Rotational skeletal

Photoisomerization Photochemical process leading to an isomerization of the substrate, either by bond rotation, skeletal rearrangement, or atom- or group-transfer. 

The vector r joining the two ends of the chain takes different values resulting from rotations about the individual bonds. For chains with more than about 50 skeletal bonds, the probability W(r)dxdydz that one end of r is at the origin and the other end is in an infinitesimal volume dV — dxdydz is satisfactorily represented by the Gaussian function [31,32]... 

In the enumeration of chirality elements of flexible molecules all arrangements are taken into account which are permitted by the given constraints under the observation conditions. Here, one must always assume a rigid skeletal model and freely rotating ligandsF That arrangement for which the lowest number of chirality elements is found equal zero determines the number of chirality elements for the whole ensemble. 

The (I ,S)-nomenclature still reminds the user of the right and left handed helical pattern arising from Fresnel s 29> interpretation of optical activity. These patterns are characterized by the combination of a translational and a rotational direction. The Ta skeletal symmetry of tetracoordinate systems submits itself to the pictorial models not applicable to other configurational types. The CIP rules may as well be used to define a configurational nomenclature on the basis of the Fischer projection. If one specified that in such a projection of an (R)-... 

The A defined in Equation 5.30 is not to be confused with the Helmholtz free energy. Should the A frequencies be limited to the external hindered translations and rotations, vi g = vi g = 0, and this is an additional simplification. In some molecules, however, there are isotope sensitive low lying internal modes (often internal rotations or skeletal bends). In that cases both terms in Equation 5.30 contribute. 

There is a special and very important feature of the anticipated open nido twelve-vertex structures in Fig. 12 repetition of single Lipscomb dsd rearrangements (denoted by the two-headed arrows) monotonically allows the six skeletal atoms about the open face to rotate about the second tier of five skeletal atoms (two-tier dsd rotation). Each dsd rearrangement [85, 163) (valence bond tautomerism) recreates the same configuration and involves only the motion of two skeletal atoms (in the ball-and-stick representation) and would allow carbons, if located in different tiers, to migrate apart. Such wholesale valence bond tautomerism is known to accompany the presence of seven-coordinate BH groups, e.g., and CBjoHu 142,155). 

Principles of skeletal structure formation of Raney catalysts are discussed, first from the perspective of phase transformation by chemical leaching. Some ideas are then proposed for making new Raney catalysts. Rapid solidification and mechanical alloying (MA) are described as potential processes for preparing particulate precursors. A rotating-water-atomization (RWA) process developed by the author and co-workers is shown as an example of rapid solidification. 

The observed low Tg s of most polyphosphazenes are consistent with the low barrier to internal rotation predicted for them and indicate the potential these polymers have for elastomeric applications, Theoretical calculations, based on rotational isomeric models assuming localized it bonding, predict the lowest ( 100 cal per mol of repeating unit) known polymer barrier to rotation for the skeletal bonds of polydifluorophosphazene,... 

Identify all skeletal bonds around which rotation is possible under the chosen conditions (a variation in bond angles can also be taken as the basis for an RIS scheme). 

Collect the statistical weights into statistical weight matrices (of dimension Vj.j X v , where v,- is the number of rotational isomeric states of bond i), one per skeletal bond subject to conformational change, indexing rows and columns of the matrices with the RIS of the bond. The generic statistical weight matrix for bond i is termed U,-. 

Although the potentials affecting the rotation about a skeletal bond in a chain molecule such as PE usually depend only on rotations of immediately adjoining bonds, the interdependence of rotational states may be transmitted over greater distances. In the case of PE or of POM the effective range of correlation is only four or five bonds. This is established by calculating a priori probabilities for rotational states of a bond as a function of its location relative to the chain termini and of the total chain length. 

The internal rotations around the skeletal bonds of PE are hindered due to interaction between the neighboring hydrogens. Since second and higher orders of interactions are not negligible, the internal rotations are interdependent. The statistics of such interdependent rotations is developed and applied to obtain the configurational partition function and the mean-square end-to-end... 

Expressions for the optical anisotropy AT of Kuhn s random link (an equivalent to the stress-optical coefficient) of stereo-irregular and multirepeat polymers are derived on the basis of the additivity principle of bond polarizabilities and the RIS approximation for rotations about skeletal bonds. Expressions for the unperturbed mean-square end-to-end distance , which are required in the calculation of Ar, are also obtained. 

A method is developed for calculating even moments of the end-to-end distance r of polymeric chains, on the basis of the RIS approximation for rotations about skeletal bonds. Expressions are obtained in a form which is applicable in principle to arbitrary k, but practical applications are limited by a tremendous increase in the order of the matrices to be treated, with increasing k. An application is made to the PE chain by using the familiar three-state model. Approximate values of the distribution function Wn (r) of the end-to-end vector r, Wn (0), and , are calculated from these even moments. 

For POM, a matrix algorithm for the statistical mechanical treatment of an unperturbed -A-B-A-B- polymer chain with energy correlation between first-neighboring skeletal rotations is described. The results of the unperturbed dimensions are in satisfactory agreement with experimental data. In addition, if the same energy data are used, the results are rather close to those obtained by the RIS scheme usually adopted. The RIS scheme is shown to be also adequate for the calculation of the average intramolecular conformational energy, if the torsional oscillation about skeletal bonds is taken into account in the harmonic approximation. 

The conformational energies of the lower members of POM, 2,4-dioxapentane and 2,4,6-trioxaheptane are estimated by the empirical force field method. The gauche states of the Internal rotation around the skeletal C—0 bonds are successfully predicted to be of lower energies in both molecules. In order to calculate the unperturbed dimension and dipole moment of POM, RIS approximations are made by using the results obtained from the force field calculations on 2,4,6-trioxaheptane. Although these parameters are significantly different from those estimated earlier, they reproduce the observed values fairly well. 

Semiempirical potentials are used to compute conformational energies as function of rotations over the backbone bonds the results of these calculations indicate that skeletal C—0 bonds are always placed in trans conformation, whereas gauche states over C—C bonds have an energy of about 2 kJ mol-1 lower than their trans conformation. 

Conformational energies of meso and racemic diads of PS are computed as functions of skeletal bond rotations. Confinement of rotations of the phenyl groups to a small range within which they are nearly perpendicular to the plane defined by the two adjoining skeletal bonds is confirmed. Steric interactions involving the relatively large planar phenyl group virtually preclude"g" conformations. A simple, two-state RIS scheme is applicable with states at 170° and 70° for both meso and racemic dyads. 

Conformational energies as function of rotational angles over two consecutive skeletal bonds for both meso and racemic diads of poly(Af-vinyl-2-pyrrolidone) are computed. The results of these calculations are used to formulate a statistical model that was then employed to calculate the unperturbed dimensions of this polymer. The conformational energies are sensitive to the Coutombic interactions, which are governed by the dielectric constant of the solvent, and to the size of the solvent molecules. Consequently, the calculated values of the polymeric chain dimensions are strongly dependent on the nature of the solvent, as it was experimentally found before. 

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