Electron-transfer mechanisms with photoactivated quinones. The encounter complex versus the Rehm-Weller paradigm

Article abstract of DOI:10.1021/ja982710z

Photoexcited quinones (Q*) are efficiently quenched by polymethylbenzenes (ArH) via electron transfer (ET). However, the second-order rate constants (k₂) exhibit Rehm-Weller (outer-sphere) dependence on the free energy (ΔG_ET), despite our new findings that the quenching occurs via a series of rather strong encounter complexes [Q*, ArH] with substantial (charge-transfer) bonding. The relatively high formation constants (K_EC) of the encounter complexes indicate that any mechanistic interpretation of the driving-force dependence of the observed rate constants is highly ambiguous since k₂ must be a composite of K_EC and the intrinsic rate constant (k_ET) for electron transfer within the intermediate (inner-sphere) complex. As such, the reorganization energies extracted from Rehm-Weller plots lack thermodynamic significance. On the other hand, the unambiguous driving-force dependence of k_ET represents a unique example for the "normal" Marcus behavior of the endergonic electron transfer between the donor/acceptor pair in van der Waals contact as extant in the encounter complex.

Full text of DOI:10.1021/ja982710z

1688
J. Am. Chem. Soc. 1999, 121, 1688-1694
Electron-Transfer Mechanisms with Photoactivated Quinones. The
Encounter Complex versus the Rehm-Weller Paradigm
Stephan M. Hubig and Jay K. Kochi*
Contribution from the Department of Chemistry, UniVersity of Houston, Houston, Texas 77204-5641
ReceiVed July 30, 1998
Abstract: Photoexcited quinones (Q*) are efficiently quenched by polymethylbenzenes (ArH) via electron
transfer (ET). However, the second-order rate constants (k2) exhibit Rehm-Weller (outer-sphere) dependence
on the free energy (∆GET), despite our new findings that the quenching occurs via a series of rather strong
encounter complexes [Q*, ArH] with substantial (charge-transfer) bonding. The relatively high formation
constants (KEC) of the encounter complexes indicate that any mechanistic interpretation of the driving-force
dependence of the observed rate constants is highly ambiguous since k2 must be a composite of KEC and the
intrinsic rate constant (kET) for electron transfer within the intermediate (inner-sphere) complex. As such, the
reorganization energies extracted from Rehm-Weller plots lack thermodynamic significance. On the other
hand, the unambiguous driving-force dependence of kET represents a unique example for the “normal” Marcus
behavior of the endergonic electron transfer between the donor/acceptor pair in van der Waals contact as
extant in the encounter complex.
Introduction
The question whether excited charge-transfer complexes (or
exciplexes) are or are not crucial intermediates in electron-trans-
fer quenching reactions is as old as the Rehm-Weller relation-
ship itself. In particular, the frequent observation of exciplex
emissions8,9 upon photoexcitation of donors and acceptors
challenges the general validity of the “outer-sphere” model, and
recent fluorescence-quenching studies in acetonitrile even
question its suitability in highly polar media.10 As a result, an
alternative mechanism for fluorescence quenching in polar media
has been proposed to account for long-lived exciplexes with
formation constants that are much greater than those for
diffusional encounters.11 In a recent study,12 we investigated
the quenching reactions of a series of donor/acceptor systems
that experience strong complex formation between the excited
acceptor and the donor quencher prior to electron transfer. Thus,
photoexcited quinones (Q*) and polymethylbenzene donors
(ArH) form encounter complexes13 with formation constants up
to 200 M-1 in various solvents of different polarity, as
determined by time-resolved absorption measurements on the
picosecond/nanosecond time scale. Most importantly, the ab-
Fluorescence quenching processes that occur via an electron-
transfer mechanism are commonly evaluated using the Rehm-
Weller correlation1,2 which relates the second-order rate con-
stants to the free-energy change (∆GET) of the electron-transfer
step. Thus, electron-transfer rate constants are frequently
calculated for donor/acceptor systems with known redox po-
tentials and excited-state energies,3 and redox potentials of
excited-state and ground-state species are estimated from the
rate constants of quenching processes with donors and acceptors
with well-known redox potentials.4 The free-energy correlation
introduced by Rehm and Weller1,2 is an empirical equation to
fit the observed driving-force dependence of the fluorescence
quenching rate constants. However, the underlying reaction
scheme is adopted from the kinetic description of an outer-sphere
electron transfer involving purely diffusional encounters between
weakly coupled donors and acceptors.5-7 As such, Rehm and
Weller concluded that an intermediate formation of excited
complexes8 must be excluded from the electron-transfer mech-
anism of the quenching process that follows their correlation.1
(8) (a) Mataga, N.; Okada, T.; Yamamoto, N. Chem. Phys. Lett. 1967,
1, 119. (b) Okada, T.; Matsui, H.; Oohari, H.; Matsumoto, H.; Mataga, N.
