Wolfgang Demtroder Molecular Physics

Transcription

1 Wolfgang Demtroder Molecular Physics

2 Related Titles Bethge, K., Gruber, G., Stohlker, T. Physik der Atome und Molekiile Eine Einfuhrung 437 pages with 192 figures 2004, Hardcover ISBN Hollas, J. M. Modern Spectroscopy 480 pages 2003, Hardcover ISBN , Softcover ISBN May, V., Kuhn, 0. Charge and Energy Transfer Dynamics in Molecular Systems 490 pages with approx. 134 figures 2004, Hardcover ISBN Brumer, P. W., Shapiro, M. Principles of the Quantum Control of Molecular Processes approx. 250 pages 2003, Hardcover ISBN Cohen-Tannoudji, C., Dupont-Roc, J., Grynberg, G. Atom-Photon Interactions Basic Processes and Applications 678 pages with 108 figures 1998, Softcover ISBN

3 Wolfgang Demtroder Molecular Physics Theoretical Principles and Experimental Methods WKEY- VCH WILEY-VCH Verlag GmbH & Co. KGaA

4 The Author Prof. Dr. Wolfgang Demtroder Department of Physics University of Kaiserslautern Germany Translation Dr. Michael Bir Original title: Molekiilphysik. Theoretische Grundlagen und experimentelle 2003 Oldenbourg Wissenschaftsverlag GmbH All rights reserved Authorized translation from German language edition published by Oldenbourg Wissenschaftsverlag GmbH All books published by Wiley-VCH are carefully produced. Nevertheless, authors, editors, and publisher do not warrant the information contained in these books, including this book, to be free of errors. Readers are advised to keep in mind that statements, data, illustrations, procedural details or other items may inadvertently be inaccurate. Library of Congress Card No.: applied for British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. Bibliographic information published by Die Deutsche Bibliothek Die Deutsche Bibliothek lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data is available in the Internet at 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Wein heim All rights reserved (including those of translation into other languages). No part of this book may be reproduced in any form - by photoprinting, microfilm, or any other means - nor transmitted or translated into a machine language without written permission from the publishers. Registered names, trademarks, etc. used in this book, even when not specifically marked as such, are not to be considered unprotected by law. Typesetting Dr. Michael Bir, Wiesloch Printing Strauss GmbH, Moerlenbach Binding Litges & Dopf Buchbinderei GmbH, Heppenheim Printed in the Federal Republic of Germany Printed on acid-free paper ISBN-13: ISBN-10:

5 Iv Contents Contents v Preface xiii Introduction 1 Short Historical Overview 2 Molecular Spectra 4 Recent Developments 8 The Concept of This Book Molecular Electronic States 15 Adiabatic Approximation and the Concept of Molecular Potentials 15 Quantum-Mechanical Description of Free Molecules 15 Separation of Electronic and Nuclear Wavefunctions 18 Born-Oppenheimer Approximation 20 Adiabatic Approximation 22 Deviations From the Adiabatic Approximation 23 Potentials, Curves and Surfaces, Molecular Term Diagrams and Spectra 25 Electronic States of Diatomic Molecules 28 Exact Treatment of the Rigid H$ Molecule 29 Classification of Electronic Molecular States 34 Energetic Ordering of Electronic States 35 Symmetries of Electronic Wavefunctions 36 Electronic Angular Momenta 38 Electron Configurations and Electronic States 42 The Approximation of Separated Atoms 42 The United Atom Approximation 45 Molecular Orbitals and the Aufbau Principle 45 Molecular Pliysi(x Theorefiral Principles and Experimental Meih0d.r. Wolfgang Demtroder. Copyright WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN:

6 vi I Contents Correlation Diagrams 48 Approximation Methods for the Calculation of Electronic Wavefunctions 51 The Variational Method 52 The LCAO Approximation 53 Application of Approximation Methods to One-electron Systems 56 A Simple LCAO Approximation for the H2f Molecule 56 Deficiencies of the Simple LCAO Method 58 Improved LCAO Approximations 60 Many-electron Molecules 63 Molecular Orbitals and the Single-particle Approximation 63 The H2 Molecule 66 The Molecular Orbital Approximation for H2 66 The Heitler-London Approximation 69 Improvements of Both Methods 70 Equivalence of Heitler-London and MO Approximation 71 Generalized MO Ansatz 71 Modem Ab Znitio Methods 72 The Hartree-Fock Approximation 73 Configuration Interaction 75 Ab Znitio Calculations and Quantum Chemistry Rotatlon, Vibration, and Potential Curves of Diatomic Molecules 79 Quantum-mechanical Treatment 79 Rotation of Diatomic Molecules 81 The Rigid Rotor 81 Centrifugal Distortion 82 The Influence of Electron Rotation 84 Molecular Vibrations 86 The Harmonic Oscillator 87 The Anharmonic Oscillator 92 Morse Potential 92 Taylor Expansion of Potentials 92 Quartic Potential 93 Generalized Potential 95 Vibration-Rotation Interaction 95 Term Values of the Vibrating Rotor; Dunham Expansion 97 Term Values for the Morse Potential 97 Term Values for a Generalized Potential 98 Dunham Expansion 99 Isotopic Shifts 100

