Rosenfeld optical activity

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 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 ... 

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. 

In order to make the connection with the usual discussion of optical rotation based on the Rosenfeld equation for a molecule49, one must express the exact states ip, of the chiral medium in terms of the states of the elementary excitations in the system, using the machinery of quantum field theory discussed in Sect. 2. Before considering this problem however it is instructive to consider first the role of the space-inversion operator P in optical activity. 

Rosenfeld (1928) has related to the electronic structure of any molecule by showing that it is a function of discrete electronic transitions and hence is related to the electronic absorption spectrum of the molecule. For regions far from the optically active absorption bands, the following equation may be derived from quantum mechanical perturbation theory. 

The relatively simple Rosenfeld equation (8.6) determines the relation between the structure of a molecule and its interaction with circularly polarized radiation. Different methods are used for the computation of R, including the direct calculation by ab initio methods from first principles. However, at least within a limited range of applications, simplified approaches can be used that make a priori assumptions about a decisive mechanism by which optical activity of a molecule originates. 

L. Rosenfeld, Z. Physik, 52, 161 (1928). Quantum-Mechanical Theory of the Natural Optical Activity of Liquids and Gases. 

The quantum mechanical expression for the average optical rotation of a molecule was first given by Rosenfeld (1928). In 1937 Kirkwood (1937) and Condon (1937) presented similar derivations. A quantum mechanical expression for the optical activity tensor... 

The quantities, e, m, r, and pi are the charge, mass, position, and momentum of the ith electron, Z/c. Af/, Ri, and P/, are the charge, mass, position, and momentum of the 7th nucleus, and c is the speed of light. The deceptively simple Rosenfeld relationship (2) has been difficult to put into practice, and de.spite a 20 year head start for CD spectroscopists, the first reliable determination of the absolute configuration of any substance was accomplished by X-ray diffraction in 1951, 100 years after Pasteur showed that optical activity has a molecular origin. In ECD, the transition is between electronic states, typically the ground state and an electronically excited state. The theoretical description of ECD therefore reduces to the task of evaluating these transition moments in a computationally viable manner. 

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