# Differences Of Circular Dichroism (CD) Fundamentals

CD is defined as the difference between absorptions of left (Al) and right (Ar) circularly polarized light beams,

CD=Al-Ar

For each absorption band, the CD of two enantiomers are always exactly opposite.

Theory.

For each electronic transition one can define an electric (µij≠0) and a magnetic (mij≠0) transition dipole. Both can lead to absorption of radiation, the intensity of which is directly related to the oscillator strength f, fij≈| µij |2+ | mij |2

In CD spectroscopy, in contrast to an electronic absorption (where electronic dipole >> magnetic dipole) spectroscopy, both transition dipole moments are important. Therefore, an integral of CD (Rij) band is proportional to the scalar product of 2 dipoles:

Rij≈ µij * mij (both should be vectors)

Rij is defined as rotational strength, which is opposite in sign for 2 chiral molecules. Integral of CD over the whole EM spectrum is zero.

Chromophore.

Chromophore is a molecular moiety, responsible for electronic transitions in UV or in the visible range. Chromophores can be classified in terms of chiral spheres. Intrinsically chiral

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If a molecule contains a chromophore of complex or not well understood nature, then 2 chromophores with absorbance shifted to the red are introduced. Chrom group (p.922, Fig. 9) of chromophores are suitable for -OH group derivatization and protonated Shiff bases are suitable for amino groups. Porphyrins possess a very intense sharp and narrow Soret band, therefore can be used as versatile chromohores, providing an unsurpassed exciton couplet amplitude of A=570 and allowing CD coupling over the large distance of 40-50 Å. In complex molecules with multiple chromophores, matrix method or computational methods can be