L6: C rad/H/OneDeC 184 0.086442 -0.037467 0.049316

L7: C rad/H/CtCs

L7: C rad/H/CbCs

L7: C rad/H/CO/Cs 41 0.053933 -0.014722 0.038508

L8: C rad/H/CO\H/Cs\H3 1 0.095705 -0.050407 0.047214

L7: C rad/H/CdCs 143 0.095805 -0.044019 0.052429

L7: C rad/H/CSCs

L6: C rad/H/OneDeO 1 0.126124 -0.059563 0.065670

Continued on next page

109

Table B.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L5: C rad/H/TwoDe 99 0.126910 -0.060266 0.068401

L6: C rad/H/CtCt

L6: C rad/H/CtCb

L6: C rad/H/CtCO

L6: C rad/H/CbCb

L6: C rad/H/CbCO

L6: C rad/H/COCO

L6: C rad/H/CdCt

L6: C rad/H/CdCb

L6: C rad/H/CdCO

L6: C rad/H/CdCd 99 0.126910 -0.060266 0.068401

L4: C ter rad 104 0.062942 -0.025701 0.035402

L5: C rad/NonDe 16 0.005813 0.000990 0.008314

L6: C rad/Cs3 15 0.007964 0.006028 0.015416

L7: C rad/Cs2/Cs\OL7: C rad/Cs3 5ring fused6

L7: C rad/Cs3 5ring adj5

L6: C rad/NDMustO 1 -0.049406 -0.128339 -0.173976

L7: C rad/Cs2O 1 -0.049406 -0.128339 -0.173976

L8: C rad/OOH/Cs/Cs

L8: C rad/O/Cs/Cs\Cs

L7: C rad/CsO2

L7: C rad/O3

L5: C rad/OneDe 87 0.070669 -0.029339 0.038898

L6: C rad/Cs2 87 0.070669 -0.029339 0.038898

L7: C rad/CtCs2

L7: C rad/CbCs2

L7: C rad/COCs2 87 0.070669 -0.029339 0.038898

L7: C rad/CdCs2

L6: C rad/CsO

L6: C rad/O2

L5: C rad/TwoDe 1 0.270660 -0.119354 0.154191

L6: C rad/Cs 1 0.270660 -0.119354 0.154191

L7: C rad/CtCtCs

L7: C rad/CtCbCs

L7: C rad/CtCOCs

L7: C rad/CbCbCs

L7: C rad/CbCOCs

L7: C rad/COCOCs

L7: C rad/CdCtCs

L7: C rad/CdCbCs

L7: C rad/CdCOCs

L7: C rad/CdCdCs 1 0.270660 -0.119354 0.154191

L6: C rad/TDMustO

L5: C rad/ThreeDe

110

B.5 Group values for new tree

Table B.2: Modified tree structure, with distance group data in A.

Groups TS count dXH (A) dHY (A) dXY (A)L1: X H or Xanyrad H 2142 1.335530 1.335350 2.666040

L2: H2 70 -0.342288 -0.039783 -0.379376

L2: C H 1832 0.029362 0.004085 0.033720

L3: Cs H 1304 0.013039 0.020558 0.034846

L4: Csnorad H 1266 0.008578 0.024975 0.034745

L5: C methane 69 0.076977 -0.054808 0.025695

L5: CsRHHH 684 0.025708 -0.000824 0.026630

L6: CsCHHH 631 0.025688 -0.001134 0.026803

L7: C/H3/Cs 357 0.050417 -0.030813 0.022318

L7: C/H3/Cd 154 -0.016229 0.054933 0.041314

L7: C/H3/Ct 36 -0.002891 0.027628 0.026874

L7: C/H3/Cb

L6: CsOHHH 53 0.025956 0.002967 0.024508

L5: CsRRHH 409 -0.022947 0.070377 0.048092

L6: CsCCHH 356 -0.028156 0.077681 0.050784

L7: C/H2/Cs/Cs 73 0.027797 -0.011348 0.019668

L7: C/H2/Cs/Cd 143 -0.039272 0.093747 0.055160

L7: C/H2/Cs/Ct

L7: C/H2/Cs/Cb

L7: C/H2/Cd/Cd 99 -0.054862 0.123563 0.070441

L7: C/H2/Cd/Ct

L7: C/H2/Cd/Cb

L7: C/H2/Ct/Ct

L7: C/H2/Ct/Cb

L7: C/H2/Cb/Cb

L6: CsCOHH 51 0.011230 0.023228 0.030972

L7: C/H2/Cs/O 50 0.013016 0.020855 0.030315

L7: C/H2/Cd/O 1 -0.064825 0.124233 0.058927

L7: C/H2/Ct/O

L7: C/H2/Cb/O

L6: CsOOHH 2 0.027312 -0.019710 0.008337

L5: CsRRRH 104 -0.024248 0.067372 0.041141

L6: CsCCCH 103 -0.023913 0.067560 0.041645

L7: C/H/Cs/Cs/Cs 15 0.013473 0.013732 0.029444

L7: C/H/Cs/Cs/Cd

L7: C/H/Cs/Cs/Ct

L7: C/H/Cs/Cs/Cb

L7: C/H/Cs/Cd/Cd 1 -0.121224 0.263641 0.145531

L7: C/H/Cs/Cd/Ct

L7: C/H/Cs/Cd/Cb

L7: C/H/Cs/Ct/Ct

L7: C/H/Cs/Ct/Cb

L7: C/H/Cs/Cb/Cb

L7: C/H/Cd/Cd/Cd

Continued on next page

111

Table B.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L7: C/H/Cd/Cd/Ct

L7: C/H/Cd/Cd/Cb

L7: C/H/Cd/Ct/Ct

L7: C/H/Cd/Ct/Cb

L7: C/H/Cd/Cb/Cb

L7: C/H/Ct/Ct/Ct

L7: C/H/Ct/Ct/Cb

L7: C/H/Ct/Cb/Cb

L7: C/H/Cb/Cb/Cb

L6: CsCCOH 1 -0.121857 0.012401 -0.106079

L7: C/H/Cs/Cs/O 1 -0.121857 0.012401 -0.106079

L7: C/H/Cs/Cd/O

L7: C/H/Cs/Ct/O

L7: C/H/Cs/Cb/O

L7: C/H/Cd/Cd/O

L7: C/H/Cd/Ct/O

L7: C/H/Cd/Cb/O

L7: C/H/Ct/Ct/O

L7: C/H/Ct/Cb/O

L7: C/H/Cb/Cb/O

L6: CsCOOH

L7: C/H/Cs/O/O

L7: C/H/Cd/O/O

L7: C/H/Ct/O/O

L7: C/H/Cb/O/O

L6: CsOOOH

L4: Csrad H 38 0.154287 -0.119281 0.038063

L5: C methyl 38 0.154287 -0.119281 0.038063

L5: CsradRH2

L6: CsradCHH

L7: Csrad/H/Cs/H

L7: Csrad/H/Cd/H

L7: Csrad/H/Ct/H

L7: Csrad/H/Cb/H

L6: CsradOH2

L5: CsradRRH

L6: CsradCCH

L7: Csrad/Cs/Cs/H

L7: Csrad/Cs/Cd/H

L7: Csrad/Cs/Ct/H

L7: Csrad/Cs/Cb/H

L7: Csrad/Cd/Cd/H

L7: Csrad/Cd/Ct/H

L7: Csrad/Cd/Cb/H

L7: Csrad/Ct/Ct/H

L7: Csrad/Ct/Cb/H

L7: Csrad/Cb/Cb/H

L6: CsradCOH

Continued on next page

112

Table B.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L7: Csrad/Cs/O/H

L7: Csrad/Cd/O/H

L7: Csrad/Ct/O/H

L7: Csrad/Cb/O/H

L6: CsradOOH

L4: CsbiradH

L5: Cs singletH

L6: Cs singletHH

L6: Cs singletRH

L7: C singletCH

L8: C singlet/Cs/H

L8: C singlet/Cd/H

L8: C singlet/Ct/H

L8: C singlet/Cb/H

L7: C singletOH

L5: Cs tripletH

L6: Cs tripletHH

L6: Cs tripletRH

L7: Cs tripletCH

L8: C triplet/Cs/H

L8: C triplet/Cd/H

L8: C triplet/Ct/H

L8: C triplet/Cb/H

L7: Cs tripletOH

L4: CstriradH

L5: Cdoublet H

L5: Cquartet H

L3: Cd H 319 0.080461 -0.066374 0.014535

L4: Cdnorad H 319 0.080461 -0.066374 0.014535

L5: Cd C/R/H 319 0.080461 -0.066374 0.014535

L6: Cd C/H2 210 0.075312 -0.063805 0.011806

L7: Cd Cds/H2 121 0.112224 -0.091421 0.021864

L7: Cd Cdd/H2 89 0.024935 -0.026114 -0.001921

L6: Cd C/C/H 109 0.090623 -0.071444 0.019920

L7: Cd Cds/Cs/H 30 0.065391 -0.049501 0.012283

L7: Cd Cds/Cd/H 53 0.133020 -0.104743 0.030985

L7: Cd Cds/Ct/H 26 0.031752 -0.027696 0.005788

L7: Cd Cds/Cb/H

L7: Cd Cdd/Cs/H

L7: Cd Cdd/Cd/H

L7: Cd Cdd/Ct/H

L7: Cd Cdd/Cb/H

L6: Cd C/O/H

L7: Cd Cds/O/H

L7: Cd Cdd/O/H

L5: Cd O/R/H

L6: Cd O/H2

L6: Cd O/C/H

Continued on next page

113

Table B.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L7: Cd O/Cs/H

L7: Cd O/Cd/H

L7: Cd O/Ct/H

L7: Cd O/Cb/H

L6: Cd O/O/H

L4: Cdrad H

L5: Cdrad C/H

L6: Cdrad Cds/H

L6: Cdrad Cdd/H

L5: Cdrad O/H

L3: Ct H 12 0.431401 -0.229422 0.108762

L3: Cb H 44 0.117925 -0.092504 0.026137

L2: O H 240 -0.118125 -0.018878 -0.139931

L3: OradH 15 -0.075951 -0.082791 -0.155556

L3: ORH 225 -0.121281 -0.014095 -0.138762

L4: OHH 14 0.070355 -0.189952 -0.151526

L4: OCH 52 -0.066073 -0.091363 -0.160225

L5: O/Cs/H 51 -0.064968 -0.091454 -0.159202

L5: O/Cd/H

L5: O/Ct/H

L5: O/Cb/H 1 -0.234679 -0.077629 -0.316172

L4: OOH 159 -0.156010 0.026510 -0.130609

L1: Y anyrad

L2: Hrad 70 -0.039495 -0.342287 -0.379190

L2: Orad 240 -0.017829 -0.118668 -0.139585

L3: OjR 225 -0.012844 -0.122031 -0.138432

L4: OjH 14 -0.193300 0.076164 -0.149391

L4: OjC 52 -0.089279 -0.068097 -0.160291

L5: OjCs 51 -0.089356 -0.066985 -0.159249

L5: OjCd

L5: OjCt

L5: OjCb 1 -0.077813 -0.234351 -0.316079

L4: OjO 159 0.027899 -0.156949 -0.130319

L3: O atom triplet 15 -0.083286 -0.074511 -0.154718

L2: Crad 1832 0.003965 0.029654 0.033918

L3: Cj 1794 0.006693 0.026902 0.033836

L4: Csj 1266 0.025234 0.008380 0.034738

L5: Cs methyl 69 -0.053769 0.075442 0.025074

L5: CsjRH2 684 -0.000760 0.025831 0.026698

L6: CsjCH2 631 -0.001101 0.025831 0.026859

L7: Csj/Cs/H2 357 -0.031137 0.050803 0.022282

L7: Csj/Cd/H2 154 0.055474 -0.016532 0.041386

L7: Csj/Ct/H2 36 0.028053 -0.002911 0.027161

L7: Csj/Cb/H2

L6: CsjOH2 53 0.003401 0.025833 0.024741

L5: CsjRRH 409 0.070627 -0.023160 0.048156

L6: CsjCCH 356 0.077902 -0.028338 0.050848

L7: Csj/Cs/Cs/H 73 -0.011458 0.028261 0.019955

Continued on next page

114

Table B.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L7: Csj/Cs/Cd/H 143 0.094158 -0.039761 0.055281

L7: Csj/Cs/Ct/H

L7: Csj/Cs/Cb/H

L7: Csj/Cd/Cd/H 99 0.124292 -0.055524 0.070403

L7: Csj/Cd/Ct/H

L7: Csj/Cd/Cb/H

L7: Csj/Ct/Ct/H

L7: Csj/Ct/Cb/H

L7: Csj/Cb/Cb/H

L6: CsjCOH 51 0.024012 0.010600 0.031199

L7: Csj/Cs/O/H 50 0.021572 0.012445 0.030539

L7: Csj/Cd/O/H 1 0.126136 -0.066634 0.058822

L7: Csj/Ct/O/H

L7: Csj/Cb/O/H

L6: CsjOOH 2 -0.017641 0.025276 0.008156

L5: CsjRRR 104 0.068516 -0.025639 0.040796

L6: CsjCCC 103 0.068715 -0.025301 0.041315

L7: Csj/Cs/Cs/Cs 15 0.013659 0.012220 0.028184

L7: Csj/Cs/Cs/Cd

L7: Csj/Cs/Cs/Ct

L7: Csj/Cs/Cs/Cb

L7: Csj/Cs/Cd/Cd 1 0.265941 -0.123578 0.145242

L7: Csj/Cs/Cd/Ct

L7: Csj/Cs/Cd/Cb

L7: Csj/Cs/Ct/Ct

L7: Csj/Cs/Ct/Cb

L7: Csj/Cs/Cb/Cb

L7: Csj/Cd/Cd/Cd

L7: Csj/Cd/Cd/Ct

L7: Csj/Cd/Cd/Cb

L7: Csj/Cd/Ct/Ct

L7: Csj/Cd/Ct/Cb

L7: Csj/Cd/Cb/Cb

L7: Csj/Ct/Ct/Ct

L7: Csj/Ct/Ct/Cb

L7: Csj/Ct/Cb/Cb

L7: Csj/Cb/Cb/Cb

L6: CsjCCO 1 0.012218 -0.121529 -0.105986

L7: Csj/Cs/Cs/O 1 0.012218 -0.121529 -0.105986

L7: Csj/Cs/Cd/O

L7: Csj/Cs/Ct/O

L7: Csj/Cs/Cb/O

L7: Csj/Cd/Cd/O

L7: Csj/Cd/Ct/O

L7: Csj/Cd/Cb/O

L7: Csj/Ct/Ct/O

L7: Csj/Ct/Cb/O

L7: Csj/Cb/Cb/O

Continued on next page

115

Table B.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L6: CsjCOO

L7: Csj/Cs/O/O

L7: Csj/Cd/O/O

L7: Csj/Ct/O/O

L7: Csj/Cb/O/O

L6: CsjOOO

L4: Cdj 319 -0.067745 0.082294 0.015358

L5: Cdj CR 319 -0.067745 0.082294 0.015358

L6: Cdj CH 210 -0.065277 0.077335 0.012609

L7: Cdj CdsH 121 -0.093854 0.115196 0.022945

L7: Cdj CddH 89 -0.026782 0.026331 -0.001313

L6: Cdj CC 109 -0.072645 0.092142 0.020817

L7: Cdj CdsCs 30 -0.052748 0.067639 0.013440

L7: Cdj CdsCd 53 -0.104889 0.134137 0.031903

L7: Cdj CdsCt 26 -0.028231 0.032656 0.006171

L7: Cdj CdsCb

L7: Cdj CddCs

L7: Cdj CddCd

L7: Cdj CddCt

L7: Cdj CddCb

L6: Cdj CO

L7: Cdj CdsO

L7: Cdj CddO

L5: Cdj OR

L6: Cdj OH

L6: Cdj OC

L7: Cdj OCs

L7: Cdj OCd

L7: Cdj OCt

L7: Cdj OCb

L6: Cdj OO

L4: Ctj 12 -0.230464 0.433568 0.110987

L5: CtjC 12 -0.230464 0.433568 0.110987

L4: Cbj 44 -0.095175 0.120179 0.026648

L3: Cjj 38 -0.118072 0.152750 0.037583

L4: Csjj 38 -0.118072 0.152750 0.037583

L5: Cs sing

L6: Cs singH2

L6: Cs singRH

L7: Cs singCH

L8: Cs sing/Cs/H

L8: Cs sing/Cd/H

L8: Cs sing/Ct/H

L8: Cs sing/Cb/H

L7: Cs singOH

L6: Cs singRR

L7: Cs singCC

L8: Cs sing/Cs/Cs

Continued on next page

116

Table B.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L8: Cs sing/Cs/Cd

L8: Cs sing/Cs/Ct

L8: Cs sing/Cs/Cb

L8: Cs sing/Cd/Cd

L8: Cs sing/Cd/Ct

L8: Cs sing/Cd/Cb

L8: Cs sing/Ct/Ct

L8: Cs sing/Ct/Cb

L8: Cs sing/Cb/Cb

L7: Cs singCO

L8: Cs sing/Cs/O

L8: Cs sing/Cd/O

L8: Cs sing/Ct/O

L8: Cs sing/Cb/O

L7: Cs singOO

L5: Cs trip 38 -0.118072 0.152750 0.037583

L6: Cs tripH2 38 -0.118072 0.152750 0.037583

L6: Cs tripRH

L7: Cs tripCH

L8: Cs trip/Cs/H

L8: Cs trip/Cd/H

L8: Cs trip/Ct/H

L8: Cs trip/Cb/H

L7: Cs tripOH

L6: Cs tripRR

L7: Cs tripCC

L8: Cs trip/Cs/Cs

L8: Cs trip/Cs/Cd

L8: Cs trip/Cs/Ct

L8: Cs trip/Cs/Cb

L8: Cs trip/Cd/Cd

L8: Cs trip/Cd/Ct

L8: Cs trip/Cd/Cb

L8: Cs trip/Ct/Ct

L8: Cs trip/Ct/Cb

L8: Cs trip/Cb/Cb

L7: Cs tripCO

L8: Cs trip/Cs/O

L8: Cs trip/Cd/O

L8: Cs trip/Ct/O

L8: Cs trip/Cb/O

L7: Cs tripOO

L4: Cdjj

L5: Cd singletR

L6: Cd singletC

L6: Cd singletO

L5: Cd tripletR

L6: Cd tripletC

Continued on next page

117

Table B.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L6: Cd tripletO

L3: Cjjj

L4: C doubletR

L4: C quartetR

L3: Cjjjj

L4: C quintet

L4: C triplet

118

B.6 List of test reactions

Table B.3: 1393 hydrogen abstraction reactions used to test the group estimates cou-pled with the automated transition state algorithm. The reactants andproducts are provided as SMILES strings. Transition states that werefound and validated are available in CML format.

Reactions Found[CH2]C(C)C(=O)C(C)C + [O]O↔ CC(C)C(=O)C(C)C + [O][O] No

C[C](C)C(=O)C(C)C + [O]O↔ CC(C)C(=O)C(C)C + [O][O] No

[CH2]C(C)C(=O)C(C)C + CC(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C[C](C)C(=O)C(C)C No

[CH2]C(C)C(=O)C(C)C + CC(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)C + CC(C)C(=O)C(C)(C)O[O] Yes

C[C](C)C(=O)C(C)C + CC(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)C + CC(C)C(=O)C(C)(C)O[O] Yes

[CH2]C(C)C(=O)C(C)C + CC(C)C(=O)C(C)COO↔ CC(C)C(=O)C(C)C + CC(C)C(=O)C(C)CO[O] Yes

C[C](C)C(=O)C(C)C + CC(C)C(=O)C(C)COO↔ CC(C)C(=O)C(C)C + CC(C)C(=O)C(C)CO[O] Yes

CC(C)C(=O)C(C)(C)O[O] + [O]O↔ CC(C)C(=O)C(C)(C)OO + [O][O] Yes

CC(C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)CO[O]↔ CC(C)C(=O)C(C)COO + CC(C)C(=O)C(C)(C)O[O] No

CC(C)C(=O)C(C)CO[O] + [O]O↔ CC(C)C(=O)C(C)COO + [O][O] Yes

CC(C)C(=O)C(C)(C)OO + [H]↔ [H][H] + CC(C)C(=O)C(C)(C)O[O] No

CC(C)C(=O)C(C)COO + [H]↔ [H][H] + CC(C)C(=O)C(C)CO[O] Yes

CC(C)C(=O)C(C)C + [O]↔ [OH] + [CH2]C(C)C(=O)C(C)C No

CC(C)C(=O)C(C)C + [O]↔ [OH] + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + [O]↔ [OH] + CC(C)C(=O)C(C)(C)O[O] No

CC(C)C(=O)C(C)COO + [O]↔ [OH] + CC(C)C(=O)C(C)CO[O] No

CC(C)C(=O)C(C)(C)OO + [OH]↔ O + CC(C)C(=O)C(C)(C)O[O] No

CC(C)C(=O)C(C)COO + [OH]↔ O + CC(C)C(=O)C(C)CO[O] No

CC(C)C(=O)C(C)(C)OO + [O]O↔ OO + CC(C)C(=O)C(C)(C)O[O] No

CC(C)C(=O)C(C)COO + [O]O↔ OO + CC(C)C(=O)C(C)CO[O] No

[CH2]C(C)C(=O)C(C)C + C#CC↔ CC(C)C(=O)C(C)C + C#C[CH2] No

CC(C)C(=O)C(C)C + C#C[CH2]↔ C#CC + C[C](C)C(=O)C(C)C No

CC(C)C(=O)C(C)(C)OO + C#C[CH2]↔ C#CC + CC(C)C(=O)C(C)(C)O[O] No

CC(C)C(=O)C(C)COO + C#C[CH2]↔ C#CC + CC(C)C(=O)C(C)CO[O] Yes

[H] + C#CC↔ [H][H] + C#C[CH2] Yes

[OH] + C#CC↔ O + C#C[CH2] Yes

[O]O + C#C[CH2]↔ C#CC + [O][O] No

OO + C#C[CH2]↔ C#CC + [O]O Yes

[CH2]C(C)C(=O)C(C)C + C=C=C↔ CC(C)C(=O)C(C)C + [CH]=C=C No

CC(C)C(=O)C(C)C + [CH]=C=C↔ C=C=C + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + [CH]=C=C↔ C=C=C + CC(C)C(=O)C(C)(C)O[O] No

CC(C)C(=O)C(C)COO + [CH]=C=C↔ C=C=C + CC(C)C(=O)C(C)CO[O] No

[H] + C=C=C↔ [H][H] + [CH]=C=C No

[OH] + C=C=C↔ O + [CH]=C=C No

[O]O + [CH]=C=C↔ C=C=C + [O][O] No

OO + [CH]=C=C↔ C=C=C + [O]O No

[c]1ccccc1 + [O]O↔ c1ccccc1 + [O][O] No

[c]1ccccc1 + CC(C)C(=O)C(C)C↔ c1ccccc1 + C[C](C)C(=O)C(C)C No

[c]1ccccc1 + CC(C)C(=O)C(C)C↔ c1ccccc1 + [CH2]C(C)C(=O)C(C)C Yes

[c]1ccccc1 + CC(C)C(=O)C(C)(C)OO↔ c1ccccc1 + CC(C)C(=O)C(C)(C)O[O] Yes

[c]1ccccc1 + CC(C)C(=O)C(C)COO↔ c1ccccc1 + CC(C)C(=O)C(C)CO[O] No

Continued on next page

119

Table B.3 – continued from previous pageReactions Found[c]1ccccc1 + [H][H]↔ c1ccccc1 + [H] Yes

c1ccccc1 + [OH]↔ O + [c]1ccccc1 Yes

[c]1ccccc1 + OO↔ c1ccccc1 + [O]O No

[c]1ccccc1 + C#CC↔ c1ccccc1 + C#C[CH2] Yes

[c]1ccccc1 + C=C=C↔ c1ccccc1 + [CH]=C=C Yes

[CH2]C(C)C(=O)C(C)C + C=CC↔ CC(C)C(=O)C(C)C + [CH2]C=C No

C[C](C)C(=O)C(C)C + C=CC↔ CC(C)C(=O)C(C)C + [CH2]C=C Yes

CC(C)C(=O)C(C)(C)OO + [CH2]C=C↔ C=CC + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + [CH2]C=C↔ C=CC + CC(C)C(=O)C(C)CO[O] Yes

