Fundamentals of molecular symmetry:
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Bristol [u.a.]
Inst. of Physics Publ.
2005
|
| Series: | Series in chemical physics
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIII, 358 S. graph. Darst. |
| ISBN: | 0750309415 9780750309417 9781138410176 |
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| 245 | 1 | 0 | |a Fundamentals of molecular symmetry |c Philip R. Bunker ; Per Jensen |
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Record in the Search Index
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| adam_text | Contents
Preface xi
PARTI
Spectroscopy and the quantum states of molecules 1
1 Molecular spectroscopy 3
1.1 Molecular spectra 3
1.2 The energies of molecules in the gas phase 6
1.3 The positions of spectral lines 9
1A The intensities of spectral lines 11
1.5 The shapes of spectral lines 12
1.6 Raman spectra 14
1.7 Problems 15
2 Quantum mechanics 17
2.1 The Schrodinger equation 17
2.2 The postulates of quantum mechanics 18
2.2.1 Operators and eigenfunctions 19
2.3 Diagonalizing the Hamiltonian matrix 21
2.4 The molecular Schrodinger equation 26
2.5 The separation of translational energy 26
2.5.1 The translational Schrodinger equation 29
2.6 The rovibronic Schrodinger equation 32
2.7 The angular momentum operator 34
2.8 The dipole moment operator and line strengths 35
2.9 Matrices and matrix algebra 37
2.10 Problems 40
3 Electronic states 42
3.1 The Bom-Oppenheimer approximation 42
3.2 Spin and the Pauli exclusion principle 46
3.3 Electronic wavefunctions and energies 48
3.3.1 The Slater determinant 49
vi Contents
3.3.2 The Hartree-Fock approximation and molecular orbitals 50
3.3.3 MOs as linear combinations of atomic orbitals 52
3.3.4 Configuration interaction 52
3.4 Molecular orbital theory 53
3.4.1 Bonding and antibonding orbitals 54
3.4.2 Hybridization 57
3.4.3 The Hiickel approximation and benzene 61
3.4.4 Polyene chain molecules 62
3.5 Problems 65
4 Vibrational states 68
4.1 Space-fixed and molecule-fixed axes 68
4.2 The vibrational Hamiltonian 70
4.3 Vibrational wavefunctions and energies 72
4.4 Anharmonicity 78
4.5 Tunnelling 81
4.6 Problems 87
5 Rotational states 89
5.1 The Euler angles 89
5.2 The principal moments of inertia 90
5.3 The rigid-rotor Hamiltonian 92
5.3.1 Symmetric top molecules 92
5.3.2 Linear molecules 94
5.3.3 Spherical top molecules 95
5.3.4 Asymmetric top molecules 95
5.4 Rovibronic wavefunctions 96
5.5 The Hamiltonian and wavefunctions in detail 97
5.5.1 The derivation of the rigid-rotor Hamiltonian 97
5.5.2 The Euler angles and angular momentum 99
5.5.3 The symmetric top wavefunctions 101
5.5.4 The asymmetric top wavefunctions and energies 101
5.6 Problems 107
PART 2
Symmetry and symmetry groups 111
6 Geometrical symmetry 113
6.1 Geometrical symmetry operations 113
6.2 Geometrical symmetry groups: Point groups 117
6.3 The point group symmetry of molecules 122
6.4 Problems 125
Contents vii
7 The symmetry of the Hamiltonian 126
7.1 Hamiltonian symmetry operations 126
7.2 Nuclear permutations and the inversion E* 127
7.3 Symmetry labels 132
7.4 Symmetry groups 133
7.5 The vanishing integral rule 136
7.5.1 Proof of the vanishing integral rule for the water molecule 138
7.6 Selection rules 139
7.7 The rovibronic symmetry label J 140
7.8 Diagonalizing the Hamiltonian matrix using symmetry 141
7.9 The Stark effect 142
7.10 The symmetry of Hf 143
7.11 Group theory 149
7.12 Problems 156
8 The symmetry groups of rigid molecules 158
8.1 The CNPI group 158
8.2 The molecular symmetry (MS) group 162
8.3 The MS group and the point group 164
8.3.1 The H2O molecule 164
8.3.2 The H3 molecule 168
8.3.3 General rules for rigid molecule symmetry groups 171
8.3.4 Linear rigid molecules 172
8.3.5 The ethylene molecule C2H4 173
8.4 Problems 175
PART 3
Applications of symmetry 177
9 Nuclear spin, statistical weights and hyperfine structure 179
9.1 The fifth postulate of quantum mechanics 179
9.2 Statistical weights 180
9.3 Missing levels 184
9.3.1 C02 184
9.3.2 H+ 185
9.4 Statistical weights for CH3F 186
9.5 Nuclear spin hyperfine structure 187
9.6 Problems 191
10 The symmetry of electronic wavefunctions 193
10.1 The water molecule 193
10.2 The benzene molecule 197
10.3 The butadiene molecule 205
10.4 Conservation of orbital symmetry 207
10.5 The non-crossing rule 217
viii Contents
10.6 The Ct and ov operations for benzene 218
10.7 Problems 220
11 The symmetry of rotation-vibration wavefunctions 222
11.1 The transformation properties of the Euler angles 222
11.2 The symmetry of rotational wavefunctions 224
11.2.1 226
11.2.2 H20 229
11.3 The symmetry of normal coordinates 230
11.3.1 H20 232
11.3.2 Benzene 233
11.4 The symmetry of vibrational wavefunctions 236
11.4.1 H20 236
11.4.2 Hj 236
11.5 Rotation-vibration coupling 238
11.6 Problems 244
12 Symmetry selection rules for optical transitions 245
12.1 Forbidden and allowed transitions 245
12.2 Zero-order transition moment integrals 247
12.3 Transitions within an electronic state 249
12.3.1 Vibrational transition moments and Hônl-London factors 249
12.3.2 The rotational spectrum of the CO molecule 255
