1. Done by Shobana.N.S 1 BY SHOBANA.N.S QUEEN MARY’S COLLEGE

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3.  Symmetry is present in nature and in human culture 3

4.  Understand what orbitals are used in bonding.  Predict optical activity of a molecule.  Predict IR and Raman spectral activity 4

5.  A molecule or object is said to possess a particular operation if that operation when applied leaves the molecule unchanged. 5

6. There are 5 kinds of operations 1. Identity 2. n-Fold Rotations 3. Reflection 4. Inversion 5. Improper n-Fold Rotation 6

7. IDENTITY  E (Identity Operation) = no change in the object.  Needed for mathematical completeness.  Every molecule has at least this symmetry operation. 7

8.  It is equal to rotation of the object 360/n degree about an axis.  The symmetry element is line.  Principle axis = axis with the largest possible n value.  C n n Is equal to identity (E) 8

9.  Symmetry element is plane.  Linear object has infinite σ.  σv- plane including principle axis  σh- plane perpendicular to principle axis.  σd- plane bisecting the dihedral angle between two σv plane. 9

10.  (x,y,z) --> (-x,-y,-z).  Symmetry element : point  Symmetry operation : inversion through a point.  i n is equal to identity (E) 10

11.  It is also known as ROTATION-REFLECTION AXIS.  Rotation followed by reflection.  S n n = E ( n= even number)  S n 2n = E ( n= odd number) 11

12.  A symmetry element is a point of reference about which symmetry operations can take place  Symmetry elements can be 1. point 2. axis and 3. plane 12

13.  Symmetry element : point  Symmetry operation : inversion 1,3-trans-disubstituted cyclobutane 13

14.  Symmetry element : plane  Symmetry operation : reflection 14

15.  Symmetry element : line  Symmetry operation : rotation 15

16. elementoperationsymbol symmetry planereflection through planeσ inversion center inversion: every point x,y,z translated to -x,-y,-z i proper axis rotation about axis by 360/n degrees CnCn improper axis 1. rotation by 360/n degrees 2. reflection through plane perpendicular to rotation axis SnSn 16

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18.  The collection of symmetry elements present in a molecule forms a ‘group’, typically called a POINT GROUP.  The symmetry elements can combine only in a limited number of ways and these combinations are called the POINT GROUP. WHY IS IT CALLED A “POINT GROUP”??  Because all the symmetry elements (points, lines, and planes) will intersect at a single point. 18

19. 19

20.  C i has 2 symmetry operations : E the identity operation i point of inversion 20 C2H2F2Cl2

21.  It has two symmetry operations E – identity operation σ – reflection 21 CH2BrCl 1- bromo, 2-chloro ethene

22.  Only one symmetry operation (E)  Molecules in this group have no symmetry  This means no symmetrical operations possible. 22 CHFBrCl Bromochlorofluoromethane

23. Rotation of the molecule to 180 degree. This point group contains only two symmetry operations: E the identity operation C 2 a twofold symmetry axis Examples : water, chlorine trifluoride, hydrogen peroxide, formaldehyde 23 hydrazine

24. 24 (2R,3R)-tartaric acidD-mannitol

25. Rotation of the molecule to 120 degree. This point group contains only two symmetry operations: E the identity operation C 3 a three fold symmetry axis Examples: ammonia, boron trifluoride, triphenyl phosphine 25

26. 26 9b H-Phenalene3,7,11-trimethyl cyclo dodeca 1,5,9-triene 2,6,7-trimethyl-1-aza-bicyclo [2.2.2]octane

27.  This point group contains the following symmetry operations E the identity operation C n n-fold symmetry axis. nσv n reflection operation 27

28.  This point group contains the following symmetry operations E the identity operation C 2 2-fold symmetry axis. 2σv reflection operation 28

29.  Examples: 1. Ozone 2. Thiophene 3. Furan 4. Pyridine 29 Sulphur dioxide Formaldehyde (Z)-1,2-DICHLORO ETHENE

30. 30 m-Xylene Phenanthrene O-dichloro benzene p-dichloro benzene

31. 31

32. 32 Cyclohexane (boat) Water

33.  This point group contains the following symmetry operations E the identity operation C 3 3-fold symmetry axis. 3σv reflection operation 33

34.  Examples: 34 Ammonia POCl3 Trichloro methane Tert-butyl bromide

35.  This point group contains the following symmetry operations E the identity operation C 4 n-fold symmetry axis. 4σv n reflection operation 35

36. 36 EXAMPLES Xenon oxytetrafluoride Sulfur chloride pentafluoride Bromine pentafluoride Fluorine pentafluoride Calix[4]arene

37.  This point group contains the following symmetry operations E the identity operation C ∞ ∞ -fold symmetry axis. ∞ σv n reflection operation 37

38.  Linear Hetero nuclear Diatomic Molecule belongs to this category  These molecules don’t have centre of inversion. 38 Chloro ethyne

39.  This point group contains the following symmetry operations E the identity operation C n n-fold symmetry axis. σh n reflection operation NOTE : If n is even ‘i’ is present. 39

40.  This point group contains the following symmetry operations E the identity operation C 2 2-fold symmetry axis. σh reflection operation i inversion 40

41. 41 EXAMPLES trans-1,2-dichloroethylene Trans-1,3-butadiene C2H2F2C2H2F2 N2F2

42. 42 1,4-dibromo-2,5-dichloro-benzene(E)-1,2-dichloro ethene

43.  This point group contains the following symmetry operations E the identity operation C 3 3-fold symmetry axis. σh reflection operation S3 improper axis of symmetry 43

44. 44 Benzene-1,3,5-triol

45. 45

46.  This point group contains the following symmetry operations E the identity operation C n n-fold symmetry axis. nC 2 2-fold symmetry axis. (perpendicular to C n ) 46

47.  This point group contains the following symmetry operations E the identity operation C 2 n-fold symmetry axis. 2C 2 2-fold symmetry axis. 47 twistan e

48. 48  This point group contains the following symmetry operations E the identity operation C 3 3-fold symmetry axis. 3C 2 2-fold symmetry axis.

