Torsional rigidity, double

In this case, the lengthening of the N-H and C=0 bonds, and the shortening of the C—N bonds as a consequence of hydrogen-bond formation can be measured by careful X-ray or neutron diffraction analyses, as described in Chapter 5. This type of -cooperativity is especially important in the main-chain hydrogen bonding of proteins, where it increases the double-bond character and hence the torsional rigidity of the peptide C-N bond. 

The torsional rigidity of an epoxide (or episulfide or ethyleneimine) group and of a carbon-carbon double bond must have a definite effect on the shape of any ring to which the former are attached or in which the latter is incorporated. When these groupings are associated with a pyranoid ring, the latter must adopt a half-chair, a boat, or a skew conformation, and it has been calculated that, for cyclohexene, the half-chair is energetically more favored than the boat by 2.7 Kcal./mole. The conformation of... 

Bending and torsional rigidity of double helices 4.1.2.1 Elastic rod model 4.1.2.1.1 General relations... 

The torsional rigidity constant may also be estimated from data on the fluorescence depolarization of dye molecules bound to the double helix [80T1, 82M1, 83A1] and on ESR spectra [82H1]. 

Frank-Kamenetskii, M.D., Lukashin, A.V., Anshelevich, A.V., and Vologodskii, A.V. (1985) Torsional and bending rigidity of double helix from data on small DNA rings. J. Biomol. Struct. Dynam. 2, 1005-1012. 

In fact, the frequency ofthe torsional oscillation mode V4 is found to be more than double that ofthe ground state. The frequency ofthe torsional oscillation mode was reevaluated by Mukheijee et al [56], using a very accurate representation of the one-dimensional vibrational Hamiltonian of the non-rigid rotor in terms of a Fourier series [76-78], and other spectroscopic parameters calculated for the first time taking care of anharmonicity. A new assignment of the experimental spectrum was given. The results are displayed in Table 8. For reference purpose the vibrational frequencies of the ionic states are also listed... 

The torsional solutions are then determined variationally by using this potential (116), together with B constants (114) evaluated in the rigid rotor approximation, and by developing the solutions on the basis of 961 double products of trigonometric functions. 

Ethylene exhibits a non-steric barrier to rotation about the molecular axis. The conventional explanation ascribes this effect to the lateral tt overlap of parallel p orbitals with spin pairing. The triple bond in acetylene is conventionally defined in terms of one sp rr-bond and two rr-bonds at right angles to each other. Triple bonds should therefore be torsionally even more rigid than double bonds. The curious fact... 

The polypeptide backbone can only bend in a very restricted way. The peptide bond itself is a hybrid of two resonance structures, one of which has double bond character, so that the carboxyl and amide groups that form the bond must, therefore, remain planar (see Fig. 7.3.). As a consequence, the peptide backbone consists of a sequence of rigid planes formed by the peptide groups (see Fig. 7.3). However, rotation within certain allowed angles (torsion angles) can occur around the bond between the a-carbon and the a-amino group and around the bond between the a-carbon and the carbonyl group. This rotation is subject to steric constraints that maximize the... 

Notice that the double switch operation exists always when there are symmetry plane in the moving moities and the frame of the molecule [10]. These operations are illustrated in figure 2. With these definitions, the restricted Non-Rigid Group (r-NRG) for the torsion and wagging mode is a group of order twelve, isomorphic to the C v symmetry point group ... 

In this work we will not treat this most general problem, but we will instead consider a special case which forms a part of the general problem. This case is the — as chemists call it — rigidity of the double bond with respect to torsion. 

We should not that the result we will arrive at, namely the stability of the double bond with respect to torsion and the planar arrangement of the substituents, would also be obtained if Eu > Eg independent of the nature of the substituents. However, we would obtain neither the rigidity nor the planar arrangement when it would depend on the nature of the substituents whether Eu < Eg or Eu> Eg. 

Polymers with double bonds in the main chain, e.g. polydienes, show different stereostructures. Figure 1.6 shows the two stereoforms of 1,4-polybutadiene cis and trans. The double bond is rigid and allows no torsion, and the cis and trans forms are not transferable into each other. Polyisoprene is another well-known example natural rubber consists almost exclusively of the cis form whereas gutta-percha is composed of the trans form. Both polymers are synthesized by... 

---