The Optical Rotation Parameter

The usefulness of TDDFT for first-principles theory based computations of chiroptical properties will become obvious after a brief discussion of the basic molecular parameters that describe the response of a molecule to the presence of an electromagnetic (EM) field. Consider, initially, the optical rotation (OR). 

On a molecular level, describes the linear response of the electric (d) and magnetic (m) dipole moment of a single chiral molecule to the presence of time-dependent electric (E) and magnetic (B) fields. We refer the reader to the books by Kauzmann [32] and Barron [1] and the review by Condon [31] for derivations of the following equations for the field-induced dipole moments  

Terms of higher order in the field amplitudes or in the multipole expansion are indicated by. . . The other two tensors in (1) are the electric polarizability ax and the magnetizability The linear response tensors in (1) are molecular properties, amenable to ab initio computations, and the tensor elements are functions of the frequency m of the applied fields. Because of the time derivatives of the fields involved with the mixed electric-magnetic polarizabilities, chiroptical effects vanish as a goes to zero (however, f has a nonzero static limit). Away from resonances, the OR parameter is given by [32] 

Equation (2) is an example of a sum-over-states (SOS) expression of a molecular response property. It suggests an easy way of computing / , but in practice the SOS approach is rarely taken because of its very slow convergence, i.e., because of the need to compute many excited states wavefunctions. The summation goes over all excited states and also needs to include, in principle, the continuum of unbound states. As it will be shown below, there are more economic ways of computing [1 within approximate first-principles electronic structure methods. 

For a medium with a standard concentration of identical noninteracting chiral molecules, the molecular OR parameter [i can be directly converted to the observed specific rotation via 

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The helix-coil transition can be demonstrated by polarization of fluorescence techniques, and the results may be compared with spectroscopic measurements to correlate the change in the hydrodynamic properties of the molecule with the change of its conformational structure. It is clear that the hydrodynamic and conformational changes do not necessarily parallel one another. Ion adsorption, breaks in the helix, and changes in helical type can occur without being reflected in the optical rotation parameters. 

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