Hammett equation multiparameter extensions

There are two main types of treatment, both involving multiparameter extensions of the Hammett equation, which essentially express the sliding scale idea. 

Finally, in this account of multiparameter extensions of the Hammett equation, we comment briefly on the origins of the a, scale. This had its beginning around 1956 in the a scale of Roberts and Moreland for substituents X in the reactions of 4-X-bicyclo[2.2.2]octane-l derivatives. However, at that time few values of o were available. A more practical basis for a scale of inductive substituent constants lay in the o values for XCHj groups derived from Taft s analysis of the reactivities of aliphatic esters into polar, steric and resonance effects . For the few o values available it was shown that o for X was related to o for XCHj by the equation o = 0.45 <7. Thereafter the factor 0.45 was used to calculate c, values of X from o values of XCH2 . ... 

Shorter, J. 1978. Multiparameter extensions of the Hammett equation. In N.B. Chapman and J. Shorter, Eds., Chapter 4, pp 119-174. Correlation Analysis in Chemistry, Plenum Press, New York. 

Shorter, J. (1978). Multiparameter Extensions of the Hammett Equation. In Correlation Analysis in Chemistry (Chapman, N.B. and Shorter, J., eds.). Plenum Press, New York (NY), pp. 119-173. 

Yukawa-Tsuno equation A multiparameter extension of the Hammett equation to quantify the role of enhanced RESONANCE effects on the reactivity of meta- and para-substituted benzene derivatives, for example,... 

The work of Hammett and others in the early 1930s led to the formulation of the best known linear free energy relationship, the Hammett equation, which describes the influence of polar meta- or para-substituents on the side-chain reactions of benzene derivatives. This equation, its refinement in various ways, and its elaboration in the form of multiparameter extensions are the subjects of Section 2. 

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