OO + [CH2]C=C↔ C=CC + [O]O Yes

[c]1ccccc1 + C=CC↔ c1ccccc1 + [CH2]C=C No

C=C1C=C[CH]C1 + [O]O↔ C=C1C=CCC1 + [O][O] Yes

C=C1[CH]CC=C1 + [O]O↔ C=C1C=CCC1 + [O][O] Yes

C=C1C=CCC1 + C[C](C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + C[C](C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C=C1[CH]CC=C1 No

C=C1C=CCC1 + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C=C1[CH]CC=C1 Yes

C=C1C=CCC1 + CC(C)C(=O)C(C)(C)O[O]↔ CC(C)C(=O)C(C)(C)OO + C=C1C=C[CH]C1 Yes

C=C1[CH]CC=C1 + CC(C)C(=O)C(C)(C)OO↔ C=C1C=CCC1 + CC(C)C(=O)C(C)(C)O[O] Yes

C=C1C=CCC1 + CC(C)C(=O)C(C)CO[O]↔ CC(C)C(=O)C(C)COO + C=C1C=C[CH]C1 Yes

C=C1[CH]CC=C1 + CC(C)C(=O)C(C)COO↔ C=C1C=CCC1 + CC(C)C(=O)C(C)CO[O] Yes

C=C1C=CCC1 + [H]↔ [H][H] + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + [H]↔ [H][H] + C=C1[CH]CC=C1 Yes

C=C1C=CCC1 + [O]↔ [OH] + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + [O]↔ [OH] + C=C1[CH]CC=C1 No

C=C1C=CCC1 + [OH]↔ O + C=C1C=C[CH]C1 No

C=C1C=CCC1 + [OH]↔ O + C=C1[CH]CC=C1 No

C=C1C=CCC1 + [O]O↔ OO + C=C1C=C[CH]C1 No

C=C1C=CCC1 + [O]O↔ OO + C=C1[CH]CC=C1 No

C=C1C=CCC1 + C#C[CH2]↔ C#CC + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + C#C[CH2]↔ C#CC + C=C1[CH]CC=C1 Yes

C=C1C=CCC1 + [CH]=C=C↔ C=C=C + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + [CH]=C=C↔ C=C=C + C=C1[CH]CC=C1 No

C=C1C=CCC1 + [c]1ccccc1↔ c1ccccc1 + C=C1C=C[CH]C1 No

C=C1C=CCC1 + [c]1ccccc1↔ c1ccccc1 + C=C1[CH]CC=C1 Yes

C=C1C=CCC1 + [CH2]C=C↔ C=CC + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + [CH2]C=C↔ C=CC + C=C1[CH]CC=C1 Yes

C=C1[CH]C=CC1 + [O]O↔ C=C1CC=CC1 + [O][O] Yes

C=C1CC=CC1 + C[C](C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C=C1[CH]C=CC1 Yes

C=C1CC=CC1 + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C=C1[CH]C=CC1 No

C=C1CC=CC1 + CC(C)C(=O)C(C)(C)O[O]↔ CC(C)C(=O)C(C)(C)OO + C=C1[CH]C=CC1 Yes

C=C1CC=CC1 + CC(C)C(=O)C(C)CO[O]↔ CC(C)C(=O)C(C)COO + C=C1[CH]C=CC1 No

C=C1CC=CC1 + [H]↔ [H][H] + C=C1[CH]C=CC1 No

C=C1CC=CC1 + [O]↔ [OH] + C=C1[CH]C=CC1 Yes

C=C1CC=CC1 + [OH]↔ O + C=C1[CH]C=CC1 No

C=C1CC=CC1 + [O]O↔ OO + C=C1[CH]C=CC1 No

C=C1CC=CC1 + C#C[CH2]↔ C#CC + C=C1[CH]C=CC1 No

C=C1CC=CC1 + [CH]=C=C↔ C=C=C + C=C1[CH]C=CC1 Yes

Continued on next page

120

Table B.3 – continued from previous pageReactions FoundC=C1CC=CC1 + [c]1ccccc1↔ c1ccccc1 + C=C1[CH]C=CC1 No

C=C1CC=CC1 + [CH2]C=C↔ C=CC + C=C1[CH]C=CC1 Yes

C=C1C=CCC1 + C=C1[CH]CC=C1↔ C=C1C=CCC1 + C=C1C=C[CH]C1 No

C=C1CC=CC1 + C=C1[CH]CC=C1↔ C=C1C=CCC1 + C=C1[CH]C=CC1 No

C=C1C=C[CH]C1 + C=C1CC=CC1↔ C=C1C=CCC1 + C=C1[CH]C=CC1 No

CC(C)C(=O)C(C)C + [CH]=C↔ C=C + [CH2]C(C)C(=O)C(C)C No

CC(C)C(=O)C(C)C + [CH]=C↔ C=C + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + [CH]=C↔ C=C + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + [CH]=C↔ C=C + CC(C)C(=O)C(C)CO[O] No

[H][H] + [CH]=C↔ C=C + [H] Yes

[OH] + C=C↔ O + [CH]=C Yes

[O]O + [CH]=C↔ C=C + [O][O] Yes

OO + [CH]=C↔ C=C + [O]O No

[c]1ccccc1 + C=C↔ c1ccccc1 + [CH]=C No

C=C1C=CCC1 + [CH]=C↔ C=C + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + [CH]=C↔ C=C + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + [CH]=C↔ C=C + C=C1[CH]C=CC1 Yes

C=C=C + [O]↔ [OH] + [CH]=C=C Yes

C=C=C + C#C[CH2]↔ C#CC + [CH]=C=C Yes

[CH]=C=C + C=CC↔ C=C=C + [CH2]C=C No

C=C=C + [CH]=C↔ C=C + [CH]=C=C No

C#CC + [O]↔ [OH] + C#C[CH2] Yes

C#C[CH2] + C=CC↔ C#CC + [CH2]C=C Yes

C#CC + [CH]=C↔ C=C + C#C[CH2] No

[C]#C + [O]O↔ C#C + [O][O] Yes

[C]#C + CC(C)C(=O)C(C)C↔ C#C + C[C](C)C(=O)C(C)C No

[C]#C + CC(C)C(=O)C(C)C↔ C#C + [CH2]C(C)C(=O)C(C)C No

[C]#C + CC(C)C(=O)C(C)(C)OO↔ C#C + CC(C)C(=O)C(C)(C)O[O] No

[C]#C + CC(C)C(=O)C(C)COO↔ C#C + CC(C)C(=O)C(C)CO[O] No

[C]#C + [H][H]↔ C#C + [H] No

[C]#C + O↔ C#C + [OH] No

[C]#C + OO↔ C#C + [O]O No

[C]#C + C#CC↔ C#C + C#C[CH2] No

[C]#C + C=C=C↔ C#C + [CH]=C=C No

[C]#C + c1ccccc1↔ C#C + [c]1ccccc1 No

[C]#C + C=CC↔ C#C + [CH2]C=C Yes

[C]#C + C=C1C=CCC1↔ C#C + C=C1[CH]CC=C1 No

[C]#C + C=C1CC=CC1↔ C#C + C=C1[CH]C=CC1 Yes

[C]#C + C=C1C=CCC1↔ C#C + C=C1C=C[CH]C1 No

[C]#C + C=C↔ C#C + [CH]=C No

CC(C)C(=O)C(C)C + [CH]=CC↔ C=CC + [CH2]C(C)C(=O)C(C)C No

CC(C)C(=O)C(C)C + [CH]=CC↔ C=CC + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + [CH]=CC↔ C=CC + CC(C)C(=O)C(C)(C)O[O] No

CC(C)C(=O)C(C)COO + [CH]=CC↔ C=CC + CC(C)C(=O)C(C)CO[O] Yes

[O]O + [CH]=CC↔ C=CC + [O][O] No

OO + [CH]=CC↔ C=CC + [O]O No

[c]1ccccc1 + C=CC↔ c1ccccc1 + [CH]=CC No

C=C1C=CCC1 + [CH]=CC↔ C=CC + C=C1C=C[CH]C1 Yes

Continued on next page

121

Table B.3 – continued from previous pageReactions FoundC=C1C=CCC1 + [CH]=CC↔ C=CC + C=C1[CH]CC=C1 No

C=C1CC=CC1 + [CH]=CC↔ C=CC + C=C1[CH]C=CC1 No

C=C=C + [CH]=CC↔ C=CC + [CH]=C=C No

C#CC + [CH]=CC↔ C=CC + C#C[CH2] Yes

[C]#C + C=CC↔ C#C + [CH]=CC No

CC(C)C(=O)C(C)C + C=[C]C↔ C=CC + [CH2]C(C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)C + C=[C]C↔ C=CC + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + C=[C]C↔ C=CC + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + C=[C]C↔ C=CC + CC(C)C(=O)C(C)CO[O] No

[O]O + C=[C]C↔ C=CC + [O][O] No

OO + C=[C]C↔ C=CC + [O]O No

[c]1ccccc1 + C=CC↔ c1ccccc1 + C=[C]C No

C=C1C=CCC1 + C=[C]C↔ C=CC + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + C=[C]C↔ C=CC + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + C=[C]C↔ C=CC + C=C1[CH]C=CC1 No

C=C=C + C=[C]C↔ C=CC + [CH]=C=C Yes

C#CC + C=[C]C↔ C=CC + C#C[CH2] Yes

[C]#C + C=CC↔ C#C + C=[C]C No

CC(C)C(=O)C(C)(C)OO + [CH3]↔ C + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + [CH3]↔ C + CC(C)C(=O)C(C)CO[O] Yes

[H] + C↔ [H][H] + [CH3] No

[OH] + C↔ O + [CH3] Yes

[O]O + [CH3]↔ C + [O][O] No

OO + [CH3]↔ C + [O]O No

[c]1ccccc1 + C↔ c1ccccc1 + [CH3] No

C=C1C=CCC1 + [CH3]↔ C + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + [CH3]↔ C + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + [CH3]↔ C + C=C1[CH]C=CC1 Yes

[C]#C + C↔ C#C + [CH3] Yes

CC(C)C(=O)C(C)C + [CH2]CC↔ CCC + [CH2]C(C)C(=O)C(C)C No

CC(C)C(=O)C(C)C + [CH2]CC↔ CCC + C[C](C)C(=O)C(C)C No

CC(C)C(=O)C(C)(C)OO + [CH2]CC↔ CCC + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + [CH2]CC↔ CCC + CC(C)C(=O)C(C)CO[O] Yes

OO + [CH2]CC↔ CCC + [O]O Yes

[c]1ccccc1 + CCC↔ c1ccccc1 + [CH2]CC No

C=C1C=CCC1 + [CH2]CC↔ CCC + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + [CH2]CC↔ CCC + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + [CH2]CC↔ CCC + C=C1[CH]C=CC1 Yes

C=C=C + [CH2]CC↔ CCC + [CH]=C=C No

C#CC + [CH2]CC↔ CCC + C#C[CH2] Yes

[C]#C + CCC↔ C#C + [CH2]CC Yes

[CH2]C(C)C(=O)C(C)C + CCC↔ CC(C)C(=O)C(C)C + C[CH]C No

CC(C)C(=O)C(C)C + C[CH]C↔ CCC + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + C[CH]C↔ CCC + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + C[CH]C↔ CCC + CC(C)C(=O)C(C)CO[O] Yes

OO + C[CH]C↔ CCC + [O]O Yes

[c]1ccccc1 + CCC↔ c1ccccc1 + C[CH]C No

C=C1C=CCC1 + C[CH]C↔ CCC + C=C1C=C[CH]C1 No

Continued on next page

122

Table B.3 – continued from previous pageReactions FoundC=C1C=CCC1 + C[CH]C↔ CCC + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + C[CH]C↔ CCC + C=C1[CH]C=CC1 Yes

C=C=C + C[CH]C↔ CCC + [CH]=C=C Yes

C#CC + C[CH]C↔ CCC + C#C[CH2] Yes

[C]#C + CCC↔ C#C + C[CH]C Yes

C=CC + [O]↔ [OH] + [CH2]C=C No

[CH]=CC + C=CC↔ C=CC + [CH2]C=C No

C=[C]C + C=CC↔ C=CC + [CH2]C=C No

[CH]=CC + C=C↔ C=CC + [CH]=C No

C=CC + [CH]=C↔ C=C + C=[C]C Yes

C=CC + [CH]=C↔ C=C + [CH2]C=C Yes

C=CC + [CH]=CC↔ C=CC + C=[C]C Yes

[CH]=CC + CCC↔ C=CC + [CH2]CC Yes

C=[C]C + CCC↔ C=CC + [CH2]CC Yes

C=CC + [CH2]CC↔ CCC + [CH2]C=C Yes

[CH]=CC + CCC↔ C=CC + C[CH]C Yes

C=[C]C + CCC↔ C=CC + C[CH]C Yes

C=CC + C[CH]C↔ CCC + [CH2]C=C Yes

[CH]=C + C↔ C=C + [CH3] Yes

[CH]=C + CCC↔ C=C + [CH2]CC Yes

[CH]=C + CCC↔ C=C + C[CH]C Yes

[CH]=C=O + [O]O↔ C=C=O + [O][O] Yes

[CH]=C=O + CC(C)C(=O)C(C)C↔ C=C=O + C[C](C)C(=O)C(C)C No

[CH]=C=O + CC(C)C(=O)C(C)C↔ C=C=O + [CH2]C(C)C(=O)C(C)C Yes

[CH]=C=O + CC(C)C(=O)C(C)(C)OO↔ C=C=O + CC(C)C(=O)C(C)(C)O[O] Yes

[CH]=C=O + CC(C)C(=O)C(C)COO↔ C=C=O + CC(C)C(=O)C(C)CO[O] Yes

[CH]=C=O + [H][H]↔ C=C=O + [H] Yes

C=C=O + [OH]↔ O + [CH]=C=O Yes

[CH]=C=O + OO↔ C=C=O + [O]O Yes

[CH]=C=O + C#CC↔ C=C=O + C#C[CH2] Yes

[CH]=C=O + C=C=C↔ C=C=O + [CH]=C=C Yes

C=C=O + [c]1ccccc1↔ c1ccccc1 + [CH]=C=O No

[CH]=C=O + C=CC↔ C=C=O + [CH2]C=C Yes

[CH]=C=O + C=C1C=CCC1↔ C=C=O + C=C1[CH]CC=C1 Yes

[CH]=C=O + C=C1CC=CC1↔ C=C=O + C=C1[CH]C=CC1 Yes

[CH]=C=O + C=C1C=CCC1↔ C=C=O + C=C1C=C[CH]C1 Yes

C=C=O + [CH]=C↔ C=C + [CH]=C=O Yes

C=C=O + [CH]=CC↔ C=CC + [CH]=C=O Yes

C=C=O + C=[C]C↔ C=CC + [CH]=C=O Yes

[CH]=C=O + C↔ C=C=O + [CH3] Yes

[CH]=C=O + CCC↔ C=C=O + [CH2]CC Yes

[CH]=C=O + CCC↔ C=C=O + C[CH]C Yes

[CH]=O + [O]O↔ C=O + [O][O] Yes

C=O + C[C](C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH]=O Yes

C=O + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH]=O Yes

[CH]=O + CC(C)C(=O)C(C)(C)OO↔ C=O + CC(C)C(=O)C(C)(C)O[O] Yes

[CH]=O + CC(C)C(=O)C(C)COO↔ C=O + CC(C)C(=O)C(C)CO[O] Yes

C=O + [H]↔ [H][H] + [CH]=O Yes

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123

Table B.3 – continued from previous pageReactions FoundC=O + [O]↔ [OH] + [CH]=O Yes

C=O + [OH]↔ O + [CH]=O No

[CH]=O + OO↔ C=O + [O]O No

C=O + C#C[CH2]↔ C#CC + [CH]=O Yes

C=O + [CH]=C=C↔ C=C=C + [CH]=O Yes

C=O + [c]1ccccc1↔ c1ccccc1 + [CH]=O No

C=O + [CH2]C=C↔ C=CC + [CH]=O Yes

[CH]=O + C=C1C=CCC1↔ C=O + C=C1[CH]CC=C1 Yes

[CH]=O + C=C1CC=CC1↔ C=O + C=C1[CH]C=CC1 Yes

[CH]=O + C=C1C=CCC1↔ C=O + C=C1C=C[CH]C1 Yes

C=O + [CH]=C↔ C=C + [CH]=O Yes

C=O + [CH]=CC↔ C=CC + [CH]=O Yes

C=O + C=[C]C↔ C=CC + [CH]=O Yes

C=O + [CH3]↔ C + [CH]=O Yes

C=O + [CH2]CC↔ CCC + [CH]=O Yes

C=O + C[CH]C↔ CCC + [CH]=O Yes

[CH2]O + [O]O↔ CO + [O][O] Yes

[CH2]O + CC(C)C(=O)C(C)C↔ CO + C[C](C)C(=O)C(C)C No

CO + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH2]O Yes

[CH2]O + CC(C)C(=O)C(C)(C)OO↔ CO + CC(C)C(=O)C(C)(C)O[O] Yes

[CH2]O + CC(C)C(=O)C(C)COO↔ CO + CC(C)C(=O)C(C)CO[O] Yes

CO + [H]↔ [H][H] + [CH2]O Yes

CO + [O]↔ [OH] + [CH2]O Yes

CO + [OH]↔ O + [CH2]O Yes

[CH2]O + C#CC↔ CO + C#C[CH2] No

[CH2]O + C=C=C↔ CO + [CH]=C=C Yes

CO + [c]1ccccc1↔ c1ccccc1 + [CH2]O Yes

[CH2]O + C=CC↔ CO + [CH2]C=C Yes

[CH2]O + C=C1C=CCC1↔ CO + C=C1[CH]CC=C1 Yes

[CH2]O + C=C1CC=CC1↔ CO + C=C1[CH]C=CC1 Yes

[CH2]O + C=C1C=CCC1↔ CO + C=C1C=C[CH]C1 Yes

CO + [CH]=C↔ C=C + [CH2]O Yes

CO + [CH]=CC↔ C=CC + [CH2]O Yes

CO + C=[C]C↔ C=CC + [CH2]O Yes

CO + [CH3]↔ C + [CH2]O Yes

CO + [CH2]CC↔ CCC + [CH2]O Yes

CO + C[CH]C↔ CCC + [CH2]O Yes

CC(C)C(=O)C(C)C + [CH2]↔ [CH3] + [CH2]C(C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)C + [CH2]↔ [CH3] + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + [CH2]↔ [CH3] + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + [CH2]↔ [CH3] + CC(C)C(=O)C(C)CO[O] Yes

[H][H] + [CH2]↔ [CH3] + [H] Yes

[O]O + [CH2]↔ [CH3] + [O][O] Yes

OO + [CH2]↔ [CH3] + [O]O No

C=C1C=CCC1 + [CH2]↔ [CH3] + C=C1C=C[CH]C1 No

C=C1C=CCC1 + [CH2]↔ [CH3] + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + [CH2]↔ [CH3] + C=C1[CH]C=CC1 Yes

C=C=C + [CH2]↔ [CH3] + [CH]=C=C Yes

Continued on next page

124

Table B.3 – continued from previous pageReactions FoundC#CC + [CH2]↔ [CH3] + C#C[CH2] Yes

C=CC + [CH2]↔ [CH3] + C=[C]C Yes

C=CC + [CH2]↔ [CH3] + [CH2]C=C Yes

C=C + [CH2]↔ [CH3] + [CH]=C Yes

C=C=O + [CH2]↔ [CH3] + [CH]=C=O Yes

C=O + [CH2]↔ [CH3] + [CH]=O No

CO + [CH2]↔ [CH3] + [CH2]O Yes

C + [O]↔ [OH] + [CH3] No

C + [CH2]↔ [CH3] + [CH3] Yes

[CH2]CO + [O]O↔ CCO + [O][O] No

C[CH]O + [O]O↔ CCO + [O][O] No

CC[O] + [O]O↔ CCO + [O][O] No

[CH2]CO + CC(C)C(=O)C(C)C↔ CCO + C[C](C)C(=O)C(C)C No

C[CH]O + CC(C)C(=O)C(C)C↔ CCO + C[C](C)C(=O)C(C)C Yes

CC[O] + CC(C)C(=O)C(C)C↔ CCO + C[C](C)C(=O)C(C)C No

[CH2]CO + CC(C)C(=O)C(C)C↔ CCO + [CH2]C(C)C(=O)C(C)C No

CCO + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C[CH]O Yes

CC[O] + CC(C)C(=O)C(C)C↔ CCO + [CH2]C(C)C(=O)C(C)C Yes

[CH2]CO + CC(C)C(=O)C(C)(C)OO↔ CCO + CC(C)C(=O)C(C)(C)O[O] Yes

C[CH]O + CC(C)C(=O)C(C)(C)OO↔ CCO + CC(C)C(=O)C(C)(C)O[O] Yes

CC[O] + CC(C)C(=O)C(C)(C)OO↔ CCO + CC(C)C(=O)C(C)(C)O[O] Yes

[CH2]CO + CC(C)C(=O)C(C)COO↔ CCO + CC(C)C(=O)C(C)CO[O] No

C[CH]O + CC(C)C(=O)C(C)COO↔ CCO + CC(C)C(=O)C(C)CO[O] Yes

CC[O] + CC(C)C(=O)C(C)COO↔ CCO + CC(C)C(=O)C(C)CO[O] Yes

CCO + [O]↔ [OH] + [CH2]CO Yes

CCO + [O]↔ [OH] + C[CH]O Yes

CCO + [OH]↔ O + [CH2]CO No

CCO + [OH]↔ O + CC[O] No

[CH2]CO + OO↔ CCO + [O]O No

CC[O] + OO↔ CCO + [O]O Yes

[CH2]CO + C#CC↔ CCO + C#C[CH2] Yes

C[CH]O + C#CC↔ CCO + C#C[CH2] Yes

CC[O] + C#CC↔ CCO + C#C[CH2] Yes

[CH2]CO + C=C=C↔ CCO + [CH]=C=C Yes

C[CH]O + C=C=C↔ CCO + [CH]=C=C Yes

CC[O] + C=C=C↔ CCO + [CH]=C=C Yes

CCO + [c]1ccccc1↔ c1ccccc1 + [CH2]CO Yes

CCO + [c]1ccccc1↔ c1ccccc1 + C[CH]O Yes

CCO + [c]1ccccc1↔ c1ccccc1 + CC[O] Yes

[CH2]CO + C=CC↔ CCO + [CH2]C=C No

C[CH]O + C=CC↔ CCO + [CH2]C=C Yes

CC[O] + C=CC↔ CCO + [CH2]C=C Yes

[CH2]CO + C=C1C=CCC1↔ CCO + C=C1[CH]CC=C1 No

C[CH]O + C=C1C=CCC1↔ CCO + C=C1[CH]CC=C1 Yes

CC[O] + C=C1C=CCC1↔ CCO + C=C1[CH]CC=C1 Yes

[CH2]CO + C=C1CC=CC1↔ CCO + C=C1[CH]C=CC1 No

C[CH]O + C=C1CC=CC1↔ CCO + C=C1[CH]C=CC1 Yes

CC[O] + C=C1CC=CC1↔ CCO + C=C1[CH]C=CC1 Yes

Continued on next page

125

Table B.3 – continued from previous pageReactions Found[CH2]CO + C=C1C=CCC1↔ CCO + C=C1C=C[CH]C1 Yes

