Dipolar model

The stereoselectivity of an addition reaction is considerably lower when the reactions are conducted in polar solvents, complexing additives such as /V./V,A. A, -tetramethylethylenedi-arnine arc used, or when the stereogenic center carries a methoxy group instead of a hydroxy group. This behavior is explained as competition between the cyclic model and a dipolar model, proposed for carbonyl compounds bearing a polar substituent such as chlorine with a highly... 

In contrast to the open-chain and dipolar models, which are based on conformations of the carbonyl compound not representing energy minima, Karabatsos proposed a different model assuming an early, reactant-like transition state in which the most stable conformation of the free carbonyl compound is preserved1314. Thus, the C-M bond eclipses the carbonyl double bond and, in order to minimize the energy of the transition state, the nucleophile approaches close to the small substituent on the stereogenic center (Figure 5). 

These results may be explained by a chelation-controlled mechanism A with M representing a complex of JVtg(ll), Ce( 111) or of both cations. The highly stereoselective addition of the organocop-per reagent can be rationalized either by the dipolar model B or the Felkin-Anh model C (see also ref 12). 

These results may be explained either by Cram s cyclic model in the case of lithium alkyls or by Cornforth s dipolar model if copper-boron trifluoride reagents are used. Boron trifluoride causes double complexation of both nitrogen and oxygen atoms which results in the formation of an adduct with rigid antiperiplanar conformation due to electrostatic repulsion (see 4 and 5)9. 

We conclude that the dipolar models may exhibit many interesting features, such as the influence of the strength of the dipole moment on the nematic-isotropic and smectic-nematic transitions. Determining the structure of the various smectic phases is clearly an area which needs more investigation. However, an appropriate simulation scheme must be used to avoid misunderstanding the behaviour caused by the method rather than the model. This may be as simple as checking for system size dependence, or running... 

An interesting comparison can be made between the experimentally determined limits on the interaction energies and those obtained from a simple dipolar model. In this case, the interaction energy difference between two coplanar dipoles is given by ... 

The existence of the surface contribution to the effective magnetostriction of nanocrystalline alloys has been confirmed theoretically in terms of the dipolar model (Szumiata et al. 1999). These authors showed that, due to the limited radius of the nanoparticles, additional magnetostrictive stresses are localised at the interfaces. The evaluation of the influence of the dipolar interaction on the magnetostriction in crystalline grains of perfect spherical shape surrounded by a magnetic environment of about 0.S nm with either crystalline or amorphous structure has been calculated. A similar method was previously used to obtain the surface and volume anisotropy (Draaisma and de Jonge 1988) and to... 

FLC phases in the surface stabilized geometry possess a single C2 axis of symmetry, and therefore polar order and non-zero x<2) in the simple electronic dipolar model. Thus, it is not surprising that experiments aimed at measuring this property were first reported shortly after the Clark-Lagerwall invention. Early studies (14-15) described second harmonic generation in (S)-2-Methylbutyl 4-(4-decyloxybenzylideneamino)cin-namate, the first ferroelectric liquid crystal, also known as DOBAMBC (1). 

When analogous treatment of AG is included, the two-sphere monopole or one-sphere dipole models predict a significant solvatochromic shift for optical ET of the CR type (i.e., in which the intial state is charge separated) e.g., a blue shift for absorption (e.g., betaine [48]) and a red shift for emission (e.g., coumarin [42]). Similar trends are typically found for CSh using the two-sphere model, while the one-sphere dipolar model is ambiguous, since it does not provide an adequate estimate of the polarity dependence of AG° [29],... 

The concentration of Grignard reagent could also be a factor in the stereochemical outcome. The addition of ethylmagnesium chloride to 26 in diethyl ether was highly selective for the R R stereoisomer at concentrations of 0.09-0.72 M (81-83%). The chloromagnesium compound is associated even at low concentrations. The stereoselectivity of addition to 26 by ethylmagnesium bromide, which is monomeric at low concentration, is concentration-dependent. Selectivity for the R R isomer varied from 74% at 0.70 M, where the dipolar model 28 should dominate, to 55% at 0.044 M, at which the cyclic model 27 should be more important. The stereoselectivity for reaction of 26 with ethylmagnesium iodide is also concentration-dependent. 

In this section we consider the possibility of applying the ion association concept to the description of the properties of electrolyte solutions in the ion-molecular or Born-Oppenheimer level approach. The simplest ion-molecular model for electrolyte solution can be represented by the mixture of charged hard spheres and hard spheres with embedded dipoles, the so-called ion-dipolar model. For simplification we consider that ions and solvent molecules are characterized by diameters R and Rs, correspondingly. The model is given by the pair potentials,... 

These trends are similar to what is observed in simpler model fluids with purely spherically s3mimotric interactions [298, 313], which is to some extent expected because the gas liquid transition in Stockmayer fluids is mainly driven by the isotropic LJ (12,6) interactions underlying this model. We show in Ref. 307 that the main effects of HS matrices on the condensation can be reproduced when the dipolar model fluid is approximated by a fluid with angle-averaged dipolar interactions that are not only spherically symmetric but also short-ranged (they decay in proportion to for r — cx)). This notion is particularly important for future simulation studies on adsorbed dipolar fluids. 

Hydrogen bonds are the most characteristic element of liquid water structure. Water models used in computer simulations are able to describe the properties of the hydrogen bond network in a realistic way, contrary to many of the dipolar model fluids used in analytical theories. Much has been learned about bulk water and solutions through an analysis of the hydrogen bond network (e.g.. Ref. 156, 157). 

In Section III, we use a more general notation in which a ir) is denoted as a° (r), a (r) is denoted as a °(r), and U ,(r) as a" (r), while d - (k) refers to a generalized Fourier transform that includes the Hankel transform introduced here. In treating simple dipolar models (in which higher ideal multipole terms may or may not be present, but are not explicitly discussed) the more general notation is unnecessary and is not used in Section II. 

Real Liquids. Real molecules usually have both dipole and quadrupole moments. Thus the results described above strongly suggest that withoi t the inclusion of higher multipole moments, simple dipolar models will be hopelessly inadequate for most real liquids. This is illustrated qualitatively in Fig. 22, which compares experimental results for a number of common liquids ... 

Figure 7. Setting angle of the herringbone phase of the quadrupolar-dipolar model (2.8) and the same model including a sixfold-modulated in-plane crystal-field (2.10) as a function of the reduced temperature T = TIT i at X = 0.9 for jSj = 2, where X = 1 note that 02 only sets the temperature scale. Solid line no crystal field. Dashed line K3 = 0.1. (Adapted from Fig. 7 of Ref. 71.)...

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