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Molecular symmetry, super-rotation, and semiclassical motion : new ideas for solving old problems

Author: Hanno Schmiedt
Publisher: Cham, Switzerland : Springer, [2017] ©2017
Series: Springer series on atomic, optical, and plasma physics, 97.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
This book presents a range of fundamentally new approaches to solving problems involving traditional molecular models. Fundamental molecular symmetry is shown to open new avenues for describing molecular dynamics beyond standard perturbation techniques. Traditional concepts used to describe molecular dynamics are based on a few fundamental assumptions, the ball-and-stick picture of molecular structure and the  Read more...
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Genre/Form: Electronic books
Electronic book
Additional Physical Format: Print version:
(OCoLC)994639540
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Hanno Schmiedt
ISBN: 9783319660714 3319660713
OCLC Number: 1003117545
Description: 1 online resource.
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.
Series Title: Springer series on atomic, optical, and plasma physics, 97.
Responsibility: Hanno Schmiedt.

Abstract:

This book presents a range of fundamentally new approaches to solving problems involving traditional molecular models. Fundamental molecular symmetry is shown to open new avenues for describing molecular dynamics beyond standard perturbation techniques. Traditional concepts used to describe molecular dynamics are based on a few fundamental assumptions, the ball-and-stick picture of molecular structure and the respective perturbative treatment of different kinds of couplings between otherwise separate motions. The book points out the conceptual limits of these models and, by focusing on the most essential idea of theoretical physics, namely symmetry, shows how to overcome those limits by introducing fundamentally new concepts. The book begins with an introduction to molecular symmetry in general, followed by a discussion of nuclear spin symmetry. Here, a new correlation between identical particle exchange and spin angular momentum symmetry of nuclei is exhibited. The central part of the book is the discussion of extremely floppy molecules, which are not describable in the framework of traditional theories. The book introduces a fundamentally new approach to describing the molecular dynamics of these molecules - the super-rotor model, which is based on a five-dimensional symmetry that has never been observed in molecules before. By applying the super-rotor theory to the prototype of floppy molecules, protonated methane, this model can consistently predict the symmetry and energy of low-energy states, which were characterized experimentally only a few years ago. The theoretical predictions agree with the experimental results, which makes the prospect of further developing the super-rotor theory and applying it to other molecules a promising one. In the final section, the book also covers the topic of ultrafast rotations, where usual quantum calculations reach their natural limits. A semi-classical method for determining rotational energies, developed in the early 1990s, is shown to be attachable to quantum calculations of the vibrational states. This new combined method is suitable for efficiently calculating ro-vibrational energies, even for molecular states with large angular momentum.

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