C[CH]O + C=C1C=CCC1↔ CCO + C=C1C=C[CH]C1 Yes

CC[O] + C=C1C=CCC1↔ CCO + C=C1C=C[CH]C1 Yes

CCO + [CH]=C↔ C=C + [CH2]CO Yes

CCO + [CH]=C↔ C=C + C[CH]O Yes

CCO + [CH]=C↔ C=C + CC[O] No

CCO + [CH]=CC↔ C=CC + [CH2]CO Yes

CCO + [CH]=CC↔ C=CC + C[CH]O Yes

CCO + [CH]=CC↔ C=CC + CC[O] No

CCO + C=[C]C↔ C=CC + [CH2]CO No

CCO + C=[C]C↔ C=CC + C[CH]O Yes

CCO + C=[C]C↔ C=CC + CC[O] Yes

[CH2]CO + CCC↔ CCO + [CH2]CC No

CCO + [CH2]CC↔ CCC + C[CH]O Yes

CC[O] + CCC↔ CCO + [CH2]CC Yes

[CH2]CO + CCC↔ CCO + C[CH]C Yes

CCO + C[CH]C↔ CCC + C[CH]O Yes

CC[O] + CCC↔ CCO + C[CH]C Yes

CCO + [CH2]↔ [CH3] + [CH2]CO No

CCO + [CH2]↔ [CH3] + C[CH]O Yes

CCO + [CH2]↔ [CH3] + CC[O] Yes

[C]#C + CCO↔ C#C + C[CH]O No

[CH]=C=O + CCO↔ C=C=O + C[CH]O No

C=O + C[CH]O↔ CCO + [CH]=O No

[CH2]O + CCO↔ CO + C[CH]O Yes

[CH2]CO + CCO↔ CCO + C[CH]O Yes

CC[O] + CCO↔ CCO + C[CH]O Yes

[C]#C + CCO↔ C#C + [CH2]CO Yes

[CH]=C=O + CCO↔ C=C=O + [CH2]CO Yes

C=O + [CH2]CO↔ CCO + [CH]=O Yes

CO + [CH2]CO↔ CCO + [CH2]O Yes

CC[O] + CCO↔ CCO + [CH2]CO Yes

[C]#C + CCO↔ C#C + CC[O] Yes

[CH]=C=O + CCO↔ C=C=O + CC[O] No

C=O + CC[O]↔ CCO + [CH]=O Yes

CO + CC[O]↔ CCO + [CH2]O Yes

[CH2]C=O + CC(C)C(=O)C(C)C↔ CC=O + C[C](C)C(=O)C(C)C No

C[C]=O + CC(C)C(=O)C(C)C↔ CC=O + C[C](C)C(=O)C(C)C Yes

CC=O + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH2]C=O Yes

CC=O + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C[C]=O Yes

[CH2]C=O + CC(C)C(=O)C(C)(C)OO↔ CC=O + CC(C)C(=O)C(C)(C)O[O] Yes

C[C]=O + CC(C)C(=O)C(C)(C)OO↔ CC=O + CC(C)C(=O)C(C)(C)O[O] Yes

[CH2]C=O + CC(C)C(=O)C(C)COO↔ CC=O + CC(C)C(=O)C(C)CO[O] Yes

C[C]=O + CC(C)C(=O)C(C)COO↔ CC=O + CC(C)C(=O)C(C)CO[O] Yes

CC=O + [H]↔ [H][H] + [CH2]C=O No

CC=O + [O]↔ [OH] + [CH2]C=O Yes

[CH2]C=O + C#CC↔ CC=O + C#C[CH2] Yes

CC=O + C#C[CH2]↔ C#CC + C[C]=O Yes

Continued on next page

126

Table B.3 – continued from previous pageReactions Found[CH2]C=O + C=C=C↔ CC=O + [CH]=C=C Yes

CC=O + [CH]=C=C↔ C=C=C + C[C]=O No

CC=O + [c]1ccccc1↔ c1ccccc1 + [CH2]C=O No

CC=O + [c]1ccccc1↔ c1ccccc1 + C[C]=O Yes

[CH2]C=O + C=CC↔ CC=O + [CH2]C=C Yes

C[C]=O + C=CC↔ CC=O + [CH2]C=C Yes

[CH2]C=O + C=C1C=CCC1↔ CC=O + C=C1[CH]CC=C1 Yes

C[C]=O + C=C1C=CCC1↔ CC=O + C=C1[CH]CC=C1 Yes

[CH2]C=O + C=C1CC=CC1↔ CC=O + C=C1[CH]C=CC1 Yes

C[C]=O + C=C1CC=CC1↔ CC=O + C=C1[CH]C=CC1 Yes

[CH2]C=O + C=C1C=CCC1↔ CC=O + C=C1C=C[CH]C1 Yes

C[C]=O + C=C1C=CCC1↔ CC=O + C=C1C=C[CH]C1 Yes

CC=O + [CH]=C↔ C=C + [CH2]C=O Yes

CC=O + [CH]=C↔ C=C + C[C]=O No

CC=O + [CH]=CC↔ C=CC + [CH2]C=O Yes

CC=O + [CH]=CC↔ C=CC + C[C]=O Yes

CC=O + C=[C]C↔ C=CC + [CH2]C=O Yes

CC=O + C=[C]C↔ C=CC + C[C]=O Yes

CC=O + [CH2]CC↔ CCC + [CH2]C=O Yes

CC=O + [CH2]CC↔ CCC + C[C]=O Yes

CC=O + C[CH]C↔ CCC + [CH2]C=O Yes

CC=O + C[CH]C↔ CCC + C[C]=O Yes

CC=O + [CH2]↔ [CH3] + [CH2]C=O Yes

CC=O + [CH2]↔ [CH3] + C[C]=O Yes

[CH2]C=O + CCO↔ CC=O + C[CH]O No

CC=O + C[CH]O↔ CCO + C[C]=O Yes

CC=O + [CH2]CO↔ CCO + [CH2]C=O Yes

CC=O + [CH2]CO↔ CCO + C[C]=O Yes

CC=O + CC[O]↔ CCO + [CH2]C=O Yes

CC=O + CC[O]↔ CCO + C[C]=O Yes

[C]#C + CC=O↔ C#C + C[C]=O Yes

[CH]=C=O + CC=O↔ C=C=O + C[C]=O No

C=O + C[C]=O↔ CC=O + [CH]=O No

[CH2]O + CC=O↔ CO + C[C]=O Yes

[CH2]C=O + CC=O↔ CC=O + C[C]=O Yes

[C]#C + CC=O↔ C#C + [CH2]C=O Yes

[CH]=C=O + CC=O↔ C=C=O + [CH2]C=O No

C=O + [CH2]C=O↔ CC=O + [CH]=O Yes

CO + [CH2]C=O↔ CC=O + [CH2]O Yes

[CH2]C(C)C(=O)C(C)C + CC↔ CC(C)C(=O)C(C)C + C[CH2] Yes

CC(C)C(=O)C(C)C + C[CH2]↔ CC + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + C[CH2]↔ CC + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + C[CH2]↔ CC + CC(C)C(=O)C(C)CO[O] Yes

[H] + CC↔ [H][H] + C[CH2] Yes

[OH] + CC↔ O + C[CH2] Yes

OO + C[CH2]↔ CC + [O]O No

[c]1ccccc1 + CC↔ c1ccccc1 + C[CH2] No

C=C1C=CCC1 + C[CH2]↔ CC + C=C1C=C[CH]C1 No

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127

Table B.3 – continued from previous pageReactions FoundC=C1C=CCC1 + C[CH2]↔ CC + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + C[CH2]↔ CC + C=C1[CH]C=CC1 Yes

C=C=C + C[CH2]↔ CC + [CH]=C=C Yes

C#CC + C[CH2]↔ CC + C#C[CH2] Yes

[C]#C + CC↔ C#C + C[CH2] Yes

[CH]=CC + CC↔ C=CC + C[CH2] No

C=[C]C + CC↔ C=CC + C[CH2] Yes

C=CC + C[CH2]↔ CC + [CH2]C=C Yes

[CH]=C + CC↔ C=C + C[CH2] Yes

[CH]=C=O + CC↔ C=C=O + C[CH2] Yes

C=O + C[CH2]↔ CC + [CH]=O No

CO + C[CH2]↔ CC + [CH2]O Yes

[CH3] + CC↔ C + C[CH2] Yes

[CH2]CO + CC↔ CCO + C[CH2] Yes

CCO + C[CH2]↔ CC + C[CH]O Yes

CC[O] + CC↔ CCO + C[CH2] Yes

CC=O + C[CH2]↔ CC + [CH2]C=O Yes

CC=O + C[CH2]↔ CC + C[C]=O Yes

CC + [O]↔ [OH] + C[CH2] Yes

CC + [CH2]CC↔ CCC + C[CH2] Yes

C[CH2] + CCC↔ CC + C[CH]C Yes

CC + [CH2]↔ [CH3] + C[CH2] Yes

[C]#C + C=C=O↔ C#C + [CH]=C=O Yes

C=O + [CH]=C=O↔ C=C=O + [CH]=O No

CO + [CH]=C=O↔ C=C=O + [CH2]O Yes

[C]#C + CO↔ C#C + [CH2]O No

C=O + [CH2]O↔ CO + [CH]=O No

C=O + [C]#C↔ C#C + [CH]=O No

CCC + [O]↔ [OH] + [CH2]CC No

CCC + [O]↔ [OH] + C[CH]C Yes

CCC + [CH2]CC↔ CCC + C[CH]C Yes

CCC + [CH2]↔ [CH3] + [CH2]CC Yes

CCC + [CH2]↔ [CH3] + C[CH]C Yes

[CH2]C=C=O + [O]O↔ CC=C=O + [O][O] Yes

[CH2]C=C=O + CC(C)C(=O)C(C)C↔ CC=C=O + C[C](C)C(=O)C(C)C Yes

CC=C=O + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH2]C=C=O Yes

[CH2]C=C=O + CC(C)C(=O)C(C)(C)OO↔ CC=C=O + CC(C)C(=O)C(C)(C)O[O] Yes

[CH2]C=C=O + CC(C)C(=O)C(C)COO↔ CC=C=O + CC(C)C(=O)C(C)CO[O] Yes

[CH2]C=C=O + OO↔ CC=C=O + [O]O Yes

CC=C=O + C#C[CH2]↔ C#CC + [CH2]C=C=O Yes

[CH2]C=C=O + C=C=C↔ CC=C=O + [CH]=C=C Yes

CC=C=O + [c]1ccccc1↔ c1ccccc1 + [CH2]C=C=O Yes

[CH2]C=C=O + C=CC↔ CC=C=O + [CH2]C=C Yes

[CH2]C=C=O + C=C1C=CCC1↔ CC=C=O + C=C1[CH]CC=C1 Yes

[CH2]C=C=O + C=C1CC=CC1↔ CC=C=O + C=C1[CH]C=CC1 Yes

[CH2]C=C=O + C=C1C=CCC1↔ CC=C=O + C=C1C=C[CH]C1 Yes

CC=C=O + [CH]=C↔ C=C + [CH2]C=C=O Yes

CC=C=O + [CH]=CC↔ C=CC + [CH2]C=C=O No

Continued on next page

128

Table B.3 – continued from previous pageReactions FoundCC=C=O + C=[C]C↔ C=CC + [CH2]C=C=O No

CC=C=O + [CH3]↔ C + [CH2]C=C=O Yes

CC=C=O + [CH2]CC↔ CCC + [CH2]C=C=O No

CC=C=O + C[CH]C↔ CCC + [CH2]C=C=O Yes

CC=C=O + [CH2]↔ [CH3] + [CH2]C=C=O Yes

CC=C=O + C[CH]O↔ CCO + [CH2]C=C=O No

CC=C=O + [CH2]CO↔ CCO + [CH2]C=C=O Yes

CC=C=O + CC[O]↔ CCO + [CH2]C=C=O Yes

[CH2]C=C=O + CC=O↔ CC=C=O + C[C]=O No

CC=C=O + [CH2]C=O↔ CC=O + [CH2]C=C=O Yes

CC=C=O + C[CH2]↔ CC + [CH2]C=C=O Yes

CC=C=O + [CH]=C=O↔ C=C=O + [CH2]C=C=O Yes

CC=C=O + [CH2]O↔ CO + [CH2]C=C=O No

CC=C=O + [C]#C↔ C#C + [CH2]C=C=O Yes

[CH2]C=C=O + C=O↔ CC=C=O + [CH]=O No

[CH2]C(C)C(=O)C(C)C + C=CC=O↔ CC(C)C(=O)C(C)C + C=C[C]=O No

CC(C)C(=O)C(C)C + C=C[C]=O↔ C=CC=O + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + C=C[C]=O↔ C=CC=O + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + C=C[C]=O↔ C=CC=O + CC(C)C(=O)C(C)CO[O] Yes

OO + C=C[C]=O↔ C=CC=O + [O]O Yes

[c]1ccccc1 + C=CC=O↔ c1ccccc1 + C=C[C]=O No

C=C1C=CCC1 + C=C[C]=O↔ C=CC=O + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + C=C[C]=O↔ C=CC=O + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + C=C[C]=O↔ C=CC=O + C=C1[CH]C=CC1 Yes

[CH]=C=C + C=CC=O↔ C=C=C + C=C[C]=O Yes

C#C[CH2] + C=CC=O↔ C#CC + C=C[C]=O No

[C]#C + C=CC=O↔ C#C + C=C[C]=O No

[CH]=CC + C=CC=O↔ C=CC + C=C[C]=O No

C=[C]C + C=CC=O↔ C=CC + C=C[C]=O No

C=CC + C=C[C]=O↔ C=CC=O + [CH2]C=C Yes

[CH]=C + C=CC=O↔ C=C + C=C[C]=O Yes

[CH]=C=O + C=CC=O↔ C=C=O + C=C[C]=O No

C=O + C=C[C]=O↔ C=CC=O + [CH]=O Yes

[CH2]O + C=CC=O↔ CO + C=C[C]=O Yes

[CH3] + C=CC=O↔ C + C=C[C]=O Yes

[CH2]CO + C=CC=O↔ CCO + C=C[C]=O Yes

C[CH]O + C=CC=O↔ CCO + C=C[C]=O Yes

CC[O] + C=CC=O↔ CCO + C=C[C]=O Yes

[CH2]C=O + C=CC=O↔ CC=O + C=C[C]=O Yes

CC=O + C=C[C]=O↔ C=CC=O + C[C]=O Yes

C[CH2] + C=CC=O↔ CC + C=C[C]=O Yes

[CH2]CC + C=CC=O↔ CCC + C=C[C]=O No

C[CH]C + C=CC=O↔ CCC + C=C[C]=O Yes

[CH2]C=C=O + C=CC=O↔ CC=C=O + C=C[C]=O Yes

C=CC=O + [CH2]↔ [CH3] + C=C[C]=O Yes

CC(C)C(=O)C(C)C + [CH]=CC#C↔ C#CC=C + [CH2]C(C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)C + [CH]=CC#C↔ C#CC=C + C[C](C)C(=O)C(C)C No

CC(C)C(=O)C(C)(C)OO + [CH]=CC#C↔ C#CC=C + CC(C)C(=O)C(C)(C)O[O] No

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129

Table B.3 – continued from previous pageReactions FoundCC(C)C(=O)C(C)COO + [CH]=CC#C↔ C#CC=C + CC(C)C(=O)C(C)CO[O] Yes

[H][H] + [CH]=CC#C↔ C#CC=C + [H] Yes

[OH] + C#CC=C↔ O + [CH]=CC#C Yes

[O]O + [CH]=CC#C↔ C#CC=C + [O][O] No

OO + [CH]=CC#C↔ C#CC=C + [O]O No

c1ccccc1 + [CH]=CC#C↔ C#CC=C + [c]1ccccc1 No

C=C1C=CCC1 + [CH]=CC#C↔ C#CC=C + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + [CH]=CC#C↔ C#CC=C + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + [CH]=CC#C↔ C#CC=C + C=C1[CH]C=CC1 No

C=C=C + [CH]=CC#C↔ C#CC=C + [CH]=C=C Yes

C#CC + [CH]=CC#C↔ C#CC=C + C#C[CH2] Yes

[C]#C + C#CC=C↔ C#C + [CH]=CC#C Yes

C=CC + [CH]=CC#C↔ C#CC=C + [CH]=CC Yes

C=CC + [CH]=CC#C↔ C#CC=C + C=[C]C Yes

C=CC + [CH]=CC#C↔ C#CC=C + [CH2]C=C Yes

C=C + [CH]=CC#C↔ C#CC=C + [CH]=C No

C=C=O + [CH]=CC#C↔ C#CC=C + [CH]=C=O Yes

C=O + [CH]=CC#C↔ C#CC=C + [CH]=O Yes

CO + [CH]=CC#C↔ C#CC=C + [CH2]O No

C + [CH]=CC#C↔ C#CC=C + [CH3] No

CCO + [CH]=CC#C↔ C#CC=C + [CH2]CO Yes

CCO + [CH]=CC#C↔ C#CC=C + C[CH]O Yes

CCO + [CH]=CC#C↔ C#CC=C + CC[O] Yes

CC=O + [CH]=CC#C↔ C#CC=C + [CH2]C=O Yes

CC=O + [CH]=CC#C↔ C#CC=C + C[C]=O Yes

CC + [CH]=CC#C↔ C#CC=C + C[CH2] Yes

CCC + [CH]=CC#C↔ C#CC=C + [CH2]CC No

CCC + [CH]=CC#C↔ C#CC=C + C[CH]C Yes

CC=C=O + [CH]=CC#C↔ C#CC=C + [CH2]C=C=O Yes

C=CC=O + [CH]=CC#C↔ C#CC=C + C=C[C]=O Yes

CC(C)C(=O)C(C)C + C#C[C]=C↔ C#CC=C + [CH2]C(C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)C + C#C[C]=C↔ C#CC=C + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + C#C[C]=C↔ C#CC=C + CC(C)C(=O)C(C)(C)O[O] No

CC(C)C(=O)C(C)COO + C#C[C]=C↔ C#CC=C + CC(C)C(=O)C(C)CO[O] Yes

[H] + C#CC=C↔ [H][H] + C#C[C]=C Yes

[OH] + C#CC=C↔ O + C#C[C]=C Yes

[O]O + C#C[C]=C↔ C#CC=C + [O][O] No

OO + C#C[C]=C↔ C#CC=C + [O]O No

[c]1ccccc1 + C#CC=C↔ c1ccccc1 + C#C[C]=C No

C=C1C=CCC1 + C#C[C]=C↔ C#CC=C + C=C1C=C[CH]C1 Yes

C=C1C=CCC1 + C#C[C]=C↔ C#CC=C + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + C#C[C]=C↔ C#CC=C + C=C1[CH]C=CC1 Yes

C=C=C + C#C[C]=C↔ C#CC=C + [CH]=C=C Yes

C#CC + C#C[C]=C↔ C#CC=C + C#C[CH2] No

[C]#C + C#CC=C↔ C#C + C#C[C]=C No

[CH]=CC + C#CC=C↔ C=CC + C#C[C]=C No

C=[C]C + C#CC=C↔ C=CC + C#C[C]=C No

C=CC + C#C[C]=C↔ C#CC=C + [CH2]C=C Yes

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130

Table B.3 – continued from previous pageReactions Found[CH]=C + C#CC=C↔ C=C + C#C[C]=C Yes

[CH]=C=O + C#CC=C↔ C=C=O + C#C[C]=C Yes

C=O + C#C[C]=C↔ C#CC=C + [CH]=O Yes

CO + C#C[C]=C↔ C#CC=C + [CH2]O Yes

[CH3] + C#CC=C↔ C + C#C[C]=C Yes

[CH2]CO + C#CC=C↔ CCO + C#C[C]=C No

CCO + C#C[C]=C↔ C#CC=C + C[CH]O No

CC[O] + C#CC=C↔ CCO + C#C[C]=C Yes

CC=O + C#C[C]=C↔ C#CC=C + [CH2]C=O Yes

CC=O + C#C[C]=C↔ C#CC=C + C[C]=O Yes

CC + C#C[C]=C↔ C#CC=C + C[CH2] Yes

CCC + C#C[C]=C↔ C#CC=C + [CH2]CC No

CCC + C#C[C]=C↔ C#CC=C + C[CH]C Yes

CC=C=O + C#C[C]=C↔ C#CC=C + [CH2]C=C=O Yes

C=CC=O + C#C[C]=C↔ C#CC=C + C=C[C]=O No

C#CC=C + [O]↔ [OH] + C#C[C]=C Yes

C#CC=C + [CH2]↔ [CH3] + C#C[C]=C Yes

C#CC=C + [CH]=CC#C↔ C#CC=C + C#C[C]=C Yes

C[C](C)C(=O)C(C)(C)OO + [O]O↔ CC(C)C(=O)C(C)(C)OO + [O][O] Yes

C[C](C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)(C)OO + C[C](C)C(=O)C(C)C Yes

CC(C)C(=O)C(C)(C)OO + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C[C](C)C(=O)C(C)(C)OO Yes

C[C](C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)(C)O[O] Yes

C[C](C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)COO↔ CC(C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)CO[O] No

CC(C)C(=O)C(C)(C)OO + [H]↔ [H][H] + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + [O]↔ [OH] + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + [OH]↔ O + C[C](C)C(=O)C(C)(C)OO No

C[C](C)C(=O)C(C)(C)OO + OO↔ CC(C)C(=O)C(C)(C)OO + [O]O No

CC(C)C(=O)C(C)(C)OO + C#C[CH2]↔ C#CC + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + [CH]=C=C↔ C=C=C + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + [c]1ccccc1↔ c1ccccc1 + C[C](C)C(=O)C(C)(C)OO No

C[C](C)C(=O)C(C)(C)OO + C=CC↔ CC(C)C(=O)C(C)(C)OO + [CH2]C=C No

C[C](C)C(=O)C(C)(C)OO + C=C1C=CCC1↔ CC(C)C(=O)C(C)(C)OO + C=C1[CH]CC=C1 Yes

C[C](C)C(=O)C(C)(C)OO + C=C1CC=CC1↔ CC(C)C(=O)C(C)(C)OO + C=C1[CH]C=CC1 Yes

C[C](C)C(=O)C(C)(C)OO + C=C1C=CCC1↔ CC(C)C(=O)C(C)(C)OO + C=C1C=C[CH]C1 Yes

CC(C)C(=O)C(C)(C)OO + [CH]=C↔ C=C + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + [CH]=CC↔ C=CC + C[C](C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + C=[C]C↔ C=CC + C[C](C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + [CH3]↔ C + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + [CH2]CC↔ CCC + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + C[CH]C↔ CCC + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + [CH2]↔ [CH3] + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + C[CH]O↔ CCO + C[C](C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + [CH2]CO↔ CCO + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + CC[O]↔ CCO + C[C](C)C(=O)C(C)(C)OO Yes

