The Taft equation is a
linear free energy relationship (LFER) used in
physical organic chemistry
Physical organic chemistry, a term coined by Louis Hammett in 1940, refers to a discipline of organic chemistry that focuses on the relationship between chemical structures and reactivity, in particular, applying experimental tools of physical c ...
in the study of
reaction mechanisms and in the development of
quantitative structure–activity relationship
Quantitative structure–activity relationship models (QSAR models) are regression or classification models used in the chemical and biological sciences and engineering. Like other regression models, QSAR regression models relate a set of "predic ...
s for
organic compound
In chemistry, organic compounds are generally any chemical compounds that contain carbon-hydrogen or carbon-carbon bonds. Due to carbon's ability to catenate (form chains with other carbon atoms), millions of organic compounds are known. T ...
s. It was developed by
Robert W. Taft in 1952 as a modification to the
Hammett equation
The Hammett equation in organic chemistry describes a linear free-energy relationship relating reaction rates and equilibrium constants for many reactions involving benzoic acid derivatives with meta- and para-substituents to each other with ju ...
. While the Hammett equation accounts for how
field
Field may refer to:
Expanses of open ground
* Field (agriculture), an area of land used for agricultural purposes
* Airfield, an aerodrome that lacks the infrastructure of an airport
* Battlefield
* Lawn, an area of mowed grass
* Meadow, a grass ...
,
inductive, and
resonance
Resonance describes the phenomenon of increased amplitude that occurs when the frequency of an applied Periodic function, periodic force (or a Fourier analysis, Fourier component of it) is equal or close to a natural frequency of the system ...
effects influence reaction rates, the Taft equation also describes the
steric effects of a
substituent. The Taft equation is written as:
:
where
is the ratio of the
rate of the substituted reaction compared to the reference reaction, ρ* is the sensitivity factor for the reaction to
polar effect
The polar effect or electronic effect in chemistry is the effect exerted by a substituent on modifying electrostatic forces operating on a nearby reaction center. The main contributors to the polar effect are the inductive effect, mesomeric effec ...
s, σ* is the polar substituent constant that describes the field and inductive effects of the substituent, δ is the sensitivity factor for the reaction to steric effects, and E
s is the steric substituent constant.
Polar substituent constants, σ*
Polar substituent constants describe the way a substituent will influence a reaction through polar (inductive, field, and resonance) effects. To determine σ
* Taft studied the
hydrolysis
Hydrolysis (; ) is any chemical reaction in which a molecule of water breaks one or more chemical bonds. The term is used broadly for substitution, elimination, and solvation reactions in which water is the nucleophile.
Biological hydrolys ...
of
methyl esters
In chemistry, an ester is a compound derived from an oxoacid (organic or inorganic) in which at least one hydroxyl group () is replaced by an alkoxy group (), as in the substitution reaction of a carboxylic acid and an alcohol. Glycerides ar ...
(RCOOMe). The use of ester hydrolysis rates to study polar effects was first suggested by Ingold in 1930. The hydrolysis of esters can occur through either
acid and base catalyzed mechanisms, both of which proceed through a
tetrahedral
In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners. The tetrahedron is the simplest of all the ...
intermediate. In the base catalyzed mechanism the reactant goes from a neutral species to negatively charged intermediate in the
rate determining (slow) step, while in the acid catalyzed mechanism a positively charged reactant goes to a positively charged intermediate.
:
Due to the similar tetrahedral intermediates, Taft proposed that under identical conditions any steric factors should be nearly the same for the two mechanisms and therefore would not influence the ratio of the rates. However, because of the difference in charge buildup in the rate determining steps it was proposed that polar effects would only influence the reaction rate of the base catalyzed reaction since a new charge was formed. He defined the polar substituent constant σ* as:
: