PHYSICAL KINETICS

By ABIGAIL WILSON

1 Introduction 1 2 Obtaining Molecular Thermochemistry from Calculations 7 1 Introduction and overview 7 2 Molecular mechanics 9 3 Semiempirical molecular orbital theory 12 4 Molecular orbital theory 14 41 Physical approximations 14 42 Numerical approximations 19 5 Density functional theory 22 6 Theory and basis set: examples 23 61 Electron affinity of fluorine 23 62 Bond dissociation energy in methane 24 63 Proton affinity of ammonia 25 64 Excitation energy of singlet O2 25 7 Thermochemistry from ab initio calculations 27 71 Temperatures besides 29815 K 34 8 Recognizing trouble, ab initio 35 9 Summary 37 References 38 3 Elements of Chemical Kinetics 43 1 Introduction 43 2 Elementary concepts 43 21 Stoichiometry 43 22 The reaction rate 45 23 The rate expression 46 24 Elementary reactions 48 25 State-to-state kinetics 49 26 The temperature dependence of the rate coefficient 51 27 Kinetic data 54 28 Mechanism 55 29 The steady state approximation 58 210 Microscopic reversibility and detailed balance 60 3 Potential energy 64 31 The Born-Oppenheimer approximation 64 32 Long-range potentials 65 33 Short-range repulsive forces 65 34 Bonding interactions 66 35 Potential energy surfaces 67 4 Bimolecular reaction rate theory 72 41 Simple collision theory 72 42 Bimolecular collision dynamics 76 43 Ion–molecule reactions 77 44 Ion–ion reactions 78 45 Bimolecular association of free radicals 79 46 Classical trajectory calculations 80 47 Transition state theory 83 48 The statistical factor 85 49 Tests of transition state theory 86 410 Microcanonical transition state theory 88 411 Variational transition state theory 88 412 The transmission coefficient 90 413 Tunneling 90 414 Electronically non-adiabatic reactions 92 5 Termolecular Reactions 95 References 97 4 The Kinetics of Pressure-Dependent Reactions 101 1 Introduction 101 2 Review of pressure-dependent reactions 102 21 Unimolecular reactions 102 22 Chemically activated reactions 110 23 Energy transfer models 113 24 The master equation approach for single-well systems 118 25 Complex pressure-dependent systems 121 3 Practical methods to analyze pressure-dependent reactions 136 31 Software for the calculation of pressure-dependent rate constants 136 32 Getting input data for the calculations 137 4 Worked-out examples of the analysis of pressure-dependent reactions 157 41 Example 1: the thermal dissociation C2H5O-CH3+CH2O 157 42 Example 2: the isomerization reaction n-C3H7 Ð i-C3H7 164 43 Example 3: the reaction C2H5+O2-products 167 44 Example 4: the reaction C2H3+O2-products 172 5 Representation of k(T, p) rate coefficients for modeling 175 51 Single-well single-channel systems 175 52 Multi-well multi-channel systems 176 6 Summary and look to the future 178 References 180 5 Constructing Reaction Mechanisms 185 1 Introduction 185 2 Identifying reactions 188 21 Finding reactions and reaction mechanisms in the literature 188 22 Identifying reactions by analogy 192 23 Identifying reactions based on ‘chemical intuition,’ or just making it up 194 3 Determining species thermochemical properties 198 31 Finding thermochemical properties in the literature 199 32 Estimating thermochemical properties using group additivity 202 33 Estimating thermochemical properties using computational quantum chemistry 203 34 Estimating thermochemical properties by analogy or educated guessing 203 4 Determining rate parameters 208 41 Finding rate parameters in the literature 209 42 Determining rate parameters using quantum chemical calculations and transition state theory 210 43 Purely empirical estimation of rate parameters 217 44 Linear free energy relationships and correlations for estimating activation energies 221 5 Applying the mechanism at conditions of interest 221 6 Reaction rate/flux analysis and sensitivity analysis 232 7 Summary and outlook 239 References 240 6 Optimization of Reaction Models With Solution Mapping 243 1 Introduction 243 2 Preliminary material and terminology 244 21 Training data 244 22 Objective function 245 23 Optimization methods 246 24 Parameter uncertainty 247 3 Pitfalls of poor uncertainty management 250 4 Statement of the problem 255 5 Parameter estimation of dynamic models with solution mapping 256 51 Solution mapping approach 256 52 Effect sparsity and active variables 258 53 Screening sensitivity analysis 258 54 Factorial designs 261 55 Optimization 268 56 Prior pruning of the reaction model 268 57 Strengths and weaknesses of solution mapping 271 6 Data collaboration 275 61 Data collaboration concepts 276 62 Looking at some feasible sets from GRI-Mech dataset 277 63 Optimization techniques primer 279 64 Prediction of model uncertainty 282 65 Consistency of a reaction dataset 283 66 Information gain due to data collaboration 285 7 Concluding remarks 288 Acknowledgments 289 References 289