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From my understanding of Kramer's Kronig relations applied to chirality: optical rotation dispersion should be correlated to circular dichroism.

Why is it then that many molecules have an optical rotation at the sodium D-line (585 nm), but they have no measurable circular dichroic effect at the same wavelength or even within 100 nm.

If a molecule is optically active at one wavelength, this should be apparent in both the circular dichroism and optical rotation of the molecule, right?

Any help would be much appreciated. Additional resources other than Barron's Molecular Light Scattering and Optical Activity would be great. Thanks in advance!

I've added some photos. These photos are from Laurence Barron's book titled 'Molecular Light Scattering and Optical Activity.' While these are simple rough sketches, they might be the source of my misunderstanding. enter image description here enter image description here

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    $\begingroup$ It is easy to measure the optical rotation of a transparent substance, the path can be made long. But it is difficult to measure small dichroism in the attenuation length of absorption bands in the ultraviolet. $\endgroup$
    – user137289
    Mar 13, 2018 at 21:30
  • $\begingroup$ Polarimetry with it's typical (10cm) path lengths is more common for chemicals where there is an abundance. Today's circular dichroism (CD) tools are really built to measure protein structures, of which the amount of material is often scarce, so the path length is smaller. That being said I've experimentally measured some CD for molecules at the sodium D line, under similar polarimetry conditions, but retrieved no CD signal. (Pathlength reduced by 10x.) $\endgroup$
    – Sean
    Mar 13, 2018 at 23:32
  • $\begingroup$ But the relevant electronic transitions will be at higher photon energies. It is the UV resonances that are the cause of the refractive index of dielectrics. And of their off-axis matrix elements when the molecule is chiral. $\endgroup$
    – user137289
    Mar 13, 2018 at 23:40

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The Kramers-Kronig relations link the real and imaginary parts of the refractive index separately for left-handed circularly polarized light and for right-handed circularly polarized light. (There is no KK-relation between CD and optical activity.)

The imaginary part is often due to electronic transitions in the UV. In chiral molecules there is a small difference for left- and right-handed CP light. This is the circular dichroism. It is difficult to measure, because the differences are small.

Because of Kramers-Kronig, this then also means differences in the real part of the refractive index in the visible part of the spectrum. This is easy to measure, because the difference $n_+ \! - n_-$ can be measured directly as the optical activity. Rotation of the plane of polarization of linearly polarized light is caused by the phase shift between the left- and right-handed CP components of the linearly polarized beam.

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  • $\begingroup$ Hi Pieter, There is a K-K relation between optical activity and circular dichroism. pubs.acs.org/doi/pdf/10.1021/jp0524328 $\endgroup$
    – Sean
    Mar 15, 2018 at 20:45
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    $\begingroup$ Unfortunately, I can't agree. K-K relates the imaginary part to the real part in normal circumstances. Because CD measures absorption, this is related to the imaginary part of the refractive index. In a similar fashion, ORD is related to the real part of the refractive index. Because these properties are related to these different components of the index, they are too related by the K-K relations. $\endgroup$
    – Sean
    Mar 15, 2018 at 20:51
  • $\begingroup$ @Sean It may be true to good approximation in such cases. But I know that it is not true in the case of magnetic circular dichroism in the x-ray region, where dichroism can be as high as 30 or 50 % at some absorption edges. $\endgroup$
    – user137289
    Mar 15, 2018 at 21:46

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