Rate Constant Calculation for Thermal Reactions

PREFACE xiii Herbert DaCosta and Maohong Fan CONTRIBUTORS xv PART I METHODS 1 1. Overview of Thermochemistry and Its Application to Reaction Kinetics 3 Elke Goos and Alexander Burcat 1.1. History of Thermochemistry 3 1.2. Thermochemical Properties 5 1.3. Consequences of Thermodynamic Laws to Chemical Kinetics 8 1.4. How to Get Thermochemical Values? 10 1.4.1. Measurement of Thermochemical Values 10 1.4.2. Calculation of Thermochemical Values 10 1.4.2.1. Quantum Chemical Calculations of Molecular Properties 10 1.4.2.2. Calculation of Thermodynamic Functions from Molecular Properties 12 1.5. Accuracy of Thermochemical Values 16 1.5.1. Standard Enthalpies of Formation 16 1.5.2. Active Thermochemical Tables 18 1.6. Representation of Thermochemical Data for Use in Engineering Applications 21 1.6.1. Representation in Tables 21 1.6.2. Representation with Group Additivity Values 21 1.6.3. Representation as Polynomials 22 1.6.3.1. How to Change Df H298K Without Recalculating NASA Polynomials 25 1.7. Thermochemical Databases 26 1.8. Conclusion 27 References 27 2. Calculation of Kinetic Data Using Computational Methods 33 Fernando P. Cossío 2.1. Introduction 33 2.2. Stationary Points and Potential Energy Hypersurfaces 34 2.3. Calculation of Reaction and Activation Energies: Levels of Theory and Solvent Effects 38 2.3.1. Hartree-Fock and Post-Hartree-Fock Methods 38 2.3.2. Methods Based on Density Functional Theory 41 2.3.3. Computational Treatment of Solvent Effects 44 2.4. Estimate of Relative Free Energies: Standard States 47 2.5. Theoretical Approximate Kinetic Constants and Treatment of Data 50 2.6. Selected Examples 51 2.6.1. Relative Reactivities of Phosphines in Aza-Wittig Reactions 52 2.6.2. Origins of the Stereocontrol in the Staudinger Reaction Between Ketenes and Imines to Form ²-Lactams 54 2.6.3. Origins of the Stereocontrol in the Reaction Between Imines and Homophthalic Anhydride 58 2.7. Conclusions and Outlook 61 References 62 3. Quantum Instanton Evaluation of the Kinetic Isotope Effects and of the Temperature Dependence of the Rate Constant 67 JiYí Vanícek 3.1. Introduction 67 3.2. Arrhenius Equation, Transition State Theory, and the Wigner Tunneling Correction 68 3.3. Quantum Instanton Approximation for the Rate Constant 69 3.4. Kinetic Isotope Effects 71 3.4.1. Transition State Theory Framework for KIE 71 3.4.2. Quantum Instanton Approach and the Thermodynamic Integration with Respect to the Isotope Mass 72 3.5. Temperature Dependence of the Rate Constant 73 3.5.1. Transition State Theory Framework for the Temperature Dependence of k(T) 73 3.5.2. Quantum Instanton Approach and the Thermodynamic Integration with Respect to the Inverse Temperature 74 3.6. Path Integral Representation of Relevant Quantities 75 3.6.1. Path Integral Formalism 75 3.6.2. Estimators 76 3.6.3. Estimators for Er 77 3.6.4. Estimators for Eii 78 3.6.5. Estimators for the Derivatives of Fr and F z with Respect to Mass 79 3.6.6. Statistical Errors and Efficiency 79 3.6.7. Treatment of Potential Energy Surfaces for Many-Dimensional Systems 80 3.7. Examples 