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Atomic & Molecular Symmetry Groups and Chemistry [Hardback]

  • Formāts: Hardback, 424 pages, height x width: 229x152 mm, weight: 698 g, 11 Tables, black and white; 69 Line drawings, black and white; 69 Illustrations, black and white
  • Izdošanas datums: 19-Aug-2021
  • Izdevniecība: CRC Press
  • ISBN-10: 1032075317
  • ISBN-13: 9781032075310
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  • Hardback
  • Cena: 249,78 €
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Atomic & Molecular Symmetry Groups and ChemistryPalielināt
  • Formāts: Hardback, 424 pages, height x width: 229x152 mm, weight: 698 g, 11 Tables, black and white; 69 Line drawings, black and white; 69 Illustrations, black and white
  • Izdošanas datums: 19-Aug-2021
  • Izdevniecība: CRC Press
  • ISBN-10: 1032075317
  • ISBN-13: 9781032075310
Citas grāmatas par šo tēmu:
Permanent link: https://www.kriso.lv/db/9781032075310.html
Keywords:

Atomic Symmetry Groups, being continuous groups, are just a fallout of the Lie Groups and Lie Algebras. Atoms are structurally simpler than molecules but atomic symmetry is more complex than molecular symmetry. In quantum mechanics we study atoms first and then the molecules. In symmetry studies, we do just the reverse. In this book, apart from theories, the description of both the symmetry groups – atomic and molecular, are attended with adequate applications.