J. Chem. Phys. 1968, 49, 4717.
(9) Gordon, M., Ware, W. R., Eds. The Exciplex; Academic Press: New
York, 1975.
(10) (a) Kikuchi, K.; Niwa, T.; Takahashi, Y.; Ikeda, H.; Miyashi, T.;
Hoshi, M. Chem. Phys. Lett. 1990, 173, 421. (b) Kikuchi, K.; Takahashi,
Y.; Katagiri, T.; Niwa, T.; Hoshi, M.; Miyashi, T. Chem. Phys. Lett. 1991,
180, 403. (c) Gould, I. R.; Farid, S. J. Phys. Chem. 1992, 96, 7635. (d)
Gould, I. R.; Young, R. H.; Mueller, L. J.; Farid, S. J. Am. Chem. Soc.
1994, 116, 8176.
(1) Rehm, D.; Weller, A. Ber. Bunsen-Ges. 1969, 73, 834.
(2) Rehm, D.; Weller, A. Isr. J. Chem. 1970, 8, 259.
(3) (a) Ballardini, R.; Varani, G.; Indelli, M. T.; Scandola, F.; Balzani,
V. J. Am. Chem. Soc. 1978, 100, 7219. (b) Caldwell, R. A.; Creed, D.;
DeMarco, D. C.; Melton, L. A.; Ohta, H.; Wine, P. H. J. Am. Chem. Soc.
1980, 102, 2369. (c) Baggott, J. E.; Pilling, M. J. J. Chem. Soc., Faraday
Trans. 1 1983, 79, 221. (d) Creutz, C.; Sutin, N. J. Am. Chem. Soc. 1977,
99, 241. (e) Allonas, X.; Jacques, P. Chem. Phys. 1997, 215, 371. (f)
Kavarnos, G. J.; Turro, N. J. Chem. ReV. 1986, 86, 401. (g) Chen, J.-M.;
Ho, T.-I.; Mou, C.-Y. J. Phys. Chem. 1990, 94, 2889.
(4) (a) Murphy, S.; Schuster, G. B. J. Phys. Chem. 1995, 99, 511. (b)
Bock, C. R.; Connor, J. A.; Gutierrez, A. R.; Meyer, T. J.; Whitten, D. G.;
Sullivan, B. P.; Nagle, J. K. J. Am. Chem. Soc. 1979, 101, 4815.
(5) (a) Marcus, R. A. J. Chem. Phys. 1956, 24, 966. (b) Marcus, R. A.
Discuss. Faraday Soc. 1960, 29, 129.
(6) (a) Hush, N. S. Trans. Faraday Soc. 1961, 57, 557. (b) Sutin, N.
Acc. Chem. Res. 1968, 1, 225.
(7) For reviews, see: (b) Cannon, R. D. Electron-Transfer Reactions;
Butterworth: London, 1980. (c) Eberson, L. AdV. Phys. Org. Chem. 1982,
18, 79.
(11) (a) Sadovskii, N. A.; Kuzmin, M. G.; Go¨rner, H.; Schaffner, K.
Chem. Phys. Lett. 1998, 282, 456. (b) Kuzmin, M. G. J. Photochem.
Photobiol. 1996, A102, 51. (c) Kuzmin, M. G. Pure Appl. Chem. 1993, 65,
1653. (d) Kuzmin, M. G.; Sadovskii, N. A.; Vainshtein, Yu. A. High Energy
Chem. 1992, 26, 416. (e) As pointed out by one of the reviewers, the
possibility of exciplex formation was already mentioned by Rehm and
Weller in ref 2. (f) For the bearing of the Kuzmin mechanism on our results,
see the Discussion.
(12) Rathore, R.; Hubig. S. M.; Kochi, J. K. J. Am. Chem. Soc. 1997,
119, 11468.
