Polarizability rotatory

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 additivity scheme for the optical rotatory power and the pair partitioning schemes for the polarizabilities and the susceptibilities are also correlated ... 

The majority of the procedures currently being used in the conformational analysis of solutes (e.g. infra-red absorption differences between conformers, optical rotatory dispersions, NMR proton shifts, etc.) are qualitative and based upon empirical observations and analogies. It is therefore claimed that the present applications of anisotropic polarizabilities, built as they are on the theoretical arguments of Lorentz, Lorenz, Langevin, Born, Gans, Debye, and others, have—where solutes are concerned—advantages both in their foundations and in the quantitatively expressible natures of the conclusions they can provide. 

We neglected the case where the tensor at would depend on the wave vector and could be non-symmetrical (rotatory power). Thus, there is an orthogonal system of axes for which the matrix representation of the polarizability is diagonal. 

This enantiomer would be dextro or levo as the rotational contributions of X and Y differ and would, of course, be zero if the two groups were identical. The term derives from the fact that the mol fraction of each conformer would be n = n = 0.5. Conformational rotatory powers, relative to Y = CH3, were assigned (Table 5) to give reasonable fits to the data for various 2-substituted alkanes (Table 6). The values in Table 5 decrease in accord with the square root of the atomic refractions of the atoms (a measure of polarizability). 

A wide variety of molecular properties can be accurately obtained with ADF. The time-dependent DFT implementation " yields UV/Vis spectra (singlet and triplet excitation energies, as well as oscillator strengths), frequency-dependent (hyper)polarizabilities (nonlinear optics), Raman intensities, and van der Waals dispersion coefficients. Rotatory strengths and optical rotatory dispersion (optical properties of chiral molecules ), as well as frequency-dependent dielectric functions for periodic structures, have been implemented as well. NMR chemical shifts and spin-spin couplingsESR (EPR) f-tensors, magnetic and electric hyperfme tensors are available, as well as more standard properties like IR frequencies and intensities, and multipole moments. Relativistic effects (ZORA and spin-orbit coupling) can be included for most properties. 

Linear Response (2nd rank tensor) Electric dipole polarizability, a, magnetic dipole susceptibihty, optical rotatory power, k, nuclear shielding tensor at... 

Relatively modest modifications are required to extend a static linear polarizability Hartree-Fock computer code to dynamic or frequency-depen-dent polarizabilities. And if the code already handles magnetic moment operators, then the conversion to optical rotatory dispersion (ORD) or circular dichroism (CD) is also straightforward. At the third derivative level, e.g., hyperpolarizabilities, modifications are more complicated. 

The quantity /3 may be looked upon as a sort of rotatory polarizability. It appears because the geometry of optically active molecules is such that that oscillating charge displacements cannot occur without the production of an accompanying magnetic moment. Like oc, /3 can also be interpreted in classical language. One says that /3 is composed of a sum of partial quantities / the /th such quantity,... 

Limitations in charge mobility can be of two kinds. Firstly, the charge may migrate to boundaries over which further transport is either restricted or totally inhibited. Under this category, the boimdary may delineate the mdecule as is the case for electronic polarizability, or extend further in for example the ion atmosphere of a polyelectroiyte in solution, or constitute a phase boundary semi- or impermeable to charge in a solid material. For the last two examples the phenomenon is termed interfacial or Maxwell-Wagner polarization. The second type of restricted mobility occurs when dipoles are present which can cause pcdarization by a redistribution of their inclinations relative to the field direction. Such orientation polarization need not involve complete rotatory diffusion of the dipole even a restricted rotation or libration can affect polarization by this mechanism. 

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