Coupled oscillator mechanism

For the optical activity of achiral chromophores with a dissymmetric environment, two types of theoretical treatments have been proposed coupled oscillator treatment and one-electron treatment. The charge distribution of the magnetic dipole transition correlates Coulombically with an electric dipole induced in the substituents, and the colinear component of the induced dipole provides, with the zero-th order magnetic moment, a non-vanishing rotational strength. 

The coupled oscillator mechanism involves coupling between the transition moments of two adjacent chromophores these must have a spatial relationship in which the interacting moments are non-parallel. (If the moments are parallel, only the absorption spectrum is affected hyperchromism is shown if the chromophores are arranged in a head-to-tail mode, and hypochromism if they are stacked one over the other in the head-to-head mode 20). By knowing the optical activity, it is possible to deduce the relative configuration between the given chromophores, and vice versa. 

Let us consider the optical activity of calycanthine 2i 22) as an example (Fig. 8). The absolute configuration in calycanthine was determined by X-ray crystallographic-al analysis23. However, it should be emphasized that the X-ray data need to be 

Reconsidering the optical activity of calycanthine, we shall focus on two chromo-phores which maintain the pertinent distance and geometry. It is assumed that the electronic states of these chromophores do not mix with those of other chromo-phores. The linear combinations of the locally excited configurations were taken to be  

Suffix 0, a, and b are the ground state, and the singly excited states of chromophores (1) and (2). In Eq. (37), the plus and minus signed wave function + and correspond to A and B symmetries, respectively, assumed to be a C2v point symmetry for the group of the chromophores (1) and (2). 

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Optical activity arises from the coupling of given electric-allowed transitions with a chiral orientation (coupled oscillator mechanism or two-electron mechanism) or from the electric or magnetic moments of a transition being pertubed by a chiral static field (asymmetrically perturbed field mechanism or one-electron mechanism) in the given one molecule. A similar mechanism of the optical activity can be expected for molecular assemblies which are composed of chiral and achiral ones. This type of optical activity is called induced optical activity and depends on types of inter-molecular interaction modes. 

The electronic transitions of the bound chromophore are coupled to the transitions of the protein, e.g., aromatic amino acid side chains and/or peptide bonds by the coupled oscillator mechanism [68-70]. 

In contrast to the trans-disubstituted phenylcyclopropanes cis-disubstituted phenylcyclopropanes, such as 23 and 30, do not show any detectable CD signals a. This is reasonable, if the optical activity of the two lowest energy electronic bands of phenylcyclopropanes are generated essentially by the coupled-oscillator mechanism (exciton mechanism for the degenerate case, such as 19). In cis-phenylcyclopropanes the interacting transition moments will lie (approximately) in the same plane. Hence, in the coupled-oscillator mechanism there will be only a very small Cotton effect (which is zero, if... 

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