MODERN SPECTROSCOPY Fourth Edition MODERN SPECTROSCOPY Fourth Edition J. Michael Hollas University of Reading Copyright # 1987, 1992, 1996, 2004 by John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (þ44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.uk Visit our Home Page on www.com or www.com All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to permreq@wiley.uk, or faxed to (þ44) 1243 770620.
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Contents Preface to first edition xiii Preface to second edition xv Preface to third edition xvii Preface to fourth edition xix Units, dimensions and conventions xxi Fundamental constants xxiii Useful conversion factors xxv 1 Some important results in quantum mechanics 1 1.1 Spectroscopy and quantum mechanics 1 1.2 The evolution of quantum theory 2 1.3 The Schrödinger equation and some of its solutions 8 1.1 The Schrödinger equation 9 1.2 The hydrogen atom 11 1.3 Electron spin and nuclear spin angular momentum 17 1.4 The Born–Oppenheimer approximation 19 1.5 The rigid rotor 21 1.6 The harmonic oscillator 23 Exercises 25 Bibliography 26 2 Electromagnetic radiation and its interaction with atoms and molecules 27 2.2 Absorption and emission of radiation 27 2.1 Natural line broadening 34 2.4 Power, or saturation, broadening 36 2.5 Removal of line broadening 37 2.1 Effusive atomic or molecular beams 37 2.2 Lamb dip spectroscopy 37 v vi CONTENTS Exercises 38 Bibliography 39 3 General features of experimental methods 41 3.1 The electromagnetic spectrum 41 3.2 General components of an absorption experiment 42 3.3 Fourier transformation and interferometers 48 3.2 Infrared, visible and ultraviolet radiation 55 3.4 Components of absorption experiments in various regions of the spectrum 59 3.1 Microwave and millimetre wave 59 3.3 Near-infrared and mid-infrared 62 3.4 Visible and near-ultraviolet 62 3.5 Vacuum- or far-ultraviolet 63 3.5 Other experimental techniques 64 3.1 Attenuated total reflectance spectroscopy and reflection–absorption infrared spectroscopy 64 3.2 Atomic absorption spectroscopy 64 3.3 Inductively coupled plasma atomic emission spectroscopy 66 3.6 Typical recording spectrophotometers for the near-infrared, mid-infrared, visible and near-ultraviolet regions 68 Exercise 70 Bibliography 70 4 Molecular symmetry 73 4.1 Elements of symmetry 73 4.1 n-Fold axis of symmetry, Cn 74 4.2 Plane of symmetry, s 75 4.3 Centre of inversion, i 76 4.4 n-Fold rotation–reflection axis of symmetry, Sn 76 4.5 The identity element of symmetry, I (or E) 77 4.6 Generation of elements 77 4.7 Symmetry conditions for molecular chirality 78 4.1 Cn point groups 82 4.2 Sn point groups 83 4.3 Cnv point groups 83 4.4 Dn point groups 83 4.5 Cnh point groups 84 4.6 Dnd point groups 84 4.7 Dnh point groups 84 CONTENTS vii 4.8 Td point group 85 4.9 Oh point group 85 4.10 Kh point group 86 4.11 Ih point group 86 4.12 Other point groups 87 4.3 Point group character tables 87 4.4 Ih character table 97 4.4 Symmetry and dipole moments 97 Exercises 102 Bibliography 102 5 Rotational spectroscopy 103 5.1 Linear, symmetric rotor, spherical rotor and asymmetric rotor molecules 103 5.2 Rotational infrared, millimetre wave and microwave spectra 105 5.1 Diatomic and linear polyatomic molecules 105 5.1 Transition frequencies or wavenumbers 105 5.4 Diatomic molecules in excited vibrational states 112 5.2 Symmetric rotor molecules 113 5.3 Stark effect in diatomic, linear and symmetric rotor molecules 115 5.4 Asymmetric rotor molecules 116 5.5 Spherical rotor molecules 117 5.6 Interstellar molecules detected by their radiofrequency, microwave or millimetre wave spectra 119 5.3 Rotational Raman