KIE for Electron-Transfer ActiVation of Hydrocarbons
J. Am. Chem. Soc., Vol. 120, No. 12, 1998 2829
by added salt.19
kS
\
[ArH+•, Q-•] + TBA+, PF6- y
z TBA+, Q-• + ArH+•, PF6
-
(3)
We therefore conclude that the critical step to form Q(H)• and
Ar• as the products of hydrogen transfer is to be identified as
proton transfer (kPT) from ArH+• to Q-• within the contact ion
pair in eq 4.20
kET
kPT
Q* + ArH 8 [Q-•, ArH+•] 8 Q(H)• + Ar•
(4)
The pathway in eq 4 might appear to be incompatible with
the observed isotope effects in Table 1, since the initial electron-
transfer step is not expected to show an appreciable isotope
effect. To resolve this paradox, let us consider the cumulative
effect of added salt on the kinetic isotope effect. In the absence
of any salt, Q* reacts appreciably slower with the perdeuterated
methylarenes, and the difference is reflected in the kinetic
isotope effect (3.1 for HMB) which is more or less that for
deprotonation of various ArH+• by pyridine bases.21 Most
Figure 4. Linear correlation of the competition between proton transfer
(kPT) and ion separation (kS) as derived from the salt effect on ArH+•
yields in Figure 3A according to the mechanism in Scheme 1.
Scheme 1
strikingly, the progressive addition of TBA+PF6 causes a
-
kET
kPT
Q(H)• + Ar•
Q* + ArH
Q– •, ArH+•
corresponding diminution in the deuterium isotope effects
(compare the open circles relative to the filled circles in Figure
3B), such that at the (highest) salt concentration of 0.2 M the
isotope effect completely vanishes in Figure 3B! Equally
striking is the concomitant increase in the ion yields of ArH+•
with increasing salt concentration in Figure 3A to establish the
salt-induced competition between ion-pair separation (kS) and
proton transfer (kPT), i.e.
k–ET
ks[salt]
Q– + ArH+•
•
the theoretical intercept of Φion ) 1.0 solidifies this prediction,
and the slope (kPT/kS) leads to the isotope effect for proton
transfer (kH/kD)PT listed in the last column in Table 1.24
Summary and Conclusions
kPT
ArH+• + Q-• 7kS
9
[ArH+•, Q-•] 8 Ar• + Q(H)• (5)
We have unambiguously demonstrated that substantial kinetic
isotope effects are observed for the hydrogen transfer in eq 1,
even when it proceeds via a two-step sequence involving
reversible electron transfer followed by proton transfer according
to Scheme 1. This mechanism is applicable to the oxidative
C-H activation of most hydrocarbons which involve endergonic
electron transfer (∆G g 0), so that reverse electron transfer
(k-ET) is competitive with proton transfer (kPT). Although
analogous electron-transfer formulations are applicable to a wide
variety of other organic reactions,25 their experimental verifica-
tion (as elucidated herein) will be difficult, since the rapidity
of the follow-up steps generally precludes the direct observation
of the ion-radical pair. Indeed, time-resolved spectroscopy,
Such a formulation emphasizes the effect of added salt on the
kinetic isotope effect to parallel its effect on the ion yield, which
is consistently greater for the deuterated analogue (ArD). The
difference, however, diminishes with increasing salt concentra-
tions, as the yield of cation radical approaches unity for both
isotopomers.
Salt effects in eq 5 predict the ion-pair separation in eq 2 to
be complete at sufficiently high salt concentrations, and this
will lead to the loss of the kinetic isotope effect. Thus the
difference in reactivity between ArH and ArD in Table 1 must
stem entirely from the proton-transfer step (kPT) in eq 4.22 Since
the overall decay rate of Q* is affected by isotopic substitution,
the kinetics of this follow-up step must feed back onto the initial
electron-transfer step. For this condition to hold, electron
transfer must be reversible. As such, the inclusion of the salt-
induced separation and reverse electron transfer leads to the
modification of the ET mechanism in eq 4 to that shown in
Scheme 1.
(24) If the ion-radical pair in Scheme 1 is assumed to be present in a
dynamic steady-state concentration, the bimolecular rate constant, k2, is given
by k2 ) kET(kPT + kS[salt])/(k
+ kPT + kS[salt]). Two limiting cases
-ET
arise from this equation. For case (i), kPT . k
+ kS[salt], k2 is simply
-ET
given by kET. No kinetic isotope effect is expected in this case. For case
(ii), k -ET . kPT + kS[salt], k2 is given by (kET/k-ET)(kPT + kS[salt]). In this
case, the kinetic isotope effect (in the absence of added salt) will be identical
to that of the intrinsic proton transfer, i.e., (kH/kD)PT in Table 1. Thus the
measured kinetic isotope effect on k2 will fall between these extremes. (b)
Digital simulation of the complete (complex) kinetics in Scheme 1, using
the method of Weigert,24c leads to the same conclusion. (c) Weigert, F. J.
Comput. Chem. 1987, 11, 273.
In this scheme, the isotope effect on the proton transfer (kPT)
is “diluted” by the competing ion separation (kS) as well as the
reversible electron transfer (k-ET). Thus, the isotope effect
decreases as the free-ion yields increase, and such an inverse
relationship is verified in Figure 3. For the competition in
Scheme 1, the ion yield is readily formulated as Φion ) kS-
[salt]/(kPT + kS[salt]),23 which leads to the linearized correlation
(25) The mechanistic ambiguity addressed in this study applies to other
hydrogen-atom transfer reactions, as well as a wide variety of organic
processes for which an initial electron-transfer process may be formulated.
For H-atom transfers, see: (a) Patz, M.: Fukuzumi, S. J. Phys. Org. Chem.
1997, 10, 129. For other reactions, see: (b) Olah, G. A.; Malhotra, R.;
Narang, S. C. Nitration: Methods and Mechanism; VCH: New York, 1989;
p 166 f (nitration). (c) Baciocchi, E.; Galli, C. J. Phys. Org. Chem. 1995,
8, 563 (halogenation). (d) Tolbert, L. M.; Sun, X. J.; Ashby, E. C. J. Am.
Chem. Soc. 1995, 117, 2681 (nucleophilic substitution). (e) Freilich, S. C.;
Peters, K. S. J. Am. Chem. Soc. 1985, 107, 3819 (cycloaddition). (f) Lopez,
L.; Troisi, L. Tetrahedron Lett. 1989, 30, 3097 (rearrangement of epoxides).
For organometallic examples, see: (g) Astruc, D. Electron Transfer and
Radical Processes in Transition-Metal Chemistry; VCH: New York, 1995.
Φion ) 1 + (kPT/kS) [salt]-1, and this is confirmed in Figure
-1
-1
4 by the linear plot of the reciprocal ion yields (Φion
)
versus the reciprocal salt concentration [salt]-1. Most notably,
(23) The bimolecular formulation of the salt effect in Scheme 1 is likely
to be an oversimplification, since it assumes that added salt reacts as a
simple molecular species and does not take into account the behavior of
the separated ions.