1. Symmetry and Group heory
Chapter4
Symmetry and Group heory
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2. FIGURE 4.1 Examples of Symmetry.

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FIGURE 4.2 Rotations The Cross section of the tobacco mosaic virus is a cover diagram from Nature,1976,259.c1976,Macmillan Journals Ltd.Reproduced with permission of Aaron Klug .

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FIGURE 4.3 Reflections.

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FIGURE 4.3-1

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FIGURE 4.3-2

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FIGURE 4.4 Inversion .

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FIGURE 4.4-TABLE-1

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FIGURE 4.4-TABLE-2

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FIGURE 4.4-TABLE-3

15. FIGURE 4.5 Figures(a)With and (b) Without Inversion Centers.
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FIGURE 4.5 Figures(a)With and (b) Without Inversion Centers.

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FIGURE 4.5-1

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FIGURE 4.5-2

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19. FIGURE 4.6 Improper Rotation or Rotation-Reflection.

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21. FIGURE 4.7 Diagram of the Point Group Assignment Method.

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23. aen＝ethylenediamine＝NH2CH2CH2NH2,represented by N︵N.
FIGURE 4.8 Molecules to be Assigned to Point Groups.
aen＝ethylenediamine＝NH2CH2CH2NH2,represented by N︵N.

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FIGURE 4.9 Rotation Axes.

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27. FIGURE 4.10 Perpendicular C2 Axes.

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29. FIGURE 4.11 Horizontal Mirror Planes.

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31. FIGURE 4.12 Vertical or Dihedral Mirror Planes or S2n Axes.

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33. FIGURE 4.13 W〔N(CH3)2〕6,a Molecule with Th Symmetry.
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FIGURE 4.13 W〔N(CH3)2〕6,a Molecule with Th Symmetry.

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35. FIGURE 4.14 Symmetry Operations for Ammonia.
(Top view) NH3 is of point group C3v,with the symmetry operations E, C3,C32, σv, σ v ’,and σ v” usually written as E,2C3 and 3σ v (note that C33 ≡ E).

36. FIGURE 4.15 Symmetry Operations of the Water Molecule.

37. FIGURE 4.16 Effect of Rotation on Coordinates of a Point.

38. FIGURE 4.17 Orbitals and Representations.

39. FIGURE 4.18 A Chiral Molecule and Other Chiral Objects.
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FIGURE 4.18 A Chiral Molecule and Other Chiral Objects.

40. FIGURE 4.19 Rotation of Plane-Polarized Light.

41. FIGURE 4.20 Chiral Isomers of 〔Ru(NH2CH2CH2NH2)3〕2+.
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FIGURE 4.20 Chiral Isomers of 〔Ru(NH2CH2CH2NH2)3〕2+.

42. FIGURE 4.21 A Set of Axes for the Water Molecule.
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FIGURE 4.21 A Set of Axes for the Water Molecule.

43. FIGURE 4.22 Coordinate Axes for XeF4.
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FIGURE 4.22 Coordinate Axes for XeF4.

44. FIGURE 4.23 Translational Modes of XeF4.
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FIGURE 4.23 Translational Modes of XeF4.

45. FIGURE 4.24 Rotational Modes of XeF4.
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FIGURE 4.24 Rotational Modes of XeF4.

46. FIGURE 4.25 Selected Vibrational Modes of XeF4.
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FIGURE 4.25 Selected Vibrational Modes of XeF4.

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FIGURE 4.26 Carbonyl Stretching Vibrations of cis-and trans-Dicarbonyl Square Planar Complexes.

48. FIGURE 4.27 Symmetry Operations and Characters for cis－ML2(CO)2.