Rate Constant Calculation for Thermal Reactions

Herbert DaCosta is currently a principal consultant at Chem-Innovations LLC and an adjunct professor of chemistry at Illinois Central College. His research interests include environmental catalysis and clean energy, nanomaterial design and synthesis, computational chemistry, and kinetics.
 
Maohong Fan is Associate Professor at the University of Wyoming and an adjunct associate professor at the Georgia Institute of Technology. His research interests include nanomaterial synthesis and application, green processes for chemical production, and new approaches to clean energy generation.

Providing an overview of the latest computational approaches to estimate rate constants for thermal reactions, this book addresses the theories behind various first-principle and approximation methods that have emerged in the last twenty years with validation examples. It presents in-depth applications of those theories to a wide range of basic and applied research areas. When doing modeling and simulation of chemical reactions (as in many other cases), one often has to compromise between higher-accuracy/higher-precision approaches (which are usually time-consuming) and approximate/lower-precision approaches (which often has the advantage of speed in providing results). This book covers both approaches. It is augmented by a wide-range of applications of the above methods to fuel combustion, unimolecular and bimolecular reactions, isomerization, polymerization, and to emission control of nitrogen oxides. An excellent resource for academics and industry members in physical chemistry, chemical engineering, and related fields.

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-Pen