The importance of precursor and successor complex formation in a bimolecular proton-electron transfer reaction

Article abstract of DOI:10.1021/ic100143s

The transfer of a proton and an electron from the hydroxylamine 1-hydroxyl-2,2,6,6-tetramethylpiperidine (TEMPOH) to [Co^III(Hbim) (H₂bim)₂]²⁺ (H₂bim = 2,2′-biimidazoline) has an overall driving force of ΔG° = -3.0 ± 0.4 kcal mol^-1 and an activation barrier of ΔG ^° = 21.9 ± 0.2 kcal mol^-1. Kinetic studies implicate a hydrogen-bonded precursor complex at high [TEMPOH], prior to proton-electron (hydrogen-atom) transfer. In the reverse direction, [Co^II(H₂bim)₃]²⁺ + TEMPO, a similar successor complex was not observed, but upper and lower limits on its formation have been estimated. The energetics of formation of these encounter complexes are the dominant contributors to the overall energetics in this system: ΔG°′ for the proton-electron transfer step is only -0.3 ± 0.9 kcal mol^-1. Thus, formation of the precursor and successor complexes can be a significant component of the thermochemistry for intermolecular proton-electron transfer, particularly in the low-driving-force regime, and should be included in quantitative analyses.

Full text of DOI:10.1021/ic100143s

Inorg. Chem. 2010, 49, 3685–3687 3685
DOI: 10.1021/ic100143s
The Importance of Precursor and Successor Complex Formation in a
Bimolecular Proton-Electron Transfer Reaction
Elizabeth A. Mader† and James M. Mayer*
Department of Chemistry, University of Washington, Box 351700, Seattle, Washington 98195-1700.
†Current address: Chemical Sciences and Engineering Division CSE/205, Argonne National Laboratory,
Argonne, IL 60439-4837. E-mail: mader@anl.gov.
Received January 22, 2010
Scheme 1. Mechanism of HAT Involving Precursor and Successor
The transfer of a proton and an electron from the hydroxylamine 1-
hydroxyl-2,2,6,6-tetramethylpiperidine (TEMPOH) to [CoIII(Hbim)-
(H2bim)2]2þ (H2bim = 2,20-biimidazoline) has an overall driving force
of ΔG° = -3.0 ( 0.4 kcal mol-1 and an activation barrier of ΔGq =
21.9 ( 0.2 kcal mol-1. Kinetic studies implicate a hydrogen-bonded
“precursor complex” at high [TEMPOH], prior to proton-electron
(hydrogen-atom) transfer. In the reverse direction, [CoII(H2bim)3]2þ þ
TEMPO, a similar “successor complex” was not observed, but
upper and lower limits on its formation have been estimated. The
energetics of formation of these encounter complexes are the
dominant contributors to the overall energetics in this system: ΔG°0
Complexesa
for the proton-electron transfer step is only -0.3 ( 0.9 kcal mol-1
.
Thus, formation of the precursor and successor complexes can be a
significant component of the thermochemistry for intermolecular
proton-electron transfer, particularly in the low-driving-force regime,
and should be included in quantitative analyses.
a kHAT is the rate-limiting step, and K1 is the overall Keq
.
electron-transfer (ET) theories such as Marcus theory.3
When Marcus theory is applied to bimolecular ET reactions,
the reactants Aþ þ D are considered to proceed by the initial
formation of a precursor or encounter complex, Aþ|D. This
undergoes ET to form a successor complex, A|Dþ, which
then dissociates to products.4 It has long been recognized that
the energetics of the ET step must be corrected for the
energetics of formation of these precursor and successor
complexes, as indicated by the use of ΔG°0 in Marcus theory
treatments.4 Precursor and successor complexes are likely to
be more important for PCET reactions because the proton-
transfer (PT) component must occur over a very short range,1
yet they have not been included in most analyses to date.
