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Understanding Symmetry Operations in Molecules - Essential Concepts & Applications

Discover the fundamentals of symmetry operations in molecules, including rotations, reflections, inversions, and more. Learn about symmetry elements, symmetry axes, and how to assign molecules to point groups. Delve into the intricacies of identifying symmetry in molecular configurations.

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Understanding Symmetry Operations in Molecules - Essential Concepts & Applications

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  1. Will stick to isolated, finite molecules (not crystals). SYMMETRY OPERATION Carry out some operation on a molecule (or other object) - e.g. rotation. If final configuration is INDISTINGUISHABLE from the initial one - then the operation is a SYMMETRY OPERATION for that object. N.B. “Indistinguishable” does not necessarily mean “identical”.

  2. e.g. for a square piece of card, rotate by 90º as shown below: Labels show final configuration is NOT identical to original. Further 90º rotations give other indistinguishable configurations - until after 4 (360º) the result is identical.

  3. SYMMETRY OPERATIONS Motions of molecule (rotations, reflections, inversions etc. - see below) which convert molecule into configuration indistinguishable from original. SYMMETRY ELEMENTS

  4. C3: Isle of Man Coat of Arms

  5. Where is the Isle of Man?

  6. C3 Picture by MC Escher

  7. When m = n we have a special case, which introduces a new type of symmetry operation.....

  8. MORE ROTATION AXES

  9. Some additional points about symmetry axes:

  10. Reflection

  11. Mirror Plane

  12. Greek letter ‘sigma’

  13. C2 σv σv’

  14. Best described in terms of cartesian axes:

  15. Centre of inversion

  16. Centre of inversion?

  17. Position of P given by x,y,z

  18. C2H6

  19. Summary of symmetry elements and operations:

  20. A collection of symmetry operations all of which pass through a single point A point group for a molecule is a quantitative measure of the symmetry of that molecule

  21. Assignment of molecules to point groups Is there a plane of symmetry? Step 1: Is there an axis of symmetry? N Y Molecule in point group Cs Y N Is there a horizontal plane of symmetry? Step 2: Are there C2 axes perpendicular to Cn? Is there a centre of symmetry? Y Molecule in point group Cj Y N Molecule in point group Cnh N N Y No symmetry except E: point group C1 Are there n vertical planes of symmetry? Step 3: There are nC2's perpendicular to Cn Is there a horizontal plane of symmetry? Y Y Molecule belongs to point group Dnh Molecule in point group Cnv N Are there n vertical planes of symmetry? Y Molecule in point group Dnd

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