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

4. Improper Axes and Improper Rotations S=C,o n h Rotations by 2 /n followed by reflection in a plane l to the s axis D D B B C A A B C 20218/21 Chemistry Departme nt of Fudan University 16

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 16 4. Improper Axes and Improper Rotations Rotations by 2/n followed by reflection in a plane ⊥ to the Sn axis. Sn=Cn h

Phydical Chemiatry I Chapter IV Molecular Symmetry and Poirmt Group 5 The Inversion Center i=S2=C20h=o, C2 (X,y,z)→(-X,-y,-z) 6 Inversion 3 5 Center of Inversion 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 17 5. The Inversion Center i i = S2 = C2h =hC2 (x, y, z) → (-x, -y, -z)

Phydical Chemiatry I Chapter IV Molecular Symmetry and Poirmt Group 84-1-2. Multiplication Table Multiplication Table of H,o 2y E 2 XZ Operate first XZ E perate second 20218/21 Chemistry Departme nt of Fudan University 18

Physical ChemistryI Chemistry Department of Fudan University Chapter IV Molecular Symmetry and Point Group 2021/8/21 18 Multiplication Table of H2O C2v E C2 xz yz E E C2 xz yz C2 C2 E yz xz xz xz yz E C2 yz yz xz C2 E Operate first Operate second §4-1-2. Multiplication Table

84-1-3. General Relations Among Symmetry Elements and Operations 1。 Products (1) The product of two reflections, intersecting at an angle leof￠2T/2n,isa rotation by 2 about the axis defined by the line of intersection 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 19 §4-1-3. General Relations Among Symmetry Elements and Operations 1. Products (1) The product of two reflections, intersecting at an angle of = 2/2n, is a rotation by 2 about the axis defined by the line of intersection

Phydical Chemiatry I Chapter IV Molecular Symmetry and Poirmt Group (2)When there is a rotation axis, Cn, and a plane containing it, there must be n such planes separated by angles of 2r c/2n; The product of two C2 rotations about axes which intersect at an angle e is a rotation by 20 about an axis perpendicular to the plane of the C2 axes; (4 )A proper rotation axis of even order and a perpendicular reflection plane generate an inversion center 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 20 (2) When there is a rotation axis, Cn , and a plane containing it, there must be n such planes separated by angles of 2/2n; (3)The product of two C2 rotations about axes which intersect at an angle  is a rotation by 2 about an axis perpendicular to the plane of the C2 axes; (4) A proper rotation axis of even order and a perpendicular reflection plane generate an inversion center