Symmetry of Intramolecular Quantum Dynamics:
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
De Gruyter
2012
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| Series: | De Gruyter Studies in Mathematical Physics
11 |
| Subjects: | |
| Online Access: | Inhaltstext Inhaltsverzeichnis |
| Item Description: | Aus dem Russ. |
| Physical Description: | XIII, 430 S. graph. Darst. 240 mm x 170 mm |
| ISBN: | 9783110267532 3110267535 |
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| adam_text |
Titel: Symmetry of intramolecular quantum dynamics
Autor: Burenin, Alexander V
Jahr: 2012
Contents
Preface v
I Foundations of the mathematical apparatus
1 Basic concepts of group theory 3
1.1 The group postulates. 3
1.2 Subgroup, direct product of groups, isomorphism, and
homomorphism. 6
1.3 Cosets. Semidirect product of groups. 7
1.4 Conjugacy classes. 9
2 Basic concepts of group representation theory 10
2.1 Linear vector spaces . 10
2.2 Operators in configuration and function spaces. 13
2.3 Representations of groups. 15
2.4 Characters. Decomposition of reducible representations . 17
2.5 Direct product of representations. Symmetrie power . 20
2.6 The Clebsch-Gordan coefficients . 23
2.7 Basis funetions of irreducible representations. 25
2.8 Irreducible tensor Operators. The Wigner-Eckart theorem. 28
3 The permutation group 31
3.1 Operations in the permutation group. Classes. 31
3.2 Irreducible representations. The Young diagrams and tableaux. 33
3.3 Basis funetions of irreducible representations. 35
3.4 The conjugate representation. 37
4 Continuous groups 39
4.1 Compact Lie groups . 39
4.2 Lie group of linear transformations. 41
4.3 Lie algebra. Three-dimensional rotation group. 42
4.4 Irreducible representations of a three-dimensional rotation group . 46
x Contents
5 Point groups 51
5.1 Operations in point groups . 51
5.2 Discrete axial groups. 53
5.3 Cubic groups. Icosahedral groups. 54
5.4 Continuous axial groups . 56
6 Dynamic groups 58
6.1 Invariant dynamic groups . 58
6.2 Noninvariant dynamic groups. 59
II Qualitative intramolecular quantum dynamics
7 The philosophy of using the symmetry properties of internal dynamics 67
7.1 Symmetry groups of internal dynamics . 67
7.2 Significance of the analysis of symmetry properties. 73
7.3 On the domain ofthe point group. 76
7.4 The chain of symmetry groups . 81
7.5 The concept of the coordinate spin . 83
7.6 The influence of numerical methods on the overall description. 86
7.7 Conclusions. 86
8 Internal dynamics of rigid molecules 89
8.1 Nonlinear molecules without inversion center . 89
8.2 Nonlinear molecules with inversion center.101
8.3 Linear molecules.108
8.4 Description of quasidegenerate vibronic states.115
8.5 Conclusions.119
9 Molecules with torsional transitions of the exchange type 123
9.1 Extended point groups. Intermediate configuration.123
9.2 Methanol molecule CH3OH.129
9.3 Ethane molecule C2H6.135
9.4 The molecules of complex hydrides L1BH4 and NaBrLj .140
9.5 The molecules of dimethyl ether (CH3)20 and acetone (CH3)2CO . 148
9.6 Conclusions.155
Contents xi
10 Molecules with pseudorotations ofthe exchange type 157
10.1 Extended point groups. 157
10.2 Cyclobutane molecule C4H8. 159
10.3 Molecules ofthe XPF4 type . 166
10.4 Phosphoras pentafluoride molecule PF5. 171
10.5 The Separation of internal motions . 179
10.6 Conclusions. 181
11 Molecules with transitions of the nonexchange type between equivalent
configurations 182
11.1 Extended point groups.182
11.2 The ammonia molecule NH3.185
11.3 The peroxide molecule HOOH .189
11.4 The hydrazine molecule N2H4 .195
11.5 Conclusions.204
12 On the meaning of the Born-Oppenheimer Approximation 205
12.1 Nondegenerate electronic states .206
12.2 Degenerate electronic states .207
12.3 Internal geometric symmetry ofthe Hamiltonian.210
12.4 Definition ofthe rotational motion .216
12.5 Selection of physically meaningful states.219
12.6 Symmetry methods in the description of intramolecular dynamics . 223
12.7 Geometric symmetry and definitions of nonrigid motions .226
12.8 Nuclear Statistical weights.229
12.9 Conclusions.230
13 Molecules with transitions of the exchange and nonexchange types
between equivalent configurations 235
13.1 Extended point groups.235
13.2 Methanol molecule CH3OH .239