Described here, for the first time, are the energetics of a
bimolecular PCET reaction including the precursor and
successor complexes (Scheme 1), showing that the formation
of these complexes can be energetically significant.5
Proton-coupled electron-transfer (PCET) reactions are
critical steps in a variety of biologically and industrially
important processes.1 Reactions in which one electron and
one proton transfer in a single kinetic step can be called
hydrogen-atom transfer (HAT) or, more generally, concerted
proton-electron transfer (CPET).2 Most current theoretical
models for proton-electron transfer have their roots in
*To whom correspondence should be addressed. E-mail: mayer@chem.
washington.edu.
(1) (a) Hydrogen-Transfer Reactions; Hynes, J. T., Klinman, J. P., Limback,
H.-H., Schowen, R. L., Eds.; Wiley-VCH: Weinheim, Germany, 2007. (b) Huynh,
M. H. V.; Meyer, T. Chem. Rev. 2007, 107, 5004–5064. (c) Mayer, J. M. Annu.
Rev. Phys. Chem. 2004, 55, 363–390.
(2) (a) The terminology in this area is in flux. “CPET”, coined by
Costentin et al.,2b refers to any process in which electron and proton transfer
are in the same kinetic step. The traditional term HAT is, in our view,1c,2c
best used to include all reactions in which electron and proton transfer from
one reactant to a single product. There are also narrower definitions of HAT,
for instance, restricting it to processes “in which the transferring electron and
proton come from the same bond”.1b Reaction (1) is HAT under both
definitions (although, according to the latter, the reverse reaction is not
The deprotonated cobalt(III) tris(2,20-biimidazoline) com-
plex CoIII(Hbim) reacts reversibly with the hydroxylamine
TEMPOH to slowly form the reduced protonated CoII(H2bim)
(3) (a) Hammes-Schiffer, S.; Soudackov, A. V. J. Phys. Chem. B 2008,
112, 14108–14123. (b) Tishchenko, O.; Truhlar, D. G.; Ceulemans, A.; Nguyen,
M. T. J. Am. Chem. Soc. 2008, 130, 7000–7010.
(4) (a) Marcus, R. A.; Sutin, N. Biochim. Biophys. Acta, Rev. Bioenerg.
1985, 811, 265–322. (b) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441–498.
ꢀ
HAT). (b) Costentin, C.; Evans, D. H.; Robert, M.; Saveant, J.-M.; Singh,
P. S. J. Am. Chem. Soc. 2005, 127, 12490–12491. (c) Waidmann, C. R.; Zhou,
Z.; Tsai, E. A.; Kaminsky, W.; Hrovat, D. A.; Borden, W. T.; Mayer, J. M. J. Am.
Chem. Soc. 2009, 131, 4729–4743.
r
2010 American Chemical Society
Published on Web 03/19/2010
pubs.acs.org/IC

3686 Inorganic Chemistry, Vol. 49, No. 8, 2010
Mader and Mayer
Table 1. Activation and Ground-State Thermodynamics for CoIII(Hbim) þ TEMPOH in MeCN
value at 298 Ka
ΔG°b
ΔH°b
ΔS°c
d
K1e
169 ( 23
61.3 ( 0.8
0.16 < KS < 2.6
-3.0 ( 0.4
-2.44 ( 0.05
0.27 ( 0.83
9.3 ( 0.4
-4 ( 2
41 ( 2
-9 ( 4
KP
KS
ΔGq
ΔHq
ΔSq
k-1 = k-HATKS
kHAT
(1.8 ( 0.5) ꢀ 10-4
22.5 ( 0.3
21.9 ( 0.2
9.0 ( 0.8
23 ( 2
-47 ( 3
3 ( 6
(5.25 ( 0.08) ꢀ 10-4
a Units: K1, unitless; KP, KS, M-1; k-1, M-1 s-1; kHAT, s-1. b In kcal mol-1 at 298 K. c In cal mol-1 K-1. d Data from ref 6. e ΔH°P and ΔS°P from Hess’ law.9
and the stable nitroxyl radical TEMPO (eq 1; N-N =
2,20-biimidazoline = H2bim). This is a net HAT reaction.
