Conceptual torsion

It is evident that 11, 12, and 13 can all be converted into their enantiomers by conceptual torsions about the bonds that link the starred atoms. The success of the operation does not depend on the number of ligands that are attached to these atoms, which constitute the terminal atoms of the lines of torsion (Fig. 3d, e, henceforth types d and e). Similarly, there is no place in this scheme for any restriction on dihedral angles a conceptual torsion can interconvert the stereoisomers of hexahelicene (8) or of dioxepin (7) (both type f, Fig. 3/) as readily as those of ordinary biphenyls (type d) with their perpendicular orientation of the rings. No idealization is required. 

The mutually dependent elements of 25 are a pherochiral double bond and a chiral center of steroisomerism. Instead, the isomerism could be viewed as the result of a conceptual torsion of the partially occupied line between C(2) and... 

Systematic searches exhaustively sample conformational space by sequentially incrementing the torsional angles of aU of the rotatable bonds in a given molecule. This conceptually simple approach is straightforward to implement, but scales exponentially with respect to the number of rotatable bonds. To control the exponential increase in the number of potential conformers obtained, systematic searches are usually combined with tree-based search techniques taken from computer science. Even the best implementations of systematic searches become impractical beyond several rotatable bonds (typically greater than 10). Stochastic searches are based on probabiHstic theories and are better suited to calculations... 

Because of the simple functions this model is too crude to be of practical use, and we must add a number of secondary terms they depend explicitly on valence, torsional, and out-of-plane angles where appropriate. Figure 2 shows the terms relevant to the work reported here. The designations primary and secondary are conceptually significant the secondary terms are necessary because the present formulations of the primary terms is not sufficently accurate. In cases where carboxyl, amido, imino and other groups occur, out-of-plane angles are usually included. 

Another approach that is conceptually similar is to make certain constants depend on bond order or bond hybridization. Thus, for instance, in the VALBOND force field, angle bending energies at metal atoms are computed from orbital properties of the metal-ligand bonds in the MM2 and MM3 force fields, stretching force constants, equilibrium bond lengths, and two-fold torsional terms depend on computed n bond orders between atoms. 

Ethane C2H8 — 2CH3. The models for the ethane molecule, C—C rupture complex, and H rupture complex are the molecule, complex 3, and complex 4, respectively, shown in Table I. For illustrative purposes and consistency with Sec. II, the 350 torsion model of ethane, rather than the internal rotation model, was used. The latter would be a better conceptual representation, but, in fact, for the relevant energies, to = 85 kcal. mole, there is little practical difference (cf. Sec. II-C,3). The calculated results which are obtained by combining the kt values, Figure 2, with the distribution function that is appropriate for the activation technique, Figure 8, are shown in Table XII. 

The calculation of G and for a number of geometries, such as peeling, double cantilever, double torsion, or blister test, can be found in textbooks. We will concentrate on the case of adherence of punches (and especially of a sphere) which is conceptually an important topic via which to understand the connection between adherence, mechanics of contact, and fracture mechanics, or, more simply, what is an area of contact. 

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