POINT GROUPS Molecular Symmetry Symmetry element Point GroupsLETS GO 2. Molecular SymmetryAll molecules can be described in terms of their symmetrySymmetry operation Reflection, rotation, or inversion Symmetry elements such as mirror, axes ofrotation, and inversion centers 3. There are two naming systems commonly used when describing symmetry elements:1. The Schoenflies notation used extensively by spectroscopists2. The Hermann-Mauguin or international notation preferred by crystallographersSymmetry elements Symmetry element Notation Hermann-Manguin Schnflies (crystallography) (spectroscopy)Point Symmetry Identity1 for 1-fold rotation C Rotation axes n Cn Mirror planes m h, v, d Centres of i inversion(centres of symmetry)Sn Axes of rotary inversion (improper rotation)Space symmetry Glide plane n, d, a, b, c - Screw axis21, 31, etc - 4.

Symmetry Elements Identitas (C E atau 1)1Rotation axes (Cnatau n)Centres of inversion (centre ofsymmetry (i atau )1inversion axes (axes of rotaryinversion)Mirror planes ( atau m) 5. Identity (C1 E or 1) Rotasi dengan sudut putar360 melalui sudut z sehinggamolekul kembali seperti posisisemula. Putaran seperti ini diberisimbol dengan C1 axis atau 1. Schoenflies: C1 Hermann-Mauguin: 1 for 1-fold rotation Operation: act of rotatingmolecule through 360 Element: axis of symmetry(i.e. The rotation axis). Rotation (Cn or n) Rotasi melalui sudut selain 360. Operation: act of rotation Element: rotation axis Symbol untuk symmetry element yang mana rotasinya adalah rotasi dari 360/n Schoenflies: Cn HermannMauguin: n.

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Molekul mempunyai n- fold axis dari symmetry. Two-fold rotation A Symmetrical Pattern = 360o/2 rotationto reproduce amotif in a 6symmetricalpattern 6 8. Two-fold rotation= 360o/2 rotation Motif to reproduce a motif in a6 symmetricalElement pattern= the symbol for a two-foldrotation 6 9. Two-fold rotation= 360o/2 rotation to reproduce a motif in a 6 first operatio n step symmetrical pattern= the symbol for a two-foldrotationsecond 6operation step 10. Three-fold rotation = 360o/3 rotationto reproduce amotif in asymmetricalpattern 11. Three-fold rotation = 360o/3 rotationto reproduce astep 1motif in asymmetricalpattern step 3step 2 12.

Said and done boyzone rare. Symmetry ElementsRotation 6 6666 6 6 61-fold 2-fold3-fold4-fold6-foldObjects with symmetry: a identity Zt9d 5-fold and > 6-fold rotations will not work in combination with translations in crystals (as we shall see later). Thus we will exclude them now. Inversion (i)inversion through acenter to reproducea motif in asymmetrical pattern Operation:inversionthrough this6point Element: point = symbol for an6 inversion center 15. Reflection ( or m)Reflection across a mirror plane reproducesa motif Mirror reflection through a plane. Operation: act of reflection Element: mirror plane = symbol for a mirror plane 17. Schoenflies notation: Horizontal mirror plane ( h): planeperpendicular to the principal rotationaxis Vertical mirror plane ( v): planeincludes principal rotation axisDiagonal mirror plane ( d): d includesthe principle rotation axis, but liesbetween C2 axes that are perpendicular tothe principle axishh v dd 18. Note inversion (i) and C2 are not equivalent 19.

Axes of rotary inversion (improper rotation Snor An improper rotation involves a combination of rotation and n)reflectionThe operation is a combination of rotation by 360/n (Cn) followed byreflection in a plane normal ( h) to the Sn axisMolecule does not need to have either a Cn or a h symmetry element 20. Combinations of symmetry elements are also possibleTo create a complete analysis of symmetry about a point inspace, we must try all possible combinations of thesesymmetry elementsIn the interest of clarity and ease of illustration, wecontinue to consider only 2-D examples 21. Try combining a 2-fold rotation axis with a mirror 22. Try combining a 2-fold rotation axis with a mirrorStep 1: reflect(could do either step first) 23. Try combining a 2-fold rotation axis with a mirrorStep 1: reflectStep 2: rotate (everything) 24. Try combining a 2-fold rotation axis with a mirror Step 1: reflect Step 2: rotate (everything)No!

A second mirror is required 25. Try combining a 2-fold rotation axis with a mirrorThe result is Point Group 2mm2mm indicates 2 mirrors 26. Now try combining a 4-fold rotation axis with a mirror 27. Now try combining a 4-fold rotation axis with a mirrorStep 1: reflect 28.

Now try combining a 4-fold rotation axis with a mirrorStep 1: reflectStep 2: rotate 1 29. Now try combining a 4-fold rotation axis with a mirrorStep 1: reflectStep 2: rotate 2 30. Now try combining a 4-fold rotation axis with a mirrorStep 1: reflectStep 2: rotate 3 31. Now try combining a 4-fold rotation axis with a mirrorAny other elements? Now try combining a 4-fold rotation axis with amirrorAny other elements?Yes, two more mirrorsPoint group name??4mm 33. 3-fold rotation axis with a mirror creates point group3m 34. 6-fold rotation axis with a mirror creates pointgroup 6mm 35.