7 Contents I vii Determination of Potential Curves from Measured Term Values The WKB Approximation 101 WKB Approximation and Dunham Expansion 104 Other Potential Expansions 105 The RKR Method 105 The Inverted Perturbation Approach 109 Potential Curves at Large Internuclear Distances 112 Multipole Expansion 113 Induction Contributions to the Interaction Potential 114 Point-charge-induced Dipole (Ion-Atom Interaction) 115 Interaction Between Two Neutral Atoms 116 Lennard-Jones Potential Spectra of Diatomic Molecules 727 Transition Probabilities 122 Einstein Coefficients 122 Transition Probabilities and Matrix Elements 125 Matrix Elements in the Born-Oppenheimer Approximation 128 Structure of the Spectra of Diatomic Molecules 129 Vibration-Rotation Spectra 129 Pure Vibrational Transitions Within an Electronic State 131 Pure Rotational Transitions 133 Vibration-Rotation Transitions 136 Electronic Transitions 138 R Centroid Approximation; the Franck-Condon Principle 139 The Rotational Structure of Electronic Transitions 145 Continuous Spectra 148 Line Profiles of Spectral Lines 151 Natural Linewidth 152 Doppler Broadening 154 Voigt Profiles 157 Collisional Broadening of Spectral Lines 158 Multi-photon Transitions 161 Two-Photon Absorption 161 Raman Transitions 165 Raman Spectra 167 Thermal Population of Molecular Levels 170 Thermal Population of Rotational Levels 170 Population of Vibration-Rotation Levels 171 Nuclear Spin Statistics 171

8 viii I Contents Molecular Symmetry and Group Theory 175 Symmetry Operations and Symmetry Elements 175 Foundations of Group Theory 179 Molecular Point Groups 181 Classification of Molecular Point Groups 184 The Point Groups C,, Cnv, and cnh 185 The Point Groups D,, Dnd, and D,h 187 The groups S, 189 The Point Groups Td and oh 190 How to Find the Point Group of a Molecule 191 Symmetry vpes and Representations of Groups 192 The Representation of the Group CzV 193 The Representation of the Group C3v 195 Characters and Character Tables 197 Sums, Products, and Reduction of Representations Rotations and Vlbratlons of Polyatomic Molecules 203 Transformation From the Laboratory System to the Molecule-fixed System 204 Molecular Rotation 207 The Rigid Rotor 207 The Symmetric Top 211 Quantum-mechanical Treatment of Rotation 212 Centrifugal Distortion of the Symmetric Top 214 The Asymmetric Top 215 Vibrations of Polyatomic Molecules 221 Normal Modes 222 Example: Calculation of the Stretching Vibrations of a Linear Molecule AB;! 225 Degenerate Vibrations 226 Quantum-mechanical Treatment 228 Anharmonic Vibrations 230 Vibration-Rotation Coupling Electronic States of Polyatomic Molecules Molecular Orbitals Hybridization Triatomic Molecules I The BeH2 Molecule The H20 Molecule 247

9 Contents I ix The C02 Molecule AB;! Molecules and Walsh Diagrams Molecules With More Than Three Atoms The NH3 Molecule Formaldehyde n-electron Systems Butadiene Benzene I Spectra of Polyatomic Molecules 263 Pure Rotational Spectra 263 Linear Molecules 264 Symmetric Top Molecules 266 Asymmetric Top Molecules 267 Intensities of Rotational Transitions 26Y Symmetry Properties of Rotational Levels 270 Statistical Weights and Nuclear Spin Statistics 272 Line Profiles of Absorption Lines 274 Vibration-Rotation Transitions 274 Selection Rules and Intensities of Vibrational Transitions Fundamental Transitions 278 Overtone and Combination Bands 279 Rotational Structure of Vibrational Bands 283 Electronic Transitions 286 Fluorescence and Raman Spectra Breakdown of the Born-Oppenheimer Approximation, Perturbations in Molecular Spectra 293 What is a Perturbation? 293 Quantitative Treatment of Perturbations 295 Adiabatic and Diabatic Basis 297 Perturbations Between Two Levels 299 Hund s Coupling Cases 300 Discussion of Different Types of Perturbations 302 Electrostatic Interaction 302 Spin-Orbit Coupling 305 Rotational Perturbations 307 Vibronic Coupling 309 Renner-Teller Coupling 311 Jahn-Teller Effect 313