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1 Symmetry Elements and Symmetry Operations
1(13)
1.1 Symmetry Elements, Symmetry Operations and Symbols
1(5)
1.2 Symmetry Planes
6(1)
1.3 Centre of Symmetry
7(1)
1.4 Roto-reflection Axis of Symmetry
8(2)
1.5 Multiple Symmetry Operations, Inverse Operations and Simplified Symbols for Symmetry Operations
10(2)
1.6 Choice of Origin and Axes
12(1)
1.7 Active and Passive Modes
13(1)
2 Groups and Molecular Point Groups
14(41)
2.1 Groups, Definition, Elucidations and Multiplication Tables
14(6)
2.2 Basic Concepts and Some Theorems
20(7)
2.2.1 Generators
20(1)
2.2.2 Subgroups
21(1)
2.2.3 Cosets
21(1)
2.2.4 Some Finite Group Theorems
21(2)
2.2.5 Generators and Generation of Group Elements
23(1)
2.2.6 Conjugate Elements and Classes
24(2)
2.2.7 Invariant Subgroup
26(1)
2.2.8 Direct Product Group
26(1)
2.3 Molecular Symmetry Groups (Point Groups)
27(22)
2.3.1 Classification of Point Symmetry Groups and Group Symbols
30(3)
2.3.2 Generation of Point Symmetry Groups: Axial Point Groups
33(4)
2.3.3 Features of Group ElementsClasses and Products
37(2)
2.3.4 Cubic Point Groups
39(7)
2.3.5 Special Groups of Linear Molecules
46(1)
2.3.6 Molecules of Very High Symmetry
46(1)
2.3.7 Point Groups - Molecules and Crystals, Schonflies and Hermann Mauguin Symbols
47(1)
2.3.8 Direct Product and Generation of Groups
48(1)
2.3.9 Point Groups and Flexibility of Molecules
49(1)
2.4 Recognition of Point Groups of Molecules
49(6)
3 Vector Spaces, Matrices and Transformations
55(27)
3.1 Linear Spaces and Basis Vectors
55(5)
3.1.1 Matrix Forms of Vectors in Linear Spaces
59(1)
3.2 Linear Subspaces and Linear Product Spaces
60(4)
3.2.1 Vector Space and Metrical Matrix
63(1)
3.3 Matrices and Diagonalisation
64(5)
3.4 Transformations in Vectorspaces and Matrices
69(4)
3.4.1 Rotations in Physical Spaces
69(2)
3.4.2 Rotations about an Arbitrary Axis
71(1)
3.4.3 Reflections, Inversion and Improper Rotations
72(1)
3.5 Matrices and Transformations in Function Spaces
73(4)
3.6 Transformations in Other Spaces
77(1)
3.7 Rotations about Arbitrary Axes. Euler Angles
78(4)
4 Representation of Groups, Equivalent Representations and Reducible Representations
82(25)
4.1 Representation of Geometrical Operations by Matrices
82(1)
4.2 Representations of Group symmetry operations and of Groups
82(4)
4.3 Multiplicity of Representations, Similarity Transformartions and Equivalent Representations
86(7)
4.4 Representations in Function Spaces. Extension of the idea of Equivalent Representations
93(3)
4.5 Representations of Variable Dimensions. Reducible and Irreducible Representations
96(3)
4.6 Reduction of Representations Qualitative Outline
99(3)
4.7 Representations of Groups C4v and C3h
102(5)
5 Reducible Representations, Irreducible Representations and Characters -- Theorems and Properties
107(51)
5.1 Metrical Matrix--Positive Definiteness
108(1)
5.2 Reducible Representations--Unitary Basis and Unitary Representation
108(4)
5.3 Theorems--- IR's and Characters
112(6)
5.4 Character Tables Principle of Construction
118(3)
5.5 Character Tables-Description; Notations for Irreducible Representations
121(5)
5.6 Projection Operators, Basis Functions and Reduction of Representations
126(11)
5.7 Direct Product Representation: (Tensor Product Representation)
137(6)
5.8 Some General Remarks-Transformations, Bases and Characters
143(9)
5.9 Regular Representation
152(6)
6 Representation Theory and Quantum Mechanics
158(18)
6.1 Symmetry Operators, Hamiltonian Operator and Wave Functions
158(2)
6.2 Representations and Molecular Orbitals as Basis Set
160(2)
6.3 Perturbations and Symmetry
162(11)
6.4 Direct Product and Quantum Mechanical Integrals
173(3)
7 Qualitative Applications and Assignment of Symmetry to Wave Functions
176(9)
7.1 General
176(1)
7.2 Qualitative Applications
177(2)
7.3 Tagging Symmetry Labels to Wave Functions and Orbitals
179(6)
8 Molecular Vibrations, Normal Co-Ordinates, Selection Rules-Infrared and Raman Spectra
185(28)
8.1 General Remarks
185(3)
8.2 Vibrations of Molecules. Normal Modes of Vibrations
188(5)
8.3 Normal Modes of Vibrations. Symmetry Aspects
193(15)
8.4 Symmetry in Vibrations of Linear Molecules
208(5)
9 Hybrid Orbitals, Symmetry Orbitals and Molecular Orbitals
213(45)
9.1 Introduction
213(1)
9.2 Principle of Constructing Hybrid Orbitals
214(2)
9.3 Hybrids For σ--- Bond Formation
216(10)
9.4 Hybrids For π---Bond Formation
226(2)
9.5 Symmetry Orbitals, Molecular Orbitals: Introduction
228(3)
9.6 π---Molecular Orbitals and Htickel Approximations: Introduction
231(2)
9.7 Symmetry Orbitals, Group Orbitals and Molecular Orbitals
233(25)
10 Symmetry Principles and Transition Metal Complexes
258(49)
10.1 General Remarks
258(1)
10.2 Basic Principles
259(5)
10.3 Symmetry and Splitting of Energy Levels
264(7)
10.3.1 Crystal Field Effect on p1, d1 and f1 Systems
264(4)
10.3.2 Crystal Field Effect (Splitting). Multielectron Configurations
268(3)
10.4 Energy of Split Levels. Energy Diagram
271(8)
10.4.1 Principles
271(3)
10.4.2 Energy Correlation Diagram
274(5)
10.5 Molecular Orbital Theory of Transition Metal Complexes
279(9)
10.6 Spectral Properties. Vibronic Coupling, Vibronic Polarisation
288(6)
10.7 Electronic Transitions. Selection Rules and Polarisation
294(4)
10.8 Double Groups. Spin Orbit Coupling and Crystal Field States
298(9)
11 Atomic Symmetry and Quantum Mechanical Problems. R(2), R(3) Su(2) and R(4) Lie Groups
307(31)
11.1 Lie Group of Transformation
307(1)
11.2 Classification of Linear Transformations
308(1)
11.3 Lie Groups: Number of Parameters and General Process of Treatment
309(1)
11.4 General Steps in Lie Group Treatment
310(1)
11.5 The Group R(2)
311(2)
11.6 General Form of Generator of Lie Group
313(1)
11.7 The group R(3) i.e, SO(3) [ sub group of the spinless Atomic Symmetry Group]
314(9)
11.8 Group Theoretical Significance of Direct Product Representation with Angular Momentum Basis Functions, Addition of Angular Momenta
323(1)
11.9 The SU(2) group (Special Unitary Group- in Two Dimensions)
324(12)
11.9.1 Diagonalization and Rotations, Isomorphism and Homomorphism, Higher Dimensional Representations
326(2)
11.9.2 Higher Dimensional IR's of SU(2) Group and their character Values
328(8)
11.10 The Lie Group R(4)- Rotations in Four Dimensions
336(2)
12 Applications of Lie Groups in Quantamechanical Problems
338(16)
12.1 General Remarks
338(1)
12.2 Total Angular Momentum, Casimir operator and the Hamiltonian operator
339(1)
12.3 Applications in some Quantamechanical Problems
340(8)
12.4 Atomic Symmetry Group SU(2)/R*(3)--- Applications in Angular Momenta Aspects
348(6)
13 Symmetry and Stereochemistry of Reactions
354(14)
13.1 Molecular Orbital Background
354(2)
13.2 Symmetry Control of Electrocyclic Reactions
356(6)
13.3 Symmetry and Cycloaddition Reactions
362(4)
13.4 Symmetry and Sigmatropic Processes
366(2)
Problems & References 368(8)
Appendix I 376(4)
Appendix II 380(26)
Appendix III 406(2)
Subject Index 408
S.C. Rakshit, Ph. D., was Professor of Chemistry at Burdwan University, India for more than three decades, where he taught various disciplines of Physical Chemistry at the postgraduate level, which included quantum mechanics, group theory, atomic spectra, crystallography and theoretical kinetics.