Group Theory for Chemistry
本課程是由 國立陽明交通大學應用化學系提供。
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.
Textbook：Physical Chemistry 3rd edition, Mortimer, 2008.
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| Instructor(s) | Department of Applied Chemistry Prof. Chao-Yuan Zhu |
|---|---|
| Course Credits | 3 Credits |
| Academic Year | 99 Academic Year |
| Level | Third year university student |
| Prior Knowledge | Chemistry (I), Chemistry(II), Applied Mathematics, Physical Chemistry (II) |
| Related Resources | Course Video Course Syllabus Course Calendar |
| Week | Course Content | Course Video |
|---|---|---|
| 單元一 Introduction Conservation law via symmetry operation Elementary operations for molecule Apply symmetry operation to molecule Summary | Watch Online | |
| 單元二 Definitions and theorems of group theory Definition of an abstract group Multiplication table for a finite group Cyclic groups Subgroups | Watch Online | |
| 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 | Watch Online | |
| Products and relations of symmetry operations The symmetry point groups | Watch Online | |
| Classes of point groups Symmetry with multiple high-order axes | Watch Online | |
| Summary of point groups Illustrative examples EXERCISES | Watch Online | |
| 單元四 Representation of groups Matrix algebra Eigenvalue and eigenvector of matrix | Watch Online | |
| Simultaneous diagonalization of matrices Irreducible representations Great orthogonality theorem | Watch Online | |
| Irreducible representations Representation for cyclic group | Watch Online | |
| Basis of representations Mulliken symbols (x,y,z) basis for tetrahedron symmetry | Watch Online | |
| 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 | Watch Online | |
| Identifying nonzero matrix elements Symmetry-adapted basis Projection operators Application of projection operators | Watch Online | |
| Application of projection operators Simplification igma bonding in MH6 | Watch Online | |
| 單元六 Molecular orbital theory and its applications in organic chemistry Benzene Tetramethylenecyclobutane | Watch Online | |
| Naphthalene | Watch Online | |
| 單元八 Molecular vibrations Cartesian coordinates | Watch Online | |
| Normal-mode coordinates Internal coordinates Fundamental vibrational transitions | Watch Online |
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 |
