Taft equation information

Constants used in the Taft equation^[1]
Substituent	E_s	σ*
–H	1.24	0.49
–CH₃	0	0
–CH₂CH₃	–0.07	–0.1
–CH(CH₃)₂	–0.47	–0.19
–C(CH₃)₃	–1.54	–0.3
–CH₂Ph	–0.38	0.22
–Ph	–2.55	0.6

The Taft equation is a linear free energy relationship (LFER) used in physical organic chemistry in the study of reaction mechanisms and in the development of quantitative structure–activity relationships for organic compounds. It was developed by Robert W. Taft in 1952^[2]^[3]^[4] as a modification to the Hammett equation.^[5] While the Hammett equation accounts for how field, inductive, and resonance effects influence reaction rates, the Taft equation also describes the steric effects of a substituent. The Taft equation is written as:

\log \left({\frac {k_{s}}{k_{{\ce {CH3}}}}}\right)=\rho ^{*}\sigma ^{*}+\delta E_{s}

where $\log {\frac {k_{s}}{k_{{\ce {CH3}}}}}$ 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 effects, 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.

^ Eric Anslyn, E.; Dougherty, D. A. Modern Physical Organic Chemistry; University Science Books, 2006, p 455.
^ Taft, Robert W. (June 1952). "Linear Free Energy Relationships from Rates of Esterification and Hydrolysis of Aliphatic and Ortho-substituted Benzoate Esters". Journal of the American Chemical Society. 74 (11): 2729–2732. doi:10.1021/ja01131a010. ISSN 0002-7863.
^ Taft, Robert W. (1952-06-01). "Polar and Steric Substituent Constants for Aliphatic and o-Benzoate Groups from Rates of Esterification and Hydrolysis of Esters1". Journal of the American Chemical Society. 74 (12): 3120–3128. doi:10.1021/ja01132a049. ISSN 0002-7863.
^ Taft, Robert W. (1953-09-01). "Linear Steric Energy Relationships". Journal of the American Chemical Society. 75 (18): 4538–4539. doi:10.1021/ja01114a044. ISSN 0002-7863.
^ Hammett, Louis P. (1937-01-01). "The Effect of Structure upon the Reactions of Organic Compounds. Benzene Derivatives". Journal of the American Chemical Society. 59 (1): 96–103. doi:10.1021/ja01280a022. ISSN 0002-7863.

[1] Eric Anslyn, E.; Dougherty, D. A. Modern Physical Organic Chemistry; University Science Books, 2006, p 455.

[2] Taft, Robert W. (June 1952). "Linear Free Energy Relationships from Rates of Esterification and Hydrolysis of Aliphatic and Ortho-substituted Benzoate Esters". Journal of the American Chemical Society. 74 (11): 2729–2732. doi:10.1021/ja01131a010. ISSN 0002-7863.

[3] Taft, Robert W. (1952-06-01). "Polar and Steric Substituent Constants for Aliphatic and o-Benzoate Groups from Rates of Esterification and Hydrolysis of Esters1". Journal of the American Chemical Society. 74 (12): 3120–3128. doi:10.1021/ja01132a049. ISSN 0002-7863.

[4] Taft, Robert W. (1953-09-01). "Linear Steric Energy Relationships". Journal of the American Chemical Society. 75 (18): 4538–4539. doi:10.1021/ja01114a044. ISSN 0002-7863.

[5] Hammett, Louis P. (1937-01-01). "The Effect of Structure upon the Reactions of Organic Compounds. Benzene Derivatives". Journal of the American Chemical Society. 59 (1): 96–103. doi:10.1021/ja01280a022. ISSN 0002-7863.

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