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Chapter 4

Chapter 4. Molecular Symmetry. Symmetry Elements and Symmetry Operations. Identity Proper axis of rotation Mirror planes Center of symmetry Improper axis of rotation. Symmetry Elements and Symmetry Operations. Identity => E. Symmetry Elements and Symmetry Operations.

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Chapter 4

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  1. Chapter 4 Molecular Symmetry Dr. S. M. Condren

  2. Dr. S. M. Condren

  3. Symmetry Elements and Symmetry Operations • Identity • Proper axis of rotation • Mirror planes • Center of symmetry • Improper axis of rotation Dr. S. M. Condren

  4. Symmetry Elements and Symmetry Operations • Identity => E Dr. S. M. Condren

  5. Symmetry Elements and Symmetry Operations • Proper axis of rotation => Cn • where n = 2, 180o rotation • n = 3, 120o rotation • n = 4, 90o rotation • n = 6, 60o rotation • n = , (1/)o rotation • principal axis of rotation, Cn Dr. S. M. Condren

  6. 2-Fold Axis of Rotation Dr. S. M. Condren

  7. 3-Fold Axis of Rotation Dr. S. M. Condren

  8. Rotations for a Trigonal Planar Molecule Dr. S. M. Condren

  9. Symmetry Elements and Symmetry Operations Mirror planes => sh => mirror plane perpendicular to a principal axis of rotation sv => mirror plane containing principal axis of rotation sd => mirror plane bisects dihedral angle made by the principal axis of rotation and two adjacent C2 axes perpendicular to principal rotation axis Dr. S. M. Condren

  10. Mirrors svsv Cl Cl sh I sd sd Cl Cl Dr. S. M. Condren

  11. Rotations and Mirrors in a Bent Molecule Dr. S. M. Condren

  12. Benzene Ring Dr. S. M. Condren

  13. Symmetry Elements and Symmetry Operations • Center of symmetry => i Dr. S. M. Condren

  14. Center of Inversion Dr. S. M. Condren

  15. Inversion vs. C2 Dr. S. M. Condren

  16. Symmetry Elements and Symmetry Operations • Improper axis of rotation => Sn • rotation about n axis followed by inversion through center of symmetry Dr. S. M. Condren

  17. Improper Rotation in a Tetrahedral Molecule Dr. S. M. Condren

  18. S1 and S2 Improper Rotations Dr. S. M. Condren

  19. Successive C3 Rotations onTrigonal Pyramidal Molecule Dr. S. M. Condren

  20. Linear Molecules Dr. S. M. Condren

  21. Selection ofPoint Group from Shape • first determine shape using Lewis Structure and VSEPR Theory • next use models to determine which symmetry operations are present • then use the flow chart Figure 3.9, Pg. 81 text to determine the point group Dr. S. M. Condren

  22. Dr. S. M. Condren

  23. Decision Tree Dr. S. M. Condren

  24. Selection ofPoint Group from Shape 1. determine the highest axis of rotation 2. check for other non-coincident axis of rotation 3. check for mirror planes Dr. S. M. Condren

  25. H2O and NH3 Dr. S. M. Condren

  26. Dr. S. M. Condren

  27. Dr. S. M. Condren

  28. Geometric Shapes Dr. S. M. Condren

  29. Orbital Symmetry, pz C2v z E + X(E) = +1 - + + C2(z) x - + - X(C2(z)) = +1 y sv(xz) - X(sv(xz)) = +1 sv(yz) + - X(sv(xz)) = +1 Dr. S. M. Condren

  30. Orbital Symmetry, py C2v X(E) = +1 - z + E + - C2(z) - x X(C2(z)) = -1 + sv(xz) y + X(sv(xz)) = -1 - sv(yz) - X(sv(xz)) = +1 + Dr. S. M. Condren

  31. Orbital Symmetry, px C2v z X(E) = +1 - + E C2(z) x + - - + X(C2(z)) = -1 sv(xz) y - + X(s(xz)) = +1 sv(yz) + - X(sv(xz)) = -1 Dr. S. M. Condren

  32. Water, C2v Point GroupTranslational motion in y z y o o HHHH x sv(xz) “asymmetric” => -1 Dr. S. M. Condren

  33. Water, C2v Point GroupTranslational motion in y z o y HH x o HH sv(yz) “symmetric” => +1 Dr. S. M. Condren

  34. Water, C2v Point GroupTranslational motion in y z y C2(z) x O H H “asymmetric” = - 1 Dr. S. M. Condren

  35. Water, C2v Point GroupTranslational motion in y Representation: E C2(z) sv(xz) sv(yz) G3 +1 -1 -1 +1 Dr. S. M. Condren

  36. Water, C2v Point GroupRotation about z axis z O rHa Hbs r - movement out of plane towards observer s - movement out of plane away from observer a,b - labeling to distinguish hydrogens before and after symmetry operations Dr. S. M. Condren

  37. Water, C2v Point GroupRotation about z axis z O E O rHa Hbs rHa Hbs +1 Dr. S. M. Condren

  38. Water, C2v Point GroupRotation about z axis z O C2z O rHa Hbs rHb Has +1 Dr. S. M. Condren

  39. Water, C2v Point GroupRotation about z axis z O sv(xz) O rHa Hbs sHb Har x -1 Dr. S. M. Condren

  40. Water, C2v Point GroupRotation about z axis z O sv(yz) O rHa Hbs sHa Hbr -1 Dr. S. M. Condren

  41. Water, C2v Point GroupRotation about z axis Representation E C2(z) sv(xz) sv(yz) G4 +1 +1 -1 -1 Dr. S. M. Condren

  42. Water, C2v Point Group Representations: Rotation E C2(z) sv(xz) sv(yz) G4 +1 +1 -1 -1 Dr. S. M. Condren

  43. Water, C2v Point Group Representation: Translation E C2(z) sv(xz) sv(yz) G1 +1 +1 +1 +1 Tz G2 +1 -1 +1 -1 Tx G3 +1 -1 -1 +1 Ty Dr. S. M. Condren

  44. Water, C2v Point Group Representation: Rotation E C2(z) sv(xz) sv(yz) G4 +1 +1 -1 -1 Rz G5 +1 -1 +1 -1 Ry G6 +1 -1 -1 +1 Rx Dr. S. M. Condren

  45. Water, C2v Point Group Character Table E C2(z) sv(xz) sv(yz) A1 +1 +1 +1 +1 Tz G1 A2 +1 +1 -1 -1 Rz G4 B1 +1 -1 +1 -1 Ry, Tx G2 , G5 B2 +1 -1 -1 +1 Rx,Ty G3, G6 Dr. S. M. Condren

  46. Dr. S. M. Condren

  47. Vibrational Modes in CO2 For linear molecules: 3N - 5 IR fundamentals Dr. S. M. Condren

  48. Vibrational Modes in SO2 For non-linear molecules: 3N - 6 IR fundamentals Dr. S. M. Condren

  49. Vibration Modes for SO3 For non-linear molecules: 3N - 6 IR fundamentals Dr. S. M. Condren

  50. Vibrational Modes for CH4 For non-linear molecules: 3N - 6 IR fundamentals Dr. S. M. Condren

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