Point group theory tables:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Oxford
Clarendon Press
1994
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XII, 704 S. graph. Darst. |
| ISBN: | 0198552262 |
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MARC
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| 100 | 1 | |a Altmann, Simon L. |d 1924- |e Verfasser |0 (DE-588)174096615 |4 aut | |
| 245 | 1 | 0 | |a Point group theory tables |c Simon L. Altmann and Peter Herzig |
| 246 | 1 | 3 | |a Point-group theory tables |
| 264 | 1 | |a Oxford |b Clarendon Press |c 1994 | |
| 300 | |a XII, 704 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 700 | 1 | |a Herzig, Peter |e Verfasser |4 aut | |
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Record in the Search Index
| _version_ | 1804124259581165568 |
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| adam_text | Contents
0 How to use this book. Notation l
1 Table numbering and general cross referencing 1
Cross references on left margins of displayed lines 1
Literature references 2
2 Symbols used 2
Part 1. Introduction to the tables
1 Introduction 7
1 Comparison with other tables 7
2 Construction of the present tables 7
2 Basic group theory: definitions and formulae 9
1 Basic group definitions 9
Group properties (postulates) 9
Group presentations 9
Group definitions 9
Group products 10
2 Operators 10
Configuration space operators 10
Function space operators 11
3 Vector (ordinary) representations 11
Definition and properties 11
Bases of the representations; representations 12
Similarity and unitary transformation of representations 13
Characters 13
Irreducible representations and their properties 13
4 Projection operators 14
Properties of the projection operators 14
Projection operator over a representation 14
5 Representation reduction 14
Notation used in this book for the indices 15
Representation reduction by projection operators 15
Representation reduction by the internal method 16
6 Direct products 16
Representations of direct product groups 16
Direct product of two representations of the same group 16
Symmetrized and antisymmetrized products of the same representation 17
7 Clebsch Gordan coefficients 17
Notation 17
Definition of the Clebsch Gordan coefficients 17
Notation for the Clebsch Gordan matrix 17
The Clebsch Gordan matrix 18
8 Matrix elements and selection rules 18
9 The Wigner Eckart theorem 19
10 Subduced and induced representations 19
Subduced representations (descent of symmetry) 19
Induced representations 19
Bibliographical note 19
vii
CONTENTS
3 Parametrization of symmetry operations 20
1 Axes and general definitions 20
2 Parametrization of proper rotations 20
Euler angles 20
Angle and axis of rotation 20
Rules for choosing a set of poles as used in the tables 21
The parameters j , n, and f n 21
Quaternion (Euler Rodrigues) parameters A, A 22
Cayley Klein parameters 22
3 Parametrization of improper operations 22
4 Parametrization of double group operations 23
5 Calculation of the Euler angles 23
6 Calculation of the angle and axis of rotation from the Euler angles 24
Bibliographical note 24
4 Symmetry operations: notation and properties 25
1 Key to the symbols for symmetry operations 25
Basic notation 25
Embellishments, subscripts, and superscripts 25
2 Special rotations and rotoreflections 26
3 Commutation of symmetry operations 26
4 Special relations for symmetry operations 27
5 Notation for point groups, single and double 28
1 Cyclic, dihedral, and related groups 28
2 Cubic groups 28
3 Icosahedral groups 29
4 Double groups 29
5 The Hermann Mauguin or international notation 29
Bibliographical note 29
6 Derivation of the proper and improper point groups 30
1 Definitions for proper point groups 30
2 Derivation of the proper point groups 31
3 Description of the proper point groups 32
Cyclic groups Cn (order n 2) 32
Dihedral groups Dn (order 2n, n 2) 32
Tetrahedral group T (order 12) 32
Octahedral group O (order 24) 32
Icosahedral group I (order 60) 33
4 Improper groups: general structure 33
5 Improper groups with inversion 33
Generated from cyclic groups Cn 33
Generated from dihedral groups Dn 34
Generated from the cubic groups O, T 34
Generated from the icosahedral group I 34
6 Improper groups without inversion 34
Generated from cyclic groups Cn 34
Generated from dihedral groups Dn 34
Generated from the cubic groups O, T 35
Generated from the icosahedral group I 35
7 Summary. The point group structure 35
Bibliographical note 36
