# GROUP THEORY ( SYMMETRY)

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1. Done by Shobana.N.S 1 BY SHOBANA.N.S QUEEN MARY’S COLLEGE 2. 2 3. Symmetry is present in nature and in human culture 3 4. Understand what orbitals are used in…
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• 1. Done by Shobana.N.S 1 BY SHOBANA.N.S QUEEN MARY’S COLLEGE
• 2. 2
• 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. n Is equal to identity (E) Cn 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. n = E ( n= even number) Sn 2n = E ( n= odd number) Sn 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. element operation symbol symmetry plane reflection through plane σ inversion center inversion: every point x,y,z translated to -x,-y,-z i proper axis rotation about axis by 360/n degrees Cn improper axis 1. rotation by 360/n degrees 2. reflection through plane perpendicular to rotation axis Sn 16
• 17. 17
• 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. Ci 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 Bromochlorofluoromethane CHFBrCl
• 23. Rotation of the molecule to 180 degree. This point group contains only two symmetry operations: E the identity operation C2 a twofold symmetry axis Examples : water, chlorine trifluoride, hydrogen peroxide, formaldehyde 23 hydrazine
• 24. 24 (2R,3R)-tartaric acid D-mannitol
• 25. Rotation of the molecule to 120 degree. This point group contains only two symmetry operations: E the identity operation C3 a three fold symmetry axis Examples: ammonia, boron trifluoride, triphenyl phosphine 25
• 26. 26 9b H-Phenalene 3,7,11-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 Cn n-fold symmetry axis. nσv n reflection operation 27
• 28. This point group contains the following symmetry operations E the identity operation C2 2-fold symmetry axis. 2σv reflection operation 28
• 29. Examples: 1. Ozone 2. Thiophene 3. Furan 4. Pyridine 29 Sulphur dioxide (Z)-1,2-DICHLORO Formaldehyde ETHENE
• 30. 30 Phenanthrene m-Xylene p-dichloro benzene O-dichloro benzene
• 31. 31
• 32. 32 Cyclohexane (boat) Water
• 33. This point group contains the following symmetry operations E the identity operation C3 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 C4 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 Cn 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 C2 2-fold symmetry axis. σh reflection operation i inversion 40
• 41. 41 EXAMPLES trans-1,2-dichloroethylene Trans-1,3-butadiene C2H2F2 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 C3 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 Cn n-fold symmetry axis. nC2 2-fold symmetry axis. (perpendicular to Cn) 46
• 47. This point group contains the following symmetry operations E the identity operation C2 n-fold symmetry axis. 2C2 2-fold symmetry axis. 47 twistane
• 48. 48 This point group contains the following symmetry operations E the identity operation C3 3-fold symmetry axis. 3C2 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 Cn n-fold symmetry axis. nC2 2-fold symmetry axis. nσd 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 C2 n-fold symmetry axis. 2C2* 2-fold symmetry axis. 2σd dihedral plane 2S4 improper axis of symmetry 52
• 53. 53 allene (propa-1,2-diene) biphenyl
• 54. 54 1,3,5,7-COT
• 55. This point group contains the following symmetry operations E the identity operation C3 n-fold symmetry axis. 2C2 2-fold symmetry axis. 3σd dihedral plane 2S6 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 2C4 n-fold symmetry axis. 4C2* 2-fold symmetry axis. 4σd dihedral plane S8 improper axis of symmetry C2 2-fold symmetry axis. 58 Mn2(CO)10
• 59. This point group contains the following symmetry operations E the identity operation 4C5 n-fold symmetry axis. 5C2* 2-fold symmetry axis. 5σd dihedral plane S10 improper axis of symmetry i inversion 59
• 60. 60
• 61. This point group contains the following symmetry operations E the identity operation Cn n-fold symmetry axis. nC2 2-fold symmetry axis. σh horizontal plane nσv vertical plane Sn improper axis of symmetry 61
• 62. 62 This point group contains the following symmetry operations E the identity operation C2 n-fold symmetry axis. 2C2 2-fold symmetry axis. σh horizontal plane 2σv vertical plane S2 improper axis of symmetry
• 63. 63 M2F6 DIBORANE ETHENE
• 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 C3 3-fold symmetry axis. 3C2 2-fold symmetry axis. σh horizontal plane 2σv vertical plane 2S3 improper axis of symmetry
• 68. 68
• 69. 69 cyclopropane
• 70. 70 This point group contains the following symmetry operations E the identity operation C4 4-fold symmetry axis. 4C2 2-fold symmetry axis. σh horizontal plane 4σv vertical plane S4 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 C5 4-fold symmetry axis. 5C2 2-fold symmetry axis. σh horizontal plane 5σv vertical plane S5 improper axis of symmetry
• 74. 74
• 75. 75 This point group contains the following symmetry operations E the identity operation C6 6-fold symmetry axis. 6C2 2-fold symmetry axis. σh horizontal plane 6σv vertical plane S6 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. ∞ C2 2-fold symmetry axis. σh horizontal plane ∞ σv 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 4C3 3-fold symmetry axis. 3C2 2-fold symmetry axis. 6σd dihedral plane 3S4 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 3C4 4-fold symmetry axis. 3C2 2-fold symmetry axis. 3σh dihedral plane 3S4 improper axis of symmetry i inversion C3 3-fold symmetry axis S6 improper axis of symmetry 6C2 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 20C3 3-fold symmetry axis. 15C2 2-fold symmetry axis. 15σh horizontal plane 20S6 improper axis of symmetry i inversion 20C3 3-fold symmetry axis 12S10 improper axis of symmetry 12C5 5-fold symmetry axis. 12S10* improper axis of symmetry TOTAL : 120 elements
• 88. 88 dodecahedran fullerenes
• 89. 89

Aug 27, 2017

#### April 11th Saturday Scholars - Ancestral Computing for Sustainability by Cueponcaxochitl Dianna Moreno Sandoval PhD

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