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Table of Contents
Preface; Contents; 1 New Ideas for Solving Old Problems
An Introduction; Part I Group Theory in Molecular Physics; 2 Basic Concepts ; 2.1 Symmetry Groups of the Molecular Hamiltonian; 2.1.1 General Representation Theory; 2.1.2 Lie Groups and Permutation Groups; 2.2 Zero-Order Models in Molecular Theory; 2.2.1 The Separation of the Molecular Hamiltonian; 2.2.2 The Zero-Order Models for Nuclear Motion; 2.3 Connecting Dynamics and Group Theory
Outlook to This Work; 3 Schur
Weyl Duality in Molecules; 3.1 Nuclear Spin States in Molecules; 3.1.1 The Natural Way; 3.1.2 Unitary Symmetry
3.1.3 Permutation Symmetry3.2 Schur
Weyl Duality; 3.2.1 Application of the Duality Theorem; 3.3 Conclusion; 4 Reactive Collisions ; 4.1 Representation Theory in Reactions of Small Molecules; 4.1.1 Mathematical Preliminaries; 4.1.2 Single Molecules; 4.1.3 A First Example; 4.2 The H3+ +H2 Reaction; 4.2.1 A Restricted Symmetry Group for the Intermediate Complex; 4.2.2 Implications for Experiments; 4.2.3 The Deuterated Version; 4.3 Discussion; Part II Extremely Floppy Molecules; 5 Introducing Extreme Floppiness; 6 Symmetry Beyond Perturbation Theory
6.1 Representation Theory of Molecular Rotation6.1.1 Example: The H3+ ion; 6.2 The Failure of the Subgroup Picture; 6.3 Concluding Remarks; 7 The Molecular Super-Rotor; 7.1 Large Amplitude Motion; 7.2 Super-Rotation; 7.2.1 The Energy Expression; 7.2.2 Degrees of Freedom; 8 Super-Rotor States and Their Symmetry; 8.1 Five-Dimensional Rotor States; 8.1.1 Parity and Dipole Selection Rules; 8.2 Permutation-Inversion Symmetry; 8.2.1 The Permutation Group of Five Identical Particles; 8.3 Conclusion; 9 Protonated Methane; 9.1 The Molecule; 9.2 The Experiment; 9.3 The Model; 9.4 The Discussion
10 Refinements and Further Applications10.1 Beyond Zero-Order; 10.1.1 Generalized Moments of Inertia; 10.1.2 Higher-Order Terms; 10.2 Additional Target Molecules; 10.3 Concluding Remarks; Part III Semi-classical Approach to Rotational Dynamics; 11 Ultrafast Rotation ; 11.1 Introduction; 11.2 The Gutzwiller Trace Formula; 11.3 The Rotational Energy Surface; 11.3.1 The Paths on the Rotational Energy Surface; 11.3.2 The Quantization Conditions; 11.3.3 Two Approaches to Generate the Rotational Energy Surface; 12 Application to Sulfur Dioxide; 12.1 The Molecule; 12.2 The Comparison; 13 Discussion
13.1 The TROVE
Generated Rotational Energy Surface13.2 Generalization of the Approach; 14 New Ideas for Solving Old Problems
A Conclusion; References ; Index
An Introduction; Part I Group Theory in Molecular Physics; 2 Basic Concepts ; 2.1 Symmetry Groups of the Molecular Hamiltonian; 2.1.1 General Representation Theory; 2.1.2 Lie Groups and Permutation Groups; 2.2 Zero-Order Models in Molecular Theory; 2.2.1 The Separation of the Molecular Hamiltonian; 2.2.2 The Zero-Order Models for Nuclear Motion; 2.3 Connecting Dynamics and Group Theory
Outlook to This Work; 3 Schur
Weyl Duality in Molecules; 3.1 Nuclear Spin States in Molecules; 3.1.1 The Natural Way; 3.1.2 Unitary Symmetry
3.1.3 Permutation Symmetry3.2 Schur
Weyl Duality; 3.2.1 Application of the Duality Theorem; 3.3 Conclusion; 4 Reactive Collisions ; 4.1 Representation Theory in Reactions of Small Molecules; 4.1.1 Mathematical Preliminaries; 4.1.2 Single Molecules; 4.1.3 A First Example; 4.2 The H3+ +H2 Reaction; 4.2.1 A Restricted Symmetry Group for the Intermediate Complex; 4.2.2 Implications for Experiments; 4.2.3 The Deuterated Version; 4.3 Discussion; Part II Extremely Floppy Molecules; 5 Introducing Extreme Floppiness; 6 Symmetry Beyond Perturbation Theory
6.1 Representation Theory of Molecular Rotation6.1.1 Example: The H3+ ion; 6.2 The Failure of the Subgroup Picture; 6.3 Concluding Remarks; 7 The Molecular Super-Rotor; 7.1 Large Amplitude Motion; 7.2 Super-Rotation; 7.2.1 The Energy Expression; 7.2.2 Degrees of Freedom; 8 Super-Rotor States and Their Symmetry; 8.1 Five-Dimensional Rotor States; 8.1.1 Parity and Dipole Selection Rules; 8.2 Permutation-Inversion Symmetry; 8.2.1 The Permutation Group of Five Identical Particles; 8.3 Conclusion; 9 Protonated Methane; 9.1 The Molecule; 9.2 The Experiment; 9.3 The Model; 9.4 The Discussion
10 Refinements and Further Applications10.1 Beyond Zero-Order; 10.1.1 Generalized Moments of Inertia; 10.1.2 Higher-Order Terms; 10.2 Additional Target Molecules; 10.3 Concluding Remarks; Part III Semi-classical Approach to Rotational Dynamics; 11 Ultrafast Rotation ; 11.1 Introduction; 11.2 The Gutzwiller Trace Formula; 11.3 The Rotational Energy Surface; 11.3.1 The Paths on the Rotational Energy Surface; 11.3.2 The Quantization Conditions; 11.3.3 Two Approaches to Generate the Rotational Energy Surface; 12 Application to Sulfur Dioxide; 12.1 The Molecule; 12.2 The Comparison; 13 Discussion
13.1 The TROVE
Generated Rotational Energy Surface13.2 Generalization of the Approach; 14 New Ideas for Solving Old Problems
A Conclusion; References ; Index