81 3.7.1. Eckart Barrier 81 3.7.2. Full-Dimensional H+H2--> H2 +H Reaction 84 3.7.3. [1,5]-Sigmatropic Hydrogen Shift in cis-1,3-Pentadiene 86 3.8. Summary 88 Appendix: Reactions 89 Acknowledgments 89 References 89 4. Activation Energies in Computational Chemistry--A Case Study 93 Michael Busch, Elisabet Ahlberg and Itai Panas 4.1. Introduction 93 4.2. Context and Theoretical Background 95 4.2.1. Density Functional Theory 95 4.2.2. Calculating Transition States 96 4.2.3. The Tyrosine/Tyrosyl-Radical Reference Potential 98 4.3. Computational Details 99 4.4. Recent Advances and New Results 99 4.4.1. Homogenous OER Catalysts 99 4.4.2. Embedded Transition Metal Dimers 102 4.5. Concluding Remarks 107 Acknowledgments 108 References 108 5. No Barrier Theory--A New Approach to Calculating Rate Constants in Solution 113 J. Peter Guthrie 5.1. Introduction 113 5.2. The Idea Behind No Barrier Theory 114 5.3. How to Define the Surface and Find the Transition State 118 5.4. What is Needed for a Calculation? 124 5.5. Applications to Date 125 5.5.1. Proton Transfer Reactions 125 5.5.2. Addition of Water to Carbonyls 126 5.5.3. Cyanohydrin Formation 130 5.5.4. The Reaction of Carbocations With Either Water or Azide Ion 131 5.5.5. Decarboxylation 134 5.5.6. The E2 Elimination Reaction 136 5.5.7. The Strecker Reaction 138 5.5.8. The Aldol Addition 138 5.6. Future Prospects for NBT 140 5.7. Summary 141 References 142 PART II MINIREVIEWS AND APPLICATIONS 147 6. Quantum Chemical and Rate Constant Calculations of Thermal Isomerizations, Decompositions, and Ring Expansions of Organic Ring Compounds, Its Significance to Cohbusion Kinetics 149 Faina Dubnikova and Assa Lifshitz 6.1. Prologue 149 6.1.1. Introduction 149 6.1.2. Quantum Chemical Calculations 150 6.1.3. Rate Constant Calculations 151 6.1.4. Experimental Methods 152 6.2. Small Organic Ring Compounds 152 6.2.1. Cyclopropane 152 6.2.2. Cyclopropane Carbonitrile 153 6.2.3. The Epoxy Family of Molecules 154 6.3. Pyrrole and Indole 156 6.3.1. Pyrrole 156 6.3.2. Indole 157 6.4. Dihydrofurans and Dihydrobenzofurans 160 6.4.1. 2,3-Dihydrofuran 160 6.4.2. 5-Methyl-2,3-Dihydrofuran 160 6.4.3. Van der Waals Interactions in H2 Elimination: 2,5-Dihydrofuran 161 6.4.4. Dihydrobenzofuran and iso-Dihydrobenzofuran 163 6.5. Naphthyl Acetylene-Naphthyl Ethylene 166 6.6. Ring Expansion Processes 168 6.6.1. Methylcyclopentadiene 169 6.6.2. Methyl Pyrrole 170 6.6.3. Methylindene and Methylindole 171 6.7. Benzoxazole-Benzisoxazoles 173 6.7.1. Benzoxazole 174 6.7.2. 1,2-Benzisoxazole 174 6.7.3. 2,1-Benzisoxazole--Intersystem Crossing 176 6.8. Conclusion 181 Acknowledgment 185 References 185 7. Challenges in the Computation of Rate Constants for Lignin Model Compounds 191 Ariana Beste and A.C. Buchanan, III 7.1. Lignin: A Renewable Source of Fuels and Chemicals 191 7.1.1. Origin and Chemical Structure 193 7.1.2. Processing Techniques and Challenges 195 7.2. Mechanistic Study of Lignin Model Compounds 196 7.2.1. Experimental Work 197 7.2.2. Computational Work 201 7.3. Computational Investigation of the Pyrolysis of ²-O-4 Model Compounds 201 7.3.1. Methodology 