spectroscopy 122 5.2 Theory of rotational Raman scattering 124 5.3 Rotational Raman spectra of diatomic and linear polyatomic molecules 126 5.4 Nuclear spin statistical weights 128 5.5 Rotational Raman spectra of symmetric and asymmetric rotor molecules 131 5.4 Structure determination from rotational constants 131 Exercises 134 Bibliography 135 6 Vibrational spectroscopy 137 6.2 Mechanical anharmonicity 142 viii CONTENTS 6.4 Vibration–rotation spectroscopy 147 6.2 Number of normal vibrations of each symmetry species 162 6.1 Non-degenerate vibrations 163 6.3 Vibrational selection rules 166 6.4 Vibration–rotation spectroscopy 173 6.1 Infrared spectra of linear molecules 174 6.2 Infrared spectra of symmetric rotors 178 6.3 Infrared spectra of spherical rotors 180 6.4 Infrared spectra of asymmetric rotors 181 6.1 Potential energy surfaces 184 6.2 Vibrational term values 186 6.3 Local mode treatment of vibrations 187 6.4 Vibrational potential functions with more than one minimum 188 6.4(b) Ring-puckering vibrations 191 6.4(c) Torsional vibrations 192 Exercises 195 Bibliography 196 7 Electronic spectroscopy 199 7.1 The periodic table 199 7.2 Vector representation of momenta and vector coupling approximations 201 7.1 Angular momenta and magnetic moments 201 7.2 Coupling of angular momenta 205 7.3 Russell–Saunders coupling approximation 206 7.3(a) Non-equivalent electrons 206 7.3 Spectra of alkali metal atoms 213 7.4 Spectrum of the hydrogen atom 216 7.5 Spectra of helium and the alkaline earth metal atoms 219 7.6 Spectra of other polyelectronic atoms 222 7.2 Electronic spectroscopy of diatomic molecules 225 7.1 Homonuclear diatomic molecules 225 7.2 Heteronuclear diatomic molecules 232 7.2 Classification of electronic states 233 7.3 Electronic selection rules 236 7.4 Derivation of states arising from configurations 237 7.5 Vibrational coarse structure 240 7.1 Potential energy curves in excited electronic states 240 7.2 Progressions and sequences 242 CONTENTS ix 7.3 The Franck–Condon principle 246 7.6 Repulsive states and continuous spectra 253 7.6 Rotational fine structure 254 7.1 1S 7 1S electronic and vibronic transitions 254 7.2 1P 7 1S electronic and vibronic transitions 257 7.3 Electronic spectroscopy of polyatomic molecules 260 7.1 Molecular orbitals and electronic states 260 7.4 Crystal field and ligand field molecular orbitals 270 7.4(a) Crystal field theory 271 7.4(b) Ligand field theory 273 7.2 Electronic and vibronic selection rules 275 7.4 Vibrational coarse structure 278 7.2(a) Totally symmetric vibrations 279 7.2(b) Non-totally symmetric vibrations 279 7.5 Rotational fine structure 283 7.6 Diffuse spectra 284 Exercises 287 Bibliography 288 8 Photoelectron and related spectroscopies 289 8.1 Sources of monochromatic ionizing radiation 291 8.2 Electron velocity analysers 294 8.2 Ionization processes and Koopmans’ theorem 295 8.3 Photoelectron spectra and their interpretation 297 8.1 Ultraviolet photoelectron spectra of atoms 297 8.2 Ultraviolet photoelectron spectra of molecules 298 8.3 X-ray photoelectron spectra of gases 307 8.4 X-ray photoelectron spectra of solids 313 8.2 Auger electron and X-ray fluorescence spectroscopy 315 8.1 Auger electron spectroscopy 317 8.1 Experimental method 317 x CONTENTS 8.2 Processes in Auger electron ejection 318 8.3 Examples of Auger electron spectra 319 8.2 X-ray fluorescence spectroscopy 322 8.2 Processes in X-ray fluorescence 324 8.3 Examples of X-ray fluorescence spectra 325 8.3 Extended X-ray absorption fine structure 327 Exercises 334 Bibliography 335 9 Lasers and laser spectroscopy 337 9.1 General discussion of lasers 337 9.1 General features and properties 337 9.2 Methods