Screw-like molecules

By ab initio MO and density functional theoretical (DPT) calculations it has been shown that the branched isomers of the sulfanes are local minima on the particular potential energy hypersurface. In the case of disulfane the thiosulfoxide isomer H2S=S of Cg symmetry is by 138 kj mol less stable than the chain-like molecule of C2 symmetry at the QCISD(T)/6-31+G // MP2/6-31G level of theory at 0 K [49]. At the MP2/6-311G //MP2/6-3110 level the energy difference is 143 kJ mol" and the activation energy for the isomerization is 210 kJ mol at 0 K [50]. Somewhat smaller values (117/195 kJ mor ) have been calculated with the more elaborate CCSD(T)/ ANO-L method [50]. The high barrier of ca. 80 kJ mol" for the isomerization of the pyramidal H2S=S back to the screw-like disulfane structure means that the thiosulfoxide, once it has been formed, will not decompose in an unimolecular reaction at low temperature, e.g., in a matrix-isolation experiment. The transition state structure is characterized by a hydrogen atom bridging the two sulfur atoms. 

Since chiral nematic liquid crystals phases have a very similar structural morphology i.e. rod-like molecules with a rotating director), the method developed to describe chiral nematic liquid crystals can be applied to the case of a solid helicoidal film. This method examines the electromagnetic response of materials with screw-like rotating electrical axes. The use of... 

Cholesteryl benzoate belongs to a special type of nematics because the molecule is chiral. Chiral means that the rod-like molecules have a handedness like a screw, which is usually right-handed but could be left-handed. Chiral molecules in a nematic phase can impart a gentle rotation on their... 

Screw-like structures are found above all for molecules such as helicenes, 1,3-disubstituted allenes, 2,2 -disubstituted biphenyls, etc., displaying C2 symmetry. With the aid of the 4-point figures indicated in the formulae the absolute helicities (P or M) can straightforwardly be ascertained. The currently still customary descriptors aS (or Sa) and aP (or Pa) regrettably correspond only inversly to the much more generally applicable helicity symbols P and M. 

Table 6-1. C2(l molecular poinl group. The electronic stales of the flat T6 molecule are classified according lo the lwo-1 old screw axis (C2). inversion (/). and glide plane reflection (o ) symmetry operations. The A and lt excited slates transform like translations Oi along the molecular axes and are optically allowed. The Ag and Bg stales arc isoniorphous with the polarizability tensor components (u), being therefore one-photon forbidden and Iwo-pholon allowed.

Helical Chirality. Helicity is a special case of chirality in which molecules are shaped as a right- or left-handed spiral like a screw or spiral stairs. The configurations are designed M and P, respectively, according to the helical direction. Viewed from the top of the axis, a clockwise helix is defined as P, whereas a counterclockwise orientation is defined as M. Thus, the configuration of example 9 is defined as M. 

Consider the axes of symmetry in the crystal. There are fourfold inversion axes, twofold axes, and twofold screw axes. Now a molecule having the chemical structure 0=C(NH2)2 cannot have a fourfold inversion axis neither can it have a screw axis (since it is a finite molecule). Hence the molecules cannot lie on these crystal axes the two molecules must be related to each other by these axes. On the other hand, a molecule of this structure may well possess a twofold axis passing through the and O atoms consequently the twofold axes (A in Fig. 175) are likely sites for molecules. Furthermore, it is to be noted that each twofold axis stands at the intersection of two mutually perpendicular planes of symmetry—and these also are likely to be possessed by a molecule of urea (see Fig. 131). Further consideration shows that all other positions are impossible for instance, if we put a molecule at By it is inevitably repeated at BB", and B, this is out of the question,... 

The helical molecules are therefore like threaded bolts which have been screwed into the net plane by randomly varying amounts. In this case it is important to recall from (iv) and (v) that... 

Thus, to go back to the bombardier beetle and the human eye, the question is whether the numerous anatomical changes can be accounted for by many small mutations. The frustrating answer is that we can t tell. Both the bombardier beetle s defensive apparatus and the vertebrate eye contain so many molecular components (on the order of tens of thousands of different types of molecules) that listing them— and speculating on the mutations that might have produced them—is currently impossible. Too many of the nuts and bolts (and screws, motor parts, handlebars, and so on) are unaccounted for. For us to debate whether Darwinian evolution could produce such large structures is like nineteenth century scientists debating whether cells could arise spontaneously. Such debates are fruitless because not all the components are known. 

Another interesting group of chiral compounds results when molecules are forced to adopt a helical geometry. Like the turn of a screw, the turn of the helix can be either right-handed or left-handed. One example is the compound known as hexahelicene, which has six aromatic rings fused together. The molecule is forced to adopt a helical... 

Rotations of 60°, 90°, 120°, or 180° are the only ones allowed,2 corresponding to six-, four-, three-, and twofold rotations. In addition, screw axes can occur, where the molecule is rotated by the same angles - 60°, 90°, 120°, 180° - and translated by a fraction of one of the lattice vectors a, b, or c. These have symbols like 21 (a 180° rotation followed by a translation of 1/2 of a lattice vector) or 43 (a 90° rotation followed by a translation of 3/4 of a lattice vector). These symmetry operators, lined up through the entire crystal, are the crystallographic symmetry operators. 

The symmetry of the atomic arrangement within the crystal can be described by space group theory, that is, the theory of the various ways of arranging objects in three dimensions such that a continuation of the symmetry operations gives the next unit cell and so forth (24). For protein molecules, which are by nature asymmetric, the important symmetry operations are rotation axes and screw axes. An object is said to have an n-fold rotation axis if, when an object is rotated (360/n)0, it appears like the original. For isolated objects, by point group theory, n may have any value. On the other hand, if the object is in a crystal (with its regular... 

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