The Raman effect: a unified treatment of the theory of Raman scattering by molecules

610 Pages·2002·5.056 MB·English

by  Derek A. Long

TheRamanEffect:AUnifiedTreatmentoftheTheoryofRamanScatteringbyMolecules.DerekA.Long
Copyright2002JohnWiley&SonsLtd
ISBNs:0-471-49028-8(Hardback);0-470-84576-7(Electronic)
The Raman Effect
The Raman Effect
A Unified Treatment of the Theory of Raman Scattering by
Molecules
Derek A. Long
Emeritus Professor of Structural Chemistry
University of Bradford
Bradford, UK
Copyright2002byJohnWiley&SonsLtd,
BaffinsLane,Chichester,
WestSussexPO191UD,England
National 01243779777
International([phone]
e-mail(forordersandcustomerserviceenquiries):[email protected]
VisitourHomePageonhttp://www.wileyeurope.com
orhttp://www.wiley.com
AllRightsReserved.Nopartofthispublicationmaybereproduced,storedinaretrieval
system,ortransmitted,inanyformorbyanymeans,electronic,mechanical,photocopying,
recording,scanningorotherwise,exceptunderthetermsoftheCopyright,DesignsandPatentsAct
1988orunderthetermsofalicenceissuedbytheCopyrightLicensingAgency,90
TottenhamCourtRoad,London,W1P9HE,withoutthepermissioninwritingofthe
Publisher.
OtherWileyEditorialOffices
JohnWiley&Sons,Inc.,605ThirdAvenue,
NewYork,NY10158-0012,USA
Wiley-VCHVerlagGmbH,Pappelallee3,
D-69469Weinheim,Germany
JohnWileyAustralia,33ParkRoad,Milton,
Queensland4064,Australia
JohnWiley&Sons(Asia)PteLtd,2ClementiLoop#02-01,
JinXingDistripark,Singapore129809
JohnWiley&Sons(Canada)Ltd,22WorcesterRoad,
Rexdale,Ontario,M9W1L1,Canada
LibraryofCongressCataloguinginPublicationData
Long,D.A.(DerekAlbert)
TheRamaneffect:aunifiedtreatmentofthetheoryofRamanscatteringbymolecules/
DerekA.Long.
p.cm.
Includesbibliographicalreferencesandindex.
ISBN0-471-49028-8(acid-freepaper)
1.Ramanspectroscopy.I.Title.
QD96.R34L662001
535.8046—dc21
2001046767
BritishLibraryCataloguinginPublicationData
AcataloguerecordforthisbookisavailablefromtheBritishLibrary
ISBN0471490288
Typesetin11/13ptTimesbyLaserwordsPrivateLimited,Chennai,India
PrintedandboundinGreatBritainbyBiddlesLtd,GuildfordandKing’sLynn
Thisbookisprintedonacid-freepaperresponsiblymanufacturedfromsustainableforestry,
inwhichatleasttwotreesareplantedforeachoneusedforpaperproduction.
Dedicated to
Edward and William Long,
grandsons.
vii
Contents
Preface xix
Acknowledgements xxiii
Part One Theory 1
1 Survey of Light-scattering Phenomena 3
1.1 Introduction 3
1.2 Some Basic Definitions 4
1.3 Rayleigh and Raman Scattering 5
1.3.1 Description 5
1.3.2 Energy transfer model 7
1.4 Hyper-Rayleigh and Hyper-Raman Scattering 10
1.4.1 Description 10
1.4.2 Energy transfer model 10
1.5 Second Hyper-Rayleigh and Second Hyper-Raman Scattering 11
1.5.1 Description 11
1.5.2 Energy transfer model 11
1.6 Coherent anti-Stokes and Coherent Stokes Raman Scattering 11
1.7 Stimulated Raman Gain and Loss Spectroscopy 13
1.8 Typical Spectra 14
1.9 Bases for the Theoretical Treatment of Rayleigh and
Raman Scattering 16
1.10 Historical Perspective 16
viii Contents
1.11 Caveat 17
References 17
2 Introduction to Theoretical Treatments of Incoherent Light Scattering 19
2.1 General Considerations 19
2.2 Induced Oscillating Electric Dipoles as Sources of
Scattered Radiation 21
2.3 Basis of the Classical Theory of Light Scattering 22
2.4 Basis of the Quantum Mechanical Treatment
of Incoherent Light-Scattering Phenomena: Electric Dipole Case 24
2.5 Extension of Quantum Mechanical Treatment of Incoherent
Light Scattering to Include Magnetic Dipole and Electric
Quadrupole Cases 27
2.6 Comparison of the Classical and Quantum Mechanical
Treatments of Light Scattering 28
2.7 The Way Ahead 29
3 Classical Theory of Rayleigh and Raman Scattering 31
3.1 Introduction 31
3.2 First-order Induced Electric Dipole 31
3.3 Frequency Dependence of the First-order Induced Electric
Dipole 34
3.4 Classical Scattering Tensors aRay and aRam 35
k
