Rotational Isomeric State RIS Approximation

In the rotational isomeric state (RIS) approximation, each bond in the chain backbone is assumed to occur in any one of a small, discrete number of... 

Appendix 2E. Restricted Rotation with Symmetrical Barrier.99 Appendix 2F. Rotational Isomeric State (RIS) Approximation... 

A common way for calculating the chemical shift of different stereosequences is based on the Rotational Isomeric State (RIS) approximation (8). In this case the effect of the conformation on the chemical shift 8 of the magnetic carbon C is ascribed to changes in populations of rotamers differing only for the C-C(a)-C(P)-C(y) dihedral angle. It can be translated into the following equation. 

Rotational isomeric state (RIS) theory, developed by Flory [19], makes the approximation of describing each of these minima as a single conformational state of the molecule. It is a very general theory, able to cope with any proposed potential and any number of minima, and to translate these into bulk data such as radius of gyration. 

Because of the third assumption, these theories are called Rotational Isomeric State (RIS) models. Adopting these approximations, the partition function can be considerably simplified and the statistical mechanics of chain molecules can be mapped onto the well-known ID Potts model with K states. [20]... 

Muller et al. focused on polybead molecules in the united atom approximation as a test system these are chains formed by spherical methylene beads connected by rigid bonds of length 1.53 A. The angle between successive bonds of a chain is also fixed at 112°. The torsion angles around the chain backbone are restricted to three rotational isomeric states, the trans (t) and gauche states (g+ and g ). The three-fold torsional potential energy function introduced [142] in a study of butane was used to calculate the RIS correlation matrix. Second order interactions , reflected in the so-called pentane effect, which almost excludes the consecutive combination of g+g- states (and vice-versa) are taken into account. In analogy to the polyethylene molecule, a standard RIS-model [143] was used to account for the pentane effect. 

A very common approximation goes by the name of rotational isomeric state model (RIS). With such a model it is assumed that the molecular population is placed exclusively in a few energy minima, always according to the Boltzmann distribution. The conformations corresponding to the minima are called conformers, or rotational isomers, and are indicated by one or more letters (G, T) for butane three conformers are considered (G, T, G ), for pentane five (TT, G T, TG, G G, G G ). A more detailed examination of pentane reveals the existence of two further wells (fl, = 65 , 2 = 260° and 0, = 100°, 02 = 295°), sometimes indicated by G G and G G , respectively, close to the forbidden G G" conformation, but with a much tower energy (157, 158). 

RMPY/HTA reference molecular Percus Yevick/high temperature approximation RIS rotational isomeric state... 

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