复旦大学：《物理化学》精品课程教学资源（PPT课件讲稿）第4章 分子对称性和点群

Physical Chemistry 20218/21 Chemistry Departme nt of Fudan University

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 1 Physical Chemistry

Chapter IV Molecular Symmetry and Point Group Reference books: (1)F. Albert, Cotton, Chemical Application of group Theory, Wiley Press, New York, 1971 (中译本:群论在化学中的应用科学出版社,1984) (2)David M. Bishop, Group Theory and Chemistry, Clarendon press. Oxford. 1973 (中译本:群论与化学高等教育出版社,1984 20218/21 Chemistry Departme nt of Fudan University

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 2 Chapter IV Molecular Symmetry and Point Group Reference Books: (1) F. Albert, Cotton, Chemical Application of Group Theory, Wiley Press, New York, 1971. (中译本:群论在化学中的应用,科学出版社,1984) (2) David M. Bishop, Group Theory and Chemistry, Clarendon Press, Oxford, 1973. (中译本:群论与化学,高等教育出版社,1984)

Symmetry is all around us and is a fundamental property of nature 备 20218/21 Chemistry Departme nt of Fudan University

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 3 Symmetry is all around us and is a fundamental property of nature

3 H 2 2 3 [B] [A] 3 3 2 [C] 20218/21 Chemistry Departme nt of Fudan University

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 4 [A] [B] [C] C3 1 N H H1 2 H3 N H H3 1 H2 N H H2 3 H1 C3 C3 C 1 3 1

Motivational factors The nature and degeneracy of vibrations The legitimate AO combinations for MOs The appearances and absences of lines in a molecules spectrum o The polarity and chirality of a molecule. 20218/21 Chemistry Departme nt of Fudan University

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 5 The nature and degeneracy of vibrations. •The legitimate AO combinations for MOs. •The appearances and absences of lines in a molecule’s spectrum. •The polarity and chirality of a molecule. Motivational Factors

84-1 Symmetry Elements and Operations The term symmetry is derived from the Greek wordsymmetria which means measured together We require a precise method to describe how an object or molecule is symmetric 20218/21 Chemistry Departme nt of Fudan University

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 6 The term symmetry is derived from the Greek word “symmetria” which means “measured together”. We require a precise method to describe how an object or molecule is symmetric. §4-1. Symmetry Elements and Operations

Symmetry Operation A symmetry operation is a movement of a body such that, after the movement has been carried out, every point of the body is coincident with an equivalent point (or perhaps the same point) of the body in its original orientation Symmetry Element A symmetry element is a geometrical entity such as a line, a plane, or a point, with respect to Which one or more symmetry operations may be carried out 20218/21 Chemistry Departme nt of Fudan University

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 7 Symmetry Operation A symmetry operation is a movement of a body such that, after the movement has been carried out, every point of the body is coincident with an equivalent point (or perhaps the same point) of the body in its original orientation. Symmetry Element A symmetry element is a geometrical entity such as a line, a plane, or a point, with respect to which one or more symmetry operations may be carried out

8 4-1-1 Symmetry Elements and Operations Required in Specifying Molecular Symmetry 20218/21 Chemistry Departme nt of Fudan University

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 8 §4-1-1. Symmetry Elements and Operations Required in Specifying Molecular Symmetry

1. The Identity Operation E No matter how asymmetrical a molecule is, it must have an identity operation, E The symbol‘E” comes from the German,“ eigen," meaning‘ the same 20218/21 Chemistry Departme nt of Fudan University

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 9 1. The Identity Operation E Ê No matter how asymmetrical a molecule is, it must have an identity operation, E •The symbol “E” comes from the German, “eigen,” meaning “the same

Phydical Chemiatry I Chapter IV Molecular Symmetry and Poirmt Group 2. Proper Axes and Proper Rotations C An n-fold rotation is symbolized by the element Cn, and represents n-1 rotational operations about the axis 20218/21 Chemistry Departme nt of Fudan University

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 10 2. Proper Axes and Proper Rotations Cn An n-fold rotation is symbolized by the element Cn , and represents n–1 rotational operations about the axis. m Cn