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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

Outline

- Historical Look…
- Introduction to Optical Activity
- Theory of Optical Activity
- Optical Activity and Group Theory
- Character Tables – Hidden Treasures

Optical Activity – A historical note

- Early 1800’s 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”.

History Cont.

- Quantum Mechanics…. 1920
- Rosenfeld’s 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.

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.

Charney, E. The molecular basis of optical activity,

John Wiley and Sons Inc.1979

Polarized Light

Lieher, A.D. J.Phys. Chem. 1964, 40, 665

Polarized Light

Davis, J.C. Advanced Physical Chemistry, John Wiley and Sons Inc.1965

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.

Optical Rotation

Lieher, A.D. J.Phys. Chem. 1964, 40, 665

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.

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 m*m(a,b) Rosenfeld

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…….

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

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.

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).

What’s 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.

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.

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

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