Isomeric state

In some systems, it may be possible to limit the sampled region of phase space by using restraint potentials, so that the overall conformation of a molecule remains unchanged. When different force constants for these restraint potentials are used, the free energy difference can be extrapolated to a system without restraint potentials. 

The existence for some molecules of many conformational states of similar potential energy presents an enormous challenge in free energy calculations. In principle, all isomeric states need to be sampled with their appropriate Boltzmann probability at every step in X. during the free energy calculation. For such systems, reliable total free energy differences may only be obtained from very long simulations. 

Because the free energy is a thermodynamic state function, an alternative solution to the problem of rotational isomeric states of similar potential energy can be achieved. - For a system a with Hamiltonian 3 , the fundamental thermodynamic state function in the canonical ensemble is the Helmholtz free energy. 

The integration in Eq. [67] is over the entire phase space, which can be divided into subspaces, 

Together, then subspaces must span the entire phase space, 

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Chain models capture the basic elements of the amphiphilic behaviour by retaining details of the molecular architecture. Ben-Shaul et aJ [ ] and others [ ] explored the organization of tlie hydrophobic portion in lipid micelles and bilayers by retaining the confonuational statistics of the hydrocarbon tail withm the RIS (rotational isomeric state) model [4, 5] while representing the hydrophilic/liydrophobic mterface merely by an... 

Sen S, Cohen J M, McCoy J D and Curro J G 1994 The structure of a rotational isomeric state alkane melt near a hard wall J Chem. Phys. 101 9010... 

Rehahn M, Mattice W L and Suter U W 1997 Rotational isomeric state models in macromolecular systems Adv. Polym. Sc/. 131/132... 

The rotational isomeric state (RIS) model assumes that conformational angles can take only certain values. It can be used to generate trial conformations, for which energies can be computed using molecular mechanics. This assumption is physically reasonable while allowing statistical averages to be computed easily. This model is used to derive simple analytic equations that predict polymer properties based on a few values, such as the preferred angle... 

RIS (rotational isomeric state) a polymer simulation technique... 

The conformational characteristics of PVF are the subject of several studies (53,65). The rotational isomeric state (RIS) model has been used to calculate mean square end-to-end distance, dipole moments, and conformational entropies. C-nmr chemical shifts are in agreement with these predictions (66). The stiffness parameter (5) has been calculated (67) using the relationship between chain stiffness and cross-sectional area (68). In comparison to polyethylene, PVF has greater chain stiffness which decreases melting entropy, ie, (AS ) = 8.58 J/(molK) [2.05 cal/(molK)] versus... 

Moller,M. Cross Polarization — Magie Angle Sample Spinning NMR Studies. With Respect to the Rotational Isomeric States of Saturated Chain Molecules. Vol. 66, pp. 59 — 80. 

With Respect to the Rotational Isomeric States of Saturated Chain Molecules... 

Rotational Isomeric States in Medium Size Cycloalkanes.67... 

The purpose of this article is to discuss conformational shift variations in some selected solid state spectra on the basis of discrete rotational isomeric states and to compare them with molecular packing effects. 

While the comparison of the OMTS and the (CH2)12 spectra helped to learn something about the kind of information solid state chemical shifts can provide, we can obtain much more detailed data about the correlation of chemical shifts and the rotational isomeric states from the spectra of larger cycloalkanes. Usually conformational shift variations are discussed by (i) the so called y-gauche effect and (ii) the vicinal gauche effect, Vg 15) ... 

The influence of the a-bond isomerism is in agreement with the slow exchange spectra of 2,3-dimethylbutane and 1,2-dimethycylohexane in solution 16,17). Taking into account the different isomeric states of the bonds in a- and P-position on both sides of the observed carbons the slow exchange spectra of CH2-chain molecules have to be explained by conformational variations in chain segments of five carbon atoms. 

Fig. 18. Staggered rotational isomeric states of the CH—CH bond of threodiisotactic poly(l,2-dimethyltetramethylene)...

Conformational shift effects could be discussed in terms of discrete rotational isomeric states. Mainly two effects could be derived empirically to explain the shift differences due to conformational isomerism they-gauche and the Vg effect. However the spectra also indicate that the y-gauche effect is not a quantity with a universal numerical value. Furthermore the spectra of the cycloalkanes show that the conformational effects do not obey simple rules of additivity. With concern to our present knowledge great care has to be taken for the interpretation of NMR-spectra on the base of conformational shift increments which were not determined for the specific molecular structures. 

A suitable approach to the equilibration of an amorphous polymer system at bulk density becomes much more likely when the fully atomistic model in continuous space is replaced by an equivalent coarse-grained model on a lattice with sufficient conformational flexibility. Different strategies, which seek results at different levels of detail, can be employed to create an appropriate coarse-grained model. Section 4 (Doruker, Mattice) describes an approach which attempts to retain a connection with the covalent bonds in the polymer. The rotational isomeric state (RIS) [35,36] model for the chain is mapped into... 

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. 

Rehahn M, Mattice WL, Suter UW (1997) Rotational isomeric state models in macromolecular systems. In Advances in Polymer Science, Springer, Berlin... 

Wiles, D. R. Search for the pj isomeric states in Tc101 and identification... 

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