Helical conductor model

The index of helicity can be used in an alternative formulation of the basic equation for the helical conductor model of optical activity (1) ... 

Fig. 3—15 show four-, five- and six-atom chains (A—C -2—B) in their non-planar staggered conformations (dihedral angles of 60° and 180°). The individual bond conformations are denoted P (positive), M (minus), consistent with the proposals of Cahn, Ingold and Prelog 15>, and T (trans), as shown in 4. Using the familiar properties of triangles and the tetrahedral bond angle (cos r = — 1/3) (see Ref. 12 for the derivation of the equation in Fig. 3) we have derived expressions for the subtended areas (A) as needed for use with the helical conductor model (Eq. (1)). It turns out that all of these expressions contain the term L... 

This equation leads to a reductio ad absurdum that may provide a significant refinement of the helical conductor model. It will be noted that as the step helices (ya = 180°) approach the absolutely planar zigzag chain structure (ya = /b = 180°) they acquire very large cross sections. The index of helieity approaches a constant value of about 0.385 but the expected residue rotations approach infinity. (See Table 12). This result is, at least intuitively, absurd. 

These considerations, thus, lay the groundwork for tests among several semi-empirical approaches to the estimation of optical rotation of bond systems regarded as helices. Should it be necessary to use Eq. (lb) rather than (la), then a sweeping reassessment of the use of the helical conductor model will be required. However that test turns out, a test between that model and the simple conformational dissymmetry model becomes possible on the basis of the material shown in Table 1. At this point it should be said that our calculations on twistane 16> support the helical conductor model but that the results obtained by Pino and his co-workers 17 18> on the chiroptical properties of isotactic polymers prepared from chiral a-olefins support the conformational dissymmetry model. [We are not able, at present anyhow, to account for their results with the helical conductor model]. 

An impressive example of the use of the helical conductor model of the optical... 

The helical conductor model is useful for the prediction of optical rotations and configurations of aliphatic helices which do not contain chromophoric skeletons, and for twisted chains of atoms. In studies of the chiroptical properties of isotactic... 

This expression is independent of molecular chain length and so is suitable for use with polymers of mixed molecular weight. The turn molecular rotation contribution can be obtained from either of the models for optical rotation we have presented 12-14), either as a sum of contributions from four-atom units or by use of helical conductor equation (Eq. 1) ... 

Fig. 30. a TEM image of a 30°-bent nanotube, b Molecular simulation model showing the change in helicity by 30° (from zigzag to armchair) - two different electronic properties (e.g. semiconductor and metallic conductor) are possible... 

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