C[C](C)C(=O)C(C)(C)OO + CC=O↔ CC(C)C(=O)C(C)(C)OO + C[C]=O No

CC(C)C(=O)C(C)(C)OO + [CH2]C=O↔ CC=O + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + C[CH2]↔ CC + C[C](C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + [CH]=C=O↔ C=C=O + C[C](C)C(=O)C(C)(C)OO Yes

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131

Table B.3 – continued from previous pageReactions FoundCC(C)C(=O)C(C)(C)OO + [CH2]O↔ CO + C[C](C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + [C]#C↔ C#C + C[C](C)C(=O)C(C)(C)OO Yes

C[C](C)C(=O)C(C)(C)OO + C=O↔ CC(C)C(=O)C(C)(C)OO + [CH]=O No

CC(C)C(=O)C(C)(C)OO + [CH2]C=C=O↔ CC=C=O + C[C](C)C(=O)C(C)(C)OO No

C[C](C)C(=O)C(C)(C)OO + C=CC=O↔ CC(C)C(=O)C(C)(C)OO + C=C[C]=O Yes

CC(C)C(=O)C(C)(C)OO + [CH]=CC#C↔ C#CC=C + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + C#C[C]=C↔ C#CC=C + C[C](C)C(=O)C(C)(C)OO Yes

[CH2]C(C)C(=O)C(C)(C)OO + [O]O↔ CC(C)C(=O)C(C)(C)OO + [O][O] No

[CH2]C(C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)(C)OO + C[C](C)C(=O)C(C)C No

CC(C)C(=O)C(C)(C)OO + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH2]C(C)C(=O)C(C)(C)OO Yes

[CH2]C(C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)(C)O[O] Yes

[CH2]C(C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)COO↔ CC(C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)CO[O] Yes

CC(C)C(=O)C(C)(C)OO + [H]↔ [H][H] + [CH2]C(C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + [O]↔ [OH] + [CH2]C(C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + [OH]↔ O + [CH2]C(C)C(=O)C(C)(C)OO No

[CH2]C(C)C(=O)C(C)(C)OO + OO↔ CC(C)C(=O)C(C)(C)OO + [O]O No

[CH2]C(C)C(=O)C(C)(C)OO + C#CC↔ CC(C)C(=O)C(C)(C)OO + C#C[CH2] Yes

[CH2]C(C)C(=O)C(C)(C)OO + C=C=C↔ CC(C)C(=O)C(C)(C)OO + [CH]=C=C Yes

CC(C)C(=O)C(C)(C)OO + [c]1ccccc1↔ c1ccccc1 + [CH2]C(C)C(=O)C(C)(C)OO Yes

[CH2]C(C)C(=O)C(C)(C)OO + C=CC↔ CC(C)C(=O)C(C)(C)OO + [CH2]C=C Yes

[CH2]C(C)C(=O)C(C)(C)OO + C=C1C=CCC1↔ CC(C)C(=O)C(C)(C)OO + C=C1[CH]CC=C1 No

[CH2]C(C)C(=O)C(C)(C)OO + C=C1CC=CC1↔ CC(C)C(=O)C(C)(C)OO + C=C1[CH]C=CC1 Yes

[CH2]C(C)C(=O)C(C)(C)OO + C=C1C=CCC1↔ CC(C)C(=O)C(C)(C)OO + C=C1C=C[CH]C1 Yes

CC(C)C(=O)C(C)(C)OO + [CH]=C↔ C=C + [CH2]C(C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + [CH]=CC↔ C=CC + [CH2]C(C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + C=[C]C↔ C=CC + [CH2]C(C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + [CH3]↔ C + [CH2]C(C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + [CH2]CC↔ CCC + [CH2]C(C)C(=O)C(C)(C)OO Yes

[CH2]C(C)C(=O)C(C)(C)OO + CCC↔ CC(C)C(=O)C(C)(C)OO + C[CH]C Yes

CC(C)C(=O)C(C)(C)OO + [CH2]↔ [CH3] + [CH2]C(C)C(=O)C(C)(C)OO No

[CH2]C(C)C(=O)C(C)(C)OO + CCO↔ CC(C)C(=O)C(C)(C)OO + C[CH]O No

CC(C)C(=O)C(C)(C)OO + [CH2]CO↔ CCO + [CH2]C(C)C(=O)C(C)(C)OO Yes

CC(C)C(=O)C(C)(C)OO + CC[O]↔ CCO + [CH2]C(C)C(=O)C(C)(C)OO Yes

[CH2]C(C)C(=O)C(C)(C)OO + CC=O↔ CC(C)C(=O)C(C)(C)OO + C[C]=O No

[CH2]C(C)C(=O)C(C)(C)OO + CC=O↔ CC(C)C(=O)C(C)(C)OO + [CH2]C=O No

[CH2]C(C)C(=O)C(C)(C)OO + CC↔ CC(C)C(=O)C(C)(C)OO + C[CH2] Yes

CC(C)C(=O)C(C)(C)OO + [CH]=C=O↔ C=C=O + [CH2]C(C)C(=O)C(C)(C)OO Yes

[CH2]C(C)C(=O)C(C)(C)OO + CO↔ CC(C)C(=O)C(C)(C)OO + [CH2]O Yes

CC(C)C(=O)C(C)(C)OO + [C]#C↔ C#C + [CH2]C(C)C(=O)C(C)(C)OO Yes

[CH2]C(C)C(=O)C(C)(C)OO + C=O↔ CC(C)C(=O)C(C)(C)OO + [CH]=O Yes

[CH2]C(C)C(=O)C(C)(C)OO + CC=C=O↔ CC(C)C(=O)C(C)(C)OO + [CH2]C=C=O No

[CH2]C(C)C(=O)C(C)(C)OO + C=CC=O↔ CC(C)C(=O)C(C)(C)OO + C=C[C]=O No

CC(C)C(=O)C(C)(C)OO + [CH]=CC#C↔ C#CC=C + [CH2]C(C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + C#C[C]=C↔ C#CC=C + [CH2]C(C)C(=O)C(C)(C)OO No

[CH2]C(C)C(=O)C(C)(C)OO + CC(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)(C)OO + C[C](C)C(=O)C(C)(C)OO Yes

[CH2]C(C)C(=O)C(C)C + CC(C)C(=O)OO↔ CC(C)C(=O)C(C)C + CC(C)C(=O)O[O] Yes

CC(C)C(=O)C(C)C + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C[C](C)C(=O)C(C)C No

[CH2]C(C)C(=O)C(C)(C)OO + CC(C)C(=O)OO↔ CC(C)C(=O)C(C)(C)OO + CC(C)C(=O)O[O] Yes

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132

Table B.3 – continued from previous pageReactions FoundCC(C)C(=O)C(C)(C)OO + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C[C](C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + CC(C)C(=O)C(C)CO[O] Yes

[H] + CC(C)C(=O)OO↔ [H][H] + CC(C)C(=O)O[O] Yes

[OH] + CC(C)C(=O)OO↔ O + CC(C)C(=O)O[O] No

[O]O + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + [O][O] No

OO + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + [O]O No

[c]1ccccc1 + CC(C)C(=O)OO↔ c1ccccc1 + CC(C)C(=O)O[O] No

C=C1C=CCC1 + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C=C1C=C[CH]C1 No

C=C1C=CCC1 + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C=C1[CH]C=CC1 Yes

C=C=C + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + [CH]=C=C No

C#CC + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C#C[CH2] Yes

[C]#C + CC(C)C(=O)OO↔ C#C + CC(C)C(=O)O[O] No

[CH]=CC + CC(C)C(=O)OO↔ C=CC + CC(C)C(=O)O[O] No

C=[C]C + CC(C)C(=O)OO↔ C=CC + CC(C)C(=O)O[O] No

C=CC + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + [CH2]C=C No

[CH]=C + CC(C)C(=O)OO↔ C=C + CC(C)C(=O)O[O] Yes

[CH]=C=O + CC(C)C(=O)OO↔ C=C=O + CC(C)C(=O)O[O] No

C=O + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + [CH]=O No

CO + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + [CH2]O No

[CH3] + CC(C)C(=O)OO↔ C + CC(C)C(=O)O[O] No

[CH2]CO + CC(C)C(=O)OO↔ CCO + CC(C)C(=O)O[O] No

CCO + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C[CH]O No

CC[O] + CC(C)C(=O)OO↔ CCO + CC(C)C(=O)O[O] Yes

CC=O + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + [CH2]C=O Yes

CC=O + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C[C]=O Yes

C[CH2] + CC(C)C(=O)OO↔ CC + CC(C)C(=O)O[O] Yes

[CH2]CC + CC(C)C(=O)OO↔ CCC + CC(C)C(=O)O[O] No

CCC + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C[CH]C No

CC=C=O + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + [CH2]C=C=O No

C=CC=O + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C=C[C]=O No

C#C[C]=C + CC(C)C(=O)OO↔ C#CC=C + CC(C)C(=O)O[O] No

[CH]=CC#C + CC(C)C(=O)OO↔ C#CC=C + CC(C)C(=O)O[O] No

CC(C)C(=O)OO + [CH2]↔ [CH3] + CC(C)C(=O)O[O] No

C[C](C)C(=O)C(C)COO + [O]O↔ CC(C)C(=O)C(C)COO + [O][O] Yes

C[C](C)C(=O)C(C)COO + CC(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)COO + C[C](C)C(=O)C(C)C No

CC(C)C(=O)C(C)COO + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C[C](C)C(=O)C(C)COO No

C[C](C)C(=O)C(C)COO + CC(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)COO + CC(C)C(=O)C(C)(C)O[O] Yes

C[C](C)C(=O)C(C)COO + CC(C)C(=O)C(C)COO↔ CC(C)C(=O)C(C)COO + CC(C)C(=O)C(C)CO[O] Yes

CC(C)C(=O)C(C)COO + [H]↔ [H][H] + C[C](C)C(=O)C(C)COO No

CC(C)C(=O)C(C)COO + [O]↔ [OH] + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + [OH]↔ O + C[C](C)C(=O)C(C)COO No

C[C](C)C(=O)C(C)COO + OO↔ CC(C)C(=O)C(C)COO + [O]O No

CC(C)C(=O)C(C)COO + C#C[CH2]↔ C#CC + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + [CH]=C=C↔ C=C=C + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + [c]1ccccc1↔ c1ccccc1 + C[C](C)C(=O)C(C)COO No

C[C](C)C(=O)C(C)COO + C=CC↔ CC(C)C(=O)C(C)COO + [CH2]C=C No

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133

Table B.3 – continued from previous pageReactions FoundC[C](C)C(=O)C(C)COO + C=C1C=CCC1↔ CC(C)C(=O)C(C)COO + C=C1[CH]CC=C1 Yes

C[C](C)C(=O)C(C)COO + C=C1CC=CC1↔ CC(C)C(=O)C(C)COO + C=C1[CH]C=CC1 Yes

C[C](C)C(=O)C(C)COO + C=C1C=CCC1↔ CC(C)C(=O)C(C)COO + C=C1C=C[CH]C1 Yes

CC(C)C(=O)C(C)COO + [CH]=C↔ C=C + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + [CH]=CC↔ C=CC + C[C](C)C(=O)C(C)COO No

CC(C)C(=O)C(C)COO + C=[C]C↔ C=CC + C[C](C)C(=O)C(C)COO No

CC(C)C(=O)C(C)COO + [CH3]↔ C + C[C](C)C(=O)C(C)COO No

CC(C)C(=O)C(C)COO + [CH2]CC↔ CCC + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + C[CH]C↔ CCC + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + [CH2]↔ [CH3] + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + C[CH]O↔ CCO + C[C](C)C(=O)C(C)COO No

CC(C)C(=O)C(C)COO + [CH2]CO↔ CCO + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + CC[O]↔ CCO + C[C](C)C(=O)C(C)COO Yes

C[C](C)C(=O)C(C)COO + CC=O↔ CC(C)C(=O)C(C)COO + C[C]=O Yes

CC(C)C(=O)C(C)COO + [CH2]C=O↔ CC=O + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + C[CH2]↔ CC + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + [CH]=C=O↔ C=C=O + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + [CH2]O↔ CO + C[C](C)C(=O)C(C)COO No

CC(C)C(=O)C(C)COO + [C]#C↔ C#C + C[C](C)C(=O)C(C)COO No

C[C](C)C(=O)C(C)COO + C=O↔ CC(C)C(=O)C(C)COO + [CH]=O Yes

CC(C)C(=O)C(C)COO + [CH2]C=C=O↔ CC=C=O + C[C](C)C(=O)C(C)COO No

C[C](C)C(=O)C(C)COO + C=CC=O↔ CC(C)C(=O)C(C)COO + C=C[C]=O Yes

CC(C)C(=O)C(C)COO + [CH]=CC#C↔ C#CC=C + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + C#C[C]=C↔ C#CC=C + C[C](C)C(=O)C(C)COO No

CC(C)C(=O)C(C)COO + C[C](C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)(C)OO + C[C](C)C(=O)C(C)COO No

CC(C)C(=O)C(C)COO + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + [CH2]C(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)(C)OO + C[C](C)C(=O)C(C)COO Yes

[CH2]C(C)=C=O + [O]O↔ CC(C)=C=O + [O][O] Yes

CC(C)=C=O + C[C](C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH2]C(C)=C=O No

CC(C)=C=O + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH2]C(C)=C=O Yes

[CH2]C(C)=C=O + CC(C)C(=O)C(C)(C)OO↔ CC(C)=C=O + CC(C)C(=O)C(C)(C)O[O] Yes

[CH2]C(C)=C=O + CC(C)C(=O)C(C)COO↔ CC(C)=C=O + CC(C)C(=O)C(C)CO[O] No

CC(C)=C=O + [H]↔ [H][H] + [CH2]C(C)=C=O Yes

CC(C)=C=O + [O]↔ [OH] + [CH2]C(C)=C=O Yes

CC(C)=C=O + [OH]↔ O + [CH2]C(C)=C=O No

[CH2]C(C)=C=O + OO↔ CC(C)=C=O + [O]O No

CC(C)=C=O + C#C[CH2]↔ C#CC + [CH2]C(C)=C=O Yes

CC(C)=C=O + [CH]=C=C↔ C=C=C + [CH2]C(C)=C=O Yes

CC(C)=C=O + [c]1ccccc1↔ c1ccccc1 + [CH2]C(C)=C=O No

CC(C)=C=O + [CH2]C=C↔ C=CC + [CH2]C(C)=C=O Yes

[CH2]C(C)=C=O + C=C1C=CCC1↔ CC(C)=C=O + C=C1[CH]CC=C1 Yes

[CH2]C(C)=C=O + C=C1CC=CC1↔ CC(C)=C=O + C=C1[CH]C=CC1 Yes

[CH2]C(C)=C=O + C=C1C=CCC1↔ CC(C)=C=O + C=C1C=C[CH]C1 Yes

CC(C)=C=O + [CH]=C↔ C=C + [CH2]C(C)=C=O Yes

CC(C)=C=O + [CH]=CC↔ C=CC + [CH2]C(C)=C=O No

CC(C)=C=O + C=[C]C↔ C=CC + [CH2]C(C)=C=O Yes

CC(C)=C=O + [CH3]↔ C + [CH2]C(C)=C=O Yes

CC(C)=C=O + [CH2]CC↔ CCC + [CH2]C(C)=C=O Yes

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134

Table B.3 – continued from previous pageReactions FoundCC(C)=C=O + C[CH]C↔ CCC + [CH2]C(C)=C=O Yes

CC(C)=C=O + [CH2]↔ [CH3] + [CH2]C(C)=C=O Yes

CC(C)=C=O + C[CH]O↔ CCO + [CH2]C(C)=C=O No

CC(C)=C=O + [CH2]CO↔ CCO + [CH2]C(C)=C=O Yes

CC(C)=C=O + CC[O]↔ CCO + [CH2]C(C)=C=O No

CC(C)=C=O + C[C]=O↔ CC=O + [CH2]C(C)=C=O No

CC(C)=C=O + [CH2]C=O↔ CC=O + [CH2]C(C)=C=O Yes

CC(C)=C=O + C[CH2]↔ CC + [CH2]C(C)=C=O Yes

CC(C)=C=O + [CH]=C=O↔ C=C=O + [CH2]C(C)=C=O Yes

CC(C)=C=O + [CH2]O↔ CO + [CH2]C(C)=C=O Yes

CC(C)=C=O + [C]#C↔ C#C + [CH2]C(C)=C=O Yes

CC(C)=C=O + [CH]=O↔ C=O + [CH2]C(C)=C=O No

CC(C)=C=O + [CH2]C=C=O↔ CC=C=O + [CH2]C(C)=C=O No

CC(C)=C=O + C=C[C]=O↔ C=CC=O + [CH2]C(C)=C=O Yes

CC(C)=C=O + [CH]=CC#C↔ C#CC=C + [CH2]C(C)=C=O Yes

CC(C)=C=O + C#C[C]=C↔ C#CC=C + [CH2]C(C)=C=O No

CC(C)=C=O + C[C](C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)(C)OO + [CH2]C(C)=C=O Yes

CC(C)=C=O + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + [CH2]C(C)=C=O Yes

CC(C)=C=O + [CH2]C(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)(C)OO + [CH2]C(C)=C=O No

CC(C)=C=O + C[C](C)C(=O)C(C)COO↔ CC(C)C(=O)C(C)COO + [CH2]C(C)=C=O Yes

[CH2]C(C)C(=O)C(C)C + C=C(C)C(=O)OO↔ CC(C)C(=O)C(C)C + C=C(C)C(=O)O[O] Yes

CC(C)C(=O)C(C)C + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C[C](C)C(=O)C(C)C No

[CH2]C(C)C(=O)C(C)(C)OO + C=C(C)C(=O)OO↔ CC(C)C(=O)C(C)(C)OO + C=C(C)C(=O)O[O] Yes

CC(C)C(=O)C(C)(C)OO + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C[C](C)C(=O)C(C)(C)OO No

CC(C)C(=O)C(C)(C)OO + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + CC(C)C(=O)C(C)(C)O[O] Yes

CC(C)C(=O)C(C)COO + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C[C](C)C(=O)C(C)COO Yes

CC(C)C(=O)C(C)COO + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + CC(C)C(=O)C(C)CO[O] Yes

[H] + C=C(C)C(=O)OO↔ [H][H] + C=C(C)C(=O)O[O] Yes

[OH] + C=C(C)C(=O)OO↔ O + C=C(C)C(=O)O[O] Yes

[O]O + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + [O][O] No

OO + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + [O]O Yes

[c]1ccccc1 + C=C(C)C(=O)OO↔ c1ccccc1 + C=C(C)C(=O)O[O] No

C=C1C=CCC1 + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C=C1C=C[CH]C1 No

C=C1C=CCC1 + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C=C1[CH]CC=C1 Yes

C=C1CC=CC1 + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C=C1[CH]C=CC1 Yes

C=C=C + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + [CH]=C=C Yes

C#CC + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C#C[CH2] No

[C]#C + C=C(C)C(=O)OO↔ C#C + C=C(C)C(=O)O[O] Yes

[CH]=CC + C=C(C)C(=O)OO↔ C=CC + C=C(C)C(=O)O[O] No

C=[C]C + C=C(C)C(=O)OO↔ C=CC + C=C(C)C(=O)O[O] No

C=CC + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + [CH2]C=C No

[CH]=C + C=C(C)C(=O)OO↔ C=C + C=C(C)C(=O)O[O] Yes

[CH]=C=O + C=C(C)C(=O)OO↔ C=C=O + C=C(C)C(=O)O[O] No

C=O + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + [CH]=O No

CO + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + [CH2]O Yes

[CH3] + C=C(C)C(=O)OO↔ C + C=C(C)C(=O)O[O] Yes

[CH2]CO + C=C(C)C(=O)OO↔ CCO + C=C(C)C(=O)O[O] No

CCO + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C[CH]O No

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135

Table B.3 – continued from previous pageReactions FoundCC[O] + C=C(C)C(=O)OO↔ CCO + C=C(C)C(=O)O[O] Yes

CC=O + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + [CH2]C=O No

CC=O + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C[C]=O Yes

C[CH2] + C=C(C)C(=O)OO↔ CC + C=C(C)C(=O)O[O] No

[CH2]CC + C=C(C)C(=O)OO↔ CCC + C=C(C)C(=O)O[O] No

CCC + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C[CH]C No

CC=C=O + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + [CH2]C=C=O Yes

C=CC=O + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + C=C[C]=O No

C#C[C]=C + C=C(C)C(=O)OO↔ C#CC=C + C=C(C)C(=O)O[O] No

[CH]=CC#C + C=C(C)C(=O)OO↔ C#CC=C + C=C(C)C(=O)O[O] No

CC(C)=C=O + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + [CH2]C(C)=C=O No

CC(C)C(=O)OO + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + CC(C)C(=O)O[O] No

C=C(C)C(=O)OO + [CH2]↔ [CH3] + C=C(C)C(=O)O[O] Yes

[CH2]C(COO)C(=O)C(C)C + [O]O↔ CC(C)C(=O)C(C)COO + [O][O] No

[CH2]C(COO)C(=O)C(C)C + CC(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)COO + C[C](C)C(=O)C(C)C No

CC(C)C(=O)C(C)COO + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH2]C(COO)C(=O)C(C)C Yes

[CH2]C(COO)C(=O)C(C)C + CC(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)COO + CC(C)C(=O)C(C)(C)O[O] Yes

[CH2]C(COO)C(=O)C(C)C + CC(C)C(=O)C(C)COO↔ CC(C)C(=O)C(C)COO + CC(C)C(=O)C(C)CO[O] Yes

CC(C)C(=O)C(C)COO + [H]↔ [H][H] + [CH2]C(COO)C(=O)C(C)C Yes

CC(C)C(=O)C(C)COO + [O]↔ [OH] + [CH2]C(COO)C(=O)C(C)C Yes

CC(C)C(=O)C(C)COO + [OH]↔ O + [CH2]C(COO)C(=O)C(C)C No

[CH2]C(COO)C(=O)C(C)C + OO↔ CC(C)C(=O)C(C)COO + [O]O No

[CH2]C(COO)C(=O)C(C)C + C#CC↔ CC(C)C(=O)C(C)COO + C#C[CH2] Yes

[CH2]C(COO)C(=O)C(C)C + C=C=C↔ CC(C)C(=O)C(C)COO + [CH]=C=C Yes

CC(C)C(=O)C(C)COO + [c]1ccccc1↔ c1ccccc1 + [CH2]C(COO)C(=O)C(C)C Yes

[CH2]C(COO)C(=O)C(C)C + C=CC↔ CC(C)C(=O)C(C)COO + [CH2]C=C No

[CH2]C(COO)C(=O)C(C)C + C=C1C=CCC1↔ CC(C)C(=O)C(C)COO + C=C1[CH]CC=C1 Yes

[CH2]C(COO)C(=O)C(C)C + C=C1CC=CC1↔ CC(C)C(=O)C(C)COO + C=C1[CH]C=CC1 No

[CH2]C(COO)C(=O)C(C)C + C=C1C=CCC1↔ CC(C)C(=O)C(C)COO + C=C1C=C[CH]C1 Yes

CC(C)C(=O)C(C)COO + [CH]=C↔ C=C + [CH2]C(COO)C(=O)C(C)C No

CC(C)C(=O)C(C)COO + [CH]=CC↔ C=CC + [CH2]C(COO)C(=O)C(C)C Yes

CC(C)C(=O)C(C)COO + C=[C]C↔ C=CC + [CH2]C(COO)C(=O)C(C)C No

CC(C)C(=O)C(C)COO + [CH3]↔ C + [CH2]C(COO)C(=O)C(C)C Yes

CC(C)C(=O)C(C)COO + [CH2]CC↔ CCC + [CH2]C(COO)C(=O)C(C)C Yes

[CH2]C(COO)C(=O)C(C)C + CCC↔ CC(C)C(=O)C(C)COO + C[CH]C Yes

CC(C)C(=O)C(C)COO + [CH2]↔ [CH3] + [CH2]C(COO)C(=O)C(C)C Yes

[CH2]C(COO)C(=O)C(C)C + CCO↔ CC(C)C(=O)C(C)COO + C[CH]O No

CC(C)C(=O)C(C)COO + [CH2]CO↔ CCO + [CH2]C(COO)C(=O)C(C)C Yes

CC(C)C(=O)C(C)COO + CC[O]↔ CCO + [CH2]C(COO)C(=O)C(C)C Yes

[CH2]C(COO)C(=O)C(C)C + CC=O↔ CC(C)C(=O)C(C)COO + C[C]=O Yes

[CH2]C(COO)C(=O)C(C)C + CC=O↔ CC(C)C(=O)C(C)COO + [CH2]C=O No

[CH2]C(COO)C(=O)C(C)C + CC↔ CC(C)C(=O)C(C)COO + C[CH2] Yes

CC(C)C(=O)C(C)COO + [CH]=C=O↔ C=C=O + [CH2]C(COO)C(=O)C(C)C Yes

[CH2]C(COO)C(=O)C(C)C + CO↔ CC(C)C(=O)C(C)COO + [CH2]O No

CC(C)C(=O)C(C)COO + [C]#C↔ C#C + [CH2]C(COO)C(=O)C(C)C Yes

[CH2]C(COO)C(=O)C(C)C + C=O↔ CC(C)C(=O)C(C)COO + [CH]=O Yes

[CH2]C(COO)C(=O)C(C)C + CC=C=O↔ CC(C)C(=O)C(C)COO + [CH2]C=C=O No

[CH2]C(COO)C(=O)C(C)C + C=CC=O↔ CC(C)C(=O)C(C)COO + C=C[C]=O Yes

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136

Table B.3 – continued from previous pageReactions FoundCC(C)C(=O)C(C)COO + [CH]=CC#C↔ C#CC=C + [CH2]C(COO)C(=O)C(C)C Yes

