Page 354 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

13
or C NMR spectroscopy. The ratio of enrichment is related to the fraction of reaction 335
completed and allows calculation of the KIE.
SECTION 3.6
ln 1−F Linear Free-Energy
KIE = (3.41)
ln 1−F R/R Relationships for
0 Substituent Effects
where F is the fractional completion and R/R is the isotopic enrichment.
0
The method can be simultaneously applied to each atom of interest. An atom that
is expected to have a negligible KIE is selected as an internal standard. For example,
with the methyl group as the internal standard, the KIE for every other position in
isoprene was determined for the Diels-Alder reaction with maleic anhydride. This
method is especially useful for the measurement of carbon isotope effects, where
normal methods require synthesis of isotopic labeled reactants.
0.96
1.00 H
CH 3 1.02 0.91
H
H 0.94
H
0.99 1.02
1.00 H
0.97
The experimental KIE can be compared with KIEs calculated from transition
structures on the basis of the vibrational frequencies associated with specific
bonds. This information is available from computed transition structures, 125 and the
comparison can provide a direct experimental means of evaluating the computed
transition structures. 126 The method has also been used to measure KIE in reactions
such as the bromination of pentene 127 and epoxidation of propene. 128 Those transition
structures that are inconsistent with the observed KIE can be excluded.
0.98 0.93
H 1.01 H
0.94 0.93 1.01
H H 0.97
CH 3
1.01 H 1.01 H
0.93
0.93 (1.00)
Kinetic isotope effects Kinetic isotope effects
for bromination for epoxidation

3.6. Linear Free-Energy Relationships for Substituent Effects

3.6.1. Numerical Expression of Linear Free-Energy Relationships

Many important relationships between substituent groups and chemical properties
have been developed. For example, in Section 1.2.5 (p. 53), we discussed the effect
125
M. Saunders, K. E. Laidig, and M. Wolfsberg, J. Am. Chem. Soc., 111, 8989 (1989).
126
J. E. Baldwin, V. P. Reddy, B. A. Hess, Jr., and L. J. Schaad, J. Am. Chem. Soc., 110, 8554 (1988);
K. N. Houk, S. M. Gustafson, and K. A. Black, J. Am. Chem. Soc., 114, 8565 (1992); J. W. Storer,
L. Raimondi, and K. N. Houk, J. Am. Chem. Soc., 116, 9675 (1994).
127 S. R. Merrigan and D. A. Singleton, Org. Lett., 1, 327 (1997).
128
D. A. Singleton, S. R. Merrigan, J. Liu, and K. N. Houk, J. Am. Chem. Soc., 119, 3385 (1997).