化學應用群論 Group Theory for Chemistry | 應用化學系朱超原老師

Group Theory for Chemistry

化學應用群論

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Group theory provides a systematic mathematical method for describing molecular symmetry. Actually each kind of symmetry corresponds to one of conservation law that is experimentally observable. Properties of a group, symmetry operations and symmetry elements, molecular symmetry groups, representations and characters all are used to describe molecular orbitals, molecular vibrations, selection rules, and so on.

課程用書：Physical Chemistry 3rd edition, Mortimer, 2008.
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授課教師	應用化學系朱超原老師
課程學分	3學分
授課年度	99學年度
授課對象	大學三年級學生
預備知識	化學(一)(二)、應用數學、物理化學(二)
課程提供	課程影音課程綱要課程行事曆

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課程內容	課程影音	課程下載
單元一 Introduction Conservation law via symmetry operation Elementary operations for molecule Apply symmetry operation to molecule Summary	線上觀看	MP4下載
單元二 Definitions and theorems of group theory Definition of an abstract group Multiplication table for a finite group Cyclic groups Subgroups	線上觀看	MP4下載
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	線上觀看	MP4下載
Products and relations of symmetry operations The symmetry point groups	線上觀看	MP4下載
Classes of point groups Symmetry with multiple high-order axes	線上觀看	MP4下載
Summary of point groups Illustrative examples EXERCISES	線上觀看	MP4下載
單元四 Representation of groups Matrix algebra Eigenvalue and eigenvector of matrix	線上觀看	MP4下載
Simultaneous diagonalization of matrices Irreducible representations Great orthogonality theorem	線上觀看	MP4下載
Irreducible representations Representation for cyclic group	線上觀看	MP4下載
Basis of representations Mulliken symbols (x,y,z) basis for tetrahedron symmetry	線上觀看	MP4下載
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	線上觀看	MP4下載
Identifying nonzero matrix elements Symmetry-adapted basis Projection operators Application of projection operators	線上觀看	MP4下載
Application of projection operators Simplification igma bonding in MH6	線上觀看	MP4下載
單元六 Molecular orbital theory and its applications in organic chemistry Benzene Tetramethylenecyclobutane	線上觀看	MP4下載
Naphthalene	線上觀看	MP4下載
單元八 Molecular vibrations Cartesian coordinates	線上觀看	MP4下載
Normal-mode coordinates Internal coordinates Fundamental vibrational transitions	線上觀看	MP4下載

目前顯示第 1 至第 17 個資料列，總計 17 個資料列

課程目標

Group theory provides a systematic mathematical method for describing molecular symmetry.
Actually each kind of symmetry corresponds to one of conservation law that is experimentally observable.
Properties of a group, symmetry operations and symmetry elements, molecular symmetry groups, representations and characters all are used to describe molecular orbitals, molecular vibrations, selection rules, and so on.

課程章節

章節	章節內容
單元一	Introduction
單元二	Definitions and theorems of group theory
單元三	Molecular symmetry and the symmetry groups
單元四	Representations of groups
單元五	Group theory with its applications in quantum chemistry
單元六	Molecular orbital theory with its applications in organic chemistry
單元七	Molecular orbital theory with its applications in inorganic chemistry
單元八	Molecular vibrations

課程書目

Physical Chemistry 3rd edition, Mortimer, 2008.

參考書目

Chemical Applications of Group Theory , Cotton, 3rd , (John Wiley and Sons) 2002.
Physical Chemistry,A Molecular Approach, McQuarrie and Simon, 1997.
Group theory with applications in chemical physics, Jacobs, 2005.

評分標準

項目	百分比
作業部分：每堂課後均有作業	25%
期中考	35%
期末考	40%

本課程行事曆提供課程進度與考試資訊參考。

章節	章節內容
單元一	Introduction
單元二	Definitions and theorems of group theory
單元三	Molecular symmetry and the symmetry groups
單元四	Representations of groups
單元五	Group theory with its applications in quantum chemistry
單元六	Molecular orbital theory with its applications in organic chemistry
單元七	Molecular orbital theory with its applications in inorganic chemistry
單元八	Molecular vibrations