12.3.3 Parallel and perpendicular bands of CH3F 255
12.3.4 Rotation-vibration interaction 261
12.4 Transitions between electronic states 264
12.5 Raman transitions 266
12.6 Problems 272
13 The symmetry groups of non-rigid molecules 274
13.1 The MS group of a non-rigid molecule 274
13.2 The ammonia molecule 275
13.3 Torsionally tunnelling ethylene 278
13.4 Intensity alternations for HSSH and DSSD 280
13.5 The water dimer and the water trimer 282
13.5.1 Water dimer 282
13.5.2 Water trimer 287
13.6 Ethylene and its Raman spectrum 288
13.7 Problems 290
Contents
IX
PART 4
Other symmetries and symmetry violation 291
14 Other symmetries 293
14.1 The fourth postulate of quantum mechanics 293
14.2 Conservation laws 294
14.3 Electron permutation symmetry 295
14.4 Translational symmetry 296
14.5 Rotational symmetry 301
14.6 Charge conjugation 304
14.7 Parity 305
14.8 Time reversal 308
15 Symmetry violation 310
15.1 The electroweak Hamiltonian 310
15.2 Parity (P) violation 311
15.3 CP violation 313
15.4 T violation 315
15.5 Testing for CPT violation 316
15.6 Testing for permutation symmetry violation 316
A Answers to selected problems 320
B Character tables 331
C Books for further reading 352
Index 354
The Series in Chemical Physics is an international series
that meets the need for up-to-date texts on theoretical and
experimental aspects in this rapidly developing field. Books
in the series range in level from introductory monographs and
practical handbooks to more advanced expositions of current
research. The books are written at a level suitable for senior
undergraduates and graduate students, and will also be useful
for practising chemists, physicists and chemical physicists
who wish to refresh their knowledge of a particular field.
Molecular symmetry is an easily applied tool for understanding
and predicting many of the properties of molecules. Traditionally,
students are taught molecular symmetry using point groups
derived from the equilibrium geometry of the molecule. However,
the true basis for molecular symmetry is not geometrical
symmetry, and this book shows how to set up symmetry groups
for molecules using more fundamental ideas. It is no more
difficult than using molecular geometry, and one obtains
Molecular Symmetry (MS) groups. Point group symmetry is
derived by approximation from MS group symmetry.
The approach taken gives a balanced account of both types
of symmetry group. Usuallythe point group is only usefulfor
isolated, non-rotating molecules, executing small amplitude
vibrations in isolated electronic states. However, for the
chemical physicist or physical chemist who wishes to go beyond
these limitations, the MS group is nearly always required.
An introductory description of molecular spectroscopy and
quantum mechanics is given in order that the book be self-
contained in describing how molecular symmetry is to be
understood and used. The book is suitable for both
undergraduates and research students in molecular science.
■ CRC Press
Taylor Francis Croup
an informa business
www.crcpress.com
I SBN 978-1- •138- 41017-é ►
9 781138 4 0176
|
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| discipline | Chemie / Pharmazie Physik Chemie |
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| spelling | Bunker, Philip R. Verfasser aut Fundamentals of molecular symmetry Philip R. Bunker ; Per Jensen Bristol [u.a.] Inst. of Physics Publ. 2005 XIII, 358 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Series in chemical physics Groupes, Théorie des Spectroscopie moléculaire Structure moléculaire Symétrie (Physique) Group theory Molecular theory Symmetry (Physics) Molekülsymmetrie (DE-588)4170385-6 gnd rswk-swf Molekülsymmetrie (DE-588)4170385-6 s DE-604 Jensen, Per Verfasser aut Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012994816&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Bayreuth - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=012994816&sequence=000002&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext |
| spellingShingle | Bunker, Philip R. Jensen, Per Fundamentals of molecular symmetry Groupes, Théorie des Spectroscopie moléculaire Structure moléculaire Symétrie (Physique) Group theory Molecular theory Symmetry (Physics) Molekülsymmetrie (DE-588)4170385-6 gnd |
| subject_GND | (DE-588)4170385-6 |
| title | Fundamentals of molecular symmetry |
| title_auth | Fundamentals of molecular symmetry |
| title_exact_search | Fundamentals of molecular symmetry |
| title_full | Fundamentals of molecular symmetry Philip R. Bunker ; Per Jensen |
| title_fullStr | Fundamentals of molecular symmetry Philip R. Bunker ; Per Jensen |
| title_full_unstemmed | Fundamentals of molecular symmetry Philip R. Bunker ; Per Jensen |
| title_short | Fundamentals of molecular symmetry |
| title_sort | fundamentals of molecular symmetry |
| topic | Groupes, Théorie des Spectroscopie moléculaire Structure moléculaire Symétrie (Physique) Group theory Molecular theory Symmetry (Physics) Molekülsymmetrie (DE-588)4170385-6 gnd |
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