Symmetry and group theory in chemistry
Contributors: Randhawa, H. S (Assistant professor)
Edition: Second edition.
Publisher: New Academic Science
Published: 2017
Place of publication: London
Language: eng
Number of pages: 521
ISBN-13: 9781523118953; 9781781830987
Subjects: Group theory; Chemistry; Mathematics; Théorie des groupes
Notes: 2.8.5 Concept of Reducible and Irreducible Representations.
Table of contents: title: Cover; Preface; Contents; Chapter 1: Introduction: Concept of Symmetry, Symmetry Elements and Symmetry Point Groups; 1.1 Symmetry; 1.2 Symmetry in Chemistry; 1.3 Cartesian Coordinate System, Right Hand Thumb Rule and Rotation about the Coordinate Axes; 1.3.1 Conventions Regarding Coordinate Systems and Axes; 1.4 Symmetry Operations; 1.4.1 Identity; 1.4.2 Centre of Symmetry or Inversion Centre; 1.4.3 Plane of Symmetry and Reflection Plane; 1.4.4 n-Fold Rotation or Symmetry Axis (Proper Axis); 1.4.5 Rotation-Reflection Axes (Improper Axis); 1.4.6 Products of Symmetry Operations.; title: 1.5 Concept of Symmetry Point Group1.5.1 Identity Number; 1.5.2 Laws of Combination; 1.5.3 Law of Associative Combination; 1.5.4 Inverse Number; 1.5.5 Cyclic Group; 1.5.6 Isomorphic Group; 1.5.7 Homomorphic Group; 1.5.8 Order of a Group; 1.5.9 Subgroups; 1.5.10 Similarity Transform and Conjugate Elements; 1.5.11 Classes; 1.5.12 Class Multiplication; 1.6 Hierarchy of Point Groups; 1.6.1 Minimum of Symmetry; 1.6.2 S2n Groups; 1.6.3 Cnh Groups; 1.6.4 Cnv Groups; 1.6.5 Dn Groups; 1.6.6 Dnd Groups; 1.6.7 Dnh Group; 1.6.8 Cubic Groups (Plato's Solids); 1.6.9 Tetrahedral Group (Td).; title: 1.6.10 Octahedron Group (Oh)1.6.11 Continuous Symmetry Point Groups; 1.6.12 O(3) Point Group; 1.7 Basic Symmetry Point Groups of Molecules; 1.7.1 Procedure for Symmetry Classification of Molecules; 1.8 Some Miscellaneous Topics; 1.8.1 Operations of the Same Class; 1.8.2 Inverse of a Symmetry Operation; 1.8.3 Equivalent Symmetry Elements and Equivalent Atoms; 1.8.4 Chemical Equivalence; 1.8.5 Symmetry and Nuclear Magnetic Resonance Spectroscopy; 1.8.6 Dipole Moments; 1.8.7 Optical Activity and Symmetry; 1.8.8 Symmetry and Origin of Absorption and Circular Dichroism Phenomena; Problems.; title: Chapter 2: Eulogy to Operators, Vectors, Matrices and Determinants2.1 Introduction; 2.2 Operator; 2.3 Vectors; 2.4 Matrices and Some of their Characteristics; 2.4.1 Matrix Multiplication; 2.4.2 Addition or Subtraction of Matrices; 2.4.3 Cofactor of a Matrix; 2.4.4 Transpose of a Matrix; 2.4.5 Adjoint of a Matrix; 2.4.6 Inverse of a Matrix; 2.4.7 Eigenvalues Eigenfunctions Equations; 2.4.8 Orthogonality; 2.4.9 Diagonal Matrix; 2.4.10 Similarity Transform; 2.4.11 Adjoint and Complex Conjugate Matrices; 2.4.12 Real Matrix; 2.4.13 Hermitian Matrix; 2.4.14 Unitary Matrix.; title: 2.4.15 Partitioned (or Factored) Matrices2.4.16 Character or Trace (or Spur in German) of Set of Irreducible Matrices; 2.4.17 Elementary Transformation of Matrices; 2.5 Characteristics of Determinants; 2.6 Concept of Symmetry Transformation of Functions; 2.7 Matrix Notation for Symmetry Transformations; 2.7.1 The Identity; 2.7.2 Proper Rotation; 2.7.3 Improper Rotation; 2.7.4 Reflection Through a Plane; 2.7.5 Inversion; 2.8 Representation; 2.8.1 Group Representation; 2.8.2 Equivalent of Representations; 2.8.3 Representation of an Atom; 2.8.4 Contribution to Trace of the Representations.