202 7.3.1.1. Overview 202 7.3.1.2. Transition State Theory 203 7.3.1.3. Anharmonic Corrections 207 7.3.2. Analytical Kinetic Models 210 7.3.2.1. Parallel Reactions 210 7.3.2.2. Series of First-Order Reactions 211 7.3.2.3. Product Selectivity for the Pyrolysis of PPE 211 7.3.3. Numerical Integration 213 7.4. Case Studies: Substituent Effects on Reactions of Phenethyl Phenyl Ethers 214 7.4.1. Computational Details 215 7.4.2. Initiation: Homolytic Cleavage 215 7.4.3. Hydrogen Abstraction Reactions and a/b-Selectivities 217 7.4.3.1. PPE and PPE Derivatives with Substituents on Phenethyl Group 217 7.4.3.2. PPE and PPE Derivatives with Substituents on Phenyl Group Adjacent to Ether Oxygen 221 7.4.4. Phenyl Rearrangement 229 7.5. Conclusions and Outlook 232 Acknowledgments 234 Appendix Summary of Kinetic Parameters 234 References 235 8. Quantum Chemistry Study on the Pyrolysis Mechanisms of Coal-Related Model Compounds 239 Baojun Wang, Riguang Zhang and Lixia Ling 8.1. Introduction to the Application of Quantum Chemistry Calculation to Investigation on Models of Coal Structure 239 8.2. The Model for Coal Structure and Calculation Methods 240 8.2.1. The Proposal of Local Microstructure Model of Coal 240 8.2.2. Coal-Related Model Compounds Describing the Properties of Coal Pyrolysis 241 8.2.3. The Pyrolysis of Model Compounds Reflecting the Pyrolysis Phenomenon of Coal 242 8.2.4. The Calculation Methods 242 8.3. The Pyrolysis Mechanisms of Coal-Related Model Compounds 243 8.3.1. The Pyrolysis Mechanisms of Oxygen-Containing Model Compounds 243 8.3.1.1. Phenol and Furan 243 8.3.1.2. Benzoic Acid and Benzaldehyde 246 8.3.1.3. Anisole 251 8.3.2. The Pyrolysis Mechanisms of Nitrogen-Containing Model Compounds 255 8.3.2.1. Pyrrole and Indole 256 8.3.2.2. Pyridine 258 8.3.2.3. 2-Picoline 260 8.3.2.4. Quinoline and Isoquinoline 263 8.3.3. The Pyrolysis Mechanisms of Sulfur-Containing Model Compounds 267 8.3.3.1. Thiophene 268 8.3.3.2. Benzenethiol 270 8.4. Conclusion 276 References 276 9. Ab Initio Kinetic Modeling of Free-Radical Polymerization 283 Michelle L. Coote 9.1. Introduction 283 9.1.1. Free-Radical Polymerization Kinetics 283 9.1.2. Scope of this Chapter 286 9.2. Ab Initio Kinetic Modeling 287 9.2.1. Conventional Kinetic Modeling 287 9.2.2. Ab Initio Kinetic Modeling 289 9.3. Quantum Chemical Methodology 291 9.3.1. Model Systems 291 9.3.2. Theoretical Procedures 293 9.4. Case Study: RAFT Polymerization 296 9.5. Outlook 300 References 301 10. Intermolecular Electron Transfer Reactivity for Organic Compounds Studied Using Marcus Cross-Rate Theory 305 Stephen F. Nelsen and Jack R. Pladziewicz 10.1. Introduction 305 10.2. Determination of deltaGiiii (fit) Values 307 10.3. Why is the Success of Cross-Rate Theory Surprising? 309 10.4. Major Factors Determining Intrinsic Reactivities of Hydrazine Couples 310 10.5. Nonhydrazine Couples 315 10.6. Comparison of DdeltaGiiii (fit) with DdeltaGiiii (self) Values 318 10.7. Estimation of Hab from Experimental Exchange Rate Constants and DFT-Computed l 320 10.8. Comparison with Gas-Phase Reactions 333 10.9. Conclusions 333 References 334 INDEX 337