CC(C)C(=O)C(C)COO + C#C[C]=C↔ C#CC=C + [CH2]C(COO)C(=O)C(C)C Yes

[CH2]C(COO)C(=O)C(C)C + CC(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)COO + C[C](C)C(=O)C(C)(C)OO Yes

[CH2]C(COO)C(=O)C(C)C + CC(C)C(=O)OO↔ CC(C)C(=O)C(C)COO + CC(C)C(=O)O[O] Yes

CC(C)C(=O)C(C)COO + [CH2]C(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)(C)OO + [CH2]C(COO)C(=O)C(C)C No

[CH2]C(COO)C(=O)C(C)C + CC(C)C(=O)C(C)COO↔ CC(C)C(=O)C(C)COO + C[C](C)C(=O)C(C)COO Yes

[CH2]C(COO)C(=O)C(C)C + CC(C)=C=O↔ CC(C)C(=O)C(C)COO + [CH2]C(C)=C=O Yes

[CH2]C(COO)C(=O)C(C)C + C=C(C)C(=O)OO↔ CC(C)C(=O)C(C)COO + C=C(C)C(=O)O[O] No

[CH2]C(C)=O + [O]O↔ CC(C)=O + [O][O] Yes

[CH2]C(C)=O + CC(C)C(=O)C(C)C↔ CC(C)=O + C[C](C)C(=O)C(C)C Yes

CC(C)=O + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH2]C(C)=O Yes

[CH2]C(C)=O + CC(C)C(=O)C(C)(C)OO↔ CC(C)=O + CC(C)C(=O)C(C)(C)O[O] Yes

[CH2]C(C)=O + CC(C)C(=O)C(C)COO↔ CC(C)=O + CC(C)C(=O)C(C)CO[O] Yes

CC(C)=O + [H]↔ [H][H] + [CH2]C(C)=O Yes

CC(C)=O + [O]↔ [OH] + [CH2]C(C)=O Yes

CC(C)=O + [OH]↔ O + [CH2]C(C)=O Yes

[CH2]C(C)=O + OO↔ CC(C)=O + [O]O No

[CH2]C(C)=O + C#CC↔ CC(C)=O + C#C[CH2] Yes

[CH2]C(C)=O + C=C=C↔ CC(C)=O + [CH]=C=C Yes

CC(C)=O + [c]1ccccc1↔ c1ccccc1 + [CH2]C(C)=O Yes

[CH2]C(C)=O + C=CC↔ CC(C)=O + [CH2]C=C Yes

[CH2]C(C)=O + C=C1C=CCC1↔ CC(C)=O + C=C1[CH]CC=C1 Yes

[CH2]C(C)=O + C=C1CC=CC1↔ CC(C)=O + C=C1[CH]C=CC1 Yes

[CH2]C(C)=O + C=C1C=CCC1↔ CC(C)=O + C=C1C=C[CH]C1 Yes

CC(C)=O + [CH]=C↔ C=C + [CH2]C(C)=O Yes

CC(C)=O + [CH]=CC↔ C=CC + [CH2]C(C)=O Yes

CC(C)=O + C=[C]C↔ C=CC + [CH2]C(C)=O Yes

CC(C)=O + [CH3]↔ C + [CH2]C(C)=O Yes

CC(C)=O + [CH2]CC↔ CCC + [CH2]C(C)=O Yes

CC(C)=O + C[CH]C↔ CCC + [CH2]C(C)=O Yes

CC(C)=O + [CH2]↔ [CH3] + [CH2]C(C)=O Yes

[CH2]C(C)=O + CCO↔ CC(C)=O + C[CH]O No

CC(C)=O + [CH2]CO↔ CCO + [CH2]C(C)=O Yes

CC(C)=O + CC[O]↔ CCO + [CH2]C(C)=O No

[CH2]C(C)=O + CC=O↔ CC(C)=O + C[C]=O Yes

[CH2]C(C)=O + CC=O↔ CC(C)=O + [CH2]C=O Yes

CC(C)=O + C[CH2]↔ CC + [CH2]C(C)=O Yes

CC(C)=O + [CH]=C=O↔ C=C=O + [CH2]C(C)=O Yes

[CH2]C(C)=O + CO↔ CC(C)=O + [CH2]O No

CC(C)=O + [C]#C↔ C#C + [CH2]C(C)=O Yes

[CH2]C(C)=O + C=O↔ CC(C)=O + [CH]=O No

[CH2]C(C)=O + CC=C=O↔ CC(C)=O + [CH2]C=C=O No

[CH2]C(C)=O + C=CC=O↔ CC(C)=O + C=C[C]=O Yes

CC(C)=O + [CH]=CC#C↔ C#CC=C + [CH2]C(C)=O Yes

CC(C)=O + C#C[C]=C↔ C#CC=C + [CH2]C(C)=O No

[CH2]C(C)=O + CC(C)C(=O)C(C)(C)OO↔ CC(C)=O + C[C](C)C(=O)C(C)(C)OO Yes

CC(C)=O + CC(C)C(=O)O[O]↔ CC(C)C(=O)OO + [CH2]C(C)=O Yes

CC(C)=O + [CH2]C(C)C(=O)C(C)(C)OO↔ CC(C)C(=O)C(C)(C)OO + [CH2]C(C)=O No

Continued on next page

137

Table B.3 – continued from previous pageReactions Found[CH2]C(C)=O + CC(C)C(=O)C(C)COO↔ CC(C)=O + C[C](C)C(=O)C(C)COO Yes

[CH2]C(C)=O + CC(C)=C=O↔ CC(C)=O + [CH2]C(C)=C=O No

CC(C)=O + C=C(C)C(=O)O[O]↔ C=C(C)C(=O)OO + [CH2]C(C)=O Yes

CC(C)=O + [CH2]C(COO)C(=O)C(C)C↔ CC(C)C(=O)C(C)COO + [CH2]C(C)=O No

[CH]=CC=C + C↔ C=CC=C + [CH3] Yes

C=CC=C + [CH3]↔ C + C=[C]C=C No

[CH]=CC=C + C=CC↔ C=CC=C + [CH2]C=C Yes

C=[C]C=C + C=CC↔ C=CC=C + [CH2]C=C No

C=CC=CC + [CH3]↔ C + [CH2]C=CC=C Yes

C=CC=CC + [CH2]C=C↔ C=CC + [CH2]C=CC=C No

C1=CCCC=C1 + [CH3]↔ C + [CH]1C=CC=CC1 Yes

C1=CCCC=C1 + [CH2]C=C↔ C=CC + [CH]1C=CC=CC1 Yes

[CH]=CC=C + CC(C)C(=O)C(C)C↔ C=CC=C + C[C](C)C(=O)C(C)C Yes

C=[C]C=C + CC(C)C(=O)C(C)C↔ C=CC=C + C[C](C)C(=O)C(C)C Yes

C=CC=CC + C[C](C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH2]C=CC=C No

C1=CCCC=C1 + C[C](C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH]1C=CC=CC1 Yes

[CH]=CC=C + CC(C)C(=O)C(C)C↔ C=CC=C + [CH2]C(C)C(=O)C(C)C Yes

C=[C]C=C + CC(C)C(=O)C(C)C↔ C=CC=C + [CH2]C(C)C(=O)C(C)C Yes

C=CC=CC + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH2]C=CC=C Yes

C1=CCCC=C1 + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH]1C=CC=CC1 Yes

[H] + C=CC=CC↔ [H][H] + [CH2]C=CC=C Yes

[C]#C + C=CC=CC↔ C#C + [CH2]C=CC=C No

[CH]=C + C=CC=CC↔ C=C + [CH2]C=CC=C Yes

[CH]=CC + C=CC=CC↔ C=CC + [CH2]C=CC=C No

C=[C]C + C=CC=CC↔ C=CC + [CH2]C=CC=C Yes

[CH]=C=C + C=CC=CC↔ C=C=C + [CH2]C=CC=C Yes

C#C[CH2] + C=CC=CC↔ C#CC + [CH2]C=CC=C Yes

[CH]=CC#C + C=CC=CC↔ C#CC=C + [CH2]C=CC=C Yes

C#C[C]=C + C=CC=CC↔ C#CC=C + [CH2]C=CC=C No

[CH]=CC=C + C=CC=CC↔ C=CC=C + [CH2]C=CC=C Yes

C=[C]C=C + C=CC=CC↔ C=CC=C + [CH2]C=CC=C Yes

[CH2]C=C=O + C=CC=CC↔ CC=C=O + [CH2]C=CC=C No

[c]1ccccc1 + C=CC=CC↔ c1ccccc1 + [CH2]C=CC=C Yes

C1=CCCC=C1 + [CH2]C=CC=C↔ C=CC=CC + [CH]1C=CC=CC1 No

[H] + C1=CCCC=C1↔ [H][H] + [CH]1C=CC=CC1 Yes

[C]#C + C1=CCCC=C1↔ C#C + [CH]1C=CC=CC1 Yes

[CH]=C + C1=CCCC=C1↔ C=C + [CH]1C=CC=CC1 No

[CH]=CC + C1=CCCC=C1↔ C=CC + [CH]1C=CC=CC1 Yes

C=[C]C + C1=CCCC=C1↔ C=CC + [CH]1C=CC=CC1 Yes

[CH]=C=C + C1=CCCC=C1↔ C=C=C + [CH]1C=CC=CC1 No

C#C[CH2] + C1=CCCC=C1↔ C#CC + [CH]1C=CC=CC1 No

[CH]=CC#C + C1=CCCC=C1↔ C#CC=C + [CH]1C=CC=CC1 No

C#C[C]=C + C1=CCCC=C1↔ C#CC=C + [CH]1C=CC=CC1 Yes

[CH]=CC=C + C1=CCCC=C1↔ C=CC=C + [CH]1C=CC=CC1 No

C=[C]C=C + C1=CCCC=C1↔ C=CC=C + [CH]1C=CC=CC1 Yes

[CH2]C=C=O + C1=CCCC=C1↔ CC=C=O + [CH]1C=CC=CC1 No

[c]1ccccc1 + C1=CCCC=C1↔ c1ccccc1 + [CH]1C=CC=CC1 Yes

[CH]=CC=C + [H][H]↔ C=CC=C + [H] No

Continued on next page

138

Table B.3 – continued from previous pageReactions FoundC=CC=C + [H]↔ [H][H] + C=[C]C=C Yes

C=CC=C + [O]↔ [OH] + C=[C]C=C Yes

C=CC=CC + [O]↔ [OH] + [CH2]C=CC=C Yes

C1=CCCC=C1 + [O]↔ [OH] + [CH]1C=CC=CC1 No

C=CC=C + [OH]↔ O + [CH]=CC=C No

C=CC=C + [OH]↔ O + C=[C]C=C Yes

C=CC=CC + [OH]↔ O + [CH2]C=CC=C No

C1=CCCC=C1 + [OH]↔ O + [CH]1C=CC=CC1 No

[CH]=CC=C + [O]O↔ C=CC=C + [O][O] No

C=[C]C=C + [O]O↔ C=CC=C + [O][O] No

[CH2]C=CC=C + [O]O↔ C=CC=CC + [O][O] Yes

[CH]1C=CC=CC1 + [O]O↔ C1=CCCC=C1 + [O][O] Yes

[CH]=CC=C + OO↔ C=CC=C + [O]O Yes

C=[C]C=C + OO↔ C=CC=C + [O]O No

C=CC=CC + [O]O↔ OO + [CH2]C=CC=C No

C1=CCCC=C1 + [O]O↔ OO + [CH]1C=CC=CC1 No

[CH]=CC=C + C#CC↔ C=CC=C + C#C[CH2] No

C=[C]C=C + C#CC↔ C=CC=C + C#C[CH2] Yes

[CH]=CC=C + C=C=C↔ C=CC=C + [CH]=C=C No

C=[C]C=C + C=C=C↔ C=CC=C + [CH]=C=C Yes

C=CC=C + [c]1ccccc1↔ c1ccccc1 + [CH]=CC=C No

C=CC=C + [c]1ccccc1↔ c1ccccc1 + C=[C]C=C Yes

C=C1C=CCC1 + [CH2]C=CC=C↔ C=CC=CC + C=C1C=C[CH]C1 Yes

C=C1[CH]CC=C1 + C=CC=CC↔ C=C1C=CCC1 + [CH2]C=CC=C Yes

C=C1C=C[CH]C1 + C1=CCCC=C1↔ C=C1C=CCC1 + [CH]1C=CC=CC1 Yes

C=C1[CH]CC=C1 + C1=CCCC=C1↔ C=C1C=CCC1 + [CH]1C=CC=CC1 Yes

C=C1CC=CC1 + [CH2]C=CC=C↔ C=CC=CC + C=C1[CH]C=CC1 Yes

C=C1CC=CC1 + [CH]1C=CC=CC1↔ C1=CCCC=C1 + C=C1[CH]C=CC1 Yes

[C]#C + C=CC=C↔ C#C + C=[C]C=C Yes

[CH]=C + C=CC=C↔ C=C + C=[C]C=C No

[CH]=CC + C=CC=C↔ C=CC + C=[C]C=C No

C=[C]C + C=CC=C↔ C=CC + C=[C]C=C Yes

[CH]=CC#C + C=CC=C↔ C#CC=C + C=[C]C=C Yes

C#CC=C + C=[C]C=C↔ C=CC=C + C#C[C]=C Yes

[CH]=CC=C + C=CC=C↔ C=CC=C + C=[C]C=C No

CC=C=O + C=[C]C=C↔ C=CC=C + [CH2]C=C=O No

C=C1C=CCC1 + C=[C]C=C↔ C=CC=C + C=C1C=C[CH]C1 No

C=C1C=CCC1 + C=[C]C=C↔ C=CC=C + C=C1[CH]CC=C1 No

C=C1CC=CC1 + C=[C]C=C↔ C=CC=C + C=C1[CH]C=CC1 No

[CH]=CC=C + C=C1C=CCC1↔ C=CC=C + C=C1[CH]CC=C1 No

[CH]=CC=C + C=C1CC=CC1↔ C=CC=C + C=C1[CH]C=CC1 Yes

[CH]=CC=C + C=C1C=CCC1↔ C=CC=C + C=C1C=C[CH]C1 No

[CH]=CC=C + C=C↔ C=CC=C + [CH]=C No

[CH]=CC=C + C=CC↔ C=CC=C + [CH]=CC Yes

[CH]=CC=C + C=CC↔ C=CC=C + C=[C]C Yes

[CH]=CC=C + CCC↔ C=CC=C + [CH2]CC Yes

C=[C]C=C + CCC↔ C=CC=C + [CH2]CC Yes

C=CC=CC + [CH2]CC↔ CCC + [CH2]C=CC=C Yes

Continued on next page

139

Table B.3 – continued from previous pageReactions FoundC1=CCCC=C1 + [CH2]CC↔ CCC + [CH]1C=CC=CC1 Yes

[CH]=CC=C + CCC↔ C=CC=C + C[CH]C Yes

C=[C]C=C + CCC↔ C=CC=C + C[CH]C Yes

C=CC=CC + C[CH]C↔ CCC + [CH2]C=CC=C Yes

C1=CCCC=C1 + C[CH]C↔ CCC + [CH]1C=CC=CC1 Yes

[CH]=C=O + C=CC=CC↔ C=C=O + [CH2]C=CC=C Yes

[CH]=C=O + C1=CCCC=C1↔ C=C=O + [CH]1C=CC=CC1 Yes

[CH]=C=O + C=CC=C↔ C=C=O + C=[C]C=C Yes

[CH]=O + C=CC=CC↔ C=O + [CH2]C=CC=C Yes

[CH]=O + C1=CCCC=C1↔ C=O + [CH]1C=CC=CC1 Yes

C=O + C=[C]C=C↔ C=CC=C + [CH]=O Yes

[CH2]O + C=CC=CC↔ CO + [CH2]C=CC=C No

[CH2]O + C1=CCCC=C1↔ CO + [CH]1C=CC=CC1 Yes

CO + C=[C]C=C↔ C=CC=C + [CH2]O Yes

C=CC=C + [CH2]↔ [CH3] + C=[C]C=C No

C=CC=CC + [CH2]↔ [CH3] + [CH2]C=CC=C Yes

C1=CCCC=C1 + [CH2]↔ [CH3] + [CH]1C=CC=CC1 Yes

[CH2]CO + C=CC=CC↔ CCO + [CH2]C=CC=C No

C[CH]O + C=CC=CC↔ CCO + [CH2]C=CC=C Yes

CC[O] + C=CC=CC↔ CCO + [CH2]C=CC=C Yes

[CH2]CO + C1=CCCC=C1↔ CCO + [CH]1C=CC=CC1 No

C[CH]O + C1=CCCC=C1↔ CCO + [CH]1C=CC=CC1 No

CC[O] + C1=CCCC=C1↔ CCO + [CH]1C=CC=CC1 Yes

[CH2]CO + C=CC=C↔ CCO + C=[C]C=C No

CCO + C=[C]C=C↔ C=CC=C + C[CH]O Yes

CC[O] + C=CC=C↔ CCO + C=[C]C=C Yes

[CH]=CC=C + CCO↔ C=CC=C + C[CH]O Yes

[CH]=CC=C + CCO↔ C=CC=C + [CH2]CO No

[CH]=CC=C + CCO↔ C=CC=C + CC[O] Yes

[CH2]C=O + C=CC=CC↔ CC=O + [CH2]C=CC=C No

C[C]=O + C=CC=CC↔ CC=O + [CH2]C=CC=C Yes

[CH2]C=O + C1=CCCC=C1↔ CC=O + [CH]1C=CC=CC1 Yes

C[C]=O + C1=CCCC=C1↔ CC=O + [CH]1C=CC=CC1 Yes

CC=O + C=[C]C=C↔ C=CC=C + [CH2]C=O Yes

CC=O + C=[C]C=C↔ C=CC=C + C[C]=O No

[CH]=CC=C + CC=O↔ C=CC=C + C[C]=O No

[CH]=CC=C + CC=O↔ C=CC=C + [CH2]C=O Yes

[CH]=CC=C + CC↔ C=CC=C + C[CH2] Yes

C=[C]C=C + CC↔ C=CC=C + C[CH2] Yes

C=CC=CC + C[CH2]↔ CC + [CH2]C=CC=C No

C1=CCCC=C1 + C[CH2]↔ CC + [CH]1C=CC=CC1 Yes

[CH]=CC=C + C=C=O↔ C=CC=C + [CH]=C=O Yes

[CH]=CC=C + CO↔ C=CC=C + [CH2]O No

C=CC=C + [C]#C↔ C#C + [CH]=CC=C Yes

[CH]=CC=C + C=O↔ C=CC=C + [CH]=O Yes

[CH]=CC=C + CC=C=O↔ C=CC=C + [CH2]C=C=O No

[CH]=CC=C + C=CC=O↔ C=CC=C + C=C[C]=O No

C=[C]C=C + C=CC=O↔ C=CC=C + C=C[C]=O Yes

Continued on next page

140

Table B.3 – continued from previous pageReactions FoundC=CC=CC + C=C[C]=O↔ C=CC=O + [CH2]C=CC=C No

C1=CCCC=C1 + C=C[C]=O↔ C=CC=O + [CH]1C=CC=CC1 Yes

C=CC=C + [CH]=CC#C↔ C#CC=C + [CH]=CC=C Yes

[CH]=CC=C + C#CC=C↔ C=CC=C + C#C[C]=C Yes

CCC(=O)C(C)C + [CH3]↔ C + C[CH]C(=O)C(C)C Yes

C[CH]C(=O)C(C)C + C=CC↔ CCC(=O)C(C)C + [CH2]C=C Yes

C[CH]C(=O)C(C)C + CC(C)C(=O)C(C)C↔ CCC(=O)C(C)C + C[C](C)C(=O)C(C)C Yes

CCC(=O)C(C)C + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C[CH]C(=O)C(C)C Yes

