Linear free energy equations

NaOMe solutions, no correlation was found between reaction rates and either or stoichiometric base concentration but where the rates were successfully correlated by a linear free energy equation similar to those given above. 

A treatment partially based on the Bunnett-Olsen one is that of Bagno, Scorrano, and More OTerrall, which formulates medium effects (changes in acidity of solvent) on acid-base equilibria. An appropriate equilibrium is chosen as reference, and the acidity dependence of other reaetions compared with it, by use of the linear free energy equation... 

The following overall nucleophilicity order for Sn2 mechanisms (in protic solvents) was given by Edwards and Pearson RS > ArS >1 >CN > OH > Nj > Br > ArO > Cl > pyridine > AcO > H2O. A quantitative relationship (the Swain-Scott equation) has been worked out similar to the linear free energy equations considered in Chapter 9 ... 

The most important results of the linear free energy equations in this study (Table IV) are the applications to which they can be used. For a new free radical initiator, belonging to any of the four radical forming reactions of this study, equation 6 should be useful to predict the rate of decomposition with reasonable accuracy. All that is needed is an HMD calculation to obtain the pi-delocalization energy for the radical formed in the reaction (R ) and an estimate of the steric A values for groups bonded to the central carbon of R. ... 

The linear free energy equations generated in this study are useful for reasonably accurate predictions of rates of radical forming decompositions of Irons-symmetric bisalkyl diazenes (1),... 

Other authors found that the enthalpies for the hydrogen bonding also give a good correlation against Hammett values. The linear free energy equations between Avq , Av q and AH obtained in their investigations were as follows ... 

A linear free energy equation for reaction between nucleophiles and certain large organic cations (e.g., tri-aryhnethyl cations, aryltropyhum cations, etc.). Thus, log /cn = log ko + N+ where is the rate constant for the reaction of a particular cation with a given nucleophile in a given solvent, ko is the corresponding rate constant for the same cation with water in water (i.e., the solvent is water), and N+ is the cation-independent parameter that is characteristic for that nucleophile system. 

The linear free energy equations (Chapter 2) do not directly give the charge characteristics of the reaction. The following discussion shows how the polar substituent effects can be treated to obtain a quantitative measure of relative charge. 

The substituent effect in the standard dissociation equilibrium could be measured by any linear free energy equation (see Chapter 2). The Bronsted Equation is preferred and in all the arguments in this chapter we shall use (3 terminology. The other terminologies (such as p, p, p, etc.) are perfectly valid vehicles for determining effective charge. 

The most popular of these approaches is multiple regression analysis, introduced by Hansch in 1968. In this method, the most favoured variables are (i) partition coefficients (P), from the system octanol/water (ii) the sigma (cr) and rho (p) values derived from Hammett s Linear Free Energy Equation (Section 17.2) and (iii) Taft s steric factors E ) which are used to determine what space for substituents exists between a nominated small region of the lead molecule and its receptor (Section 16.2). These variables are correlated in the following equation ... 

Values of Yots and Nots for selected solvents are shown in Table 8.3. Many other Y scales have been developed for particular reaction systems. As noted in Chapter 6, however, writing a linear free energy relationship implies the modeling of one reaction on another. The ability of the linear free energy equation to correlate experimental data thus depends to some extent on the degree to which the model reaction is appropriately chosen. 

A closer inspection of Table 2 and a large body of other experimental data leads to the conclusion that uniform ap<,ro and values for each amine substituent do not appear to exist. Some of the difficulties may result from the susceptibility of the electron pair of the amine nitrogen to interaction with the reaction media. Frequent deviations from the linear free-energy equation are observed with these groups and appropriate interpretation with factors already known is difficult. Some idea of the complexity of this situation can be gained from the fact that the 17 values reported for /-N(CH3)2 range from —0-206 to — 1-049 . 

The fact that sigma parameters are inapplicable to reactions involving highly polarizable substituents , such as amino groups, and other related phenomena, inevitably necessitates improvements in correlating substituent effects, and the proposed structure-reactivity relations are still only partially successful. An excellent and critical examination of the various linear free-energy equations is found in a recent and valuable publication of Ritchie and Sager . 

A knowledge of the effects of various substituents on any ionizable group allows each substituent to be classed as electron-attracting or electron-releasinga and placed in ranking order. This operation was quantified about 194O3 by the introduction of Hammett s Linear Free Energy Equation ... 

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