Induced dipole moment optical activity

The interaction of light with a molecule can be described by the influence of its eleetric field on the electron density. The eleetric field E acting on the molecule (or material) induces a distortion of the electron density, with (induced) dipole moment / ind (or polarization P on the maeroscopic level). For weak electric fields the magnitude of this induced moment (polarization) can be expected to be linear with the amplitude of the electric field. This linear proportionality suffiees to explain the linear optical properties, e.g., refraction and optical activity. Yet, when the electric... 

Macromolecules are constituted by a number of small monomeric units that are often considered as independent molecules. Their optical activity should thus depend on the configuration, on the conformation and on the chemical reactivity of these monomeric units. However the situation is complicated by a further factor shown at first for biopolymers and then considered of importance for all polymers, that is to say by the molecular conformation. For highly stereoregular biological molecules the existence of sequences in which the chromophores are distributed in an ordered array in space is revealed by a coupling of the induced dipole moments. This excitonic-type coupling is able to provoke modifications in the COTTON effects that depend on the spatial disposition of the chromophores [19]. In the case of poly-a-amino-acids in the a-helix form one can observe a splitting of the n-n COTTON effect of the C= O of the peptide in random coil into two COTTON effects and — of opposite... 

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. 

Equation 7 shows that in cyclopropanes helix optical activity is not only induced by the groups polarizabilities, but to a large extent also by the groups polarities (4 a, is a rough measure for the group dipole moments). 

Thus the polarizability tensor of the molecule is written as a sum of local atomic polarizabilities, each modified through dipolar interactions with the electric dipole moments on all the other atoms induced by the electric vector of the incident light wave. Similarly for the local atomic polarizabilities appearing in the origin-dependent parts of the optical activity tensors. But unlike the bond polarizability development, no allowance can be made for intrinsic local optical activity tensors Gj ap and Aj since these now pertain to spherical atoms. We refer to the original articles for the explicit Raman intensity and optical activity expressions generated by the atom dipole interaction theory. 

In the ligand polarization mechanism for optical activity, the potential of the electric hexadecapole component, Hxy(x>-y>), produces a determinate correlation of the induced electric dipole moment in each ligand group which does not lie in an octahedral symmetry plane of the [Co Ng] chromophore (Fig. 8). The resultant first-order electric dipole transition moment has a non-vanishing component collinear with the zero-order magnetic moment of the dxy dxj yj transition in chiral complexes, and the scalar product of these two moments affords the z-component of the rotational strength, RJg, of the Aj -> Ti octahedral excitation. 

Indeed, around 1980, first experimental results on atomic parity violation have been reported, in particular measurements of the optical activity of bismuth, thallium and lead vapours as well as measurements of an induced electric dipole (El) amplitude to a highly forbidden magnetic dipole transition (Ml) in caesium. These experiments have nowadays reached very high resolution so that even effects from the nuclear anapole moment, which results from weak interactions within the nucleus, have been observed in caesium. The electronic structure calculations for caesium are progressing to a sub-percent accuracy for atomic parity violating effects and the reader is referred to chapter 9 of the first part of this book [12]. 

Figure 2 Cartoon illustrating the photon-induced transitions in a molecule. (A) Electronic absorption from ground to excited state is expressed as shown, where is the electric dipole moment operator (B) magnetic absorption and the mathematical expression, where is the magnetic dipole moment operator and (C) interaction of electronic and magnetic absorption, yielding optical activity.

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