13.3 Methylamine molecule CH3NH2.245
13.4 Cyclopentane molecule C5H10.250
13.5 Conclusions.255
xü Contents
14 On the construction of extended point groups 256
14.1 Hydrogen fluoride dimer (HF)2.256
14.2 Ionic complexes ArH^~ and ArD^ .261
14.3 Carbocation C2H£ .268
14.4 Conclusions.277
15 Nonrigid molecular Systems with continuous axial symmetry groups 278
15.1 Systems ofthe HCN/HNC type.279
15.2 Complexes ofthe XCO type.282
15.3 Nonrigid water molecules H20.283
15.4 Conclusions.290
16 Molecules with different isomeric forms in a Single electronic State 291
16.1 Distorted molecular Systems.291
16.2 The methanol molecule CH2DOH .293
16.3 The ethane molecule CH2D-CH2D .297
16.4 The ethanol molecule CH3CH2OH.302
16.5 The cyclobutane-l,l-d2 molecule.307
16.6 The tetrahydrofuran molecule C4H8O .315
16.7 Conclusions.327
17 Molecules with different isomeric forms in different electronic states 329
17.1 Formaldehyde molecule H2CO.329
17.2 The ethylene molecule CH2-CD2.336
17.3 Conclusions.348
18 Algebraic modeis of the global description of molecular spectrum 349
18.1 The rigid water molecule H20 .350
18.2 The nonrigid methanol molecule CH3OH.354
18.3 The nonrigid water molecule H20 .359
18.4 Conclusions.361
19 Description of the Zeeman and Stark effects 363
19.1 External field and symmetry ofthe stationary states.363
19.2 The Zeeman effect in the case of a rigid molecule.364
19.3 The Zeeman effect in the case of a nonrigid molecule .367
19.4 The Stark effect in the case of a rigid molecule .368
19.5 The Stark effect in the case of a nonrigid molecule _.373
19.6 Conclusions.377
Contents_xiii
20 Additional remarks on describing intramolecular dynamics 379
20.1 The nonrigid trimethylborane molecule B(CH3)3.379
20.2 Hyperfine interactions in the methane molecule CH4.394
20.3 Parity violation effects in molecules with stereoisomers.396
20.4 Parity violation effects in the molecules without stereoisomers.398
20.5 Conclusions .401
Conclusion 403
Appendices 405
Bibliography 417
Index 423 |
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| dewey-tens | 530 - Physics |
| discipline | Physik |
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| spelling | Burenin, Alexander V. Verfasser aut Symmetry of Intramolecular Quantum Dynamics Alexander V. Burenin Berlin [u.a.] De Gruyter 2012 XIII, 430 S. graph. Darst. 240 mm x 170 mm txt rdacontent n rdamedia nc rdacarrier De Gruyter Studies in Mathematical Physics 11 Aus dem Russ. Molekülsystem (DE-588)4507233-4 gnd rswk-swf Intramolekulare Wechselwirkung (DE-588)4336499-8 gnd rswk-swf Quantenmechanisches System (DE-588)4300046-0 gnd rswk-swf Molekülsystem (DE-588)4507233-4 s Intramolekulare Wechselwirkung (DE-588)4336499-8 s Quantenmechanisches System (DE-588)4300046-0 s DE-604 De Gruyter Studies in Mathematical Physics 11 (DE-604)BV040141722 11 X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=4010531&prov=M&dok_var=1&dok_ext=htm Inhaltstext HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=025424300&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Burenin, Alexander V. Symmetry of Intramolecular Quantum Dynamics De Gruyter Studies in Mathematical Physics Molekülsystem (DE-588)4507233-4 gnd Intramolekulare Wechselwirkung (DE-588)4336499-8 gnd Quantenmechanisches System (DE-588)4300046-0 gnd |
| subject_GND | (DE-588)4507233-4 (DE-588)4336499-8 (DE-588)4300046-0 |
| title | Symmetry of Intramolecular Quantum Dynamics |
| title_auth | Symmetry of Intramolecular Quantum Dynamics |
| title_exact_search | Symmetry of Intramolecular Quantum Dynamics |
| title_full | Symmetry of Intramolecular Quantum Dynamics Alexander V. Burenin |
| title_fullStr | Symmetry of Intramolecular Quantum Dynamics Alexander V. Burenin |
| title_full_unstemmed | Symmetry of Intramolecular Quantum Dynamics Alexander V. Burenin |
| title_short | Symmetry of Intramolecular Quantum Dynamics |
| title_sort | symmetry of intramolecular quantum dynamics |
| topic | Molekülsystem (DE-588)4507233-4 gnd Intramolekulare Wechselwirkung (DE-588)4336499-8 gnd Quantenmechanisches System (DE-588)4300046-0 gnd |
| topic_facet | Molekülsystem Intramolekulare Wechselwirkung Quantenmechanisches System |
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