3.5 Selection Rules for Fundamental Vibrations 36
3.5.1 General considerations 36
3.5.2 Diatomic molecules 36
3.5.3 Polyatomic molecules 38
3.6 Selection Rules for Overtones and Combinations 43
3.7 Coherence Properties of Rayleigh and Raman Scattering 44
3.8 Limitations of the Classical Theory 45
3.9 Example of Rayleigh and Raman Scattering 45
3.10 Presentation of Raman Spectra 47
References 48
4 Quantum Mechanical Theory of Rayleigh and Raman Scattering 49
4.1 Introduction 49
4.2 Time-dependent Perturbation Theory and (cid:1)a(cid:2) 50
fi
4.3 Qualitative Discussion of (cid:1)˛ (cid:2) 54
(cid:3)(cid:4) fi
4.3.1 Frequency denominators 55
4.3.2 Transition electric dipole numerators 56
4.3.3 Selection rules 58
4.4 Tensorial Nature of the Transition Polarizability and its Symmetry 58
4.5 Born–Oppenheimer Approximation and the Transition
Polarizability Tensor 61
Contents ix
4.6 Simplification of (cid:1)˛ (cid:2) : General Considerations 64
(cid:3)(cid:4) efvf:egvi
4.7 Simplification by Radical Approximation: the Placzek
Transition Polarizability 65
4.8 Simplification of (cid:1)˛ (cid:2) by Stages 68
(cid:3)(cid:4) efvf:eivi
4.8.1 Introduction of Herzberg–Teller vibronic coupling 68
4.8.2 Identification of non-resonance and resonance
situations 75
4.9 Normal Electronic (and Vibronic) Raman Scattering 77
4.10 Normal Pure Vibrational Raman Scattering 78
4.11 Electronic (and Vibronic) Resonance Raman Scattering 81
4.12 Vibrational Resonance Raman Scattering 83
4.13 Units and Orders of Magnitude 83
References 84
5 Vibrational Raman Scattering 85
5.1 Introduction 85
5.2 The Placzek Vibrational Transition Polarizability:
Recapitulation 86
5.2.1 Cartesian basis 86
5.2.2 The spherical basis 88
5.3 Definition of Illumination–Observation Geometry 89
5.4 Intensity of Scattered Radiation: Some General Considerations 94
5.4.1 Development of a symbol for scattered intensity 94
5.4.2 Scattering cross-section 95
5.5 Intensity Formulae and Polarization Characteristics for a General
Vibrational Transition in Various Illumination–Observation
Geometries 97
5.5.1 General considerations 97
5.5.2 Linearly polarized incident radiation 98
5.5.3 Natural incident radiation 102
5.5.4 Angular dependence of scattered intensity 103
5.5.5 Circularly polarized incident radiation 106
5.5.6 Symmetry and depolarization ratios, reversal
coefficients and degrees of circularity 109
5.6 Stokes Parameters for Scattered Radiation 113
5.7 Specific Vibrational Transitions 116
5.8 Vibrational Selection Rules 120
5.9 Patterns of Vibrational Spectra 123
5.10 Orders of Magnitude 126
5.11 Epilogue 127
References 131
Reference Tables for Chapter 5 132
Reference Table 5.1: Definitions for I(cid:1)(cid:5);ps,pi(cid:2) 132
x Contents
Reference Table 5.2(a) to 5.2(g): Intensities, Polarization
Properties and Stokes Parameters for Vibrational Raman
(and Rayleigh) Scattering 132
Reference Table 5.3: Symmetry classes for x, y, z, the rotations
R , R and R , and the components of the cartesian basis
x y z
tensor ca. 145
6 Rotational and Vibration–Rotation Raman Scattering 153
6.1 Introduction 153
6.2 Irreducible Transition Polarizability Components 154
6.3 Symmetric Top 156
6.3.1 Selection rules 156
6.3.2 Placzek invariants (cid:1)G (cid:1)j(cid:2)(cid:2) 157
fi
6.3.3 Intensities 167
6.3.4 Subsequent development 169
6.4 Rotational and Vibrational Terms 169
6.5 Statistical Distribution of Molecular Population 171
6.6 Diatomic Molecule 173
6.6.1 Introduction 173
6.6.2 Heteronuclear diatomic molecule: pure rotation 174
6.6.3 Heteronuclear diatomic molecule: vibration–rotation 175
6.6.4 Homonuclear diatomic molecule: nuclear spin degeneracy 179
6.6.5 Intensity distribution 180
6.7 Symmetric Top Molecule 186
6.7.1 Introduction 186
6.7.2 Symmetric top: pure rotation 187
6.7.3 Symmetric top: vibration–rotation 191
6.7.4 Intensities 203
6.8 Linear Molecules 204