10.1021/ja982710z CCC: $18.00 © 1999 American Chemical Society
Published on Web 02/13/1999

Electron-Transfer Mechanisms with PhotoactiVated Quinones
J. Am. Chem. Soc., Vol. 121, No. 8, 1999 1689
Chart 1
quinones in their excited triplet states (Q*) with unit efficiency
in acetonitrile solution.12,16 The characteristic absorption spec-
trum of Q* 17 decayed to the spectral baseline on the micro-
second time scale with rate constants of kd < 5 × 104 s-1 18
.
However, in the presence of the aromatic donors (ArH in Chart
1), Q* decayed significantly faster, and the concomitant for-
mation of the quinone anion radical (Q•-)19 and the arene cation
radical (ArH•+)20 was observed with identical (first-order) rate
constants for Q* decay and ion formation. Quantitative analysis
of the time-resolved absorption spectra established the forma-
tion of the ion radicals Q•- and ArH•+ to occur in a 1:1 ratio
with unit efficiency,12 i.e.
k2
Q* + ArH
8 Q•- + ArH•+
(1)
(CH3CN)
A. Kinetic Evaluation Using the Pseudo-First-Order
Approximation. The kinetics of the electron-transfer quenching
of Q* in eq 1 was examined by monitoring the decay of Q*
(or the simultaneous growth of Q•- and ArH•+) as a function
of added arene. Figure 1A shows a typical plot of the observed
(first-order) rate constant (kobs) for the decay of Q* versus [ArH]
as exemplified by the electron-transfer quenching of photoex-
cited dichloroxyloquinone (CX*) by 1,2,4-trimethylbenzene
(TMB) in acetonitrile. Thus, for concentrations [TMB] < 0.02
M, a linear dependence of kobs on the arene concentration was
obtained, and the slope of the pseudo-first-order plot yielded
the second-order rate constant k2 ) 4 × 107 M-1 s-1 for the
electron transfer from TMB to CX* (compare eq 1). A slightly
lower value of k2 ) 1.5 × 107 M-1 s-1 was obtained for the
same quenching reaction in dichloromethane,21 and the k2 values
for the other quinone/arene combinations in acetonitrile and
dichloromethane solution are compiled in Table 1.
sorption spectra of the intermediate [Q*, ArH] complexes exhibit
characteristic near-IR absorptions, the analysis of which points
to high degrees of charge transfer.14 Thus, these donor/acceptor
systems clearly do not meet the criterion set by a weak-coupling
limit for outer-sphere electron transfer.5
In this study, we now examine an extended series of poly-
methylbenzene donors (see Chart 1) to scrutinize the driving-
force (∆GET) dependence of the electron-transfer quenching of
the excited quinone acceptors. We will show that, despite the
strong donor/acceptor interactions between photoexcited quino-
nes and polymethylbenzenes,12 the quenching rate constants can
follow a driving-force dependence that is readily fitted to the
Rehm-Weller relationship.1,2 As such, the data presented here
will demonstrate that Rehm-Weller-type free-energy relation-
ships cannot provide conclusive evidence for the outer-sphere
electron-transfer mechanism. Indeed, we will show that, due to
the two-step quenching mechanism, the second-order rate
constants are in fact composite quantities. Thus, the ambiguous
driving-force dependence raises serious questions about the
validity of reorganization energies formally extracted from the
Rehm-Weller plots. Since the driving-force dependence of the
intrinsic electron transfer within the encounter complex is
conjectural, we describe how it may be used to verify electron-
transfer theories.
B. Kinetics Evaluation Including the Preequilibrium Step.
At higher (>0.02 M) arene concentrations, kobs did not increase
linearly with [ArH], but approached a plateau value for [TMB]
> 0.6 M (see Figure 1A). Such a saturation (asymptotic)
behavior of kobs was symptomatic of a preequilibrium intermedi-
ate22 between the excited quinone and the aromatic donor, which
(15) Mulliken theory describes the wave function (ΨAD) of a charge-
transfer complex primarily as the sum of the dative (bonding) function (ψ1)
and the “no-bond” function (ψ0), i.e., ΨAD ) a ψ0(A,D) + b ψ1(A-,D+)
+ ... See: (a) Mulliken, R. S. J. Am. Chem. Soc. 1950, 72, 600. (b) Mulliken,
R. S. J. Am. Chem. Soc. 1952, 74, 811. (c) Mulliken, R. S.; Person, W. B.
Molecular Complexes; Wiley: New York, 1969.
