Molecular quantum mechanics

588 Pages·2005·5.358 MB·English

by  Peter Atkins, Ronald Friedman

MOLECULAR
QUANTUM
MECHANICS,
FOURTH EDITION
Peter Atkins
Ronald Friedman
OXFORD UNIVERSITY PRESS
MOLECULAR QUANTUM MECHANICS
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MOLECULAR
QUANTUM
MECHANICS
FOURTH EDITION
Peter Atkins
University of Oxford
Ronald Friedman
Indiana Purdue Fort Wayne
AC
AC
GreatClarendonStreet,OxfordOX26DP
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Table of contents
Preface xiii
Introductionandorientation 1
1 Thefoundationsofquantummechanics 9
2 Linearmotionandtheharmonicoscillator 43
3 Rotationalmotionandthehydrogenatom 71
4 Angularmomentum 98
5 Grouptheory 122
6 Techniquesofapproximation 168
7 Atomicspectraandatomicstructure 207
8 Anintroductiontomolecularstructure 249
9 Thecalculationofelectronicstructure 287
10 Molecularrotationsandvibrations 342
11 Molecularelectronictransitions 382
12 Theelectricpropertiesofmolecules 407
13 Themagneticpropertiesofmolecules 436
14 Scatteringtheory 473
Furtherinformation 513
Furtherreading 553
Appendix1Charactertablesanddirectproducts 557
Appendix2Vectorcouplingcoefficients 562
Answerstoselectedproblems 563
Index 565
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Detailed Contents
Introductionandorientation 1 TheplausibilityoftheSchro¨dingerequation 36
1.22 Thepropagationoflight 36
0.1 Black-bodyradiation 1
1.23 Thepropagationofparticles 38
0.2 Heatcapacities 3
1.24 Thetransitiontoquantummechanics 39
0.3 ThephotoelectricandComptoneffects 4
PROBLEMS 40
0.4 Atomicspectra 5
0.5 Thedualityofmatter 6 2 Linearmotionandtheharmonic
PROBLEMS 8 oscillator 43
1 Thefoundationsofquantummechanics 9 Thecharacteristicsofacceptablewavefunctions 43
SomegeneralremarksontheSchro¨dingerequation 44
Operatorsinquantummechanics 9 2.1 Thecurvatureofthewavefunction 45
1.1 Linearoperators 10 2.2 Qualitativesolutions 45
1.2 Eigenfunctionsandeigenvalues 10 2.3 Theemergenceofquantization 46
1.3 Representations 12 2.4 Penetrationintonon-classicalregions 46
1.4 Commutationandnon-commutation 13
Translationalmotion 47
1.5 Theconstructionofoperators 14
2.5 Energyandmomentum 48
1.6 Integralsoveroperators 15
2.6 Thesignificanceofthecoefficients 48
1.7 Diracbracketnotation 16
2.7 Thefluxdensity 49
1.8 Hermitianoperators 17
2.8 Wavepackets 50
Thepostulatesofquantummechanics 19
Penetrationintoandthroughbarriers 51
1.9 Statesandwavefunctions 19
2.9 Aninfinitelythickpotentialwall 51
1.10 Thefundamentalprescription 20
2.10 Abarrieroffinitewidth 52
1.11 Theoutcomeofmeasurements 20
2.11 TheEckartpotentialbarrier 54
1.12 Theinterpretationofthewavefunction 22
1.13 Theequationforthewavefunction 23 Particleinabox 55
1.14 TheseparationoftheSchro¨dingerequation 23 2.12 Thesolutions 56
2.13 Featuresofthesolutions 57
Thespecificationandevolutionofstates 25
2.14 Thetwo-dimensionalsquarewell 58
1.15 Simultaneousobservables 25
2.15 Degeneracy 59
1.16 Theuncertaintyprinciple 27
1.17 Consequencesoftheuncertaintyprinciple 29 Theharmonicoscillator 60
1.18 Theuncertaintyinenergyandtime 30 2.16 Thesolutions 61
1.19 Time-evolutionandconservationlaws 30 2.17 Propertiesofthesolutions 63
2.18 Theclassicallimit 65
Matricesinquantummechanics 32
1.20 Matrixelements 32 Translationrevisited:Thescatteringmatrix 66
1.21 Thediagonalizationofthehamiltonian 34 PROBLEMS 68
viii j CONTENTS
3 Rotationalmotionandthehydrogenatom 71 Theangularmomentaofcompositesystems 112
4.9 Thespecificationofcoupledstates 112
Particleonaring 71 4.10 Thepermittedvaluesofthetotalangular
momentum 113
3.1 ThehamiltonianandtheSchro¨dinger
equation 71 4.11 Thevectormodelofcoupledangular
momenta 115
3.2 Theangularmomentum 73
4.12 Therelationbetweenschemes 117
3.3 Theshapesofthewavefunctions 74
4.13 Thecouplingofseveralangularmomenta 119
3.4 Theclassicallimit 76
PROBLEMS 120
Particleonasphere 76
3.5 TheSchro¨dingerequationand 5 Grouptheory 122
itssolution 76
3.6 Theangularmomentumoftheparticle 79
Thesymmetriesofobjects 122
3.7 Propertiesofthesolutions 81
