2
(viewed through a microscope)](https://image.slidesharecdn.com/chemistry445lecture7grouptheory-130312141920-phpapp02/85/Chemistry445lecture7-grouptheory-3-320.jpg)
![The actual structure of the [Cd(DPP)2]2+
complex cation:
N N
N N
Cd(II) DPP
cation
DPP ligand
G. M. Cockrell, R. D. Hancock, D. G. VanDerveer, G. Zhang, R. P. Thummel,
J. Am. Chem. Soc., 2008, 130, 1420.](https://image.slidesharecdn.com/chemistry445lecture7grouptheory-130312141920-phpapp02/85/Chemistry445lecture7-grouptheory-6-320.jpg)
![Importance of X-ray crystallography
N-U-O angle oxo (O2-) anion PDA ligand
= 63.8(2)o
uranium atom
U-O bond = 2.279(6) Å
Structure of [UO2(PDA)] determined by X-ray crystallography
Nolan E. Dean, R. D. Hancock, M Frisch, C. Cahill, Inorg. Chem., 2008 in the press.](https://image.slidesharecdn.com/chemistry445lecture7grouptheory-130312141920-phpapp02/85/Chemistry445lecture7-grouptheory-7-320.jpg)
![Unit cell of [UO2(PDA)]](https://image.slidesharecdn.com/chemistry445lecture7grouptheory-130312141920-phpapp02/85/Chemistry445lecture7-grouptheory-8-320.jpg)
Chemistry445lecture7 grouptheory
- 1. Group Theory and Symmetry. two-fold rotational axis water molecule
- 2. Molecular Structure: The most powerful idea in chemistry is the idea of the three- dimensional structures of molecules. Two techniques have been invaluable in this regard. One is NMR (Nuclear Magnetic Resonance), and the other is X-ray crystallography. X-ray crystallography has been intensively developed as a technique, which involves the ideas of symmetry of molecules. Understanding NMR also involves an understanding of symmetry. Group theory is also vital in understanding and predicting infra-red and Uv-visible (electronic) spectra. On the next two slides are structures of complexes of metal ions determined by X-ray crystallography. These are shown simply to illustrate the power of X-ray crystallography in determining molecular structure. Determining such structures relies heavily on a knowledge of symmetry and group theory.
- 3. Crystals of [Cd(DPP)2](ClO4)2 (viewed through a microscope)
- 4. X-ray diffractometer: Monochromatic X-ray source, e.g. Cu Kα X-rays
- 6. The actual structure of the [Cd(DPP)2]2+ complex cation: N N N N Cd(II) DPP cation DPP ligand G. M. Cockrell, R. D. Hancock, D. G. VanDerveer, G. Zhang, R. P. Thummel, J. Am. Chem. Soc., 2008, 130, 1420.
- 7. Importance of X-ray crystallography N-U-O angle oxo (O2-) anion PDA ligand = 63.8(2)o uranium atom U-O bond = 2.279(6) Å Structure of [UO2(PDA)] determined by X-ray crystallography Nolan E. Dean, R. D. Hancock, M Frisch, C. Cahill, Inorg. Chem., 2008 in the press.
- 8. Unit cell of [UO2(PDA)]
- 10. Facial symmetry
- 11. Invariance to transformation as an indicator of facial symmetry: Mirror image
- 13. a a
- 14. Transformations of the benzene molecule: The presence of a symmetry element is identified by the fact that we can carry out a symmetry operation without the molecule appearing to have changed. Thus, for the benzene molecule, rotation by 60 o about the six-fold rotation axis does not change its appearance: six-fold rotation axis a rotate by 60o a The rotation axis is a six-fold rotation axis because we can repeat the operation six times before we get back to the original orientation of the benzene molecule
- 16. C3 C3 or three-fold rotational axis of the ammonia molecule. If we rotate the ammonia molecule by 360/3 or 120º about this axis, its appearance is unchanged.
- 17. Rotational axes of BF3 principal axis (highest value of Cn) C3 C3 C2 C2 . three-fold axis three-fold axis two-fold axis two-fold axis viewed from viewed from viewed from viewed from above the side the side above Note: there are 3 C2 axes
- 19. Mirror planes (σ) of BF3: Mirror planes can contain the principal axis (σv) or be at right angles to it (σh). BF3 has one σh and three σv planes: (v = vertical, h = horizontal) σv σh mirror plane C3 mirror plane principal axis C3 principal axis σv mirror plane σh mirror plane contains the C axis is at right angles to the C axis
- 20. center of symmetry center of symmetry (Note: The center of symmetry is important in deciding whether orbitals are g or u (lecture 2.))
- 21. rotate by 360o/4 The S4 improper rotation axis here is also a C2 axis
- 23. Rotational axes and mirror planes of the water molecule: C2 σv C2 σv C2 principal axis mirror plane mirror plane The water molecule has only one rotational axis, its C2 axis, which is also its principal axis. It has two mirror planes that contain the principal axis, which are therefore σv planes. It has no σh mirror plane, and no center of symmetry.
- 24. Rotational axes and mirror planes of benzene C6 C2 principal axis C2 C2 C6 σh C2 σv σv C6 principal axis C6 principal axis
- 25. Rotational axes and mirror planes of boron trifluoride C3 C2 principal axis C2 C2 σh σv σv σh boron trifluoride has a C3 principal C3 axis and three C2 axes, a σh mirror plane principal axis three σv mirror planes, but no center of inversion