7
276 J . Org. Chem., Vol. 63, No. 21, 1998
Lee and J eoung
The reactions of present interest are shown in the most
The first term on the right-hand side of eq 7 can be
general way in eq 1. Since the reactants and products
defined as the parallel effect, or Leffler-Hammond
7
effect, and the second term is the perpendicular effect,
Ai+ + A H f A H + A
j
+
(1)
or Thornton effect on R.8 The third term is negligible in
j
i
2
most applications because (RT/λ) will usually be very
r
2
small. It has been shown that both of the first two terms
∆
G* ) W + (1 + ∆G°/λ) λ/4
(2)
(3)
6
,15
in eq 7 are required for a satisfactory estimate of R.
λ ) (λ + λ )/2
The upper signs are used in eq 7 if the structural
variation is in the acceptor, and the lower signs are used
if the structural variation is in the donor.9 The present
system has the structural variation in the hydride donor
so we used the lower signs consistently.
i
j
K ) exp(-∆G°/RT)
k ) k T/h exp(-∆G*/RT)
(4)
(5)
2
B
τ is related to the sum of the bond orders of the in-
flight hydrogen at the critical configuration. Theoretical
work suggests that it is approximately constant over a
long range of K values, as long as the end atoms are
unchanged. Approximate midpoint λ and K values could
are structurally related and of the same charge type, it
can be assumed that the free energy required to form a
reactive complex from separated reactants is the same
in both directions. In that case the standard free energy
of reaction, ∆G°, is the same as the standard free energy
of reaction within a reactive complex, ∆G°′. This simpli-
fies the Marcus theory to the form shown in eqs 2 and 3.
Equations 4 and 5 give the standard thermodynamic
expression for K and the quasithermodynamic expression
10
be measured or estimated for each of the two reaction
systems. From these RPy+, RIQ+, and their ratio could be
calculated for comparison with the experimental value.
+
The ratio of the Brønsted R for the two systems Py ,
+
1
, and IQ , 2, can be written as shown in eq 9.
2
for k . The standard free energy of formation of the
r
precursor complex from reactants,W , is regarded as
structure insensitive. This is the standard free energy
for combining the two reactants into a single unit,
reducing the number of large-excursion degrees of free-
RIQ
+
/RPy
+
) [d(ln kIQ
+
)/d(ln kPy )]/
+
d(ln KIQ )/d(ln KPy
+ +
[ )] (9)
6
dom. It has been assigned a value of -8 kJ /mol, because
The numerator in eq 9, the derivative involving rate
constants, is accessible experimentally by measuring the
rate constants, k , for the two reaction systems, and the
2
there is thought to be a charge-transfer interaction
between the reactants, and that estimation is used for
the present work. As long as the assigned value is not
too far from zero, it does not have an important effect on
the conclusions.6
derivative involving equilibrium constants is unity for
the present system because the same hydride donors, 3H
and 4H, are used with each of the two acceptors. Since
the rate constants are measured with greater accuracy
than the equilibrium constants, the ratio of R values is
known more accuracy than the individual values. This
is useful in comparing the experimental results with
Marcus theory.
r
If ∆G° is zero, λ/4 ) ∆G* - W , where λ/4 is called the
intrinsic barrier, i.e., the barrier in the absence of an
overall driving force. For the two degenerate reactions
related to that shown in eq 1, ∆G° is necessarily zero,
and λ
i
j
/4 and λ /4 are the intrinsic barriers for those
reactions. For a family of structurally similar hydride
+
acceptors, such as A
variation of λ with the hydride acceptor tendency of A
can be approximated by eq 6, which also defines the
i
, it has been shown that the
Exp er im en ta l Section
i
i
6
Heteroaromatic carboxylic acids were purchased from Ald-
rich Chemical Co. They were used as supplied. 2-Propanol
was purchased from Fisher Scientific, HPLC grade, 99.9%
assay, and distilled before use. Water was also redistilled
before use. The mixed solvent was made up from 2-propanol
and water in a 4:1 ratio, by volume, at a temperature of 25 (
τ - 1 ) dλ /d(∆G °°)
(6)
i
i
parameter τ. In this equation ∆G
Gibbs free energy of the reaction of A
i
°° is the standard
+
i
with acridan as
0
.1 °C.
a hydride donor. (Any other hydride donor could have
been used as the standard instead of acridan, but acridan
was found to be convenient. ) Using eq 6, the variation
Compounds 1, 2, and their dihydro derivatives, 1H and 2H,
are previously known compounds. Their melting points and
spectroscopic properties agreed with those previously re-
6
1
1
ported.
described.12 The compounds 3c-f were prepared similarly to
a ,b and 4a -c by the modification of the procedure of Craig
Compounds 3a ,b and 4a -c have been previously
in rate constants of degenerate reactions with ∆G
i
°° can
be used to evaluate the parameter τ. Or, conversely, the
3
+
effect of changes in hydride affinity of A
i
on the value
°°, which is
13
et al. as shown in Scheme 1.
of λ can be evaluated from the change in ∆G
i
i
measurable. For hydride transfer between various ni-
(
7) Leffler, J . E. Science (Washington, D.C.) 1953, 117, 340-341.
trogen heterocycles, τ was found to be reasonably con-
(8) Thornton, R. E. J . Am. Chem. Soc. 1967, 89, 2915-2927.
6
(9) Kreevoy, M. M.; Lee, I.-S. H. Z. Naturforsch. 1989, 44a, 418-
stant with an average value of 0.81, and this value is
4
26.
used in the present work. All the other symbols in eqs
(
10) Kim. Y.; Truhler, D. G.; Kreevoy, M. M. J . Am. Chem. Soc. 1991,
113, 7837-7847.
11) Bunting, J . W.; Norris, D. J . J . Am. Chem. Soc. 1977, 99, 1189-
196.
12) Lee, I.-S. H.; J eoung, E. H.; Lee, C. K. J . Heterocycl. Chem.
1996, 32, 1711-1716.
13) Craig, J . C.; Ekwuribe, N. N.; Fu, C. C.; Walker, K. A. M.
6
2
-5 have their usual significance and values.
(
Using eqs 3-6, a Marcus theory expression for the
1
Brønsted R [≡d(ln k)/d(ln K)] can be derived from eq 2 in
(
terms of two parameters, ø and τ. It is shown in eq 7.
(
1
2
Synthesis 1981, 303-305.
(14) Frost, A. A.; Pearson, R. G. Kinetics and Mechanism, 2nd ed.;
Wiley: New York, 1961; p 29.
R ) ø ( / {(τ - 1) - [(RT/λ) ln K] (τ - 1)} (7)
2
1
(15) Lee, I.-S. H.; J eoung, E. H.; Kreevoy, M. M. J . Am. Chem. Soc.
1997, 119, 2722-2728.
ø ) / [1 - (RT/λ) ln K]
(8)
2