Circular Dichroism (CD)

Measures: Different absorption of RCP and LCP due to chirality.
Uses: Chirality.
Formula: $Δ A = \frac{A_{-} - A_{+}}{A_{-} + A_{+}}$
Selection Rules:
Excellent website for visualizing light waves and CD.
Wavelength: 300 - 190 nm.
Basis:
- Relies on refraction of light, not absorbance.
- Absorption changes the light amplitude, not the frequency specdef.
- Refraction changes the frequency, not the amplitude specdef.
- Circularly polarized light can rotate in two directions.
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  - Interaction
    - Linear (Alignment)
      - Circular (Chirality)
  - Refractive index
    - Linear Birefringence
      - Circular Birefringence
    - Linear Dichroism (LD)
      - Circular Dichroism (CD)
Linear Dichroism (LD)
- Many aligned (Anisotropy) materials are linearly dichromic (LD). Hence, LD cannot be done on solutions.
- When many dipole moments are aligned, we observe linear dichroism. The molecules absorb light along the dipole moment axis.
- $Δ A = A_{v} - A_{H}$ where H and V indicate vertical and horizontal absorptions.
- We are interested in seeing $Δ A$ as this is a measurable property and hence it needs to be non-zero, therefore Linear Dichroism (LD).
- We measure horizontally and vertically polarized light separately.
- Flow chemistry or highly organized crystals can give alignment enough for LD spectroscopy.
- A DNA molecule gives horizontal but not vertical absorbance since the moment is along the backbone.
- Materials with different H and V refractive indexes are Birefringent specdef.
Circular Dichroism (CD)
- Requirements: Differences in absorbance, chirality.
- The differential absorption between RCP and LCP light is measured.
- CD tells us whether we have chiral samples, and quantum chemistry can be used to give R or S.
- Here we measure right and left polarized absorption: $Δ A = A_{L} - A_{R}$ .
  Hence the Beer-Lambert Law $Δ A = (ϵ_{L} - ϵ_{R}) c l$ .
- We have opposite CD for R and S stereoisomers, and hence mirror image $Δ A$ plots in the form of a sine wave.
- Energy gaps are different for RH and LH energy transitions, and therefore we get shifting in absorbances for these.
- Chiral molecules also have different refractive indices for RHCP and LHCP. This results in optical activity.
- - Right: Two circularly polarized light waves of the same magnitude in an RCP and LCP mixture result in linearly polarized light.
  - Left: The two waves after passing through an absorbing medium with different magnitudes between the waves, hence resulting in ellipticity.
- We can report the degree of ellipticity as $\tan θ = \frac{E_{r} - E_{l}}{E_{l} + E_{r}}$ where E is the magnitude of the electric field vector (the light intensity).
- Quantum mechanical basis:
  - Method: