Non-rigidity

Bunker P R and Howard B J 1983 Symmetries and Properties of Non-Rigid Molecules a Gomprehensive Survey (Studies In Physical and Theoretical Ghemistry 23) ed J Maruani and J Serre (Amsterdam Elsevier) p 29... 

Allows the interpretation of [UJ data for non-spherical, non-rigid molecules... 

Zannoni C 1985 An internal order parameter formalism for non-rigid molecules Nuclear Magnetic Resonance of Liquid Crystals ed J W Emsiey (Dordrecht Reidel)... 

For the selection of descriptors, GA simulated evolution of a population. Each individual of the population represents a subset of descriptors and is defined by a chromosome of binary values. The chromosome has as many genes as there are possible descriptors (92 for the aromatic group, 119 for non-rigid aliphatic,... 

Often, Hertz s work [27] is presented in a very simple form as the solution to the problem of a compliant spherical indentor against a rigid planar substrate. The assumption of the modeling make it clear that this solution is the same as the model of a rigid sphere pressed against a compliant planar substrate. In these cases, the contact radius a is related to the radius of the indentor R, the modulus E, and the Poisson s ratio v of the non-rigid material, and the compressive load P by... 

Flexible duct A non-rigid duct that can be bent, expanded, or compressed within set limits without fracturing its cloth, metallic, or plastic covering. 

Concept of " pseudorotation introduced by R. S. Berry to interpret the stereochemical non-rigidity of trigonal bipyramidal PF5 (and SF4, ClFi) the 5 F atoms are equivalent (1953) due to interconversion via a square pyramidal intermediate. 

BalKSO Balasubramanian, K. Graph theoretical characterization of NMR groups, non-rigid nuclear spin species and the construction of symmetry adapted NMR spin functions. J. Chem. Phys. 73 (1980) 3321-3337. 

The anionic pentafluorophenyls have square pyramidal structures but are evidently non-rigid in solution (19F NMR shows all ligands equivalent). The neutral adducts are also square pyramidal (apical C6F5, trans-L) [192],... 

Procedures are now available that allow for the presence of several solvent molecules around a solute molecule. This approach takes into account the effect of molecular interactions with the solvent on properties such as the enthalpy of formation and the shape adopted by a non-rigid molecule, such as a protein or a region of DNA. These studies are important for investigating the structures and reactions of biological molecules in their natural environment. 

The d5Tiamic stereochemistries of M(dtc)3 and [M(dtc)3] (M = Fe, Co, or Rh) complexes have been studied (315). The cobalt complex is non-rigid, but the mechanism of optical inversion could not be determined. The Rh complex is stereochemically rigid up to 200°. The optical inversion of (-l-)546 [Colpyr-dtcla] in chloroform has been studied, by loss of optical activity, by polarimetry (316). 

In recent times, the study of molecular non-rigidity has been characterized by new and important developments in both experimental and theoretical directions. From the theoretical point of view, the pioneer work of Longuet-Higgins initiated numerous further studies The aim of this work was to extend the concept of symmetry to non-rigid molecules undergoing certain internal movements, the so-called feasible transformations. Some recent discussion of these problems may be found in Refs. for example. 

Non-rigidity has important consequences for the rotation and vibration spectra. Extensive experimental investigations exist in this domain they are based on the elaboration of model hamiltonians to describe the external motions. Recently, non-rigid molecule effects on the rovi-bronic levels of PF5 have been examined , so leading to the prediction of the spectroscopic consequences of Berry processes. 

The pentacoordinate molecules of trigonal bipyramidal form, like PF5, are a very nice example for the study of the formal properties of stereoisomerizations. They are characterized by an appreciable nonrigidity and they permit the description of kinetics among a reasonable number of isomers, at least in particular cases (see below). Therefore the physical and chemical properties of these molecules have been thoroughly investigated in relation to stereoisomerization. Recent reviews may be found in the literature on some aspects of this problem. Mislow has described the role of Berry pseudorotation on nucleophilic addition-elimination reactions and Muetterties has reviewed the stereochemical consequences of non-rigidity, especially for five- and six-atom families as far as their nmr spectra are concerned. 

More concretely, the aim of our investigation is to examine, from a theoretical point of view, the relation between the non-rigidity of pentacoordinate molecules and the characteristics of the temporal evolution of systems of such molecules towards chemical equilibrium. We also want to indicate the type of experimental information needed concerning the time evolution of these systems, in order to sharpen our ideas on the feasibility of the internal movements. We here give an account of the main aspects of our attempt and try to present it in a unified and synthesizing fashion. 

The most significant outcome of om study is that a qualitative understanding ofvibrational averaging effects is possible along the line of reasoning developed above. This opens the opportunity for a more dynamically based analysis of EPR parameters for large non rigid radicals. 

In Science, every concept, question, conclusion, experimental result, method, theory or relationship is always open to reexamination. Molecules do exist Nevertheless, there are serious questions about precise definition. Some of these questions lie at the foundations of modem physics, and some involve states of aggregation or extreme conditions such as intense radiation fields or the region of the continuum. There are some molecular properties that are definable only within limits, for example, the geometrical stmcture of non-rigid molecules, properties consistent with the uncertainty principle, or those limited by the negleet of quantum-field, relativistic or other effects. And there are properties which depend specifically on a state of aggregation, such as superconductivity, ferroelectric (and anti), ferromagnetic (and anti), superfluidity, excitons. polarons, etc. Thus, any molecular definition may need to be extended in a more complex situation. 

It is possible that the complexes benzene- -HX can be described in a similar way, but in the absence of any observed non-rigid-rotor behaviour or a vibrational satellite spectrum, it is not possible to distinguish between a strictly C6v equilibrium geometry and one of the type observed for benzene- ClF. In either case, the vibrational wavefunctions will have C6v symmetry, however. 

In another reaction dendritic pyridine derivatives such as 82 or 83 were tested as co-catalysts for enantioselective cyclopropanation of styrene with ethyl diazoacetate [102]. Using catalyst 82, enantiomer ratios of up to 55 45 were obtained. However, with catalyst 83 bearing larger branches yields and selectivities did not increase. The relatively low selectivities were rationalized by the presence of a large number of different conformations that this non-rigid system may adopt. 

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