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Symmetry

Symmetry. Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology. Symmetry Effects. Simplifies the amount of work needed to solve a problem reduces it by a factor of 2, 3 or more. -. Symmetry Effects. Symmetric atoms in a molecule are energetically equivalent.

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Symmetry

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  1. Symmetry Edward A. Mottel Department of Chemistry Rose-Hulman Institute of Technology

  2. Symmetry Effects • Simplifies the amount of work needed to solve a problem • reduces it by a factor of 2, 3 or more.

  3. - Symmetry Effects Symmetric atoms in a molecule are energetically equivalent. Simplifies the appearance of spectra (the symmetric bonds absorb energy at identical energies): nmr, ir, etc. cyclopentadienide ion C5H5- Simplifies crystallography (fewer unique atoms have to be located). Simplifies chemistry (symmetric atoms in a molecule react the same way).

  4. NH3 HCCH H2O PtCl42- BF3 CH2Cl2 HCN C6H6 Elements of Symmetry • Look at diagrams or models of the following molecules • What is symmetric about each? • Are they symmetric in the same way? • Are some more symmetric than others?

  5. O H H NH3 HCCH H2O PtCl42- BF3 CH2Cl2 HCN C6H6 Rotational Symmetry Rotation about an axis produces two or more equivalent structures. How many equivalent positions are there? C2 What is the rotational order for each molecule?

  6. NH3 HCCH H2O PtCl42- BF3 CH2Cl2 HCN C6H6 Rotational Symmetry Rotation about an axis produces two or more equivalent structures. Can a molecule have more than one rotation axis?

  7. Rotational Symmetry Rotation about an axis produces two or more equivalent structures. C2 C2’ C6 Can a molecule have more than one rotation axis? HCCH C∞ ∞C2

  8. O H H NH3 HCCH H2O PtCl42- BF3 CH2Cl2 HCN C6H6 Reflection Symmetry A mirror plane reflects one half of a molecule into the other half of the molecule. sv How many mirror planes are there? sv’ How many mirror planes does each molecule have?

  9. sv sv’ Reflection Symmetry Are there different kinds of mirror planes? How many of each type of mirror plane are there?

  10. NH3 HCCH H2O PtCl42- BF3 CH2Cl2 HCN C6H6 Reflection Symmetry Are there different kinds of mirror planes? sh How many mirror planes are there? Which of these molecules have different types of mirror planes?

  11. atom above the plane atom below the plane atom on the plane Alternate Diagram of Atom Positions CH4 What is the order of the major rotation axis? Where are the mirror planes? Are there C2 axes?

  12. 2- Br Cl Cu Cl Br NH3 HCCH H2O PtCl42- BF3 CH2Cl2 HCN C6H6 Inversion Symmetry Every position in a molecule can pass through the center of the molecule to give an equivalent position. trans-dibromodichlorocuprate(II) ion i Which of these molecules has a center of inversion?

  13. atom above the plane atom below the plane atom on the plane Improper Rotation Symmetry Rotation about an n-fold (improper axis) followed by reflection through a perpendicular plane gives an equivalent structure. S4 CH4

  14. S8 C6H12 (chair) C2H6 (staggered) Improper Rotation Symmetry Rotation about an n-fold (improper axis) followed by reflection through a perpendicular plane gives an equivalent structure. What is the order of the improper rotation axis in each of these molecules?

  15. Combination of Symmetry Operations The combination of a two-fold rotation followed by a horizontal reflection is equivalent to what symmetry operation? C2 sh

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