7 Direct product, semidirect product and coset expansion forms of the point groups 37
8 The crystallographic point groups 40
9 Group chains 41
1 Definitions and structure of the tables 41
Possible difficulties in group chains, for G D H 41
Construction of the tables 41
viii
CONTENTS
2 Description of the group chain graphs 42
3 An index of the groups in the graphs 42
4 Examples 44
5 The graphs 44
10 Double groups. Spinor and projective representations 51
1 The double group 5j
Definitions 51
Class structure (Opechowski s theorem) 51
Irreducible representations 52
2 Projective representations 52
Motivation 52
Definitions 53
Properties 53
Bibliographical note 53
11 The matrices of SU(2) and SU (2) 54
1 Definitions 54
2 Form of the matrices 54
3 Relation between SU(2) and SU (2) to the rotation group 54
Definitions 54
Relation between SO(3) and SU(2) 54
Relation between 0(3), SU(2), and SU (2) 54
The bilateral binary rotation matrices 55
The Pauli matrices 55
Bibliographical note 55
12 The continuous groups. Rotations, their matrices, and the irreducible
representations of 0(3) 56
1 The continuous groups 56
2 Action of a rotation on a vector 56
3 Rotation matrices 56
Notation 56
The matrices 56
4 The irreducible representations of 0(3) 57
Basis and form of the representation 57
Improper rotations 58
Special cases 58
The characters 58
Bibliographical note 58
13 Bases: spherical harmonics, spinors, cartesian tensors, and the functions s, p, d, f 59
1 Integral angular momentum: the spherical harmonics 59
2 Half integral angular momentum: spinors 59
Higher order spinors: spin harmonics 60
3 Relation between the bases of SO(3) and those of 0(3) 60
4 Cartesian tensors 61
5 The s, p, d, and / functions 62
Bibliographical note 62
14 Notation for the irreducible representations G3
1 The basic symbols 63
2 Embellishments 63
3 Lower case symbols 64
15 Stereographic projections and three dimensional drawings of point groups 65
1 Key to the symbols for the stereographic projections 65
2 Key to the symbols for the three dimensional drawings 66
Bibliographical note 66
ix
CONTENTS
16 How to use the tables 67
General instructions 67
Description of the tables 67
0 Subgroup elements 68
1 Parameters 68
Notation for the headers of T n.l 68
Instructions 68
2 Multiplication table 69
Notation for the headers of T n.2 69
Instructions 69
Example. Obtention of the multiplication table for D2 69
3 Factor table 70
Notation for the headers of T n.3 70
Instructions 70
4 Character table 71
Obtention of the character table for the double group 71
Example. Obtention of the character table for D2 71
Time reversal: column headed r in the tables 71
5 Cartesian tensors. The s, p, d, and / functions 72
The cartesian tensors (up to and including rank 3) 72
The s, p, d, and / functions 72
Example. Cartesian tensors and s, p, d, and / functions for D8 73
6 Symmetrized bases 74
General notes 74
The cyclic, dihedral, and related groups 74
The cubic and icosahedral groups 75
7 Matrix representations 77
Notation for the headers of T n.7, and for its first row 77
Vector representations 78
Double group representations 78
Projective representations (full table, including vector representations) 79
Examples. Representations of D3 79
Icosahedral group I 80
8 Direct product of representations 81
Notation for the headers of T n.8, and for its first column 81
Use of the table 81
Example. Direct products for representations of T 8h 81
9 Subduction (descent of symmetry) 82
Example. Subgroups D2 of O 82
10 Subduction from O(3) 82
Example. Subduction from 0(3) to C2h 83
11 Clebsch Gordan coefficients 83
Notation for the headers of T n.ll 83
Notation required to use the tables 84
Description of the tables 84
Example. Coupling of the representations Ei/2 and E5/2 of D6 84
Bibliographical note 85
17 Problems 86
Cross references 86
1 Multiplication rules 86
2 The regular representation 87
3 Transformation of the components of a vector 87
4 A rotation acting on the function space 88
5 The faithful (Jones) representation 88
6 Hybrids: general form 88
7 Reduction of a representation by the internal method 89
8 Cubic hybrids 89
x
CONTENTS
9 Eight equivalent hybrids not requiring / orbitals 90
10 Hybrids: their full expression 91
11 Symmetrized molecular orbitals 91
The symmetry group 91
How to find the irreducible representations that appear in the molecular orbitals 92
Use of the projection operator 92
The symmetrized functions (bases) 92
The full symmetry of the molecular orbitals in De/j, 93
