Rigid systems

Ciccotti G, Ferrario M and Ryckaert J-P 1982 Molecular dynamics of rigid systems in cartesian coordinates. A general formulation Mol. Phys. 47 1253-64... 

Beratan D N and Hopfield J J 1984 Calculation of electron tunneling matrix elements in rigid systems mixed valence dithiaspirocyclobutane molecules J. Am. Chem. Soc. 106 1584-94... 

Naturally occurring molecular ensembles such as proteins from photosyntlietic systems (plants, algae, photosyntlietic bacteria, etc) are usually relatively rigid systems tliat contain various cliromophores and hold tliem at fixed positions and orientations relative to each otlier. That is why, despite tire numerous energy jumps between tire cliromophores, tlie resulting emitted fluorescence is polarized. The extent of tliis polarization tlius affords invaluable infonnation about tlie internal stmcture of molecular complexes. 

Rigid Systems. Literature pertaining to the theoretical analysis of the three-plane rigid piping system is voluminous (30). This Hterature is expanding steadily and, as it is becoming more abstract, tends to obscure the basic problem which is the analysis of a three-dimensional statically iadeterminate stmcture. 

The Stress-Rang e Concept. The solution of the problem of the rigid system is based on the linear relationship between stress and strain. This relationship allows the superposition of the effects of many iadividual forces and moments. If the relationship between stress and strain is nonlinear, an elementary problem, such as a siagle-plane two-member system, can be solved but only with considerable difficulty. Most practical piping systems do, ia fact, have stresses that are initially ia the nonlinear range. Using linear analysis ia an apparendy nonlinear problem is justified by the stress-range concept... 

It can be observed from the previous expression that when rigid support), then Lu t = lu or the natural frequency of the rigid system. For a system with a finite stiffness at the supports, or K/, = Kr, then lu is less than Lu t. Hence, flexibility causes the natural frequency of the system to be lowered. Plotting the natural frequency as a function of bearing stiffness on a log scale provides a graph as shown in Figure 5-15. 

In rigid systems only r/3-difunciional groups are oxidized, the specificity arising from the... 

The rearrangement proceeds from the Si-state of the 1,4-diene 1. The Ti-state would allow for different reactions like double bond isomerization. Rigid systems like cyclic dienes, where EfZ -isomerization of a double bond is hindered for steric reasons, can react through the Ti-state. When the rearrangement proceeds from the Si-state, it proves to be stereospecific at C-1 and C-5 no -isomerization is observed. Z-l,l-Diphenyl-3,3-dimethyl-l,4-hexadiene 5 rearranges to the Z-configured vinylcyclopropane 6. In this case the reaction also is regiospecific. Only the vinylcyclopropane 6 is formed, but not the alternative product 7. ... 

As suggested by Roberts and Moreland many years ago (1953), the acidity constants of 4-substituted bicyclooctane-l-carboxylic acids provide a very suitable system for defining a field/induction parameter. In this rigid system the substituent X is held firmly in place and there is little possibility for mesomeric delocalization or polarization interactions between X and COOH (or COO-). Therefore, it can be assumed that X influences the deprotonation of COOH only through space (the field effect) and through intervening o-bonds. On this basis Taft (1956, p. 595) and Swain and Lupton (1968) were able to calculate values for o and crR. 

This is actually observed, except when either potentially aromatic molecules such as thiepin dioxide (358) or when (relatively) sterically/conformationally rigid systems are involved. 

In steroids and other rigid systems, a functional group in one part of the molecule can strongly affect the rate of a reaction taking place at a remote part of the same molecule by altering the conformation of the whole skeleton. 

The m-dimethyl substituents in the 3-position of 2-anisylcamphenilyl result in a major increase in the exo/endo rate ratio. This can only be a steric phenomenon. The results with the trimethylnorbornyl derivatives supports the importance of steric effects in this rigid system (25, 26). 

The quantity S defined by Eq.II-2 is the order parameter describing the restricted motion of the C-H vector for a rigid system = 1, while for a completely flexible system = 0. 

Steric and conformational factors are also important, especially in cyclic systems.233 There is a preference for the migration of the group that is antiperiplanar with respect to the peroxide bond. In relatively rigid systems, this effect can outweigh the normal preference for the migration of the more branched group.234... 

If fluorescence and cis-trans isomerization (9.26)-(9.29) are the main competing reactions upon direct excitation, then inhibition of rotation about the central bond should produce an increase in the fluorescence quantum yield. The rigid systems (3) and (4) both have fluorescence quantum yields of 1.0 at room temperature.<44,52) While the fluorescence of /rmy-stilbene is a... 

The structures of the new bicyclic peroxides have been established by the usual combination of physical techniques and chemical transformations. Here we highlight features of the H and 13C n.m.r. spectroscopic data that provide the best characterization of these compounds their reactions are discussed later. Information about the C-O-O-C dihedral angle in organic peroxides is potentially available from photoelectron (PE) spectroscopy. Measurements on comparatively rigid systems play an important part in establishing a soundly based experimental correlation, and the results obtained on several of these bicyclic peroxides are presented in this section also. 

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. 

In molecularly rigid systems, the direct (through-space) dipole-dipole interaction between nuclear spins I = fe is normally the dominant source of broadening of the NMR lineshape. For a pair of similar nuclear spins i and j in a magnetic field Hq the dipolar splitting in their spectrum is given by... 

A form of cellular rubber in which the cells are non-intercommunicating, self-contained units. It has low thermal conductivity. Expanded rubber is buoyant and does not absorb water and was therefore initially used in both the soft rubber and ebonite forms in the construction of lifebuoys and other marine buoyancy equipment. The most commonly used polymer is now polyurethane for both flexible and rigid systems. 

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