List of Study Boxes .......................................... xiii
Acknowledgements ............................................... xv
Biographies .................................................. xvii
Chapter 1 Introduction ......................................... 1
Mark Brouard and Claire Vallance
1.1 Introduction ............................................... 1
1.2 Cross Sections and Rate Constants .......................... 3
1.2.1 The Impact Parameter and Orbital Angular Momentum ... 4
1.2.2 Opacity Functions and Cross Sections ................ 5
1.2.3 Differential Cross Sections and Angular
Distributions ....................................... 7
1.2.4 State-to-state Cross Sections and Rate Constants .... 8
1.2.5 Thermal Rate Constants .............................. 9
1.3 Experimental Considerations ................................ 9
1.3.1 Single-collision Conditions ......................... 9
1.3.2 Crossed Molecular Beams ............................ 10
1.3.3 Motion in the Laboratory and Centre-of-mass
Frames ............................................. 11
1.3.4 Pump-probe Experiments ............................. 13
1.4 Guiding Principles in Dynamical Studies ................... 15
1.4.1 The Born-Oppenheimer Approximation and Potential
Energy Surfaces .................................... 18
1.4.2 Energy and Momentum Conservation and Kinematics .... 19
1.4.3 Effective Potentials and Centrifugal Barriers ...... 21
1.4.4 Statistical versus Non-statistical Reactions ....... 23
1.4.5 Transition States and Transition State
Spectroscopy ....................................... 24
1.5 Summary ................................................... 26
1.6 Problems .................................................. 26
Chapter 2 Potential Energy Surfaces: the Forces of Chemistry .. 28
Matthew A. Addicoat and Michael A. Collins
2.1 Introduction .............................................. 28
2.2 The Born-Oppenheimer Approximation ........................ 28
2.2.1 Dynamics ........................................... 31
2.3 Coordinates ............................................... 31
2.4 Methods to Calculate the Energy ........................... 33
2.5 Simple Examples ........................................... 35
2.5.1 Diatomic Molecule .................................. 35
2.5.2 Constrained Triatomic .............................. 36
2.6 Polyatomic PESs ........................................... 37
2.7 Methods for Constructing PESs ............................. 42
2.7.1 Functional Form Fitting ............................ 43
2.7.2 Interpolation ...................................... 45
2.8 Outlook ................................................... 47
2.9 Problems .................................................. 47
Chapter 3 Scattering Theory: Predicting the Outcome of
Chemical Events ................................................ 49
Anthony J.H.M. Meijer and Evelyn M. Goldfield
3.1 Introduction .............................................. 49
3.2 Classical Mechanics ....................................... 49
3.2.1 Newton's Laws and Conservation Laws ................ 49
3.2.2 Lagrangian & Hamiltonian Mechanics ................. 50
3.2.3 Example: Scattering in a Central Potential ......... 51
3.3 Quantum Scattering ........................................ 53
3.3.1 Preamble ........................................... 53
3.3.2 Fundamental Theory ................................. 54
3.3.3 Overview of Methods ................................ 67
3.3.4 Time-independent Methods ........................... 68
3.3.5 Time-dependent Methods ............................. 73
3.3.6 Approximation Methods .............................. 82
3.3.7 Case study: H + O2 ................................. 83
3.4 Outlook ................................................... 85
3.5 Problems .................................................. 86
Chapter 4 Processes Involving Multiple Potential Energy
Surfaces ....................................................... 88
Bertrand Retail and Andrew J. Orr-Ewing
4.1 Introduction .............................................. 88
4.2 Breakdown of the Born-Oppenheimer Approximation ........... 89
4.2.1 Non-adiabatic Couplings between Adiabatic PESs ..... 90
4.2.2 Diabatic and Adiabatic Representations of the
Coupled PESs ....................................... 92
4.2.3 The Landau-Zener Model for Non-Adiabatic Dynamics .. 95
4.2.4 A Case Study in Non-Adiabatic Dynamics - The
Ultraviolet Photodissociation of HC1 ............... 95
4.2.5 Multi-dimensional PESs and Conical Intersections ... 99
4.2.6 Vibronic, Coriolis and Spin-orbit Couplings
between PESs ...................................... 106
4.3 Experimental Probes of Non-Adiabatic Reactivity and
Dynamics ................................................. 109
4.4 Outlook .................................................. 113
4.5 Problems ................................................. 114
Chapter 5 Elastic and Inelastic Scattering: Energy Transfer
in Collisions ................................................. 116
David W. Chandler and Steven Stolte
5.1 Introduction ............................................. 116
5.2 Modelling Energy Transfer Processes ...................... 117
5.2.1 Vibration to Translation Energy Transfer .......... 117
5.2.2 Dynamics of a Single Hard Sphere Collision ........ 120
5.2.3 Translation to Translation Energy Transfer ........ 121
5.2.4 Classical Treatment of Translational to
Rotational Energy Transfer ........................ 130
5.3 Experimental Studies of Energy Transfer .................. 135
5.3.1 Early Measurements of DCSs and Rotational
Rainbows .......................................... 135
