Optical Activity of Inorganic Complexes

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Optical Activity of Inorganic Complexes

• Chem 510
• Adam Daly
• 29-Oct-04

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Why this topic?

• Every organic chemistry textbook..
• Classical or Quantum phenomenon?
• Of all the natural phenomenon observed in
  nature, none has had so profound effect on
  chemical thought as that of natural optical
  rotatory power.1

1. Lieher, A.D. J.Phys. Chem. 1964, 40, 1965
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Outline

• Historical Look
• Introduction to Optical Activity
• Theory of Optical Activity
• Optical Activity and Group Theory
• Character Tables Hidden Treasures

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Optical Activity A historical note

• Early 1800s polarized light in quartz crystals
  by Arago, Biot
• Structural information of optically active
  tartaric acid by Pasteur 1846-1860.
• Electromagnetic Equations by Maxwell 1860.
• Initial paper of the Journal of the American
  Chemical Society (1879) A method for the
  detection of artificial or dextro-glucose in cane
  sugar and the exact determination of cane-sugar
  by the polariscope.

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History Cont.

• Quantum Mechanics. 1920
• Rosenfelds theory of rotational strength an
  exact theory of chromophores that are small
  relative to wavelength of light. But the math is
  tooooooo complicated!
• Much more but this is enough history. Refer to
  Charney, E. The molecular basis of optical
  activity, John Wiley and Sons Inc.1979 Ch 1.

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Electromagnetic Waves

• Linear polarized light contains two vectors
  perpendicular to axis of propagation.
• Oscillating Electric and Magnetic Fields
• Superposition of Both Right and Left circularly
  polarized light.

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Charney, E. The molecular basis of optical
activity, John Wiley and Sons Inc.1979
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Polarized Light
Lieher, A.D. J.Phys. Chem. 1964, 40, 665
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Polarized Light
Davis, J.C. Advanced Physical Chemistry, John
Wiley and Sons Inc.1965
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Optical Rotation Model (Classically)

• Angle of rotation is attributed to the difference
  in the indices of refraction of left and right
  circularly polarized light.
• Elliptization (Circular Dichroism) of the
  polarized light is attributed to the absorption
  (extinction coefficients) differences of left and
  right circularly polarized light.

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Optical Rotation
Lieher, A.D. J.Phys. Chem. 1964, 40, 665
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Circular Dichroism
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Classical Theory Cont.

• The index of refraction contains two terms
• The index of refraction in a transparent medium
  the rotation term .
• The absorption (non-transparent) term where the
  extinction coefficient differences appear the
  circular dichroism.
• The rotation term is labeled

The Beta term relates the response of the
molecule in the radiation field. Zero Beta, no
optical activity.
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Quantum Theory

• Beta The chiral response parameter.
• Rotational Strength is related to the electric
  transition moment and the magnetic transition
  moment by

Where m(a,b) is
Where rotational strength is the term of mm(a,b)
Rosenfeld
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What to take from this

• To have optical activity from Q.M. stand point
  the induced electric dipole (m) and the induced
  magnetic dipole (m) must have components that are
  parallel.
• So that the dot product is not zero.
• Where is this going.

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Group Theory and Quantum Mechanics Connection

• Symmetry
• The electronic transition dipole moment integral
  given by quantum mechanics is equal to
• To have a finite value this integral must be
  invariant in the space integrated ! Ie.. Must
  not be affected by the symmetry operations of the
  group.

Where A and B are states different energy
states Like 1A1g and 1T1g
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Group Theory Takes Over

• The implication m (transition dipole term)
  belongs to or contains one of the totally
  symmetric representations A.
• What about m?
• To have rotational strength be non-zero both term
  must belong to the same totally symmetric
  representation.

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Lets Look at Some Character Tables

• First Groups with inversions or improper
  rotations are not optically active.
• Second Groups with degenerate states
• (x,y) and (Rx and Ry) on the same line can be
  chiral with degeneracy removed.
• Third Chiral group characteristics
• (z and Rz in the same line gives transitions that
  are naturally active).

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Whats hot in this field?

• Predictive models based on ligands to give
  rotational power.
• Synthesis of chiral catalysts and use of optical
  activity/NMR for characterization.

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Conclusions

• Optical activity has both classical and quantum
  mechanical roots.
• Character tables give more info then first
  suspected!
• The foundation of inorganic/organic structure and
  light interaction with matter is conveyed in this
  theory.

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References

• Lieher, A.D. J.Phys. Chem. 1964, 40, 665
• Charney, E. The molecular basis of optical
  activity, John Wiley and Sons Inc.1979
• Jorge, F. Autschbach, J, Ziegler, T Inorg. Chem.
  2003, 42, 8902-8910 (On the origin of the optical
  activity in the d-d transition region of
  Tris-Didentate Co(III) and Rh(III) complexes.
• Huyeey, J.E., Keiter, E.A. and Keiter, R.L.
  Inorganic Chemistry, HarperCollins College
  Publishers, 4th Ed. 1993, pgs 62, 492-3.
• Davis, J.C. Advanced Physical Chemistry, John
  Wiley and Sons Inc.1965