LDRS equation

When the composition of the electrical effect, Pd. is held constant the LDR equation simplifies to the CR equation ... 

If the sensitivity to electronic demand is held constant, the LDR equation reverts to the LD equation (equation 5). By means of an equation analogous to the MYT equation, the modified LD (MLD) equation is ... 

In the general case electrical effects are also present and the general form of the LDRS equation ... 

If the data sets were studied in aqueous organic solvents, they can be combined into a single large set by the addition of the term Ff where (j> is the mole fraction of organic solvent in the medium. Thus, the LDR equation becomes the LDRF equation ... 

Diparametric equation A relationship in which the effect of structure on a property is represented by two parameters, one of which is generally composite. Examples discussed in this work include the LD, CR and MYT equations. Other examples are the Taft, Ehrenson and Brownlee DSP (dual substituent parameter), Yukawa-Tsuno YT and the Swain, Unger, Rosenquist and Swain SURS equations. The DSP equation is a special case of the LDR equation with the intercept set equal to zero. It is inconvenient to use and has no advantages. The SURS equation uses composite parameters which are of poorer quality than... 

From this equation we may calculate the value of m for which 17 is zero to be 3.12. Values of a for this exponent were calculated from equation 25 (with c equal to 10) for 52 substituents. They were then correlated with the LDR equation in the form ... 

The correlation of pXa values of 4-substituted benzoic acids in aqueous ethanol52 has been carried out with a correlation equation53,54 resulting from the addition of terms in the mole fraction of ethanol, cpEtou, and the polarizability of X, ax, to the LDR equations. Thus ... 

Kuznesoff and Jolly56 have reported a pKa value of 3.5 for the acid GeHsCC H, 12, in water. We have correlated the pKa values of XCO2H in water with the LDR equation to obtain the relationship ... 

We have reported elsewhere51 the results of the correlation of dipole moments for MeX and PhX where X is a symmetric substituent with the LDR equation. The regression equations obtained are for the MeX ... 

It is claimed that, The LDR equation is the first successful model for electronic effects of substituents bonded to carbon in all substrates 257. 

Electrical effects are conveniently described by the triparametric (three independent variables) LDR equation 1 ... 

The intercept of this linear relationship represents the intrinsic delocalized (resonance) effect, Odx- This is the delocalized effect observed when the electronic demand of the data set studied is zero. The slope represents the sensitivity of the X group to the electronic demand of the active site. On substituting equation 9 into the LD equation (equation 10) we obtain the triparametric LDR equation ... 

This makes possible the combination of rate constants at different temperatures into a single data set. Thus, the LDR equation becomes the LDRT equation (equation 49) ... 

On the condition that two subsets have a structural feature whose parameterization is essentially the same, they can be combined into a single data set. As an example consider set 0X13, anfi-Ak—iyw-X—C=NOH, where Ak is either Me or Et. The electrical effects of these groups for Me and Et, respectively, are a , —.01, —,Q ad, —.14, —.12 ae, —.030, —. 036 the values of the steric parameter v are. 52 and. 56. A significant difference is found only in the polarizability parameter a, where the values for Me and Et are. 046 and. 093, respectively. Combination of oxime pXa values for Ak = Me or Et results in set 0X13 the best correlation was with the LDR equation. As only three substituent types are present in this data set and is 0.33, this data set cannot be considered as proof of anything. The only acceptable conclusion is that it is in accord with the combination of the two subsets. 

Correlation of the pXa values of XCONHOH with the LDR equation (set HA12) gave the regression equation 55 ... 

In XC(0)NHOH for NH acidity n = 2, for OH acidity n = 3. Clearly, best agreement is with n = 3. This suggests that in water, hydroxamic acids are oxygen acids. Also examined were the XCH2C(0)NHOH (set HA13) for which the n values of the NH and OH sites are 3 and 4, respectively. Correlation of the pXa values for these acids with the LDR equation gave the regression equation 56 ... 

Multiparametric equation An equation which uses three or more parameters all of which may be either pure or composite. The LDR equation used in this work is an example of a triparametric equation. The Taft-Topsom equation is an alternative triparametric equation. ... 

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