ATOMIC and MOLECULAR SYMMETRY GROUPS and CHEMISTRY

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. Please note: Taylor & Francis does not sell or distribute the Hardback in India, Pakistan, Nepal, Bhutan, Bangladesh and Sri Lanka. Cover Half Title Title Page Copyright Page Dedication Preface Table of Contents 1 Symmetry Elements and Symmetry Operations 1.1 Symmetry Elements, Symmetry Operations and Symbols 1.2 Symmetry Planes 1.3 Centre of Symmetry 1.4 Roto-reflection Axis of Symmetry 1.5 Multiple Symmetry Operations, Inverse Operations and Simplified Symbols for Symmetry Operations 1.6 Choice of Origin and Axes 1.7 Active and Passive Modes 2 Groups and Molecular Point Groups 2.1 Groups, Definition, Elucidations and Multiplication Tables 2.2 Basic Concepts and Some Theorems 2.2.1 Generators 2.2.2 Subgroups 2.2.3 Cosets 2.2.4 Some Finite Group Theorems 2.2.5 Generators and Generation of Group Elements 2.2.6 Conjugate Elements and Classes 2.2.7 Invariant Subgroup 2.2.8 Direct Product Group 2.3 Molecular Symmetry Groups (Point Groups) 2.3.1 Classification of Point Symmetry Groups and Group Symbols 2.3.2 Generation of Point Symmetry Groups: Axial Point Groups 2.3.3 Features of Group ElementsClasses and Products 2.3.4 Cubic Point Groups 2.3.5 Special Groups of Linear Molecules 2.3.6 Molecules of Very High Symmetry 2.3.7 Point Groups - Molecules and Crystals, Schonflies and Hermann Mauguin Symbols 2.3.8 Direct Product and Generation of Groups 2.3.9 Point Groups and Flexibility of Molecules 2.4 Recognition of Point Groups of Molecules 3 Vector Spaces, Matrices and Transformations 3.1 Linear Spaces and Basis Vectors 3.1.1 Matrix Forms of Vectors In Linear Spaces 3.2 Linear Subspaces and Linear Product Spaces 3.2.1 Vector Space and Metrical Matrix 3.3 Matrices and Diagonalisation 3.4 Transformations in Vectorspaces and Matrices 3.4.1 Rotations in Physical Spaces 3.4.2 Rotations about an Arbitrary Axis 3.4.3 Reflections, Inversion and Improper Rotations 3.5 Matrices And Transformations in Function Spaces: 3.6 Transformations in Other Spaces 3.7 Rotations about Arbitrary Axes. Euler Angles 4 Representation of Groups, Equivalent Representations and Reducible Representations 4.1 Representation of Geometrical Operations By Matrices 4.2 Representations of Group symmetry operations and of Groups: 4.3 Multiplicity of Representations, Similarity Transformations and Equivalent Representations 4.4 Representations in Function Spaces. Extension of the idea of Equivalent Representations 4.5 Representations of Variable Dimensions. Reducible and Irreducible Representations 4.6 Reduction of Representations Qualitative Outline: 4.7 Representations of Groups C4v and C3h 5 Reducible Representations, Irreducible Representations and Characters – Theorems and Properties 5.1 Metrical Matrix—Positive Definiteness 5.2 Reducible Representations—Unitary Basis and Unitary Representation 5.3 Theorems— IR's and Characters 5.4 Character Tables Principle Of Construction 5.5 Character Tables-Description; Notations for Irreducible Representations 5.6 Projection Operators, Basis Functions and Reduction of Representations 5.7 Direct Product Representation:(Tensor Product Representation) 5.8 Some General Remarks-Transformations, Bases and Characters 5.9 Regular Representation 6 Representation Theory and Quantum Mechanics 6.1 Symmetry Operators, Hamiltonian Operator and Wave Functions 6.2 Representations and Molecular Orbitals as Basis Set 6.3 Perturbations and Symmetry 6.4 Direct Product and Quantum Mechanical Integrals 7 Qualitative Applications and Assignment of Symmetry to Wave Functions 7.1 General 7.2 Qualitative Applications 7.3 Tagging Symmetry Labels to Wave FUnctions and Orbitals 8 Molecular Vibrations, Normal Co-Ordinates, Selection Rules-Infrared and Raman Spectra 8.1 General Remarks 8.2 Vibrations of Molecules. Normal Modes of Vibrations 8.3 Normal Modes of Vibrations. Symmetry Aspects 8.4 Symmetry in Vibrations of Linear Molecules 9 Hybrid Orbitals, Symmetry Orbitals and Molecular Orbitals 9.1 Introduction : 9.2 Principle of Constructing Hybrid Orbitals 9.3 Hybrids For σ– Bond Formation 9.4 Hybrids For π–Bond Formation 9.5 Symmetry Orbitals, Molecular Orbitals : Introduction 9.6 π–Molecular Orbitals and Htickel Approximations: Introduction 9.7 Symmetry Orbitals, Group Orbitals and Molecular Orbitals 10 Symmetry Principles and Transition Metal Complexes 10.1 General Remarks 10.2 Basic Principles 10.3 Symmetry and Splitting of Energy Levels 10.3.1 Crystal Field Effect on p1, d1 and f1 Systems 10.3.2 Crystal Field Effect (Splitting). Multielectron Configurations 10.4 Energy of Split Levels. Energy Diagram 10.4.1 Principles: 10.4.2 Energy Correlation Diagram 10.5 Molecular Orbital Theory of Transition Metal Complexes 10.6 Spectral Properties. Vibronic Coupling, Vibronic Polarisation 10.7 Electronic Transitions. Selection Rules and Polarisation 10.8 Double Groups. Spin Orbit Coupling and Crystal Field States 11 Atomic Symmetry and Quantum Mechanical Problems. R(2), R(3) SU(2) and R(4) Lie Groups 11.1 Lie Group of Transformation 11.2 Classification of Linear Transformations: 11.3 Lie Groups: Number of Parameters and General Process of Treatment 11.4 General Steps in Lie Group Treatment: 11.5 The Group R (2) 11.6 General Form of Generator of Lie Group 11.7 The group R(3) i.e, S0(3) [sub group of the spinless Atomic Symmetry Group] 11.8 Group Theoretical Significance of Direct Product Representation with Angular Momentum Basis Functions, Addition of Angular Momenta: 11.9 The SU(2) group (Special Unitary Group- In Two Dimensions): 11.9.1 Diagonalization and Rotations, Isomorphism and Homomorphism, Higher Dimensional Representations: 11.9.2 Higher Dimensional IR's of SU(2) Group and their character Values: 11.10 The Lie Group R(4)- Rotations in Four Dimensions: 12 Applications of Lie Groups in Quantamechanical Problems 12.1 General Remarks 12.2 Total Angular Momentum, Casimir operator and the Hamiltonian operator 12.3 Applications in some Quantamechanical Problems 12.4 Atomic Symmetry Group SU(2)/ R*(3)– Applications in Angular Momenta Aspects 13 Symmetry and Stereochemistry of Reactions 13.1 Molecular Orbital Background 13.2 Symmetry Control of Electrocyclic Reactions 13.3 Symmetry and Cycloaddition Reactions 13.4 Symmetry and Sigmatropic Processes Problems & References Appendix I Appendix II Appendix III Subject Index 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. Publisher's website 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.Please note: T&F does not sell or distribute the Hardback in South Asia.