C[CH]C(=O)C(C)C + C=CC=CC↔ CCC(=O)C(C)C + [CH2]C=CC=C Yes

C[CH]C(=O)C(C)C + C1=CCCC=C1↔ CCC(=O)C(C)C + [CH]1C=CC=CC1 Yes

CCC(=O)C(C)C + [H]↔ [H][H] + C[CH]C(=O)C(C)C Yes

CCC(=O)C(C)C + [O]↔ [OH] + C[CH]C(=O)C(C)C Yes

CCC(=O)C(C)C + [OH]↔ O + C[CH]C(=O)C(C)C Yes

C[CH]C(=O)C(C)C + [O]O↔ CCC(=O)C(C)C + [O][O] No

C[CH]C(=O)C(C)C + OO↔ CCC(=O)C(C)C + [O]O No

C[CH]C(=O)C(C)C + C#CC↔ CCC(=O)C(C)C + C#C[CH2] Yes

C[CH]C(=O)C(C)C + C=C=C↔ CCC(=O)C(C)C + [CH]=C=C Yes

CCC(=O)C(C)C + [c]1ccccc1↔ c1ccccc1 + C[CH]C(=O)C(C)C No

CCC(=O)C(C)C + C=[C]C=C↔ C=CC=C + C[CH]C(=O)C(C)C Yes

C[CH]C(=O)C(C)C + C=C1C=CCC1↔ CCC(=O)C(C)C + C=C1[CH]CC=C1 Yes

C[CH]C(=O)C(C)C + C=C1CC=CC1↔ CCC(=O)C(C)C + C=C1[CH]C=CC1 Yes

C[CH]C(=O)C(C)C + C=C1C=CCC1↔ CCC(=O)C(C)C + C=C1C=C[CH]C1 Yes

CCC(=O)C(C)C + [CH]=C↔ C=C + C[CH]C(=O)C(C)C Yes

CCC(=O)C(C)C + [CH]=CC↔ C=CC + C[CH]C(=O)C(C)C Yes

CCC(=O)C(C)C + C=[C]C↔ C=CC + C[CH]C(=O)C(C)C No

CCC(=O)C(C)C + [CH2]CC↔ CCC + C[CH]C(=O)C(C)C No

CCC(=O)C(C)C + C[CH]C↔ CCC + C[CH]C(=O)C(C)C Yes

CCC(=O)C(C)C + [CH2]↔ [CH3] + C[CH]C(=O)C(C)C Yes

C[CH]C(=O)C(C)C + CCO↔ CCC(=O)C(C)C + C[CH]O No

CCC(=O)C(C)C + [CH2]CO↔ CCO + C[CH]C(=O)C(C)C Yes

CCC(=O)C(C)C + CC[O]↔ CCO + C[CH]C(=O)C(C)C Yes

C[CH]C(=O)C(C)C + CC=O↔ CCC(=O)C(C)C + C[C]=O No

C[CH]C(=O)C(C)C + CC=O↔ CCC(=O)C(C)C + [CH2]C=O Yes

CCC(=O)C(C)C + C[CH2]↔ CC + C[CH]C(=O)C(C)C Yes

CCC(=O)C(C)C + [CH]=C=O↔ C=C=O + C[CH]C(=O)C(C)C Yes

C[CH]C(=O)C(C)C + CO↔ CCC(=O)C(C)C + [CH2]O Yes

CCC(=O)C(C)C + [C]#C↔ C#C + C[CH]C(=O)C(C)C Yes

C[CH]C(=O)C(C)C + C=O↔ CCC(=O)C(C)C + [CH]=O Yes

C[CH]C(=O)C(C)C + CC=C=O↔ CCC(=O)C(C)C + [CH2]C=C=O No

C[CH]C(=O)C(C)C + C=CC=O↔ CCC(=O)C(C)C + C=C[C]=O Yes

CCC(=O)C(C)C + [CH]=CC#C↔ C#CC=C + C[CH]C(=O)C(C)C Yes

CCC(=O)C(C)C + C#C[C]=C↔ C#CC=C + C[CH]C(=O)C(C)C Yes

CCC(=O)C(C)C + [CH]=CC=C↔ C=CC=C + C[CH]C(=O)C(C)C Yes

C=CCC + [CH3]↔ C + C=C[CH]C No

C=CCC + [CH2]C=C↔ C=CC + C=C[CH]C Yes

C=CCC + C[C](C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C=C[CH]C Yes

C=CCC + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + C=C[CH]C Yes

C=C[CH]C + C=CC=CC↔ C=CCC + [CH2]C=CC=C Yes

Continued on next page

141

Table B.3 – continued from previous pageReactions FoundC=C[CH]C + C1=CCCC=C1↔ C=CCC + [CH]1C=CC=CC1 Yes

C=CCC + [H]↔ [H][H] + C=C[CH]C Yes

C=CCC + [O]↔ [OH] + C=C[CH]C No

C=CCC + [OH]↔ O + C=C[CH]C No

C=C[CH]C + [O]O↔ C=CCC + [O][O] No

C=CCC + [O]O↔ OO + C=C[CH]C Yes

C=CCC + C#C[CH2]↔ C#CC + C=C[CH]C No

C=CCC + [CH]=C=C↔ C=C=C + C=C[CH]C Yes

C=CCC + [c]1ccccc1↔ c1ccccc1 + C=C[CH]C No

C=CCC + C=[C]C=C↔ C=CC=C + C=C[CH]C Yes

C=CCC + C=C1[CH]CC=C1↔ C=C1C=CCC1 + C=C[CH]C No

C=C[CH]C + C=C1CC=CC1↔ C=CCC + C=C1[CH]C=CC1 Yes

C=C[CH]C + C=C1C=CCC1↔ C=CCC + C=C1C=C[CH]C1 Yes

C=CCC + [CH]=C↔ C=C + C=C[CH]C Yes

C=CCC + [CH]=CC↔ C=CC + C=C[CH]C Yes

C=CCC + C=[C]C↔ C=CC + C=C[CH]C Yes

C=CCC + [CH2]CC↔ CCC + C=C[CH]C Yes

C=CCC + C[CH]C↔ CCC + C=C[CH]C No

C=CCC + [CH2]↔ [CH3] + C=C[CH]C Yes

C=CCC + C[CH]O↔ CCO + C=C[CH]C No

C=CCC + [CH2]CO↔ CCO + C=C[CH]C Yes

C=CCC + CC[O]↔ CCO + C=C[CH]C Yes

C=CCC + C[C]=O↔ CC=O + C=C[CH]C No

C=CCC + [CH2]C=O↔ CC=O + C=C[CH]C Yes

C=CCC + C[CH2]↔ CC + C=C[CH]C Yes

C=CCC + [CH]=C=O↔ C=C=O + C=C[CH]C Yes

C=CCC + [CH2]O↔ CO + C=C[CH]C Yes

C=CCC + [C]#C↔ C#C + C=C[CH]C Yes

C=CCC + [CH]=O↔ C=O + C=C[CH]C No

C=CCC + [CH2]C=C=O↔ CC=C=O + C=C[CH]C No

C=CCC + C=C[C]=O↔ C=CC=O + C=C[CH]C No

C=CCC + [CH]=CC#C↔ C#CC=C + C=C[CH]C Yes

C=CCC + C#C[C]=C↔ C#CC=C + C=C[CH]C Yes

C=CCC + [CH]=CC=C↔ C=CC=C + C=C[CH]C No

C=CCC + C[CH]C(=O)C(C)C↔ CCC(=O)C(C)C + C=C[CH]C Yes

C1=CCC=C1 + [CH3]↔ C + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [CH2]C=C↔ C=CC + [CH]1C=CC=C1 Yes

C1=CCC=C1 + C[C](C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [CH2]C(C)C(=O)C(C)C↔ CC(C)C(=O)C(C)C + [CH]1C=CC=C1 Yes

[CH]1C=CC=C1 + C=CC=CC↔ C1=CCC=C1 + [CH2]C=CC=C No

[CH]1C=CC=C1 + C1=CCCC=C1↔ C1=CCC=C1 + [CH]1C=CC=CC1 Yes

C1=CCC=C1 + [H]↔ [H][H] + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [O]↔ [OH] + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [OH]↔ O + [CH]1C=CC=C1 No

[CH]1C=CC=C1 + [O]O↔ C1=CCC=C1 + [O][O] No

C1=CCC=C1 + [O]O↔ OO + [CH]1C=CC=C1 Yes

C1=CCC=C1 + C#C[CH2]↔ C#CC + [CH]1C=CC=C1 No

C1=CCC=C1 + [CH]=C=C↔ C=C=C + [CH]1C=CC=C1 Yes

Continued on next page

142

Table B.3 – continued from previous pageReactions FoundC1=CCC=C1 + [c]1ccccc1↔ c1ccccc1 + [CH]1C=CC=C1 No

C1=CCC=C1 + C=[C]C=C↔ C=CC=C + [CH]1C=CC=C1 Yes

C1=CCC=C1 + C=C1[CH]CC=C1↔ C=C1C=CCC1 + [CH]1C=CC=C1 No

[CH]1C=CC=C1 + C=C1CC=CC1↔ C1=CCC=C1 + C=C1[CH]C=CC1 Yes

[CH]1C=CC=C1 + C=C1C=CCC1↔ C1=CCC=C1 + C=C1C=C[CH]C1 Yes

C1=CCC=C1 + [CH]=C↔ C=C + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [CH]=CC↔ C=CC + [CH]1C=CC=C1 No

C1=CCC=C1 + C=[C]C↔ C=CC + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [CH2]CC↔ CCC + [CH]1C=CC=C1 No

C1=CCC=C1 + C[CH]C↔ CCC + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [CH2]↔ [CH3] + [CH]1C=CC=C1 Yes

C1=CCC=C1 + C[CH]O↔ CCO + [CH]1C=CC=C1 No

C1=CCC=C1 + [CH2]CO↔ CCO + [CH]1C=CC=C1 Yes

C1=CCC=C1 + CC[O]↔ CCO + [CH]1C=CC=C1 No

C1=CCC=C1 + C[C]=O↔ CC=O + [CH]1C=CC=C1 No

C1=CCC=C1 + [CH2]C=O↔ CC=O + [CH]1C=CC=C1 Yes

C1=CCC=C1 + C[CH2]↔ CC + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [CH]=C=O↔ C=C=O + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [CH2]O↔ CO + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [C]#C↔ C#C + [CH]1C=CC=C1 No

C1=CCC=C1 + [CH]=O↔ C=O + [CH]1C=CC=C1 No

C1=CCC=C1 + [CH2]C=C=O↔ CC=C=O + [CH]1C=CC=C1 No

C1=CCC=C1 + C=C[C]=O↔ C=CC=O + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [CH]=CC#C↔ C#CC=C + [CH]1C=CC=C1 Yes

C1=CCC=C1 + C#C[C]=C↔ C#CC=C + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [CH]=CC=C↔ C=CC=C + [CH]1C=CC=C1 No

C1=CCC=C1 + C[CH]C(=O)C(C)C↔ CCC(=O)C(C)C + [CH]1C=CC=C1 Yes

C1=CCC=C1 + C=C[CH]C↔ C=CCC + [CH]1C=CC=C1 Yes

C1=CCC=C1 + [CH3]↔ C + [C]1=CCC=C1 Yes

[C]1=CCC=C1 + C=CC↔ C1=CCC=C1 + [CH2]C=C Yes

[C]1=CCC=C1 + CC(C)C(=O)C(C)C↔ C1=CCC=C1 + C[C](C)C(=O)C(C)C Yes

[C]1=CCC=C1 + CC(C)C(=O)C(C)C↔ C1=CCC=C1 + [CH2]C(C)C(=O)C(C)C Yes

[C]1=CCC=C1 + C=CC=CC↔ C1=CCC=C1 + [CH2]C=CC=C Yes

[C]1=CCC=C1 + C1=CCCC=C1↔ C1=CCC=C1 + [CH]1C=CC=CC1 Yes

C1=CCC=C1 + [H]↔ [H][H] + [C]1=CCC=C1 Yes

C1=CCC=C1 + [O]↔ [OH] + [C]1=CCC=C1 Yes

C1=CCC=C1 + [OH]↔ O + [C]1=CCC=C1 Yes

[C]1=CCC=C1 + [O]O↔ C1=CCC=C1 + [O][O] No

[C]1=CCC=C1 + OO↔ C1=CCC=C1 + [O]O No

[C]1=CCC=C1 + C#CC↔ C1=CCC=C1 + C#C[CH2] Yes

[C]1=CCC=C1 + C=C=C↔ C1=CCC=C1 + [CH]=C=C Yes

C1=CCC=C1 + [c]1ccccc1↔ c1ccccc1 + [C]1=CCC=C1 No

[C]1=CCC=C1 + C=CC=C↔ C1=CCC=C1 + C=[C]C=C Yes

[C]1=CCC=C1 + C=C1C=CCC1↔ C1=CCC=C1 + C=C1[CH]CC=C1 Yes

[C]1=CCC=C1 + C=C1CC=CC1↔ C1=CCC=C1 + C=C1[CH]C=CC1 Yes

[C]1=CCC=C1 + C=C1C=CCC1↔ C1=CCC=C1 + C=C1C=C[CH]C1 Yes

C1=CCC=C1 + [CH]=C↔ C=C + [C]1=CCC=C1 Yes

C1=CCC=C1 + [CH]=CC↔ C=CC + [C]1=CCC=C1 Yes

Continued on next page

143

Table B.3 – continued from previous pageReactions FoundC1=CCC=C1 + C=[C]C↔ C=CC + [C]1=CCC=C1 No

[C]1=CCC=C1 + CCC↔ C1=CCC=C1 + [CH2]CC No

[C]1=CCC=C1 + CCC↔ C1=CCC=C1 + C[CH]C Yes

C1=CCC=C1 + [CH2]↔ [CH3] + [C]1=CCC=C1 No

[C]1=CCC=C1 + CCO↔ C1=CCC=C1 + C[CH]O No

C1=CCC=C1 + [CH2]CO↔ CCO + [C]1=CCC=C1 Yes

C1=CCC=C1 + CC[O]↔ CCO + [C]1=CCC=C1 Yes

[C]1=CCC=C1 + CC=O↔ C1=CCC=C1 + C[C]=O Yes

[C]1=CCC=C1 + CC=O↔ C1=CCC=C1 + [CH2]C=O Yes

[C]1=CCC=C1 + CC↔ C1=CCC=C1 + C[CH2] Yes

C1=CCC=C1 + [CH]=C=O↔ C=C=O + [C]1=CCC=C1 Yes

[C]1=CCC=C1 + CO↔ C1=CCC=C1 + [CH2]O Yes

C1=CCC=C1 + [C]#C↔ C#C + [C]1=CCC=C1 Yes

[C]1=CCC=C1 + C=O↔ C1=CCC=C1 + [CH]=O Yes

[C]1=CCC=C1 + CC=C=O↔ C1=CCC=C1 + [CH2]C=C=O No

[C]1=CCC=C1 + C=CC=O↔ C1=CCC=C1 + C=C[C]=O Yes

C1=CCC=C1 + [CH]=CC#C↔ C#CC=C + [C]1=CCC=C1 Yes

[C]1=CCC=C1 + C#CC=C↔ C1=CCC=C1 + C#C[C]=C Yes

C1=CCC=C1 + [CH]=CC=C↔ C=CC=C + [C]1=CCC=C1 Yes

[C]1=CCC=C1 + CCC(=O)C(C)C↔ C1=CCC=C1 + C[CH]C(=O)C(C)C Yes

[C]1=CCC=C1 + C=CCC↔ C1=CCC=C1 + C=C[CH]C Yes

[C]1=CCC=C1 + C1=CCC=C1↔ C1=CCC=C1 + [CH]1C=CC=C1 Yes

[CH2]C(C)C(=O)C(C)C + C=C=C=C↔ CC(C)C(=O)C(C)C + [CH]=C=C=C Yes

CC(C)C(=O)C(C)C + [CH]=C=C=C↔ C=C=C=C + C[C](C)C(=O)C(C)C Yes

[H] + C=C=C=C↔ [H][H] + [CH]=C=C=C No

[CH3] + C=C=C=C↔ C + [CH]=C=C=C Yes

[C]#C + C=C=C=C↔ C#C + [CH]=C=C=C Yes

[CH]=C + C=C=C=C↔ C=C + [CH]=C=C=C No

[CH]=CC + C=C=C=C↔ C=CC + [CH]=C=C=C Yes

C=[C]C + C=C=C=C↔ C=CC + [CH]=C=C=C Yes

C=CC + [CH]=C=C=C↔ C=C=C=C + [CH2]C=C Yes

C=C=C + [CH]=C=C=C↔ C=C=C=C + [CH]=C=C No

C#CC + [CH]=C=C=C↔ C=C=C=C + C#C[CH2] No

[CH]=CC#C + C=C=C=C↔ C#CC=C + [CH]=C=C=C No

C#C[C]=C + C=C=C=C↔ C#CC=C + [CH]=C=C=C Yes

[CH]=CC=C + C=C=C=C↔ C=CC=C + [CH]=C=C=C Yes

C=[C]C=C + C=C=C=C↔ C=CC=C + [CH]=C=C=C Yes

CC=C=O + [CH]=C=C=C↔ C=C=C=C + [CH2]C=C=O Yes

C=CC=CC + [CH]=C=C=C↔ C=C=C=C + [CH2]C=CC=C No

[C]1=CCC=C1 + C=C=C=C↔ C1=CCC=C1 + [CH]=C=C=C No

C1=CCC=C1 + [CH]=C=C=C↔ C=C=C=C + [CH]1C=CC=C1 Yes

[c]1ccccc1 + C=C=C=C↔ c1ccccc1 + [CH]=C=C=C No

C1=CCCC=C1 + [CH]=C=C=C↔ C=C=C=C + [CH]1C=CC=CC1 Yes

C[CH]C(=O)C(C)C + C=C=C=C↔ CCC(=O)C(C)C + [CH]=C=C=C No

[OH] + C=C=C=C↔ O + [CH]=C=C=C Yes

[O]O + [CH]=C=C=C↔ C=C=C=C + [O][O] Yes

OO + [CH]=C=C=C↔ C=C=C=C + [O]O No

C=C1C=CCC1 + [CH]=C=C=C↔ C=C=C=C + C=C1C=C[CH]C1 No

Continued on next page

144

Table B.3 – continued from previous pageReactions FoundC=C1C=CCC1 + [CH]=C=C=C↔ C=C=C=C + C=C1[CH]CC=C1 No

C=C1CC=CC1 + [CH]=C=C=C↔ C=C=C=C + C=C1[CH]C=CC1 No

[CH]=C=O + C=C=C=C↔ C=C=O + [CH]=C=C=C Yes

C=O + [CH]=C=C=C↔ C=C=C=C + [CH]=O Yes

[CH2]O + C=C=C=C↔ CO + [CH]=C=C=C No

[CH2]CO + C=C=C=C↔ CCO + [CH]=C=C=C Yes

C[CH]O + C=C=C=C↔ CCO + [CH]=C=C=C Yes

CC[O] + C=C=C=C↔ CCO + [CH]=C=C=C Yes

[CH2]C=O + C=C=C=C↔ CC=O + [CH]=C=C=C Yes

CC=O + [CH]=C=C=C↔ C=C=C=C + C[C]=O Yes

C[CH2] + C=C=C=C↔ CC + [CH]=C=C=C Yes

[CH2]CC + C=C=C=C↔ CCC + [CH]=C=C=C No

C[CH]C + C=C=C=C↔ CCC + [CH]=C=C=C Yes

C=CC=O + [CH]=C=C=C↔ C=C=C=C + C=C[C]=O Yes

C=CCC + [CH]=C=C=C↔ C=C=C=C + C=C[CH]C Yes

C=C=C=C + [O]↔ [OH] + [CH]=C=C=C Yes

C=C=C=C + [CH2]↔ [CH3] + [CH]=C=C=C Yes

C=CCC + [CH3]↔ C + [CH2]CC=C Yes

[CH2]CC=C + C=CC↔ C=CCC + [CH2]C=C Yes

[CH2]CC=C + CC(C)C(=O)C(C)C↔ C=CCC + C[C](C)C(=O)C(C)C Yes

[CH2]CC=C + CC(C)C(=O)C(C)C↔ C=CCC + [CH2]C(C)C(=O)C(C)C No

[CH2]CC=C + C=CC=CC↔ C=CCC + [CH2]C=CC=C Yes

[CH2]CC=C + C1=CCCC=C1↔ C=CCC + [CH]1C=CC=CC1 Yes

C=CCC + [H]↔ [H][H] + [CH2]CC=C No

C=CCC + [O]↔ [OH] + [CH2]CC=C Yes

C=CCC + [OH]↔ O + [CH2]CC=C Yes

[CH2]CC=C + [O]O↔ C=CCC + [O][O] No

[CH2]CC=C + OO↔ C=CCC + [O]O No

[CH2]CC=C + C#CC↔ C=CCC + C#C[CH2] No

[CH2]CC=C + C=C=C↔ C=CCC + [CH]=C=C Yes

C=CCC + [c]1ccccc1↔ c1ccccc1 + [CH2]CC=C Yes

[CH2]CC=C + C=CC=C↔ C=CCC + C=[C]C=C Yes

[CH2]CC=C + C=C1C=CCC1↔ C=CCC + C=C1[CH]CC=C1 No

[CH2]CC=C + C=C1CC=CC1↔ C=CCC + C=C1[CH]C=CC1 No

[CH2]CC=C + C=C1C=CCC1↔ C=CCC + C=C1C=C[CH]C1 No

C=CCC + [CH]=C↔ C=C + [CH2]CC=C Yes

C=CCC + [CH]=CC↔ C=CC + [CH2]CC=C Yes

C=CCC + C=[C]C↔ C=CC + [CH2]CC=C Yes

[CH2]CC=C + CCC↔ C=CCC + [CH2]CC Yes

[CH2]CC=C + CCC↔ C=CCC + C[CH]C Yes

C=CCC + [CH2]↔ [CH3] + [CH2]CC=C Yes

[CH2]CC=C + CCO↔ C=CCC + C[CH]O No

C=CCC + [CH2]CO↔ CCO + [CH2]CC=C Yes

C=CCC + CC[O]↔ CCO + [CH2]CC=C Yes

[CH2]CC=C + CC=O↔ C=CCC + C[C]=O Yes

[CH2]CC=C + CC=O↔ C=CCC + [CH2]C=O Yes

[CH2]CC=C + CC↔ C=CCC + C[CH2] Yes

C=CCC + [CH]=C=O↔ C=C=O + [CH2]CC=C Yes

Continued on next page

145

Table B.3 – continued from previous pageReactions Found[CH2]CC=C + CO↔ C=CCC + [CH2]O Yes

C=CCC + [C]#C↔ C#C + [CH2]CC=C Yes

[CH2]CC=C + C=O↔ C=CCC + [CH]=O No

[CH2]CC=C + CC=C=O↔ C=CCC + [CH2]C=C=O No

[CH2]CC=C + C=CC=O↔ C=CCC + C=C[C]=O Yes

C=CCC + [CH]=CC#C↔ C#CC=C + [CH2]CC=C Yes

[CH2]CC=C + C#CC=C↔ C=CCC + C#C[C]=C Yes

[CH2]CC=C + C=C=C=C↔ C=CCC + [CH]=C=C=C Yes

C=CCC + [CH]=CC=C↔ C=CC=C + [CH2]CC=C Yes

[CH2]CC=C + CCC(=O)C(C)C↔ C=CCC + C[CH]C(=O)C(C)C Yes

[CH2]CC=C + C=CCC↔ C=CCC + C=C[CH]C Yes

[CH2]CC=C + C1=CCC=C1↔ C=CCC + [CH]1C=CC=C1 Yes

C=CCC + [C]1=CCC=C1↔ C1=CCC=C1 + [CH2]CC=C Yes

CC(C)C + [CH3]↔ C + [CH2]C(C)C Yes

[CH2]C(C)C + C=CC↔ CC(C)C + [CH2]C=C Yes

[CH2]C(C)C + CC(C)C(=O)C(C)C↔ CC(C)C + C[C](C)C(=O)C(C)C Yes

[CH2]C(C)C + CC(C)C(=O)C(C)C↔ CC(C)C + [CH2]C(C)C(=O)C(C)C No

[CH2]C(C)C + C=CC=CC↔ CC(C)C + [CH2]C=CC=C Yes

[CH2]C(C)C + C1=CCCC=C1↔ CC(C)C + [CH]1C=CC=CC1 Yes

CC(C)C + [H]↔ [H][H] + [CH2]C(C)C Yes

CC(C)C + [O]↔ [OH] + [CH2]C(C)C Yes

CC(C)C + [OH]↔ O + [CH2]C(C)C Yes

[CH2]C(C)C + [O]O↔ CC(C)C + [O][O] No

[CH2]C(C)C + OO↔ CC(C)C + [O]O No

[CH2]C(C)C + C#CC↔ CC(C)C + C#C[CH2] Yes

[CH2]C(C)C + C=C=C↔ CC(C)C + [CH]=C=C Yes

CC(C)C + [c]1ccccc1↔ c1ccccc1 + [CH2]C(C)C Yes

CC(C)C + C=[C]C=C↔ C=CC=C + [CH2]C(C)C No

[CH2]C(C)C + C=C1C=CCC1↔ CC(C)C + C=C1[CH]CC=C1 No

[CH2]C(C)C + C=C1CC=CC1↔ CC(C)C + C=C1[CH]C=CC1 Yes

[CH2]C(C)C + C=C1C=CCC1↔ CC(C)C + C=C1C=C[CH]C1 Yes

CC(C)C + [CH]=C↔ C=C + [CH2]C(C)C No

CC(C)C + [CH]=CC↔ C=CC + [CH2]C(C)C Yes

CC(C)C + C=[C]C↔ C=CC + [CH2]C(C)C Yes

CC(C)C + [CH2]CC↔ CCC + [CH2]C(C)C Yes

[CH2]C(C)C + CCC↔ CC(C)C + C[CH]C Yes

CC(C)C + [CH2]↔ [CH3] + [CH2]C(C)C Yes

[CH2]C(C)C + CCO↔ CC(C)C + C[CH]O No

CC(C)C + [CH2]CO↔ CCO + [CH2]C(C)C Yes

CC(C)C + CC[O]↔ CCO + [CH2]C(C)C Yes

[CH2]C(C)C + CC=O↔ CC(C)C + C[C]=O Yes

[CH2]C(C)C + CC=O↔ CC(C)C + [CH2]C=O Yes

[CH2]C(C)C + CC↔ CC(C)C + C[CH2] Yes

CC(C)C + [CH]=C=O↔ C=C=O + [CH2]C(C)C Yes

[CH2]C(C)C + CO↔ CC(C)C + [CH2]O Yes

CC(C)C + [C]#C↔ C#C + [CH2]C(C)C Yes

[CH2]C(C)C + C=O↔ CC(C)C + [CH]=O No

[CH2]C(C)C + CC=C=O↔ CC(C)C + [CH2]C=C=O No

Continued on next page

146

Table B.3 – continued from previous pageReactions Found[CH2]C(C)C + C=CC=O↔ CC(C)C + C=C[C]=O Yes