(16) (a) Gschwind, R.; Haselbach, E. HelV. Chim. Acta 1979, 62, 941.
(b) Kemp, D. R.; Porter, G. J. Chem. Soc. (D) 1969, 1029. (c) Porter, G.;
Topp, M. R. Proc R. Soc. London 1970, A315, 163. (d) Kobashi, H.; Gyoda,
H.; Morita, T. Bull. Chem. Soc. Jpn. 1977, 50, 1731.
(17) The transient spectrum of the triplet excited states of CA and CX
exhibit double maxima at 380 and 510 nm and at 370 and 500 nm,
respectively.12,16 The transient absorption spectrum obtained upon 10-ns
laser excitation (at 355 nm) of DDQ in acetonitrile exhibits a single
absorption band centered at 640 nm.
Results
I. Electron-Transfer Quenching of Photoexcited Quinones
by Polymethylbenzene Donors. Photoexcitation of the quinones
(Q in Chart 1) with a 10-ns laser pulse at 355 nm generated the
(18) Hubig, S. M. Unpublished results. See also ref 16a.
(19) (a) The anion radicals of CA, CX, and DDQ absorb at 450 nm,19b
430 nm,12 and 440/600 nm,19c respectively. (b) Andre´, J. J.; Weill, G. Mol.
Phys. 1968, 15, 97. (c) Desbe`ne-Monvernay, A.; Lacaze, P. C.; Cherigui,
A. J. Electroanal. Chem. 1989, 260, 75.
(13) (a) Complexes between excited acceptors and donors (in the ground
state) are also termed “exciplexes”.8-11 Since the term exciplex is frequently
used in a wider, but rather ambiguous way that includes both charge-transfer
complexes in the excited state (as defined here) as well as ion-radical
pairs,13b,c we avoid this terminology to minimize confusion. (b) Levin, P.
P.; Kuzmin, V. A. Russ. Chem. ReV. 1987, 56, 307. (c) Tahara, T.;
Hamaguchi, H.-O. J. Phys. Chem. 1992, 96, 8252. See also ref 30.
(14) On the basis of Mulliken theory,15 the degree of charge transfer
can be estimated from the formation enthalpy (∆Hf) and the absorption
maximum (hνCT) of the charge-transfer complex as (b/a)2 = -∆Hf/(hνCT).
See: (a) Ketalaar, J. A. A. J. Phys. Radium 1954, 15, 197. (b) Tamres, M.;
Brandon, M. J. Am. Chem. Soc. 1960, 82, 2134. (c) See also Rathore et al.
in ref 12.
(20) (a) The polymethylbenzene cation radicals absorb between 450 and
500 nm.20b,c (b) Bockman, T. M.; Karpinski, Z. J.; Sankararaman, S.; Kochi,
J. K. J. Am. Chem. Soc. 1992, 114, 1970. (c) Sehestad, K.; Holcman, J.;
Hart, E. J. J. Phys. Chem. 1977, 81, 1363.
(21) In dichloromethane solution, the quenching of Q* by polymethyl-
benzenes (ArCH3) results in the formation of semiquinone (QH•) and benzyl
•
(ArCH2 ) radicals. However, salt-effect studies unambiguously show that
the hydrogen transfer occurs via (rate-determining) electron transfer followed
by fast proton transfer. See: Bockman, T. M.; Hubig, S. M.; Kochi, J. K.
J. Am. Chem. Soc. 1998, 120, 2826.
(22) Bunnett, J. F. In InVestigation of Rates and Mechanisms of
Reactions; Part 1; Bernasconi, C. F., Ed.; Wiley: New York, 1986; p 286f.

1690 J. Am. Chem. Soc., Vol. 121, No. 8, 1999
Hubig and Kochi
Figure 1. (A) Saturation (asymptotic) behavior of the observed (first-order) rate constants for the electron-transfer quenching of CX* by 1,2,4-
trimethylbenzene (TMB) in acetonitrile and (B) its double-reciprocal evaluation according to eq 3. The inset in (A) magnifies the linear portion of
the plot for [TMB] < 0.02 M.