5.3.2 Molecular Beam Studies of the NO - Rare Gas
System ............................................ 139
5.3.3 Scalar Measurements ............................... 144
5.3.4 Vector Measurements of Rotational Energy Transfer . 148
5.4 Outlook .................................................. 163
5.5 Problems ................................................. 165
Chapter 6 Reactive Scattering: Reactions in Three Dimensions . 167
Piergiorgio Casavecchia, Kopin Liu and Xueming Yang
6.1 Introduction ............................................. 167
6.1.1 Crossed Molecular Beams ........................... 167
6.1.2 Determining Cross Sections from CMB Experiments ... 168
6.2 CMB Experiments with Mass Spectrometric Detection ........ 169
6.2.1 Angular Scattering and Reaction Mechanisms ........ 174
6.2.2 Soft-Ionization Detection ......................... 179
6.2.3 Multichannel Polyatomic Reactions ................. 180
6.3 CMB Experiments with Rydberg-Tagging Detection ........... 186
6.3.1 Quantum Phenomena and Reaction Resonances ......... 188
6.3.2 The OH + D2 Reaction: Mode Specific Chemistry ..... 200
6.4 CMB Experiments with REMPI Detection ..................... 201
6.4.1 Product Pair Correlations ......................... 202
6.4.2 Product Pair-Correlated DCSs ...................... 208
6.5 Outlook .................................................. 210
6.6 Problems ................................................. 212
Chapter 7 Reactive Scattering: Quantum State-Resolved
Chemistry ..................................................... 214
F. Fleming Сrim
7.1 Introduction ............................................. 214
7.2 Motion over a Potential Energy Surface ................... 215
7.3 State-to-state Bimolecular Reactions ..................... 218
7.3.1 Changing the Reaction Cross Section ............... 218
7.3.2 Changing the Reaction Pathways: Populating
Different States .................................. 220
7.3.3 Changing the Reaction Pathways: Breaking
Different Bonds ................................... 223
7.4 Vibrational Energy Flow .................................. 224
7.4.1 Chemical Activation: Rabinovitch's Bicycle ........ 225
7.4.2 Laser Excitation .................................. 226
7.4.3 Intramolecular Vibrational Redistribution:
Observing Energy Flow ............................. 228
7.5 Statistical Reactions .................................... 230
7.5.1 The Cumulative Reaction Probability ............... 230
7.5.2 The Statistical Assumption: Microcanonical
Transition State Theory ........................... 232
7.5.3 Quantum State Structure in Unimolecular Reactions . 233
7.6 Outlook .................................................. 235
7.7 Problems ................................................. 237
Chapter 8 Photodissociation Dynamics: the Fragmentation of
Molecules by Light ............................................ 240
David H. Parker, Andre T.J.B. Eppink and Claire Vallance
8.1 Introduction ............................................. 240
8.2 Photodissociation and Potential Energy Surfaces .......... 240
8.3 An Introduction: the Photodissociation of Br2 ............ 244
8.4 Femtosecond Probes of Photodissociation Dynamics ......... 249
8.5 Femtosecond Dynamics of the Photodissociation of O2 to
0+-0- Ion Pairs .......................................... 251
8.6 Photofragment Angular Distributions in Br2
Photodissociation ........................................ 254
8.6.1 Above-threshold Photodissociation of Br2 at
266 nm ............................................ 256
8.6.2 Near-threshold Photodissociation of Br2 at
510 nm ............................................ 257
8.7 Atomic Product Polarization .............................. 258
8.7.1 Atomic Polarization Effects in the
Photodissociation of Br2 and I2 ................... 260
8.8 Theoretical Treatment of Photodissociation ............... 263
8.8.1 Adiabatic Model of Photodissociation .............. 265
8.8.2 Prediction of Atomic Polarization using the
Adiabatic Model ................................... 266
8.8.3 Sudden Model for Photodissociation ................ 267
8.8.4 Example: Photodissociation of the OH Radical ...... 267
8.8.5 Predissociation of the A2Σ+ state of OH:
Interference Effects .............................. 271
8.8.6 The 'Bad News': Fully Quantum Analysis of Models
for Photodissociation of HX ....................... 274
8.9 Outlook .................................................. 274
8.10 Problems ................................................. 275
Chapter 9 Stereodynamics: Orientation and Alignment in
Chemistry ..................................................... 278
F. Javier Aoiz and Marcelo P. de Miranda
9.1 Introduction ............................................. 278
9.2 Concepts and Quantities .................................. 279
9.2.1 Polarization, Orientation, Alignment .............. 279
9.2.2 Vector Correlations ............................... 280
9.2.3 Probability Density Functions ..................... 283
9.2.4 Polarization Moments of Probability Density
Functions ......................................... 285
9.2.5 Density Matrices .................................. 289
9.2.6 Polarization Moments of Density Matrices .......... 290
9.2.7 Limiting Values of Real Polarization Moments ...... 292
9.3 Experimental and Theoretical Stereodynamics .............. 292
9.3.1 Theoretical Methods ............................... 293
9.3.2 Experimental Production of Polarized Reactants .... 299
9.4 A Detailed Example ....................................... 310
9.4.1 Quantification of Known Reaction Mechanisms ....... 311
9.4.2 Rationalization of the Complete Set of
