Structural effects equations

The Hammett equation is not the only LFER." ° Some, like the Hammett equation, correlate structural changes in reactants, but the Grunwald-Winstein relationship (see p. 452) correlates changes in solvent and the Brpnsted relation (see p. 337) relates acidity to catalysis. The Taft equation is a structure-reactivity equation that correlates only field effects. ... 

There is greatly renewed interest in electron solvation, due to improved laser technology. However it is apparent that a simple theoretical description such as implied by Eq. (9.15) would be inadequate. That equation assumes a continuum dielectric with a unique relaxation mechanism, such as molecular dipole rotation. There is evidence that structural effects are important, and there could be different mechanisms of relaxation operating simultaneously (Bagchi, 1989). Despite a great deal of theoretical work, there is as yet no good understanding of the evolution of free-ion yield in polar media. 

Structural effects on dienes and polyenes The only equation available for the estimation of cre constants is ... 

It is indicated that these transport parameters are functions of A. The hydraulic permeability (D Arcy coefficient), /Cp (A), exhibits strong dependence on A because larger water contents result in an increased number of pores used for water transport and better connectivity in the porous network, as well as in larger mean radii of these pores. A modification of the Hagen-Poiseuille-Kozeny equation was considered by Eikerling et aU- to account for these structural effects ... 

Some information about structure effects on the rate of dehydrogenation of alcohols to aldehydes and ketones on metals is found in the older literature 129-132) from which it follows that secondary alcohols react more easily than the primary alcohols 129) and that the reactivity decreases with the length of the carbon chain 131). Some series can be correlated by the Taft equation using a constants (Ref. 131, series 103, Cu-Cr203 catalyst, 350°C, four points, slope 18 Ref 132, series 104, Cu catalyst, four points, slope 22). Linear relationships have been used in a systematic way by... 

Conflation analysis Is the most effective simple generally applicable method for the quantification of structural effects on chemical physical or biological properties. It was first successfully applied to biological activities by Hansoh and his ooworkers(X) In an equation of the form... 

Because the entropy of formation in Hildebrand theory is ideal, this approach should be restricted to those systems in which there are no structure effects due to solute-solvent and solvent-solvent interactions. The implication of this is that the solute should be non-ionic and not have functional groups which can interact with the solvent. According to Equation (4.8), the maximum solubility occurs when the Hildebrand parameter of the solvent is equal to the Hildebrand parameter of the solute. That is, when plotting the solubility versus the Hildebrand parameter, the solubility exhibits a maximum when the solubility parameter of the solvent is equal to the solubility parameter of the solute. 

Johnson CK (1969) Addition of higher cumulants to the crystallographic structure-factor equation a generalized treatment for thermal-motion effects. Acta Crystallogr A 25 187-194... 

In addition to the structural effects due to the geometry of a substituted magnesium enolate, the stereochemistry of the reaction with a chiral aldehyde can be controlled, as described in equation 85. The aldol reaction based on the addition of magnesium enolate 56 to aldehyde 55 has been applied to the synthesis of monensin. The chiral center in the aldehyde induces the preferential approach of one diastereotopic face of the aldehyde by... 

In a parallel development, structural effects on the chemical reactivity and physical properties of organic compounds were modelled quantitatively by the Hammett equation 8). The topic is well reviewed by Shorter 9>. Hansen 10) attempted to apply the Hammett equation to biological activities, while Zahradnik U) suggested an analogous equation applicable to biological activities. The major step forward is due to the work of Hansch and Fujita12), who showed that a correlation equation which accounted for both electrical and hydrophobic effects could successfully model bioactivities. In later work, steric parameters were included 13). 

In earlier sections it has been shown that the reaction of a magnesium dialkyl with one equivalent of a primary amine usually affords the primary amido derivative. However, it is also possible to effect elimination of the second equivalent of alkane to give magnesium imides. The reaction of MgEt2 with aniline in thf proceeded via an amido intermediate which eliminated ethane to yield the hexameric imido compound [ (thflMgNPhJg] which was the first homometallic magnesium imide to be structurally characterized. Equation (3.9). 

As a consequence of the model employed, values of Hb(H20) and N ought to be independent of the choice of the cosolvent as long as specific structural effects are absent. Therefore, we applied Equation 3 to the enthalpies of solution of n-Bu4NBr in DMSO-water mixtures (iO), since DMSO is a dipolar aprotic solvent like DMF. The best fit of the AHE values in this mixture yields Hb(H20) = —49.2 kj mol-1 and N/4 = 6.4, in excellent agreement with our values at 25°C given in Table III. 

A quantitative correlation of structural effects of four esters and four alcohols in the vapour phase transesterification on a macroreticular ion exchanger at 120°C was made using the Taft equation [441]. The authors found that rate coefficients [from eqn. (27)] yielded better correlation with steric (Es) than with polar (a ) parameters, while there was no significant difference between the correlations of the adsorption coefficients of alcohols, Kb, with both parameters. The correlations with Es yielded the slopes 1.4 and 0.6 for the reactivity of the esters and the alcohols, respectively, and —0.4 for the adsorptivity of the alcohols. The observed... 

A kinetic study of structural effects on the A-nitrosation of amino acids by nitrite in aqueous solution has established that the dominant term in the rate equation corresponds to nitrosation by dinitrogen trioxide.189 Nitrosation by intramolecular migration of the nitroso group from an initially nitrosated carboxylate group can compete when the transition state has a five- or six-membered ring structure. Nitrosation of A-methyl-4-tolylsulfonylguanidine involves rapid nitrosation of the N-... 

Fluid dynamics in a tubular fuel cell has significant effects on different other phenomena such as the electrochemical reactions, which need species to be transported to the reaction site, and mass and heat transfer. In the porous structures, an equation that accounts for the fluid flowing in the pores - such as Brinkman s or Darcy s equations (Equation (3.4)) - must be used usually the velocities are low. Fluid-dynamic is modelled through Navier-Stokes equation in the channels (Equation (3.3)). 

The selection of a Tanimoto coefficient corresponding to a 2 log unit difference in activity between a compounds in the test studies effectively equates to a resolution of our bioactivity space. We consider a 2 log unit resolution to this space to be ideal for searching for lead structures. Note that two independent research groups arrived at similar Tanimoto values in slightly different studies. 

Discrete and continuum models of transfer of molecules over various sorption sites of a microheterogeneous membrane were considered for systems with weak intermolecular interactions and membranes with constant composition and structure. An equation for estimating size effects on permeability coefficient II of microheterogeneous membranes was derived [188], and the possibility of applying the continuum model to calculate the n value in thin films of thickness L is numerically analyzed. The effect of the composition and structure of a uniformly microheterogeneous membrane on the permeability coefficients II was studied. The dependence of n on the composition is a convex function if the migration between different sorption sites proceeds more quickly than between identical sites and a concave one in the opposite case [189],... 

In 1,2,3-triphosphetenes the amino group acts as an effective Jt-electron donor and the mesomeric form makes a considerable contribution to the ground-state structure 31 (Equation 1) <1996GEJ208>. 

The goodness of fit is in accord with the experimental error in the data. Both equations 42 and 43 are significant at the 99.9% confidence level. Though 07 is significantly collinear in a dependence on both parameters is fairly certain. Electrical effects are the predominant factor in the structural effect with the localized effect making the greater contribution. 

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