Equilibrium measurements, as previously described, gave K1 =
169 ( 23 at 298 K and the ΔH°1 and ΔS°1 values in Table 1.6
The kinetics of CoIII(Hbim) þ TEMPOH have been mea-
sured by observing the conversion of CoIII(Hbim) to CoII-
(H2bim) using UV-vis spectroscopy.7 Under conditions of
excess TEMPOH, the reactions proceed to completion and
are first-order in cobalt, based on studies with varying
[CoIII(Hbim)] and global analysis of the spectra from 350 to
800 nm over the course of 4-5 half-lives.7 The pseudo-first-
order rate constants kobs vary linearly with [TEMPOH] at
low concentrations but level off above 40 mM (Figure 1). The
Figure 1. 0.3 mM CoIII(Hbim) þ TEMPOH in MeCN at 298 K: (A)
UV-vis spectra vs time (45.5 mM TEMPOH) (inset: first-order fit of
absorbance at 586 nm). (B) Plot of pseudo-first-order rate constants vs
[TEMPOH].
where the intermediate is the dominant species present in
solution, are within error of the λmax and ε values predicted
for the sum of separated starting reagents. This indicates
that the intermediate is a hydrogen-bonded CoIII(Hbim)|
TEMPOH precursor complex, only slightly perturbed
from the starting materials, rather than a charge-transfer
complex or a species with a different coordination about
cobalt.
kinetics are well fit by a saturation rate law8 (eq 2); kHAT
=
(5.25 ( 0.08) ꢀ 10-4 s-1, and KP = 61.3 ( 0.8 M-1 (ΔG°P =
-2.44 kcal mol-1) at 298 K.
Alternative formulations of the intermediate involving
preequilibrium ET or PT are ruled out by the optical spectra
and thermodynamic arguments.7 In these cases, reactions
with high [TEMPO] at short times would predominantly
contain CoII(Hbim) or CoIII(H2bim), but these have optical
spectra distinct from what is observed.13a In addition, ET
from TEMPOH to CoIII(H2bim) would be endoergic by 30
kcal mol-1, based on the known E1/2 values for CoIII(Hbim)10
and TEMPOH.6 PT from TEMPOH to CoIII(Hbim) is even
more endoergic, 44 kcal mol-1 based on the known pKa
values.6,10
KPkHAT½TEMPOHꢁ
kobs
¼
ð2Þ
1 þ KP½TEMPOHꢁ
The temperature dependences (278-313 K) of the rates
from both the linear and saturated regions yield the activa-
tion parameters and the ground-state thermodynamics given
in Table 1. The values for ΔH°P and ΔS°P are in agreement
with those independently (and more precisely) determined
from the overall thermochemistry and activation parameters
using a thermochemical cycle (Hess’ law).9
The simplest kinetic saturation model is the preequili-
brium formation of an intermediate prior to the rate-
limiting step. Optical spectra of reactions at short times
and TEMPOH concentrations up to 0.2 M, conditions
To probe the properties of the successor complex, the
1
kinetics of the reverse reaction were measured both by H
NMR [5-10 mM CoII(H2bim) and 3-15 equiv of TEMPO]
and by UV-vis [1-2 mM CoII(H2bim) and up to 0.38 M
TEMPO].7 The 1H NMR spectra indicate good mass balance
and that equilibrium is reached with ∼10% conversion of
(5) (a) HAT precursor complex formation is suggested to be rate-limiting
in: Temprado, M.; McDonough, J. E.; Mendiratta, A.; Tsai, Y.-C.;
Fortman, G. C.; Cummins, C. C.; Rybak-Akimova, E. V.; Hoff, C. D.
Inorg. Chem. 2008, 47, 9380-9389. (b) For initial hydrogen-bonded complexes
that inhibit HAT, see: Litwinienko, G.; Ingold, K. U. Acc. Chem. Res. 2007, 40,
222–230.
(6) Mader, E. A.; Manner, V. W.; Markle, T. F.; Wu, A.; Franz, J. A;
Mayer, J. M. J. Am. Chem. Soc. 2009, 131, 4335–4345.
(7) See the Supporting Information.
(10) Roth, J. P.; Yoder, J. C.; Won, T. J.; Mayer, J. M. Science 2001, 294,
2524–2526.
