Skeletal rotations

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. 

Many applications of Kilpatrick and Pitzer s procedure for calculating thermodynamic properties of molecules with compound rotation have been reported. In all cases possible potential energy cross-terms between rotating tops have been neglected. Contributions from internal rotation of symmetric tops have been calculated using the appropriate tables." These tables have also been used in calculations for the internal rotation of asymmetric tops hindered by a simple -fold cosine potential. 3-Fold potential barriers have been assumed in calculations for the —OH rotations in propanol and 1-methylpropanol, the —SH rotations in propane-1-thiol, butane-2-thiol, 2-methylpropane-l-thiol, and 2-methylbutane-2-thiol, the C—S skeletal rotations in ethyl methyl sulphide, diethyl sulphide, isopropyl methyl sulphide, and t-butyl methyl sulphide, and the C—C skeletal rotations in 2,3-dimethylbutane, and 2-methylpropane-l-thiol. 2-Fold cosine potential barriers have been assumed in calculations in the S—S skeletal rotations in dimethyl disulphide and diethyl disulphide. ... 

The classical approximation described on p. 294 by equations (26), (27), and (28) has been used for calculating thermodynamic contributions for the C—C skeletal rotation in 2-methylbutane, and for the C—S skeletal rotation in diethyl disulphide, by using assumed restricting potentials. Contributions from the skeletal torsion in 2-methylbutane-2-thiol and... 

Molecular force field calculations frequently provide information useful in assessing the. overall conformational energy surface as a function of the skeletal rotational angles. Such calculations also provide very important information regarding the high energy conformations, which generally elude direct observation by conventional techniques. 

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). 

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