6.8.1 Rotation and vibration-rotation Raman spectra 204
6.8.2 Intensities 207
6.9 Contributions from Electronic Orbital and Spin Angular Momenta 208
6.10 Spherical Top Molecules 210
6.11 Asymmetric Top Molecules 211
6.12 Epilogue 211
References 213
Reference Tables for Chapter 6 214
Introduction 214
Reference Tables 6.1 to 6.4 216
7 Vibrational Resonance Raman Scattering 221
7.1 Introduction 221
7.2 Vibrational Transition Polarizability Tensor Components in the
Resonance Case, Based on Perturbation Theory 222
Contents xi
7.3 Comparison of the AVI,BVI,CVI and DVI Terms 224
7.3.1 The AVI term 224
7.3.2 The BVI term 227
7.3.3 The CVI term 229
7.3.4 The DVI term 229
7.3.5 Subsequent developments 230
7.4 AVI Term Raman Scattering from Molecules with Totally
Symmetric Modes 231
7.4.1 AVI term Raman scattering from molecules with one
totally symmetric mode 231
7.4.2 AVI term Raman scattering from molecules
with more than one totally symmetric mode: general
considerations 237
7.4.3 AVI term Raman scattering from totally symmetric modes
when  is very small 238
k
7.5 AVI Term Raman Scattering Involving Non-Totally Symmetric
Modes 239
7.5.1 General considerations 239
7.5.2 AVI term scattering involving a change of molecular
symmetry of the resonant excited state 239
7.5.3 AVI term scattering involving excited state Jahn–Teller
coupling 240
7.5.4 Summary of excited state Jahn–Teller effects in
resonance Raman scattering 240
7.6 BVI Term Scattering Involving Vibronic Coupling of the Resonant
Excited State to a Second Excited State 241
7.6.1 Introduction 241
7.6.2 BVI term scattering from molecules with non-totally
symmetric modes 241
7.6.3 BVI term scattering from molecules with totally
symmetric modes 244
7.7 Symmetry, Raman Activity and Depolarization Ratios 246
7.7.1 General symmetry considerations 246
7.7.2 The AVI term 247
7.7.3 The BVI term 250
7.8 Time-Dependent Formulation of Resonance Raman Scattering 262
7.8.1 Introduction 262
7.8.2 Transformation of the AVI term to a time-dependent
expression 263
7.8.3 The time-dependent interpretation of resonance Raman
scattering 264
7.9 Continuum Resonance Raman Scattering 266
References 270
xii Contents
8 Rotational and Vibration–Rotation Resonance Raman Scattering 271
8.1 Introduction 271
8.2 General Expression for (cid:1)˛ (cid:2) for a Symmetric Top Molecule 272
(cid:7)(cid:1)(cid:8) fi
(cid:1)j(cid:2)
8.3 General Expression for (cid:1)˛ (cid:2) 274
m fi
(cid:1)j(cid:2)
8.4 Contraction of General Expression for (cid:1)˛ (cid:2) 274
m fi
8.5 The Quadratic Term 275
8.6 Selection Rules 276
8.7 Evaluation of j(cid:1)˛(cid:1)j(cid:2)(cid:2) j2 277
m fi
8.8 Intensities and Depolarization Ratios 279
8.9 An Illustrative Example 283
8.10 Concluding Remarks 287
Reference 287
9 Normal and Resonance Electronic and Vibronic Raman Scattering 289
9.1 Introduction 289
9.2 Normal Electronic and Vibronic Raman Scattering 289
9.2.1 General considerations 289
9.2.2 AIII-term scattering 290
9.2.3 (cid:1)BIIICCIII(cid:2)-term scattering 291
9.2.4 DIII-term scattering 292
9.2.5 Transition tensor symmetry 292
9.3 Resonant Electronic and Vibronic Raman Scattering 292
9.3.1 General considerations 292
9.3.2 AV-term scattering 293
9.3.3 BV-term scattering 296
9.3.4 CV-term scattering 297
9.3.5 DV-term scattering 297
9.4 Selection Rules in Electronic Raman Spectra 297
9.4.1 General symmetry considerations 297
9.5 Intensities and Polarization Properties of Electronic Raman
Scattering 301
9.5.1 Intensities: general considerations 301
9.5.2 Excitation profiles 301
9.5.3 Depolarization ratios 302
10 Rayleigh and Raman Scattering by Chiral Systems 303
10.1 Introduction 303
10.2 Outline of the Theoretical Treatment 305
10.3 Intensities of Optically Active Rayleigh Scattering 310
10.3.1 General considerations 310
10.3.2 Intensity formulae 314
10.3.3 Stokes parameters 317