(11) (a) King, E. L. Int. J. Chem. Kinet. 1982, 14, 1285–1286. (b) Pladziewicz
J. R.; Lesniak, J. S.; Abrahamson, A. J. J. Chem. Educ. 1986, 63, 850–851.
(12) (a) In bimolecular reactions, equilibrium constants for weak en-
counter complexes are typically estimated from the average collisional
distance.4 The estimate of 0.16 M-1 follows: (b) Eberson, L. Electron
Transfer reactions in Organic Chemistry; Springer-Verlag: Berlin, Germany,
1987; pp 32-34. (c) If the value for KS were smaller than 0.16 M-1, the
discrepancy between ΔG°0HAT and ΔG°1 would be even larger.
(8) Espenson, J. H. Chemical Kinetics and Reaction Mechanisms, 2nd ed.;
McGraw Hill, Inc.: New York, 1995.
(9) ΔH°1 = ΔH°P þ ΔHqHAT - (ΔHq-HAT þ ΔH°S). ΔH°P can be derived
using the independently determined values for ΔH°1, ΔHq
, and
HAT
(ΔHq
þ ΔH°S). An equivalent entropic relationship can be defined.
(13) Radius of {CoII(H2bim) þ TEMPO} ≈ 0.8 nm: (a) Yoder, J. C.; Roth,
J. P.; Gussenhoven, E. M.; Larsen, A. S.; Mayer, J. M. J. Am. Chem. Soc.
2003, 125, 2629–2640. (b) Roth, J. P.; Lovell, S.; Mayer, J. M. J. Am. Chem.
Soc. 2000, 122, 5486–5498.
-HAT
The calculated values of ΔH°P (Table 1) are consistent with those measured
directly (ΔH°P = -6 ( 4 kcal mol-1; ΔS°P = -13 ( 12 cal mol-1 K-1) but
have smaller error bars.

Communication
Inorganic Chemistry, Vol. 49, No. 8, 2010 3687
CoII(H2bim). The data are well fit by an opposing second-
order approach-to-equilibrium kinetic model (eq 3),11 with
k-1 = (1.8 ( 0.5) ꢀ 10-4 M-1 s-1 at 298 K. Eyring analysis
of the rate constants from 273 to 313 K is shown in Table 1.
No saturation was observed up to 0.38 M TEMPO.
d½CoIII
ꢁ
kHATKP½CoIIIꢁ½TEMPOHꢁ -k-HATKS½CoIIꢁ½TEMPOꢁ
1 þ KPð½CoIIIꢁ þ ½TEMPOHꢁÞ
-
¼
dt
ð3Þ
The first-order kinetic behavior in [TEMPO] indicates that
under these conditions the successor complex CoII(H2bim)|
TEMPO is formed only to a small extent. Analysis with a full
kinetic model based in Scheme 1 (see the Supporting In-
formation) indicates that KS must be less than 2.6 M-1. The
successor complex, although not observed, likely involves a
hydrogen bond from CoII(H2bim) to the nitroxyl radical.
This analysis assumes that the formation of the precursor and
successor complexes is fast on the time scale of the HAT
reaction, which is reasonable given that the formation of
hydrogen-bonded adducts is usually fast and that kHAT is
small, <10-3 s-1. A standard collisional model12 can be used
to estimate a lower limit for the formation of the successor
complex, KS ≈ 0.16 M-1, using molecular radii roughly
estimated from crystallographic data.13 The range 2.6 M-1
> KS > 0.16 M-1 indicates that the free energy of formation
of the successor complex is 1.1 > ΔG°S > -0.56 kcal mol-1
Figure 2. Free-energy surface for the reaction of CoIII(Hbim) þ TEM-
POH in MeCN (eq 1). The uncertainty in ΔG°S for the formation of
CoII(H2bim)|TEMPO is indicated by the error bar. The top half of the
figure is not to scale, as indicated by the breaks in the lines.
steric interactions and hydrogen bonding are energetically
significant. The CoIII(Hbim)|TEMPOH complex implicated
here is likely to be structurally very similar to the precursor
complex although that may not always be the case. The
energetics of PCET precursor and successor complexes could
in some cases be estimated using empirical models for hydro-
gen-bond energies,7,14 although the parameters needed are
often not available for metal complexes or organic radicals.