CC(C)C + [CH]=CC#C↔ C#CC=C + [CH2]C(C)C Yes

CC(C)C + C#C[C]=C↔ C#CC=C + [CH2]C(C)C Yes

[CH2]C(C)C + C=C=C=C↔ CC(C)C + [CH]=C=C=C Yes

CC(C)C + [CH]=CC=C↔ C=CC=C + [CH2]C(C)C Yes

[CH2]C(C)C + CCC(=O)C(C)C↔ CC(C)C + C[CH]C(=O)C(C)C Yes

[CH2]C(C)C + C=CCC↔ CC(C)C + C=C[CH]C Yes

[CH2]C(C)C + C1=CCC=C1↔ CC(C)C + [CH]1C=CC=C1 Yes

CC(C)C + [C]1=CCC=C1↔ C1=CCC=C1 + [CH2]C(C)C Yes

CC(C)C + [CH2]CC=C↔ C=CCC + [CH2]C(C)C Yes

[CH2]C(C)C(=O)C(C)C + C=CCC=C↔ CC(C)C(=O)C(C)C + C=C[CH]C=C Yes

C[C](C)C(=O)C(C)C + C=CCC=C↔ CC(C)C(=O)C(C)C + C=C[CH]C=C Yes

[H] + C=CCC=C↔ [H][H] + C=C[CH]C=C Yes

[CH3] + C=CCC=C↔ C + C=C[CH]C=C Yes

[C]#C + C=CCC=C↔ C#C + C=C[CH]C=C Yes

[CH]=C + C=CCC=C↔ C=C + C=C[CH]C=C No

[CH]=CC + C=CCC=C↔ C=CC + C=C[CH]C=C No

C=[C]C + C=CCC=C↔ C=CC + C=C[CH]C=C Yes

[CH2]C=C + C=CCC=C↔ C=CC + C=C[CH]C=C No

[CH]=C=C + C=CCC=C↔ C=C=C + C=C[CH]C=C Yes

C#C[CH2] + C=CCC=C↔ C#CC + C=C[CH]C=C No

[CH]=CC#C + C=CCC=C↔ C#CC=C + C=C[CH]C=C Yes

C#C[C]=C + C=CCC=C↔ C#CC=C + C=C[CH]C=C Yes

[CH]=CC=C + C=CCC=C↔ C=CC=C + C=C[CH]C=C No

C=[C]C=C + C=CCC=C↔ C=CC=C + C=C[CH]C=C No

[CH2]C=C=O + C=CCC=C↔ CC=C=O + C=C[CH]C=C No

[CH2]C=CC=C + C=CCC=C↔ C=CC=CC + C=C[CH]C=C Yes

[C]1=CCC=C1 + C=CCC=C↔ C1=CCC=C1 + C=C[CH]C=C Yes

[CH]1C=CC=C1 + C=CCC=C↔ C1=CCC=C1 + C=C[CH]C=C Yes

[c]1ccccc1 + C=CCC=C↔ c1ccccc1 + C=C[CH]C=C Yes

[CH]1C=CC=CC1 + C=CCC=C↔ C1=CCCC=C1 + C=C[CH]C=C No

C[CH]C(=O)C(C)C + C=CCC=C↔ CCC(=O)C(C)C + C=C[CH]C=C Yes

[OH] + C=CCC=C↔ O + C=C[CH]C=C Yes

[O]O + C=C[CH]C=C↔ C=CCC=C + [O][O] No

[O]O + C=CCC=C↔ OO + C=C[CH]C=C No

C=C1C=C[CH]C1 + C=CCC=C↔ C=C1C=CCC1 + C=C[CH]C=C No

C=C1[CH]CC=C1 + C=CCC=C↔ C=C1C=CCC1 + C=C[CH]C=C Yes

C=C1CC=CC1 + C=C[CH]C=C↔ C=CCC=C + C=C1[CH]C=CC1 Yes

[CH]=C=O + C=CCC=C↔ C=C=O + C=C[CH]C=C Yes

[CH]=O + C=CCC=C↔ C=O + C=C[CH]C=C Yes

[CH2]O + C=CCC=C↔ CO + C=C[CH]C=C Yes

[CH2]CO + C=CCC=C↔ CCO + C=C[CH]C=C Yes

C[CH]O + C=CCC=C↔ CCO + C=C[CH]C=C Yes

CC[O] + C=CCC=C↔ CCO + C=C[CH]C=C Yes

[CH2]C=O + C=CCC=C↔ CC=O + C=C[CH]C=C Yes

C[C]=O + C=CCC=C↔ CC=O + C=C[CH]C=C No

C[CH2] + C=CCC=C↔ CC + C=C[CH]C=C Yes

[CH2]CC + C=CCC=C↔ CCC + C=C[CH]C=C No

Continued on next page

147

Table B.3 – continued from previous pageReactions FoundC[CH]C + C=CCC=C↔ CCC + C=C[CH]C=C Yes

C=C[C]=O + C=CCC=C↔ C=CC=O + C=C[CH]C=C Yes

[CH2]C(C)C + C=CCC=C↔ CC(C)C + C=C[CH]C=C Yes

C=C[CH]C + C=CCC=C↔ C=CCC + C=C[CH]C=C Yes

[CH2]CC=C + C=CCC=C↔ C=CCC + C=C[CH]C=C Yes

[CH]=C=C=C + C=CCC=C↔ C=C=C=C + C=C[CH]C=C Yes

C=CCC=C + [O]↔ [OH] + C=C[CH]C=C No

C=CCC=C + [CH2]↔ [CH3] + C=C[CH]C=C No

148

B.7 Effect of increasing force constants and reducing the difference between upper

and lower limits

Figure B.2: Decreasing the distance and increasing the force constants for the reac-tion center each minimized error in the dHY distance introduced duringthe construction of the 3-dimensional transition state estimate. The errorreduction is additive as seen when combining the modifications.

149

Figure B.3: Decreasing the distance and increasing the force constants for the reac-tion center each minimized error in the dXY distance introduced duringthe construction of the 3-dimensional transition state estimate. The errorreduction is additive as seen when combining the modifications.

C. Kinetic calculations

C.1 Molecular group trees

C.1.1 Hydrogen Abstraction

Table C.1: Molecular group tree with distance group data in A for the hydrogen ab-straction reaction family.

Groups TS count dXH (A) dHY (A) dXY (A)L1: X H or Xrad H Xbirad H Xtrirad H 2160 1.302340 1.301790 2.587830

L2: H2 99 -0.334232 -0.026237 -0.348259

L2: C H 1531 0.042361 0.013802 0.056955

L3: Cs H 983 0.021965 0.030462 0.055401

L4: Csnorad H 949 0.021077 0.032448 0.056390

L5: C methane 63 0.084181 -0.043153 0.053187

L5: CsRHHH 542 0.032564 0.016179 0.053140

L6: CsCHHH 469 0.034758 0.013193 0.054628

L7: C/H3/Cs 257 0.056230 -0.015089 0.049210

L7: C/H3/Cd 128 -0.005007 0.066501 0.066401

L7: C/H3/Ct 20 0.033807 0.014522 0.055796

L7: C/H3/Cb

L6: CsOHHH 73 0.018498 0.035323 0.043597

L6: CsClHHH

L6: CsNHHH

L6: CsSiHHH

L6: CsSHHH

L5: CsRRHH 308 -0.011445 0.077412 0.063968

L6: CsCCHH 249 -0.016637 0.083646 0.068467

L7: C/H2/Cs/Cs 71 0.024854 0.014441 0.043693

L7: C/H2/Cs/Cd 101 -0.029327 0.104563 0.074517

L7: C/H2/Cs/Ct

L7: C/H2/Cs/Cb

L7: C/H2/Cd/Cd 60 -0.041748 0.129523 0.089601

L7: C/H2/Cd/Ct

L7: C/H2/Cd/Cb

L7: C/H2/Ct/Ct

L7: C/H2/Ct/Cb

L7: C/H2/Cb/Cb

L6: CsCOHH 59 0.010319 0.051278 0.045111

L7: C/H2/Cs/O 59 0.010319 0.051278 0.045111

L7: C/H2/Cd/O

L7: C/H2/Ct/O

L7: C/H2/Cb/O

L6: CsCClHH

Continued on next page

150

151

Table C.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L6: CsCNHH

L6: CsCSiHH

L6: CsCSHH

L6: CsOOHH

L5: CsRRRH 36 0.002993 0.038881 0.045616

L6: CsCCCH 29 0.000142 0.038829 0.043770

L7: C/H/Cs/Cs/Cs 12 -0.003029 0.034764 0.040281

L7: C/H/Cs/Cs/Cd

L7: C/H/Cs/Cs/Ct

L7: C/H/Cs/Cs/Cb

L7: C/H/Cs/Cd/Cd

L7: C/H/Cs/Cd/Ct

L7: C/H/Cs/Cd/Cb

L7: C/H/Cs/Ct/Ct

L7: C/H/Cs/Ct/Cb

L7: C/H/Cs/Cb/Cb

L7: C/H/Cd/Cd/Cd

L7: C/H/Cd/Cd/Ct

L7: C/H/Cd/Cd/Cb

L7: C/H/Cd/Ct/Ct

L7: C/H/Cd/Ct/Cb

L7: C/H/Cd/Cb/Cb

L7: C/H/Ct/Ct/Ct

L7: C/H/Ct/Ct/Cb

L7: C/H/Ct/Cb/Cb

L7: C/H/Cb/Cb/Cb

L6: CsCCOH 7 0.015687 0.039114 0.053833

L7: C/H/Cs/Cs/O 7 0.015687 0.039114 0.053833

L7: C/H/Cs/Cd/O

L7: C/H/Cs/Ct/O

L7: C/H/Cs/Cb/O

L7: C/H/Cd/Cd/O

L7: C/H/Cd/Ct/O

L7: C/H/Cd/Cb/O

L7: C/H/Ct/Ct/O

L7: C/H/Ct/Cb/O

L7: C/H/Cb/Cb/O

L6: CsCCClH

L6: CsCCNH

L6: CsCCSiH

L6: CsCCSH

L6: CsCOOH

L7: C/H/Cs/O/O

L7: C/H/Cd/O/O

L7: C/H/Ct/O/O

L7: C/H/Cb/O/O

L6: CsOOOH

L4: Csrad H 32 0.046940 -0.021165 0.033333

Continued on next page

152

Table C.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L5: C methyl 17 0.090667 -0.061808 0.037283

L5: CsradRH2 15 -0.008411 0.030282 0.028332

L6: CsradCHH 15 -0.008411 0.030282 0.028332

L7: Csrad/H/Cs/H

L7: Csrad/H/Cd/H

L7: Csrad/H/Ct/H 15 -0.008411 0.030282 0.028332

L7: Csrad/H/Cb/H

L6: CsradOH2

L5: CsradRRH

L6: CsradCCH

L7: Csrad/Cs/Cs/H

L7: Csrad/Cs/Cd/H

L7: Csrad/Cs/Ct/H

L7: Csrad/Cs/Cb/H

L7: Csrad/Cd/Cd/H

L7: Csrad/Cd/Ct/H

L7: Csrad/Cd/Cb/H

L7: Csrad/Ct/Ct/H

L7: Csrad/Ct/Cb/H

L7: Csrad/Cb/Cb/H

L6: CsradCOH

L7: Csrad/Cs/O/H

L7: Csrad/Cd/O/H

L7: Csrad/Ct/O/H

L7: Csrad/Cb/O/H

L6: CsradOOH

L4: CsbiradH 2 0.046729 -0.150684 -0.143516

L5: Cs singletH

L6: Cs singletHH

L6: Cs singletRH

L7: C singletCH

L8: C singlet/Cs/H

L8: C singlet/Cd/H

L8: C singlet/Ct/H

L8: C singlet/Cb/H

L7: C singletOH

L5: Cs tripletH 2 0.046729 -0.150684 -0.143516

L6: Cs tripletHH 2 0.046729 -0.150684 -0.143516

L6: Cs tripletRH

L7: Cs tripletCH

L8: C triplet/Cs/H

L8: C triplet/Cd/H

L8: C triplet/Ct/H

L8: C triplet/Cb/H

L7: Cs tripletOH

L4: CstriradH

L5: Cdoublet H

L5: Cquartet H

Continued on next page

153

Table C.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L3: Cd H 310 0.089459 -0.051663 0.040317

L4: Cdnorad H 284 0.097443 -0.057949 0.043368

L5: Cd C/R/H 284 0.097443 -0.057949 0.043368

L6: Cd C/H2 180 0.098347 -0.058882 0.042131

L7: Cd Cds/H2 113 0.120638 -0.076649 0.048701

L7: Cd Cdd/H2 67 0.062945 -0.030666 0.031698

L6: Cd C/C/H 104 0.095841 -0.056294 0.045563

L7: Cd Cds/Cs/H 38 0.089965 -0.048448 0.047802

L7: Cd Cds/Cd/H 51 0.105603 -0.066739 0.044881

L7: Cd Cds/Ct/H 15 0.077044 -0.039990 0.042408

L7: Cd Cds/Cb/H

L7: Cd Cdd/Cs/H

L7: Cd Cdd/Cd/H

L7: Cd Cdd/Ct/H

L7: Cd Cdd/Cb/H

L6: Cd C/O/H

L7: Cd Cds/O/H

L7: Cd Cdd/O/H

L5: Cd O/R/H

L6: Cd O/H2

L6: Cd O/C/H

L7: Cd O/Cs/H

L7: Cd O/Cd/H

L7: Cd O/Ct/H

L7: Cd O/Cb/H

L6: Cd O/O/H

L4: Cdrad H 26 0.006512 0.013635 0.008624

L5: Cdrad C/H 26 0.006512 0.013635 0.008624

L6: Cdrad Cds/H

L6: Cdrad Cdd/H 26 0.006512 0.013635 0.008624

L5: Cdrad O/H

L3: Ct H 20 0.459597 -0.204392 0.207500

L3: Cb H 30 0.119688 -0.081353 0.044020

L2: O H 520 -0.065043 -0.037997 -0.107342

L3: OradH 30 -0.035310 -0.089621 -0.121745

L3: ORH 490 -0.067028 -0.034550 -0.106381

L4: OHH 70 0.116491 -0.170432 -0.075411

L4: OCH 105 -0.013657 -0.113478 -0.132370

L5: O/Cs/H 99 -0.014675 -0.114277 -0.133992

L5: O/Cd/H 4 -0.069779 -0.048202 -0.119096

L5: O/Ct/H

L5: O/Cb/H

L4: OOH 315 -0.129641 0.024288 -0.105867

L2: Cl H 1 0.395488 -0.184160 0.069450

L2: Si H 7 0.304476 0.226924 0.533363

L2: N H

L3: N3 H

L4: N3s H

Continued on next page

154

Table C.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L5: NH3

L5: N3s/H2/R

L6: N3s/H2/C

L6: N3s/H2/N

L6: N3s/H2/O

L6: N3s/H2/Si

L6: N3s/H2/S

L6: N3s/H2/Cl

L5: N3s/H/R/R

L6: N3s/H/C/C

L6: N3s/H/C/N

L6: N3s/H/C/O

L6: N3s/H/C/Si

L6: N3s/H/C/S

L6: N3s/H/C/Cl

L6: N3s/H/N/N

L6: N3s/H/N/O

L6: N3s/H/N/Si

L6: N3s/H/N/S

L6: N3s/H/N/Cl

L6: N3s/H/O/O

L6: N3s/H/O/Si

L6: N3s/H/O/S

L6: N3s/H/O/Cl

L6: N3s/H/Si/Si

L6: N3s/H/Si/S

L6: N3s/H/Si/Cl

L6: N3s/H/S/S

L6: N3s/H/S/Cl

L6: N3s/H/Cl/Cl

L4: N3d H

L3: N5 H

L4: N5s H

L4: N5d H

L2: S H 2 0.225939 0.128426 0.248627

L3: SradH

L3: SRH 2 0.225939 0.128426 0.248627

L4: SHH 1 0.151101 0.201654 0.199974

L4: SClH

L4: SOH

L4: SCH 1 0.285809 0.069844 0.287550

L5: S/Cs/H 1 0.285809 0.069844 0.287550

L5: S/Cd/H

L5: S/Ct/H

L5: S/Cb/H

L4: SSH

L4: SNH

L4: SSiH

Continued on next page

155

Table C.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L1: Y rad birad trirad quadrad

