Intrinsic rotational strength

The first term in eq. [21] is the contribution of the intrinsic rotational strengths if oscillators a and/or b are themselves chiral. The second term is the coupled oscillator contribution due to the intrinsic moments and the third term is the coupled oscillator contribution due to the geometric arrangement of the two electric dipole oscillators. The latter two contributions give rise to a conservative bisignate couplet in the observed spectrum, if the coupled modes are sufficiently separated in frequency such that the positive and negative contributions do not cancel. 

V mon is simply the sum of the intrinsic rotational strengths of the individual molecules, with the contribution of each subunit weighted by the square of the corresponding coefficient in Pb - This term, sometimes called the one-electron contribution, is independent of how the two molecules are arranged with respect to each other in the dimer, assuming that the intermolecular interactions do not affect the magnetic and electronic transition dipoles of the individual molecules. However, it could reflect perturbations of or by the electrostatic environment in the dimer. 

The rotational strength calculated for I is as large as that of a butadiene twisted by 20°. In II, with an out-of-plane methyl, R increases by a factor of about 2. This shows that the contributions to R of dissymmetric substituents of chiral cisoid dienes may be comparable to and even outweigh the contributions arising from the intrinsic dissymmetry of the chromophore. 

Dienes in quasi-s-fraws conformation are found only in cyclic structures where perfect planarity is hindered. The DR also holds valid for this kind of conformation, as demonstrated by the considerations of Section II.D.l.a and also confirmed by all the reported calculations. Indeed, contrary to what is sometimes found for cisoid systems, the rotational strength evaluated by many types of calculation is invariably found to follow the diene rule for transoid systems. However, very small skew angles are usually found in real molecules and this implies that the main contribution to the observed optical activity cannot come from the weak intrinsic distortion, but is more likely to stem from the dissymmetric perturbations, notably of the allylic axial substituents. 

In the skewed form, instead, the transition is allowed both electrically and magnetically, with parallel transition moments. The product in equation 1 is hence non-vanishing, implying that this transition has finite rotational strength. This observation leads to the conclusion that skewed 1,3-butadiene is an intrinsically dissymmetric chromophore. 

Chromophores which are asymmetric by nature are characterized by the absence of a center and plane of symmetry in the group of atoms participating in the optical transition. The rotational strength of these are usually larger when compared with chromophores that become optically active due to substitution. This is demonstrated in Mason and Schnepp s8 study of trans-cyclooctene, a-pinene and /1-pi none. They pointed out that the g (anisotropy factor, g = Ae/e) value of the major bands in trans -cyclooctene is relatively high as expected for an intrinsically asymmetric chromophore when compared with the other two olefins. 

For intrinsically chiral species that are inert enough to be resolved conventionally, the measurement of natural optical activity in crystals has the same advantages as single crystal absorption measurements. In addition, however, it also affords the opportunity to determine rotational strengths of species which do not exhibit optical activity in solution. There are two classes of such materials 1) intrinsically achiral chromophores which crystallize in enantiomorphous space groups, and 2) intrinsically chiral but labile chromophores which spontaneously resolve on crystallization. 

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