Theory of optical activity

In 1892, Biot confirmed that the colors on propagating white light parallel to the optical axis of a quartz crystal placed between crossed polarizers arise from two distinct effects, the rotation of the plane of polarization of monochromatic light and dispersion of the rotation with respect to wavelength. Biot s discovery was extended to the optical rotation of natural products in solution or in the liquid phase, and this is of chemical significance, as it indicates that rotation is a molecular effect. 

Pasteur 15) had arrived at the general stereochemical criterion for a chiral or dissymmetric molecular structure. Thus, the specific rotations of the two sets of sodium ammonium tartrate crystals in solution, isolated from the racemic mixture by hand-picking, were equal in magnitude and opposite in sign, from which Pasteur inferred that enantiomorphism of the dextro- and laevorotatory crystals is reproduced in the microscopic stereochemistry of the (+)- and (—)-tartaric acid molecules. The term dissymmetry or chirality is used when there is no superimposability between the two enantiomers, as seen in Sect. 2.1. 

On the other hand, the stereochemical concept in inorganic chemistry was establish- 

The first attempt to formulate a theory of optical rotation in terms of the general equations of wave motion was made by MacCullagh17). His theory was extensively developed on the basis of Maxwell s electromagnetic theory. Kuhn 18) showed that the molecular parameters of optical rotation were elucidated in terms of molecular polarizability (J connecting the electric moment p of the molecule, the time-derivative of the magnetic radiation field //, and the magnetic moment m with the time-derivative of the electric radiation field E as follows  

The quantum-mechanical treatment of optical activity was initiated by Rosenfeld 19) who showed that rotatory polarizability (3 of Eqs. (33) and (34) is represented by  

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A particularly useful probe of remote-substituent influences is provided by optical rotatory dispersion (ORD),106 the frequency-dependent optical activity of chiral molecules. The quantum-mechanical theory of optical activity, as developed by Rosenfeld,107 establishes that the rotatory strength R0k ol a o —> k spectroscopic transition is proportional to the scalar product of electric dipole (/lei) and magnetic dipole (m,rag) transition amplitudes,... 

The theory of optical activity would be understood in terms of symmetry considerations at the first stage. The elements of symmetry are the geometric elements in relation to which the symmetry operations are carried out, and are classified in the following ... 

Caldwell, D. J., Eyring, H. "The Theory of Optical Activity . Wiley-Interscience, New York (1971)... 

The structure of this contribution is as follows. After a brief summary of the theory of optical activity, with particular emphasis on the computational challenges induced by the presence of the magnetic dipole operator, we will focus on theoretical studies of solvent effects on these properties, which to a large extent has been done using various polarizable dielectric continuum models. Our purpose is not to give an exhaustive review of all theoretical studies of solvent effects on natural optical activity but rather to focus on a few representative studies in order to illustrate the importance of the solvent effects and the accuracy that can be expected from different theoretical methods. 

Molecular Theory of Optical Activity Optical Rotation... 

Sect. 2), and must be disposed of before a theory of optical activity can be considered. It will appear that exactly analogous discussions apply to other areas of physics - nuclei, elementary particles and so on. I propose to reinterpret the classical building-blocks of matter as the quasi-particles or elementary excitations of the quantum (field) theory of matter. 

The next section (Sect. 2) is devoted to a lengthy discussion of the molecular hypothesis from the point of view of quantum field theory, and this provides the basis for the subsequent discussion of optical activity. Having used linear response theory to establish the equations for optical activity (Sect. 3), we pause to discuss the properties of the wavefunctions of optically active isomers in relation to the space inversion operator (Sect. 4), before indicating how the general optical activity equations can be related to the usual Rosenfeld equation for the optical rotation in a chiral molecule. Finally (Sect. 5), there are critical remarks about what can currently be said in the microscopic quantum-mechanical theory of optical activity based on some approximate models of the field theory. 

E.g., Caldwell DJ, Eyring H. The Theory of Optical Activity. New York Wiley-Interscience, 1971, Chap. 6. 

In testing theories of optical activity and their relationship to intimate spectroscopic levels in molecules, a good deal of emphasis has been given to work on octahedral transition metal complexes, notably those of the... 

Caldwell DJ, Eyring H (1971) The theory of optical activity. Wiley, New York London Sydney Toronto... 

Moffitt (9) introduced the first quantum mechanical theory of optical activity in chiral transition metal complexes. He... 

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