12 Symmetrized molecular orbitals: projecting over the representations 93
13 A transition metal complex 94
14 Use of the projection operator on a direct product 95
15 Selection rules 95
16 The form of the secular determinant 96
17 Normal coordinates 96
18 Infrared and Raman activity of normal vibrations 98
19 Overtones and combination frequencies 98
20 Normal vibrations in methane 99
21 Jahn Teller effect 100
22 Electronic states in an octahedral complex 100
23 Splitting of a doublet in a magnetic field 100
24 Subduction (descent of symmetry) 100
25 Double group: term splitting 100
Double group method 101
Projective representation method 102
26 A crystal field 102
27 Time reversal 103
28 Vector coupling 103
Part 2. The tables
The proper cyclic groups Cn 107
T 1 Ci 108 T 2 C2 110
T 3 C3 112 T 4 C4 114
T 5 C5 116 T 6 C6 119
T 7 C7 122 T 8 C8 125
T 9 C9 128 T 10 Cio 132
The improper cyclic groups Cj and Cs 137
T 11 Ci 138 T 12 Cs 140
The improper cyclic groups Sn 143
T 13 S4 144 T 14 S6 146
T 15 S8 149 T 16 Sio 152
T 17 Si2 156 T 18 Su 161
T 19 Sia 166 T 20 S,8 173
T21 S20 181
The dihedral groups Dn 193
T22 D2 194 T23 D3 196
T24 D4 199 T25 D5 203
T26 D6 207 T27 D 213
T 28 D8 220 T 29 D9 227
T 30 Dio 235
The groups D^ 245
T31 D2h 246 T32 T 3h 250
T33 V4h 256 T34 D5h 263
T35 D6fc 273 T 36 T 7h 284
T37 Bsh 304 T38 B9h 314
T39 D10h 343 T 40 D^ 357
xi
CONTENTS
The groups Dnd 365
T41 V2d 366 T42 D3(i 370
T43 D4d 375 T 44 D5d 382
T45 D6d 388 T 46 D7d 404
T 47 D8d 413 T 48 D9d 436
T 49 Diod 448
The groups Cnv 481
T50 C2v 482 T51 C3u 484
T 52 Civ 489 T 53 C5v 492
T 54 C6v 497 T 55 C7, 501
T 56 C8v 507 T 57 C9v 510
T 58 C1Ov 519 T 59 C^, 523
The groups Cnh 531
T 60 C2h 532 T 61 C3h 534
T 62 C4h 537 T 63 C5h 541
T 64 Ceh 545 T 65 C7h 550
T 66 C8^ 556 T 67 C9h 562
T 68 Cwh 570
The cubic groups 579
T 69 O 580 T 70 T 590
T 71 Oh 595 T 72 T^ 632
T 73 Td 637
The icosahedral groups 641
T 74 I 642 T 75 Ih 659
References 9i
Index 701
xii
|
| any_adam_object | 1 |
| author | Altmann, Simon L. 1924- Herzig, Peter |
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| author_facet | Altmann, Simon L. 1924- Herzig, Peter |
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| building | Verbundindex |
| bvnumber | BV009898896 |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 548 - Crystallography |
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| dewey-sort | 3548 17 |
| dewey-tens | 540 - Chemistry and allied sciences |
| discipline | Chemie / Pharmazie Physik Mathematik |
| format | Book |
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| id | DE-604.BV009898896 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:42:49Z |
| institution | BVB |
| isbn | 0198552262 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006555651 |
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| physical | XII, 704 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Clarendon Press |
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| spelling | Altmann, Simon L. 1924- Verfasser (DE-588)174096615 aut Point group theory tables Simon L. Altmann and Peter Herzig Point-group theory tables Oxford Clarendon Press 1994 XII, 704 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Punktgruppe (DE-588)4176373-7 gnd rswk-swf Tabelle (DE-588)4184303-4 gnd rswk-swf Punktgruppe (DE-588)4176373-7 s Tabelle (DE-588)4184303-4 s DE-604 Herzig, Peter Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006555651&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Altmann, Simon L. 1924- Herzig, Peter Point group theory tables Punktgruppe (DE-588)4176373-7 gnd Tabelle (DE-588)4184303-4 gnd |
| subject_GND | (DE-588)4176373-7 (DE-588)4184303-4 |
| title | Point group theory tables |
| title_alt | Point-group theory tables |
| title_auth | Point group theory tables |
| title_exact_search | Point group theory tables |
| title_full | Point group theory tables Simon L. Altmann and Peter Herzig |
| title_fullStr | Point group theory tables Simon L. Altmann and Peter Herzig |
| title_full_unstemmed | Point group theory tables Simon L. Altmann and Peter Herzig |
| title_short | Point group theory tables |
| title_sort | point group theory tables |
| topic | Punktgruppe (DE-588)4176373-7 gnd Tabelle (DE-588)4184303-4 gnd |
| topic_facet | Punktgruppe Tabelle |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006555651&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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