Stereodynamical Parameters ........................ 314
9.4.3 Incomplete Information ............................ 321
9.4.4 Manipulation of Collision (stereo)Dynamics ........ 325
9.5 Conclusion and Outlook ................................... 328
9.6 Problems ................................................. 329
Chapter 10 Surface Scattering: Molecular Collisions at
Interfaces .................................................... 333
Andrew Hodgson and George Darling
10.1 Introduction ............................................. 333
10.1.1 Overview of Different Gas-Surface Scattering
Channels .......................................... 334
10.1.2 Importance of Building an Atomic-Level
Understanding of these Channels ................... 335
10.1.3 A Brief Comparison with Gas Phase Scattering ...... 336
10.2 The Molecule-Surface Potential Energy Surface ............ 336
10.3 Scattering and Trapping .................................. 342
10.3.1 Elastic Scattering ................................ 342
10.3.2 Inelastic Scattering .............................. 344
10.4 Non-Activated Dissociation ............................... 348
10.5 Direct Dissociation ...................................... 351
10.5.1 Early versus Late Barriers - Polanyi Rules ........ 351
10.5.2 Incidence Angle Dependence and Surface
Corrugation ....................................... 352
10.5.3 Molecular Rotations ............................... 353
10.5.4 Mode/Bond Specific Surface Chemistry .............. 354
10.5.5 Excitations of the Surface and Dissociation ....... 354
10.5.6 Non-Adiabatic Effects in Molecular Dissociation
Reactions ......................................... 355
10.6 Recombinative Desorption ................................. 355
10.6.1 Detailed Balance .................................. 356
10.6.2 One Dimensional Models for Activated Adsorption-
Desorption ........................................ 359
10.6.3 Weakly Coupled Systems (Hydrogen Recombination) ... 359
10.6.4 Heavy Molecules ................................... 361
10.7 Outlook .................................................. 362
10.8 Problems ................................................. 362
Chapter 11 Femtochemistry and the Control of Chemical
Reactivity .................................................... 363
Helen H. Fielding and Abigail D.G. Nunn
11.1 Introduction ............................................. 363
11.2 Femtosecond lasers ....................................... 365
11.2.1 Femtosecond Laser Oscillators ..................... 365
11.2.2 Femtosecond Amplifiers ............................ 370
11.2.3 Wavelength Tuning of Femtosecond Pulses ........... 373
11.3 Probes for Ultrafast Chemical Dynamics ................... 374
11.4 Ultrafast Photoinduced Processes ......................... 377
11.4.1 Wavepackets ....................................... 378
11.4.2 Photodissociation ................................. 378
11.4.3 Femtochemistry of Larger Molecules ................ 381
11.4.4 The Condensed Phase ............................... 382
11.5 Femtosecond Coherent Control ............................. 382
11.5.1 Pulse Trains ...................................... 383
11.5.2 Chirped Pulses .................................... 384
11.5.3 Programmable Pulse Shaping ........................ 385
11.6 Outlook .................................................. 389
11.7 Problems ................................................. 390
Chapter 12 Cold and Ultracold Collisions ...................... 392
Gerrit C. Groenenboom and Liesbeth M.C. Janssen
12.1 Introduction ............................................. 392
12.2 Classical Capture Theory ................................. 393
12.2.1 Classical Central Force Problem ................... 393
12.2.2 Cross Sections .................................... 401
12.2.3 Canonical Reaction Rates .......................... 401
12.2.4 Isotropic Interactions ............................ 403
12.2.5 Anisotropic Interactions .......................... 406
12.3 Quantum Capture Theory ................................... 407
12.3.1 Quantum Scattering Theory ......................... 408
12.3.2 Connection with Classical Capture Theory .......... 410
12.3.3 Coupled Channels Capture Theory ................... 411
12.3.4 Quantum Adiabatic Capture Theory .................. 414
12.3.5 Thermal Capture Rates ............................. 414
12.3.6 Total Angular Momentum Representation ............. 415
12.4 Wigner Threshold Laws .................................... 416
12.4.1 Bouncing Off a Cliff .............................. 417
12.4.2 S-Wave Elastic Scattering ......................... 418
12.4.3 Scattering Length ................................. 419
12.4.4 Inelastic Scattering at Low Energy ................ 420
12.5 Ultracold Phenomena ...................................... 424
12.5.1 Particle in a Box ................................. 426
12.5.2 Bose-Einstein Condensation ........................ 428
12.5.3 A Bose-Einstein Condensate in a Harmonic Trap ..... 431
12.5.4 The Gross-Pitaevskii Equation ..................... 431
12.5.5 Thomas-Fermi Approximation ........................ 438
12.5.6 Bose-enhancement and Pauli-blocking ............... 438
12.6 Outlook .................................................. 440
12.7 Problems ................................................. 440
Further Reading ............................................... 442
Glossary of Acronyms .......................................... 447
Bibliography .................................................. 450
Subject Index ................................................. 474
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