Application of projection operators, Simplification, sigma bonding in MH6

週次課程內容課程影音
單元一 Introduction
Conservation law via symmetry operation
Elementary operations for molecule
Apply symmetry operation to molecule
Summary
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單元二 Definitions and theorems of group theory
Definition of an abstract group
Multiplication table for a finite group
Cyclic groups
Subgroups
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單元三 Molecular symmetry and the symmetry groups
Symmetry planes and reflections
Center of inversion
Proper axes and proper rotations
Improper axes and improper rotations
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Products and relations of symmetry operations
The symmetry point groups
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Classes of point groups
Symmetry with multiple high-order axes
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Summary of point groups
Illustrative examples
EXERCISES
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單元四 Representation of groups
Matrix algebra
Eigenvalue and eigenvector of matrix
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Simultaneous diagonalization of matrices
Irreducible representations
Great orthogonality theorem
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Irreducible representations
Representation for cyclic group
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Basis of representations
Mulliken symbols
(x,y,z) basis for tetrahedron symmetry
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單元五 Group theory with its applications in quantum chemistry
Hydrogen atom as basis representation
General wave functions for group representation
The direct product
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Identifying nonzero matrix elements
Symmetry-adapted basis
Projection operators
Application of projection operators
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Application of projection operators
Simplification
igma bonding in MH6
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單元六 Molecular orbital theory and its applications in organic chemistry
Benzene
Tetramethylenecyclobutane
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Naphthalene線上觀看
單元八 Molecular vibrations
Cartesian coordinates
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Normal-mode coordinates
Internal coordinates
Fundamental vibrational transitions
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