of obtaining population inversion 340 9.3 Laser cavity modes 341 9.2 Examples of lasers 346 9.1 The ruby and alexandrite lasers 346 9.2 The titanium–sapphire laser 348 9.3 The neodymium–YAG laser 349 9.4 The diode or semiconductor laser 350 9.5 The helium–neon laser 352 9.6 The argon ion and krypton ion lasers 354 9.7 The nitrogen (N2) laser 355 9.8 The excimer and exciplex lasers 356 9.9 The carbon dioxide laser 358 9.10 The dye lasers 359 9.11 Laser materials in general 362 9.3 Uses of lasers in spectroscopy 362 9.1 Hyper Raman spectroscopy 363 9.2 Stimulated Raman spectroscopy 365 9.3 Coherent anti-Stokes Raman scattering spectroscopy 367 9.4 Laser Stark (or laser electron resonance) spectroscopy 368 9.5 Two-photon and multiphoton absorption 371 9.6 Multiphoton dissociation and laser separation of isotopes 374 9.7 Single vibronic level, or dispersed, fluorescence 377 9.8 Light detection and ranging (LIDAR) 379 9.9 Cavity ring-down spectroscopy 382 9.11 Spectroscopy of molecules in supersonic jets 393 9.1 Properties of a supersonic jet 393 9.2 Fluorescence excitation spectroscopy 396 9.3 Single vibronic level, or dispersed, fluorescence spectroscopy 400 9.4 Zero kinetic energy photoelectron spectroscopy 402 Exercises 404 Bibliography 405 CONTENTS xi Appendix A Character tables 407 B Symmetry species of vibrations 423 Index of Atoms and Molecules 429 Subject Index 439 Preface to first edition Modern Spectroscopy has been written to fulfil a need for an up-to-date text on spectroscopy.
It is aimed primarily at a typical undergraduate audience in chemistry, chemical physics, or physics in the United Kingdom and at undergraduate and graduate student audiences elsewhere. Spectroscopy covers a very wide area which has been widened further since the mid- 1960s by the development of lasers and such techniques as photoelectron spectroscopy and other closely related spectroscopies. The importance of spectroscopy in the physical and chemical processes going on in planets, stars, comets and the interstellar medium has continued to grow as a result of the use of satellites and the building of radiotelescopes for the microwave and millimetre wave regions. In planning a book of this type I encountered three major problems.
The first is that of covering the analytical as well as the more fundamental aspects of the subject. The importance of the applications of spectroscopy to analytical chemistry cannot be overstated, but the use of many of the available techniques does not necessarily require a detailed understanding of the processes involved. I have tried to refer to experimental methods and analytical applications where relevant. The second problem relates to the inclusion, or otherwise, of molecular symmetry arguments.
There is no avoiding the fact that an understanding of molecular symmetry presents a hurdle (although I think it is a low one) which must be surmounted if selection rules in vibrational and electronic spectroscopy of polyatomic molecules are to be understood. This book surmounts the hurdle in Chapter 4, which is devoted to molecular symmetry but which treats the subject in a non-mathematical way. For those lecturers and students who wish to leave out this chapter much of the subsequent material can be understood but, in some areas, in a less satisfying way. The third problem also concerns the choice of whether to leave out certain material.
In a book of this size it is not possible to cover all branches of spectroscopy. Such decisions are difficult ones but I have chosen not to include spin resonance spectroscopy (NMR and ESR), nuclear quadrupole resonance spectroscopy (NQR), and Mössbauer spectroscopy.