5.1 Symmetryoperationsandelements 123
3.8 Therigidrotor 82
5.2 Theclassificationofmolecules 124
MotioninaCoulombicfield 84
Thecalculusofsymmetry 129
3.9 TheSchro¨dingerequationfor
hydrogenicatoms 84 5.3 Thedefinitionofagroup 129
3.10 Theseparationoftherelativecoordinates 85 5.4 Groupmultiplicationtables 130
3.11 TheradialSchro¨dingerequation 85 5.5 Matrixrepresentations 131
3.12 Probabilitiesandtheradial 5.6 Thepropertiesofmatrixrepresentations 135
distributionfunction 90 5.7 Thecharactersofrepresentations 137
3.13 Atomicorbitals 91 5.8 Charactersandclasses 138
3.14 Thedegeneracyofhydrogenicatoms 94 5.9 Irreduciblerepresentations 139
PROBLEMS 96 5.10 Thegreatandlittleorthogonalitytheorems 142
Reducedrepresentations 145
5.11 Thereductionofrepresentations 146
4 Angularmomentum 98
5.12 Symmetry-adaptedbases 147
Thesymmetrypropertiesoffunctions 151
Theangularmomentumoperators 98
5.13 Thetransformationofp-orbitals 151
4.1 Theoperatorsandtheircommutation
relations 99 5.14 Thedecompositionofdirect-productbases 152
4.2 Angularmomentumobservables 101 5.15 Direct-productgroups 155
4.3 Theshiftoperators 101 5.16 Vanishingintegrals 157
5.17 Symmetryanddegeneracy 159
Thedefinitionofthestates 102
4.4 Theeffectoftheshiftoperators 102 Thefullrotationgroup 161
4.5 Theeigenvaluesoftheangularmomentum 104 5.18 Thegeneratorsofrotations 161
4.6 Thematrixelementsoftheangular 5.19 Therepresentationofthefullrotationgroup 162
momentum 106 5.20 Coupledangularmomenta 164
4.7 Theangularmomentumeigenfunctions 108 Applications 165
4.8 Spin 110 PROBLEMS 166
CONTENTS j ix
6 Techniquesofapproximation 168 7.10 Thespectrumofhelium 224
7.11 ThePauliprinciple 225
Time-independentperturbationtheory 168
Many-electronatoms 229
6.1 Perturbationofatwo-levelsystem 169
7.12 Penetrationandshielding 229
6.2 Many-levelsystems 171
7.13 Periodicity 231
6.3 Thefirst-ordercorrectiontotheenergy 172
7.14 Slateratomicorbitals 233
6.4 Thefirst-ordercorrectiontothewavefunction 174
7.15 Self-consistentfields 234
6.5 Thesecond-ordercorrectiontotheenergy 175
7.16 Termsymbolsandtransitionsof
6.6 Commentsontheperturbationexpressions 176 many-electronatoms 236
6.7 Theclosureapproximation 178 7.17 Hund’srulesandtherelativeenergiesofterms 239
6.8 Perturbationtheoryfordegeneratestates 180 7.18 Alternativecouplingschemes 240
Variationtheory 183 Atomsinexternalfields 242
6.9 TheRayleighratio 183 7.19 ThenormalZeemaneffect 242
6.10 TheRayleigh–Ritzmethod 185 7.20 TheanomalousZeemaneffect 243
7.21 TheStarkeffect 245
TheHellmann–Feynmantheorem 187
Time-dependentperturbationtheory 189 PROBLEMS 246
6.11 Thetime-dependentbehaviourofa
two-levelsystem 189
6.12 TheRabiformula 192 8 Anintroductiontomolecularstructure 249
6.13 Many-levelsystems:thevariationofconstants 193
6.14 Theeffectofaslowlyswitchedconstant TheBorn–Oppenheimerapproximation 249
perturbation 195
8.1 Theformulationoftheapproximation 250
6.15 Theeffectofanoscillatingperturbation 197
8.2 Anapplication:thehydrogenmolecule–ion 251
6.16 Transitionratestocontinuumstates 199
Molecularorbitaltheory 253
6.17 TheEinsteintransitionprobabilities 200
6.18 Lifetimeandenergyuncertainty 203 8.3 Linearcombinationsofatomicorbitals 253
8.4 Thehydrogenmolecule 258
PROBLEMS 204
8.5 Configurationinteraction 259
7 Atomicspectraandatomicstructure 207 8.6 Diatomicmolecules 261
8.7 Heteronucleardiatomicmolecules 265
Thespectrumofatomichydrogen 207 Molecularorbitaltheoryofpolyatomic
molecules 266
7.1 Theenergiesofthetransitions 208
7.2 Selectionrules 209 8.8 Symmetry-adaptedlinearcombinations 266
7.3 Orbitalandspinmagneticmoments 212 8.9 Conjugatedp-systems 269
7.4 Spin–orbitcoupling 214 8.10 Ligandfieldtheory 274
7.5 Thefine-structureofspectra 216 8.11 Furtheraspectsofligandfieldtheory 276
7.6 Termsymbolsandspectraldetails 217
Thebandtheoryofsolids 278
7.7 Thedetailedspectrumofhydrogen 218
8.12 Thetight-bindingapproximation 279
Thestructureofhelium 219 8.13 TheKronig–Penneymodel 281
7.8 Theheliumatom 219 8.14 Brillouinzones 284
7.9 Excitedstatesofhelium 222 PROBLEMS 285