It is a modified version of the Hammett equation that accounts for enhanced resonance effects in electrophilic reactions of para- and meta-substituted organic compounds.
This equation does so by introducing a new term to the original Hammett relation that provides a measure of the extent of resonance stabilization for a reactive structure that builds up charge (positive or negative) in its transition state.
For a particular substituent, the value of σ is generally assumed to be a constant, irrespective of the nature of the reaction; however, it has been shown that for reactions of para-substituted compounds in which the transition state bears a nearly full charge, σR does not remain constant, and thus, the sum
In other words, for such reactions, application of the standard Hammett Equation does not produce a linear plot.
To correlate these deviations from linearity, Yasuhide Yukawa and Yuho Tsuno proposed a modification to the original Hammett equation which accounts exclusively for enhanced resonance effects due to the high electron demand during such reactions.
In their 1959 publication, Yukawa and Tsuno attributed observed deviations from Hammett Plot linearity in electrophilic reactions to additional resonance effects occurring through the pi bonds of substituent groups in their compounds.
From this assumption, the two scientists defined a new resonance substituent constant, G(R), that is mathematically represented as follows: for a reaction in which positive charge is built up at the reactive center in the transition state.
Also, Yukawa and Tsuno note that, even within a group of similar reactions, r-values for more electron-withdrawing substituents tend to be higher than predicted—seen as a slight increase in slope on a Yukawa–Tsuno plot—and thus, are not as strongly correlated with the remainder of the data.