Molecular ellipticity

Figure 21. Elliptical molecular conformation of 179c from the X-ray structure of the 179c (acetone)(dichloromethane) complex. (Reprinted with permission from 96JCS(P2)2359, Copyright 1996, Royal Society of Chemistry.)...

A quite different means for the experimental determination of surface excess quantities is ellipsometry. The technique is discussed in Section IV-3D, and it is sufficient to note here that the method allows the calculation of the thickness of an adsorbed film from the ellipticity produced in light reflected from the film covered surface. If this thickness, t, is known, F may be calculated from the relationship F = t/V, where V is the molecular volume. This last may be estimated either from molecular models or from the bulk liquid density. 

Protein molecules extracted from Escherichia coli ribosomes were examined by viscosity, sedimentation, and diffusion experiments for characterization with respect to molecular weight, hydration, and ellipticity. These dataf are examined in this and the following problem. Use Fig. 9.4a to estimate the axial ratio of the molecules, assuming a solvation of 0.26 g water (g protein)"V At 20°C, [r ] = 27.7 cm g" and P2 = 1.36 for aqueous solutions of this polymer. 

The molecular ellipticity is analogous to specific rotation in that two enantiomers have exactly opposite values of 0 at every wavelength. Two enantiomers will thus show CD spectra having opposite signs. A compound with several absorption bands may show both... 

Figure 2. Schematic drawing of a control apparatus. A laser of frequency coi is focused by lens L into a cell containing a tripling medium such as Hg vapor. Mirrors Ml and M2 are mounted inside a phase tuning cell (not shown) containing a refractive medium such as H2. The folded mirror geometry produces a pair of elliptical astigmatic foci, one of which overlaps the molecular beam (MB) at a distance zm from the beam axis. (Reproduced with permission from Ref. 62, Copyright 2006 American Physical Society.)...

Figure 6.17 Contour map of p in the interatomic surface associated with the CC bond critical point in ethene. The plane of the plot is perpendicular to the molecular plane. The C and two H nuclei are projected onto the plane of the plot to indicate the orientation of the molecule. We see that electronic charge is preferentially accumulated in the direction perpendicular to the molecular plane, giving an elliptical shape to the electron density in this plane.

Comparison of the optical activity showed that the dendrimer 63 with branches of (S)-configuration has a specific rotation and a molecular ellipticity which clearly deviate from the expected values [88,90]. All other 2nd-generation dendrimers (even those with additional spacers between the branches and the core) have specific rotations that are comparable to those expected by simple addition of appropriate values for their building blocks. The deviation may therefore signal the presence of chiral conformational substructures in the 2nd-generation dendrimer 63. 

Diffusion and mass transfer effects cause the dimensions of the separated spots to increase in all directions as elution proceeds, in much the same way as concentration profiles become Gaussian in column separations (p. 86). Multiple path, molecular diffusion and mass transfer effects all contribute to spreading along the direction of flow but only the first two cause lateral spreading. Consequently, the initially circular spots become progressively elliptical in the direction of flow. Efficiency and resolution are thus impaired. Elution must be halted before the solvent front reaches the opposite edge of the plate as the distance it has moved must be measured in order to calculate the retardation factors (Rf values) of separated components (p. 86). 

Optical activity also manifests itself in small differences in the molar extinction coefficients el and er of an enantiomer toward the right and left circularly polarized light. The small differences in e are expressed by the term molecular ellipticity [9 J = 3300(el — r). As a result of the differences in molar extinction coefficients, a circularly polarized beam in one direction is absorbed more than the other. Molecular ellipticity is dependent on temperature, solvent, and wavelength. The wavelength dependence of ellipticity is called circular dichroism (CD). CD spectroscopy is a powerful method for studying the three-dimensional structures of optically active chiral compounds, for example, for studying their absolute configurations or preferred conformations.57... 

The wavelength dependence of specific rotation and/or molecular ellipticity is called the Cotton effect. The Cotton effect can provide a wealth of information on relative or absolute configurations. The sign of the Cotton effect reflects the stereochemistry of the environment of the chromophore. By comparing the Cotton effect of a compound of known absolute configuration with that of a structurally similar compound, it is possible to deduce the absolute configuration or conformation of the latter. 

The classical potential energy term is just a sum of the Coulomb interaction terms (Equation 2.1) that depend on the various inter-particle distances. The potential energy term in the quantum mechanical operator is exactly the same as in classical mechanics. The operator Hop has now been obtained in terms of second derivatives with respect to Cartesian coordinates and inter-particle distances. If one desires to use other coordinates (e.g., spherical polar coordinates, elliptical coordinates, etc.), a transformation presents no difficulties in principle. The solution of a differential equation, known as the Schrodinger equation, gives the energy levels Emoi of the molecular system... 

Related to the elliptic integral of the third kind are the Lame functions, which arise in the generalisation of spherical harmonics to confocal ellipsoidal coordinates. Applications of these in molecular electrostatics can be found... 

Fig. 51a. Circular dichroism spectra for hydrated lipid 27 (0.24 mM). b Temperature dependencies of [01 values for hydrated lipid 27(0.24 mM). The circles and triangles show the molecular ellipticity at 246 and 231 nm, respectively [367]...

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