L2: Hrad 99 -0.024278 -0.336325 -0.348540

L2: Orad 520 -0.036287 -0.067237 -0.107779

L3: OjR 490 -0.032816 -0.069208 -0.106764

L4: OjH 70 -0.168565 0.112385 -0.077781

L4: OjC 105 -0.111642 -0.016796 -0.133448

L5: OjCs 99 -0.112816 -0.017241 -0.134989

L5: OjCd 4 -0.043477 -0.072532 -0.114891

L5: OjCt

L5: OjCb

L4: OjO 315 0.026408 -0.131559 -0.105565

L3: O atom triplet 30 -0.087969 -0.037898 -0.122902

L2: Crad 1531 0.013032 0.043069 0.056882

L3: Cj 1466 0.013231 0.043776 0.058116

L4: Csj 949 0.031271 0.021748 0.056109

L5: Cs methyl 63 -0.041935 0.082581 0.052634

L5: CsjRH2 542 0.015359 0.033128 0.052856

L6: CsjCH2 469 0.012334 0.035364 0.054236

L7: Csj/Cs/H2 257 -0.016078 0.056620 0.048624

L7: Csj/Cd/H2 128 0.065052 -0.003387 0.066373

L7: Csj/Ct/H2 20 0.015649 0.032400 0.055232

L7: Csj/Cb/H2

L6: CsjOH2 73 0.034532 0.018962 0.044109

L5: CsjRRH 308 0.074972 -0.009945 0.063748

L6: CsjCCH 249 0.081137 -0.015097 0.068088

L7: Csj/Cs/Cs/H 71 0.013072 0.025416 0.043575

L7: Csj/Cs/Cd/H 101 0.101037 -0.027099 0.074047

L7: Csj/Cs/Ct/H

L7: Csj/Cs/Cb/H

L7: Csj/Cd/Cd/H 60 0.127932 -0.040702 0.089349

L7: Csj/Cd/Ct/H

L7: Csj/Cd/Cb/H

L7: Csj/Ct/Ct/H

L7: Csj/Ct/Cb/H

L7: Csj/Cb/Cb/H

L6: CsjCOH 59 0.049303 0.011508 0.045677

L7: Csj/Cs/O/H 59 0.049303 0.011508 0.045677

L7: Csj/Cd/O/H

L7: Csj/Ct/O/H

L7: Csj/Cb/O/H

L6: CsjOOH

L5: CsjRRR 36 0.038420 0.002291 0.045182

L6: CsjCCC 29 0.037866 -0.000153 0.042817

L7: Csj/Cs/Cs/Cs 12 0.037019 -0.005761 0.040111

L7: Csj/Cs/Cs/Cd

L7: Csj/Cs/Cs/Ct

L7: Csj/Cs/Cs/Cb

L7: Csj/Cs/Cd/Cd

Continued on next page

156

Table C.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L7: Csj/Cs/Cd/Ct

L7: Csj/Cs/Cd/Cb

L7: Csj/Cs/Ct/Ct

L7: Csj/Cs/Ct/Cb

L7: Csj/Cs/Cb/Cb

L7: Csj/Cd/Cd/Cd

L7: Csj/Cd/Cd/Ct

L7: Csj/Cd/Cd/Cb

L7: Csj/Cd/Ct/Ct

L7: Csj/Cd/Ct/Cb

L7: Csj/Cd/Cb/Cb

L7: Csj/Ct/Ct/Ct

L7: Csj/Ct/Ct/Cb

L7: Csj/Ct/Cb/Cb

L7: Csj/Cb/Cb/Cb

L6: CsjCCO 7 0.040874 0.013126 0.055667

L7: Csj/Cs/Cs/O 7 0.040874 0.013126 0.055667

L7: Csj/Cs/Cd/O

L7: Csj/Cs/Ct/O

L7: Csj/Cs/Cb/O

L7: Csj/Cd/Cd/O

L7: Csj/Cd/Ct/O

L7: Csj/Cd/Cb/O

L7: Csj/Ct/Ct/O

L7: Csj/Ct/Cb/O

L7: Csj/Cb/Cb/O

L6: CsjCOO

L7: Csj/Cs/O/O

L7: Csj/Cd/O/O

L7: Csj/Ct/O/O

L7: Csj/Cb/O/O

L6: CsjOOO

L4: Cdj 284 -0.058313 0.098243 0.043562

L5: Cdj CR 284 -0.058313 0.098243 0.043562

L6: Cdj CH 180 -0.059457 0.099451 0.042356

L7: Cdj CdsH 113 -0.077882 0.122527 0.049057

L7: Cdj CddH 67 -0.030443 0.063113 0.031804

L6: Cdj CC 104 -0.056290 0.096106 0.045695

L7: Cdj CdsCs 38 -0.048294 0.089904 0.047720

L7: Cdj CdsCd 51 -0.067373 0.106593 0.045123

L7: Cdj CdsCt 15 -0.038068 0.075533 0.042704

L7: Cdj CdsCb

L7: Cdj CddCs

L7: Cdj CddCd

L7: Cdj CddCt

L7: Cdj CddCb

L6: Cdj CO

L7: Cdj CdsO

Continued on next page

157

Table C.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L7: Cdj CddO

L5: Cdj OR

L6: Cdj OH

L6: Cdj OC

L7: Cdj OCs

L7: Cdj OCd

L7: Cdj OCt

L7: Cdj OCb

L6: Cdj OO

L4: Ctj 20 -0.202539 0.459642 0.208324

L5: CtjC 20 -0.202539 0.459642 0.208324

L4: Cbj 30 -0.083989 0.123085 0.044324

L3: Cjj 58 -0.004950 0.028166 0.021371

L4: Csjj 32 -0.022049 0.047291 0.032235

L5: Cs sing

L6: Cs singH2

L6: Cs singRH

L7: Cs singCH

L8: Cs sing/Cs/H

L8: Cs sing/Cd/H

L8: Cs sing/Ct/H

L8: Cs sing/Cb/H

L7: Cs singOH

L6: Cs singRR

L7: Cs singCC

L8: Cs sing/Cs/Cs

L8: Cs sing/Cs/Cd

L8: Cs sing/Cs/Ct

L8: Cs sing/Cs/Cb

L8: Cs sing/Cd/Cd

L8: Cs sing/Cd/Ct

L8: Cs sing/Cd/Cb

L8: Cs sing/Ct/Ct

L8: Cs sing/Ct/Cb

L8: Cs sing/Cb/Cb

L7: Cs singCO

L8: Cs sing/Cs/O

L8: Cs sing/Cd/O

L8: Cs sing/Ct/O

L8: Cs sing/Cb/O

L7: Cs singOO

L5: Cs trip 32 -0.022049 0.047291 0.032235

L6: Cs tripH2 17 -0.059322 0.087916 0.036802

L6: Cs tripRH 15 0.027153 -0.006333 0.026207

L7: Cs tripCH 15 0.027153 -0.006333 0.026207

L8: Cs trip/Cs/H

L8: Cs trip/Cd/H

L8: Cs trip/Ct/H 15 0.027153 -0.006333 0.026207

Continued on next page

158

Table C.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L8: Cs trip/Cb/H

L7: Cs tripOH

L6: Cs tripRR

L7: Cs tripCC

L8: Cs trip/Cs/Cs

L8: Cs trip/Cs/Cd

L8: Cs trip/Cs/Ct

L8: Cs trip/Cs/Cb

L8: Cs trip/Cd/Cd

L8: Cs trip/Cd/Ct

L8: Cs trip/Cd/Cb

L8: Cs trip/Ct/Ct

L8: Cs trip/Ct/Cb

L8: Cs trip/Cb/Cb

L7: Cs tripCO

L8: Cs trip/Cs/O

L8: Cs trip/Cd/O

L8: Cs trip/Ct/O

L8: Cs trip/Cb/O

L7: Cs tripOO

L4: Cdjj 26 0.013999 0.006970 0.009330

L5: Cd singletR

L6: Cd singletC

L6: Cd singletO

L5: Cd tripletR 26 0.013999 0.006970 0.009330

L6: Cd tripletC 26 0.013999 0.006970 0.009330

L6: Cd tripletO

L3: Cjjj 2 -0.152991 0.048485 -0.144094

L4: C doubletR

L4: C quartetR 2 -0.152991 0.048485 -0.144094

L3: Cjjjj

L4: C quintet

L4: C triplet

L2: Clrad 1 -0.186277 0.397424 0.069321

L2: Sirad 7 0.226142 0.305217 0.533278

L2: Srad 2 0.125799 0.228185 0.248529

L3: Srad H 1 0.198989 0.152974 0.199177

L3: Srad R 1 0.067246 0.288355 0.288011

L4: Srad C 1 0.067246 0.288355 0.288011

L4: Srad N

L4: Srad O

L4: Srad Si

L4: Srad S

L4: Srad Cl

L2: Nrad

L3: N3 rad

L4: N3s rad

L4: NH2

Continued on next page

159

Table C.1 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L4: N3s/H/R

L4: N3s/R/R

L4: N3d rad

L3: N5 rad

L4: N5s rad

L4: N5d rad

160

C.1.2 Intra-hydrogen migration

Table C.2: Molecular group tree with distance group data in A for the Intra-hydrogenmigration reaction family.

Groups TS count dXH (A) dHY (A) dXY (A)L1: RnH 140 2.312110 1.285790 1.285570

L2: R2Hall 14 -0.423185 -0.002694 -0.002561

L3: R2H s 14 -0.423185 -0.002694 -0.002561

L3: R2H r

L4: R2H d

L4: R2H t

L4: R2H b

L2: R3Hall 6 -0.210247 0.038629 0.042609

L3: R3H ss 6 -0.210247 0.038629 0.042609

L3: R3H sr

L4: R3H sd

L4: R3H st

L4: R3H sb

L3: R3H rs

L4: R3H ds

L4: R3H ts

L4: R3H bs

L3: R3H rr

L4: R3H bb

L2: R4Hall 50 0.096514 0.018029 0.017229

L3: R4H sss 46 0.081186 0.013837 0.012979

L3: R4H ssr

L4: R4H ssd

L4: R4H sst

L4: R4H ssb

L3: R4H srs 4 0.220103 0.051828 0.051493

L4: R4H sds 4 0.220103 0.051828 0.051493

L4: R4H sts

L4: R4H sbs

L3: R4H rss

L4: R4H dss

L4: R4H tss

L4: R4H bss

L3: R4H srr

L3: R4H rrs

L3: R4H rsr

L4: R4H dsd

L4: R4H tsd

L4: R4H bsd

L4: R4H dst

L4: R4H tst

L4: R4H bst

L4: R4H dsb

Continued on next page

161

Table C.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L4: R4H tsb

L4: R4H bsb

L3: R4H rrr

L2: R5Hall 58 0.134017 -0.016606 -0.016403

L3: R5H ssss 56 0.126439 -0.018537 -0.018273

L3: R5H sssr

L4: R5H sssd

L4: R5H ssst

L4: R5H sssb

L3: R5H ssrs 1 0.259051 0.013097 0.016608

L4: R5H ssds 1 0.259051 0.013097 0.016608

L4: R5H ssts

L4: R5H ssbs

L3: R5H srss 1 0.259051 0.017417 0.012288

L4: R5H sdss 1 0.259051 0.017417 0.012288

L4: R5H stss

L4: R5H sbss

L3: R5H rsss

L4: R5H dsss

L4: R5H tsss

L4: R5H bsss

L3: R5H ssrr

L3: R5H srsr

L4: R5H sdsd

L4: R5H stsd

L4: R5H sbsd

L4: R5H sdst

L4: R5H stst

L4: R5H sbst

L4: R5H sdsb

L4: R5H stsb

L4: R5H sbsb

L3: R5H rssr

L4: R5H dssd

L4: R5H tssd

L4: R5H bssd

L4: R5H dsst

L4: R5H tsst

L4: R5H bsst

L4: R5H dssb

L4: R5H tssb

L4: R5H bssb

L3: R5H srrs

L3: R5H rsrs

L4: R5H dsds

L4: R5H tsds

L4: R5H bsds

L4: R5H dsts

Continued on next page

162

Table C.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L4: R5H tsts

L4: R5H bsts

L4: R5H dsbs

L4: R5H tsbs

L4: R5H bsbs

L3: R5H rrss

L3: R5H srrr

L3: R5H rsrr

L3: R5H rrsr

L3: R5H rrrs

L3: R5H rrrr

L2: R6Hall 10 0.158073 -0.030703 -0.030480

L3: R6H sssss 10 0.158073 -0.030703 -0.030480

L3: R6H ssssr

L4: R6H ssssd

L4: R6H sssst

L4: R6H ssssb

L3: R6H sssrs

L4: R6H sssds

L4: R6H sssts

L4: R6H sssbs

L3: R6H ssrss

L4: R6H ssdss

L4: R6H sstss

L4: R6H ssbss

L3: R6H srsss

L4: R6H sdsss

L4: R6H stsss

L4: R6H sbsss

L3: R6H rssss

L4: R6H dssss

L4: R6H tssss

L4: R6H bssss

L3: R6H sssrr

L3: R6H ssrsr

L4: R6H ssdsd

L4: R6H sstsd

L4: R6H ssbsd

L4: R6H ssdst

L4: R6H sstst

L4: R6H ssbst

L4: R6H ssdsb

L4: R6H sstsb

L4: R6H ssbsb

L3: R6H srssr

L4: R6H sdssd

L4: R6H stssd

L4: R6H sbssd

Continued on next page

163

Table C.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L4: R6H sdsst

L4: R6H stsst

L4: R6H sbsst

L4: R6H sdssb

L4: R6H stssb

L4: R6H sbssb

L3: R6H rsssr

L4: R6H dsssd

L4: R6H tsssd

L4: R6H bsssd

L4: R6H dssst

L4: R6H tssst

L4: R6H bssst

L4: R6H dsssb

L4: R6H tsssb

L4: R6H bsssb

L3: R6H ssrrs

L3: R6H srsrs

L4: R6H sdsds

L4: R6H stsds

L4: R6H sbsds

L4: R6H sdsts

L4: R6H ststs

L4: R6H sbsts

L4: R6H sdsbs

L4: R6H stsbs

L4: R6H sbsbs

L3: R6H rssrs

L4: R6H dssds

L4: R6H tssds

L4: R6H bssds

L4: R6H dssts

L4: R6H tssts

L4: R6H bssts

L4: R6H dssbs

L4: R6H tssbs

L4: R6H bssbs

L3: R6H srrss

L3: R6H rsrss

L4: R6H dsdss

L4: R6H tsdss

L4: R6H bsdss

L4: R6H dstss

L4: R6H tstss

L4: R6H bstss

L4: R6H dsbss

L4: R6H tsbss

L4: R6H bsbss

Continued on next page

164

Table C.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L3: R6H rrsss

L3: R6H ssrrr

L3: R6H srsrr

L3: R6H rssrr

L3: R6H srrsr

L3: R6H rsrsr

L4: R6H dsdsd

L4: R6H tsdsd

L4: R6H bsdsd

L4: R6H dstsd

L4: R6H tstsd

L4: R6H bstsd

L4: R6H dsbsd

L4: R6H tsbsd

L4: R6H bsbsd

L4: R6H dsdst

L4: R6H tsdst

L4: R6H bsdst

L4: R6H dstst

L4: R6H tstst

L4: R6H bstst

L4: R6H dsbst

L4: R6H tsbst

L4: R6H bsbst

L4: R6H dsdsb

L4: R6H tsdsb

L4: R6H bsdsb

L4: R6H dstsb

L4: R6H tstsb

L4: R6H bstsb

L4: R6H dsbsb

L4: R6H tsbsb

L4: R6H bsbsb

L3: R6H rrssr

L3: R6H srrrs

L3: R6H rsrrs

L3: R6H rrsrs

L3: R6H rrrss

L3: R6H srrrr

L3: R6H rsrrr

L3: R6H rrsrr

L3: R6H rrrsr

L3: R6H rrrrs

L3: R6H rrrrr

L2: R7Hall 2 0.179079 -0.032439 -0.032230

L1: Y rad out

L2: Cj out 83 -0.005563 -0.003776 0.048410

L3: Csj out 77 0.007296 -0.008351 0.050820

Continued on next page

165

Table C.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L4: Csj out H2 44 0.020405 -0.023450 0.067691

L4: Csj out RH 14 0.181348 0.008883 0.038264

L5: Csj out CH 9 0.246944 -0.003708 0.040665

L6: Csj out CsH 9 0.246944 -0.003708 0.040665

L6: Csj out CdH

L6: Csj out CtH

L6: Csj out CbH

L5: Csj out OH 5 0.061090 0.031967 0.033862

L4: Csj out RR 19 -0.138239 0.020487 0.014328

L5: Csj out CC 15 -0.166212 0.021962 0.013029

L6: Csj out CsCs 12 -0.026739 0.017774 0.029485

L6: Csj out CsCd 1 -0.543722 -0.002171 -0.010414

L6: Csj out CsCt

L6: Csj out CsCb

L6: Csj out CdCd

L6: Csj out CdCt

L6: Csj out CdCb

L6: Csj out CtCt

L6: Csj out CtCb

L6: Csj out CbCb

L5: Csj out CO 4 0.020270 0.012129 0.021685

L6: Csj out CsO 4 0.020270 0.012129 0.021685

L6: Csj out CdO

L6: Csj out CtO

L6: Csj out CbO

L5: Csj out OO

L3: Cdj out 6 -0.188803 0.061424 0.014066

L4: Cdj out C 1 -0.618172 0.007499 0.010916

L5: Cdj out Cd 1 -0.618172 0.007499 0.010916

L5: Cdj out Cdd

L4: Cdj out O 5 -0.045681 0.079398 0.015116

L3: Ctj out

L3: Cbj out

L2: Oj out 57 0.005262 0.003571 -0.045783

L1: XH out

L2: C H out 83 -0.007593 0.048254 -0.002939

L3: Cs H out 77 0.005050 0.050600 -0.007410

L4: Cs H out H2 44 0.016883 0.067164 -0.022003

L4: Cs H out RH 14 0.181230 0.037898 0.009553

L5: Cs H out CH 9 0.246795 0.040402 -0.003138

L6: Cs H out CsH 9 0.246795 0.040402 -0.003138

L6: Cs H out CdH

L6: Cs H out CtH

L6: Cs H out CbH

L5: Cs H out OH 5 0.061027 0.033306 0.032818

L4: Cs H out RR 19 -0.138915 0.014388 0.020814

L5: Cs H out CC 15 -0.167162 0.013250 0.022171

L6: Cs H out CsCs 12 -0.027330 0.029543 0.018090

Continued on next page

166

Table C.2 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L6: Cs H out CsCd 1 -0.545671 -0.009742 -0.002262

L6: Cs H out CsCt

L6: Cs H out CsCb

L6: Cs H out CdCd

L6: Cs H out CdCt

L6: Cs H out CdCb

L6: Cs H out CtCt

L6: Cs H out CtCb

L6: Cs H out CbCb

L5: Cs H out CO 4 0.021151 0.020838 0.013129

L6: Cs H out CsO 4 0.021151 0.020838 0.013129

L6: Cs H out CdO

L6: Cs H out CtO

L6: Cs H out CbO

L5: Cs H out OO

L3: Cd H out 1 -0.620121 0.011588 0.007408

L4: Cd H out C 1 -0.620121 0.011588 0.007408

L5: Cd H out Cd 1 -0.620121 0.011588 0.007408

L6: Cd H out CdH

L6: Cd H out CdC

L7: Cd H out CdCs

L7: Cd H out CdCd

L7: Cd H out CdCt

L7: Cd H out CdCb

L6: Cd H out CdO

L5: Cd H out Cdd

L6: Cd H out CddH

L6: Cd H out CddC

L7: Cd H out CddCs

L7: Cd H out CddCd

L7: Cd H out CddCt

L7: Cd H out CddCb

L6: Cd H out CddO

L4: Cd H out O

L5: Cd H out OdH

L5: Cd H out OdC

L6: Cd H out OdCs

L6: Cd H out OdCd

L6: Cd H out OdCt

L6: Cd H out OdCb

L5: Cd H out OdO

L3: Ct H out

L3: Cb H out

L2: O H out 57 0.007022 -0.044626 0.002718

167

C.1.3 β-scission

Table C.3: Molecular group tree with distance group data in A for the β-scission re-action family.

Groups TS count dXH (A) dHY (A) dXY (A)L1: R R 158 1.307210 2.612790 2.004480

L2: Cn R 144 0.004967 0.011510 0.023505

L3: Cd R 134 0.011442 0.006411 0.022726

L4: Cds R 90 0.046130 0.077838 0.059501

L5: Cds Cd H2 34 0.045291 0.146565 0.087210

L6: Cds Cds/H2 30 0.046912 0.147575 0.095151

L6: Cds Cdd/H2 4 0.028197 0.135915 0.003470

L5: Cds Cd RH 37 0.046434 0.055242 0.054617

L6: Cds Cds/Cs/H 24 0.044214 0.038586 0.053166

L6: Cds Cds/Cd/H 1 0.043742 0.053180 -0.012341

L6: Cds Cds/Ct/H

L6: Cds Cds/Cb/H

L6: Cds Cdd/Cs/H 1 0.038510 0.209643 0.106540

L6: Cds Cdd/Cd/H

L6: Cds Cdd/Ct/H

L6: Cds Cdd/Cb/H

L5: Cds Cd RR 19 0.047561 -0.044953 -0.000354

L6: Cds Cds/Cs/Cs 9 0.044092 -0.069790 0.005843

L6: Cds Cds/Cs/Cd

L6: Cds Cds/Cs/Ct

L6: Cds Cds/Cs/Cb

L6: Cds Cds/Cd/Cd

L6: Cds Cds/Cd/Ct

L6: Cds Cds/Cd/Cb

L6: Cds Cds/Ct/Ct

L6: Cds Cds/Ct/Cb

L6: Cds Cds/Cb/Cb

L6: Cds Cdd/Cs/Cs 1 0.025502 -0.043910 -0.051901

L6: Cds Cdd/Cs/Cd

L6: Cds Cdd/Cs/Ct

L6: Cds Cdd/Cs/Cb

L6: Cds Cdd/Cd/Cd

L6: Cds Cdd/Cd/Ct

L6: Cds Cdd/Cd/Cb

L6: Cds Cdd/Ct/Ct

L6: Cds Cdd/Ct/Cb

L6: Cds Cdd/Cb/Cb

L5: Cds Od H2

L5: Cds Od RH

L6: Cds Od/Cs/H

L6: Cds Od/Cd/H

L6: Cds Od/Ct/H

L6: Cds Od/Cb/H

Continued on next page

168

Table C.3 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L5: Cds Od RR

L6: Cds Od/Cs/Cs

L6: Cds Od/Cs/Cd

L6: Cds Od/Cs/Ct

L6: Cds Od/Cs/Cb

L6: Cds Od/Cd/Cd

L6: Cds Od/Cd/Ct

L6: Cds Od/Cd/Cb

L6: Cds Od/Ct/Ct

L6: Cds Od/Ct/Cb

L6: Cds Od/Cb/Cb

L4: Cdd RR 10 0.006662 -0.087249 -0.017622

L5: Cdd CC 4 0.009779 0.023941 0.118288

L6: Cdd Cds/Cds 4 0.009779 0.023941 0.118288

L6: Cdd Cds/Cdd

L6: Cdd Cdd/Cdd

L5: Cdd CO 5 0.027151 -0.090485 -0.038746

L6: Cdd Cds/O 5 0.027151 -0.090485 -0.038746

L6: Cdd Cdd/O

L5: CO2 1 -0.085430 -0.435677 -0.374830

L3: Ct R 10 -0.086860 0.083830 0.034556

L4: Ct Ct/H 7 -0.086533 0.126234 0.065931

L4: Ct Ct/R 3 -0.088331 -0.106990 -0.106634

L5: Ct Ct/C 3 -0.088331 -0.106990 -0.106634

L6: Ct Ct/Cs 1 -0.090958 -0.119910 -0.099841

L6: Ct Ct/Cd 1 -0.088088 -0.112460 -0.102411

L6: Ct Ct/Ct 1 -0.085948 -0.088600 -0.117651

L6: Ct Ct/Cb

L5: Ct Ct/O

L2: Od R 14 -0.067256 -0.155852 -0.318274

L3: Od C 14 -0.067256 -0.155852 -0.318274

L4: Od Cds 12 -0.059610 -0.162289 -0.354429

L4: Od Cdd 2 -0.091044 -0.135826 -0.205789

L3: O2

L1: YJ

L2: Hj 44 -0.013882 -0.203432 -0.187527

L2: Cj 77 -0.009370 0.166583 0.143727

L3: Csj 54 -0.011070 0.196126 0.155730

L4: Csj methyl 29 -0.002435 0.216852 0.168683

L4: Csj RH2 18 -0.013060 0.191287 0.155259

L5: Csj CH2 11 -0.017731 0.197404 0.143925

L6: Csj Cs/H2 10 -0.023349 0.197492 0.141981

L6: Csj Cd/H2

L6: Csj Ct/H2

L6: Csj Cb/H2

L5: Csj OH2 7 -0.006466 0.182651 0.171261

L4: Csj RRH 7 -0.055722 0.089168 0.080161

L5: Csj CCH 4 -0.080798 0.001713 0.027160

Continued on next page

169

Table C.3 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L6: Csj Cs/Cs/H 3 -0.083531 0.019894 0.035911

L6: Csj Cs/Cd/H

L6: Csj Cs/Ct/H

L6: Csj Cs/Cb/H

L6: Csj Cd/Cd/H

L6: Csj Cd/Ct/H

L6: Csj Cd/Cb/H

L6: Csj Ct/Ct/H

L6: Csj Ct/Cb/H

L6: Csj Cb/Cb/H

L5: Csj COH 3 -0.030646 0.176623 0.133162

L6: Csj Cs/O/H 3 -0.030646 0.176623 0.133162

L6: Csj Cd/O/H

L6: Csj Ct/O/H

L6: Csj Cb/O/H

L5: Csj OOH

L4: Csj RRR

L5: Csj CCC

L6: Csj Cs/Cs/Cs

L6: Csj Cs/Cs/Cd

L6: Csj Cs/Cs/Ct

L6: Csj Cs/Cs/Cb

L6: Csj Cs/Cd/Cd

L6: Csj Cs/Cd/Ct

L6: Csj Cs/Cd/Cb

L6: Csj Cs/Ct/Ct

L6: Csj Cs/Ct/Cb

L6: Csj Cs/Cb/Cb

L6: Csj Cd/Cd/Cd

L6: Csj Cd/Cd/Ct

L6: Csj Cd/Cd/Cb

L6: Csj Cd/Ct/Ct

L6: Csj Cd/Ct/Cb

L6: Csj Cd/Cb/Cb

L6: Csj Ct/Ct/Ct

L6: Csj Ct/Ct/Cb

L6: Csj Ct/Cb/Cb

L6: Csj Cb/Cb/Cb

L5: Csj CCO

L6: Csj Cs/Cs/O

L6: Csj Cs/Cd/O

L6: Csj Cs/Ct/O

L6: Csj Cs/Cb/O

L6: Csj Cd/Cd/O

L6: Csj Cd/Ct/O

L6: Csj Cd/Cb/O

L6: Csj Ct/Ct/O

L6: Csj Ct/Cb/O

Continued on next page

170

Table C.3 – continued from previous pageGroups TS count dXH (A) dHY (A) dXY (A)

L6: Csj Cb/Cb/O

L5: Csj COO

L6: Csj Cs/O/O

L6: Csj Cd/O/O

L6: Csj Ct/O/O

L6: Csj Cb/O/O

L5: Csj OOO

L3: Cdj 9 -0.011836 0.214972 0.175425

L4: Cdj Cd 9 -0.011836 0.214972 0.175425

L5: Cdj CdH 4 -0.043276 0.220166 0.200290

L6: Cdj CdsH 4 -0.043276 0.220166 0.200290

L6: Cdj CddH

L5: Cdj CdC 5 0.006795 0.211895 0.160691

L6: Cdj Cds/Cs 2 -0.027209 0.232747 0.174633

L6: Cdj Cds/Cd 1 0.012251 0.293781 0.262610

L6: Cdj Cds/Ct

L6: Cdj Cds/Cb

L6: Cdj Cdd/Cs 2 0.029571 0.155313 0.099274

L6: Cdj Cdd/Cd

L6: Cdj Cdd/Ct

L6: Cdj Cdd/Cb

L5: Cdj CdO

L6: Cdj CdsO

L6: Cdj CddO

L4: Cdj Od

L5: Cdj OdH

L5: Cdj OdC

L6: Cdj OdCs

L6: Cdj OdCd

L6: Cdj OdCt

L6: Cdj OdCb

L5: Cdj OdO

L3: Ctj

L4: Ctj Ct

L3: Cbj

L2: Oj 37 0.029544 -0.079245 -0.056477

L3: OH 11 0.013221 -0.105878 0.056824

L3: OjC

L4: OjCs

L4: OjCd

L4: OjCt

L4: OjCb

L3: OjO 26 0.035945 -0.068801 -0.100909