Fig. 2.9 Positive Cotton effect curve in the optical rotation dispersion (ORD) calculated by the Drude equation. Above 300 nm a positive ORD curve is given. By passing the critical wavelength Xc =295nm, the optical rotation changes sign and shows negative values! Below 290nm the dispersion is given as negative ORD plain curve. In the selected and calculated example, the compound specific constant A is arbitrarily chosen as A = 20 500degnmdm—^ A Cotton effect of a chiral analyte recorded by an ORD spectropolarimeter shows a typical tangential curve. For comparison with values for the specific rotation [«]d, one has to be aware of its X = 589.3 nm. As a consequence of the Cotton effect, the (+) and (—)-categorization of enantiomers requires a fixed wavelength
In order to determine the critical wavelength Xc and the compound specific constant A for a given chiral molecule, the Drude equation can be transformed into Eq. 2.5.
Plotted values for X2[a] versus [a] provide a linear relationship giving access to the center distance A and the inclination Xc. Typical values for Cotton effects with [a] = 0 degrees dm—1 are at Xc = 232 nm for the peptide chymotrypsin or Xc = 295 nm for 3-P-hydroxy-5-androstan-17-one.
In the literature on chiroptical properties, rotation dispersion curves are often expressed by giving the molecular rotation [O] as a function of wavelength. The molecular rotation [O] is directly proportional to the specific rotation [a] and defined in Eq. 2.6, where MW is the molecular weight of the optically active substance in g mol—1.
What about measuring the optical rotation dispersion of more complex molecules than an amino acid such as proteins? For biomolecules like proteins (enzymes) in their polymer form, the optical rotation dispersion is not only determined by the stereogenic centers of the monomers in the primary structure, but also by its helical chirality of the secondary structure. In proteins, the helical contribution to the
ORD signal is often not negligible8 and can therefore be used to gain information on the three-dimensional structure of folded proteins. In order to distinguish between the ORD contribution caused by the stereogenic centers of the monomers and the helical chirality, the Moffit-Young equation 2.7 was developed particularly for interpretation of ORD signals of proteins.
In this virial equation [M] designates the specific molar rotation. The a0-term of the Moffit-Young equation corresponds to the Drude equation 2.4. Values for b0 correlate with the helical character of the ORD signal; b0 varies between 0 and 1 or 0 and 100% and tells one directly the degree of "helicity" of the polymer in question. For the experimental determination of a0 and b0, the Moffit-Young equation is to be transformed into Eq. 2.8.
Plotting of the left side of this equation versus (A2 - AC)-1 results in a linear function with a center distance a0AC and an inclination of b0A£. Following this way, the helical term b0 can be determined by ORD measurements for a wide variety of helical analytes.
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