Hydrogen bonds are also important in organic HAT reactions,
but for a somewhat different reason: a hydrogen-atom donor
such as phenol must shed its hydrogen-bonded solvent prior to
reaction with an organic radical.5b
In conclusion, precursor and successor complexes are an
important part of PCET reactions. These complexes have
specific orientations that are important to the PCET process.
The energetics of their formation, as indicated by the CoIII-
(Hbim) þ TEMPOH reaction analyzed here, can be a sub-
stantial component of the overall energy change. This is
particularly the case in the low-driving-force regime that is
important in biological and energy-conversion PCET pro-
cesses.1 Because the precursor and successor complexes have
both steric interactions and hydrogen bonds, their energies
of formation cannot be estimated with the electrostatic
models common for ET reactions. These conclusions have
important implications for analyses of PCET systems, from
mechanistic arguments1,15 to the application of the Marcus
cross relation10,16 to sophisticated quantum theories.1,3a
or ΔG°S = 0.27 ( 0.83 kcal mol-1
.
The free energies of activation and complex formation for
reaction (1) are illustrated in Figure 2. The free energy for
unimolecular HAT, ΔG°0HAT, is given by the overall free energy
ΔG°1 minus the difference between the energies of forming
the precursor (P) and successor (S) complexes, ΔG°S and ΔG°P
(eq 4).4 ΔG°0HAT is clearly very different from the overall free
energy change, ΔG°1. Quantitatively, ΔG°0HAT = -0.3 (
0.9 kcal mol-1, roughly isoergic. In contrast, the overall
ΔG°1 is significantly downhill, -3.0 ( 0.4 kcal mol-1 (K1 =
169). The 2.7 ( 0.9 kcal mol-1 difference between ΔG°0HAT
and ΔG°1 is due to the much higher equilibrium constant for
the precursor complex than for the successor complex. This is
likely due to the TEMPOH f CoIII(Hbim) hydrogen bond
being stronger than the CoII(H2bim) f TEMPO hydrogen
bond.
ΔG°0HΑΤ ¼ ΔG°1 þ ΔG°S -ΔG°P
ð4Þ
The precursor and successor (P and S) complexes for
PCET are quite different from those for ET. Electrons can
tunnel over multiple-angstrom distances, so there are usually
no orientation requirements for the P and S complexes. These
are typically treated as weak “encounter” complexes whose
energies of formation can be estimated by electrostatic
models.12 In PCET, however, the transfer of the proton
occurs over tenths of angstroms, typically along a specific
axis and often within a hydrogen bond. Therefore, the simple
electrostatic models used for ET are not appropriate for
PCET. For instance, they predict that ΔG°P = ΔG°S because
no net charge is transferred [for reaction (1), there is no
electrostatic work because TEMPO and TEMPOH are
neutral reactants].
Acknowledgment. We thank the U.S. National Insti-
tutes of Health (Grant GM50422 to J.M.M.) and the
Natural Sciences and Engineering Research Council of
Canada (Grant NSERC PGS-D2 to E.A.M.) for financial
support. The authors are also indebted to Drs. J. P. Roth
and J. C. Yoder for their prior studies on this system.
Supporting Information Available: Experimental details and
kinetic thermochemical analysis. This material is available free
of charge via the Internet at http://pubs.acs.org.
(14) Abraham, M. H. Chem. Soc. Rev. 1993, 22, 73–83.
(15) Compare refs 1, 13, 16, and: Concepcion, J. J.; Brennaman, M. K.;
Deyton, J. R.; Lebedeva, N. V.; Forbes, M. D. E.; Papanikolas, J. M.;
Meyer, T. J. J. Am. Chem. Soc. 2007, 129, 6968–6969.
(16) Warren, J. J.; Mayer, J. M. Proc. Natl. Acad. Sci. U.S.A., doi:10.1073/
pnas.0910347107.
Precursor and successor complexes for PCET (and PT)
likely have specific orientation requirements in which both