49. 49 Ru(en)3 Perchlorotriphenylamine

50. 50 Tris(oxalato)iron111 Molecular knot

51.  This point group contains the following symmetry operations E the identity operation C n n-fold symmetry axis. nC 2 2-fold symmetry axis. n σ d dihedral plane 51 NOTE : ‘i’ is present when n is odd and S2n coincident to C2 axis

52.  This point group contains the following symmetry operations E the identity operation C 2 n-fold symmetry axis. 2C 2* 2-fold symmetry axis. 2 σ d dihedral plane 2S 4 improper axis of symmetry 52

53. 53 allene (propa-1,2-diene)biphenyl

54. 54 COT1,3,5,7-

55.  This point group contains the following symmetry operations E the identity operation C 3 n-fold symmetry axis. 2C 2 2-fold symmetry axis. 3 σ d dihedral plane 2S 6 improper axis of symmetry 55

56. 56 Cyclohexane chair form

57. 57 Ethane staggered form

58.  This point group contains the following symmetry operations E the identity operation 2C 4 n-fold symmetry axis. 4C 2* 2-fold symmetry axis. 4 σ d dihedral plane S 8 improper axis of symmetry C 2 2-fold symmetry axis. 58 Mn2(CO)10

59.  This point group contains the following symmetry operations E the identity operation 4C 5 n-fold symmetry axis. 5C 2* 2-fold symmetry axis. 5σ d dihedral plane S 10 improper axis of symmetry i inversion 59

60. 60

61.  This point group contains the following symmetry operations E the identity operation C n n-fold symmetry axis. nC 2 2-fold symmetry axis. σ h horizontal plane nσ v vertical plane S n improper axis of symmetry 61

62. 62  This point group contains the following symmetry operations E the identity operation C 2 n-fold symmetry axis. 2C 2 2-fold symmetry axis. σ h horizontal plane 2σ v vertical plane S 2 improper axis of symmetry

63. 63 M2F6 ETHENE DIBORANE

64. 64

65. 65 1,4-DICHLOROBENZENE

66. 66 [2,2] PARACYCLOPHANE

67. 67  This point group contains the following symmetry operations E the identity operation C 3 3-fold symmetry axis. 3C 2 2-fold symmetry axis. σ h horizontal plane 2σ v vertical plane 2S 3 improper axis of symmetry

68. 68

69. 69 cyclopropane

70. 70  This point group contains the following symmetry operations E the identity operation C 4 4-fold symmetry axis. 4C 2 2-fold symmetry axis. σ h horizontal plane 4σ v vertical plane S 4 improper axis of symmetry

71. 71 Nickel tetracarbonyl

72. 72 [AlCl₄]−Xenon tetrafluoride

73. 73  This point group contains the following symmetry operations E the identity operation C 5 4-fold symmetry axis. 5C 2 2-fold symmetry axis. σ h horizontal plane 5σ v vertical plane S 5 improper axis of symmetry

74. 74

75. 75  This point group contains the following symmetry operations E the identity operation C 6 6-fold symmetry axis. 6C 2 2-fold symmetry axis. σ h horizontal plane 6σ v vertical plane S 6 improper axis of symmetry i inversion

76. 76

77. 77  This point group contains the following symmetry operations E the identity operation C ∞ 4-fold symmetry axis. ∞ C 2 2-fold symmetry axis. σ h horizontal plane ∞ σ v vertical plane S ∞ improper axis of symmetry i inversion

78. 78 POSSESS CENTER OF SYMMETRY

79. 79

80. 80  This point group contains the following symmetry operations E the identity operation 4C 3 3-fold symmetry axis. 3C 2 2-fold symmetry axis. 6σ d dihedral plane 3S 4 improper axis of symmetry Total: 24 elements

81. 81 METHANE

82. 82 NEOPENTANE

83. 83  This point group contains the following symmetry operations E the identity operation 3C 4 4-fold symmetry axis. 3C 2 2-fold symmetry axis. 3σ h dihedral plane 3S 4 improper axis of symmetry i inversion C 3 3-fold symmetry axis S 6 improper axis of symmetry 6 C 2 2-fold symmetry axis. 6σd dihedral plane TOTAL :48 elements

84. 84 Cr(CO)6 [PtCl6]2-

85. 85 PF6-CUBANE

86. 86 SF6

87. 87  This point group contains the following symmetry operations E the identity operation 20C 3 3-fold symmetry axis. 15C 2 2-fold symmetry axis. 15σh horizontal plane 20S6 improper axis of symmetry i inversion 20C 3 3-fold symmetry axis 12S10 improper axis of symmetry 12C 5 5-fold symmetry axis. 12S10* improper axis of symmetry TOTAL : 120 elements

88. 88 dodecahedran fullerenes

89. 89