Education

GROUP THEORY ( SYMMETRY)

Description
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…
Categories
Published
of 89
All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Share
Transcript
  • 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
  • We Need Your Support
    Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

    Thanks to everyone for your continued support.

    No, Thanks
    SAVE OUR EARTH

    We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

    More details...

    Sign Now!

    We are very appreciated for your Prompt Action!

    x