10 x I Contents Predissociation 316 Autoionization 31 7 Radiationless Transitions Molecules in External Fields 325 Diamagnetic and Paramagnetic Molecules 326 Zeeman Effect in Linear Molecules 327 Spin-Orbit Coupling and External Magnetic Fields Molecules in Electric Fields: The Stark Effect Van der Waals Molecules and Clusters 343 Van der Waals Molecules 345 Clusters 350 Alkali Metal Clusters 352 Rare-gas Clusters 355 Water Clusters 357 Covalently Bonded Clusters 358 Generation of Clusters Experimental Techniques in Molecular Physics Microwave Spectroscopy Infrared and Fourier Spectroscopy Classical Spectroscopy in the Visible and Ultraviolet Laser Spectroscopy Laser Absorption Spectroscopy Intracavity Laser Spectroscopy Absorption Measurements Using the Resonator Decay Time Photoacoustic Spectroscopy Laser-magnetic Resonance Spectroscopy Laser-induced Fluorescence Laser Spectroscopy in Molecular Beams Doppler-free Nonlinear Laser Spectroscopy Multi-photon Spectroscopy Double Resonance Techniques Coherent Anti-Stokes Raman Spectroscopy Time-resolved Laser Spectroscopy Femtochemistry 41 I Coherent Control 412

11 Contents I xi Photoelectron Spectroscopy 415 Experimental Setups 416 Photoionization Processes 41 7 ZEKE Spectroscopy 4 I8 Angular Distribution of Photoelectrons 420 X-ray Photoelectron Spectroscopy (XPS) 421 Mass Spectroscopy 422 Magnetic Mass Spectrometers 423 Quadrupole Mass Spectrometers 424 Time-of-flight Mass Spectrometers 426 Radiofrequency Spectroscopy 427 Nuclear Magnetic Resonance Spectroscopy 429 Electron Spin Resonance 432 Conclusion 434 Appendix: Character Tables of Some Point Groups 437 Bibliography 447 Index 467

12 I xiii During the last few decades, molecular physics has gained increasing importance in physics, chemistry and biology. There are several reasons for this progress. The development of new experimental techniques with vastly improved sensitivity and spectral resolution has allowed detailed measurements of structure and dynamics even for large molecules in minute concentrations. This opens the way for studying chemical reactions and biological processes on a molecular level. Using ultrashort laser pulses, very fast dynamical processes in excited molecular states can be measured with a time resolution of a few femtoseconds. Examples are the dissociation of excited molecules, or the redistribution of the energy pumped into a selectively excited molecular state by photon absorption. This energy redistribution onto many vibronic states can be caused by collisions or by couplings between different molecular states, and it often results in a permanent change of molecular structure (isomerization). For the first time in the development of molecular physics, such ultrashort phenomena can be measured in realtime. Another important reason for the progress in molecular physics is the development of fast computers and sophisticated software, which allow the calculation of molecular structures and potential energy surfaces in molecular ground states and even in excited states with an astonishing accuracy. Also, the dynamics of excited molecular states can be today visualized on a computer screen in slow motion to give a vivid and detailed picture of the way molecular processes occur on a femtosecond scale. This allows a much better understanding of chemical and biological reaction paths. Quantum chemistry, working in this field, has therefore received more attention in chemistry and biology. The success of molecular biology is partly based both on the new experimental techniques and on such computer simulations. In order to gain a more profound understanding of these developments, one has to acquire sufficient knowledge about the basic physics of molecules. This volume tries to make the fundamentals of molecular physics accessible, starting with diatomic molecules as the simplest molecular species. The different approximation methods used for the calculation of molecular structure, their physical meaning and their limitations are presented. The principles that are valid for diatomics are then transferred Molecular Physics. Theorrrical Principles and Experimental Methods. Wolfgang Demtroder. Copyright WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim ISBN:

13 xiv I Preface to and extended to polyatomic molecules, where additional phenomena occur, such as vibronic couplings or Coriolis effects in rotating molecules. The last chapter discusses classical and modem experimental techniques used in molecular physics, giving the reader a better understanding of the possibilities, advantages, and drawbacks of the different experimental approaches to the investigation of molecules. It is in particular laser spectroscopy that has contributed in an outstanding way to the progress in molecular spectroscopy. This book is a thoroughly revised edition of a German edition published two years ago. The author would like to thank Michael Bk who translated the German book and took care of the typesetting for his careful work and for many valuable suggestions. The author hopes that this textbook will foster the interest in molecular physics in the communities of physicists, chemists and biologists. Since no book is perfect, the author appreciates any comments, hints to possible errors, or suggestions for improvements. Wolfgang Demtriider Kaiserslautern, August 2005