For 10 points, name this equation that relates reaction rates and equilibria constants for benzoic acid derivatives.
Takahata et al showed that one parameter in this equation correlated linearly with the change in core-electron binding energy. One modification of this equation uses 80% ethanol as a reference to determine changes due to solvent effects; that modification is named for Grunwald and Weinstein. One parameter of this equation can be redefined as a linear combination of resonance and field effects. A different modification to this equation includes a delta term that accounts for steric effects and is named for (*) Taft. This quantitative structure-activity relationship was developed when its discoverer attempted to correlate the rate of ester hydrolysis with the pKa of the corresponding acid. This linear free-energy relationship predicts that the effect of meta- and para- substitutents can be described by the product of a reaction constant, rho, and a substituent constant, sigma. The developer of this equation also names a function used to measure the strength of superacids. For 10 points, name this equation that relates reaction rates and equilibria constants for benzoic acid derivatives. 
Takahata et al showed that one parameter in this equation correlated linearly with the change in core-electron binding energy.
Hammett equation