Table 1. Kinetic Parameters for the Electron-Transfer Quenching
of Photoexcited Quinones by Polymethylbenzene Donors
corresponded to the intrinsic rate constant (kET) of the electron
transfer within the encounter complex. [Note that we find that
back electron transfer (k-ET) in Scheme 1 is negligible for the
donor/acceptor couples in Chart 1 owing to the high ion-radical
yields (φion > 0.9).41] Accordingly, the curved kinetics plots
such as in Figure 1A were evaluated in a double-reciprocal
(linearized) representation12 (see Figure 1B), from which the
preequilibrium constant (KEC) and the intrinsic electron-transfer
rate constant (kET) were extracted (see eq 323). [Note that the
direct relationship in eq 3 is valid under the conditions in which
(i) the natural decay (k0) of Q* (in the absence of donors) is
∆GET
k2d [106 KEC
kET
KECkETg [106
b
e
f
Q*/ArHa [eV] solventc M-1 s-1] [M-1] [106 s-1
CX*/MES +0.49
]
M-1 s-1
]
A
D
A
D
A
D
A
D
A
D
D
A
D
A
D
A
D
D
A
D
A
4.0 1.7
5.3 4.0
6.3 4.3
2.2 2.4
2.3
2.1
2.4
1.9
17
4.5
11
2
3.9
8.4
10.3
4.6
46
18
10
CX*/XYL +0.44
CX*/TMB +0.27
CA*/TOL +0.25
40
15
2.7
4.0
7.0 0.9
15
2600
300
8.7
15
14
39
h
67
h
17
CX*/DUR +0.21
170
27
55
h
110
h
2550
378
2145
h
7370
h
1080
h
1200
h
negligibly slow as compared to the electron-transfer step
12,18
(kET
)
and (ii) the preequilibrium step (KEC) in eq 2 is
CX*/PMB +0.13
CX*/HMB (0
1500
5140
5500
4400
1150
5400
1200
12000
8000
12000
21000
established much faster than the follow-up electron transfer.23]
Thus, the double-reciprocal plot in Figure 1B yielded KEC
)
2.7 M-1 and kET ) 1.7 × 107 s-1 for the electron transfer from
CA*/MES -0.04
30
h
36
h
TMB to CX* in acetonitrile. The same kinetic evaluation in
CA*/XYL
-0.09
dichloromethane solution yielded KEC ) 4.0 M-1 and kET
)
<10
120
h
4.5 × 106 s-1, and the KEC and kET values for the other quinone/
arene combinations in acetonitrile and dichloromethane solutions
are listed in Table 1. The most striking result of this kinetic
evaluation was that the KEC values in Table 1 deviated
substantially from the unit value24 calculated for purely diffu-
sional encounters (see the Discussion).
CA*/DUR -0.32
CA*/HMB -0.53
h
h
h
h
h
h
h
h
h
h
DDQ*/HMB -1.02
a See Chart 1. b Free energy of the electron-transfer reaction as
calculated using eq 5. c A ) acetonitrile, D ) dichloromethane. d Rate
constant for bimolecular electron transfer as determined from the slope
of the initial linear portion of the kinetics plots such as in Figure 1A.
e Equilibrium constant ((10-20%) for encounter-complex formation
as determined using eq 3. f Intrinsic (first-order) rate constant ((10-
20%) for electron transfer within the encounter complex as determined
using eq 3. g As determined from the slope of the double-reciprocal
plot such as in Figure 1B (see eq 3). h Not determined owing to
insufficient curvature in the kinetics plots (see text).
(23) (a) The following double-reciprocal relationship between the
observed rate constant (kobs) and the arene concentration ([ArH]) was
applied:12
1
1
1
k
1
)
+
(3)
kobs kET KEC
ET [ArH]
(b) For the general kinetics basis of eq 3, see: Espenson, J. D. Chemical
Kinetics and Reaction mechanisms, 2nd ed.; McGraw-Hill: New York,
1995; p 89f. (c) For the decay kinetics of photoexcited quinones, see:
Kobashi, H.; Okada, T.; Mataga, N. Bull. Chem. Soc. Jpn. 1986, 59, 1975.
(d) Equation 3 is based on the assumptions that k-d . kET and k-d + kd
[ArH] > 2kET(k-d - kd[ArH]), with kd and k-d being the rate constants for
diffusional formation and dissociation of the encounter complex, re-
spectively.23e Both conditions are met even for the fastest electron transfers
(kET = 108 s-1). (e) Ware, W. R.; Watt, D.; Holmes, J. D. J. Am. Chem.
Soc. 1974, 96, 7853.
(24) The equilibrium constant K depends on the effective encounter
distance R between the donor and the acceptor. For the encounter complex
between uncharged species with distance R ) 7 Å, the formation constant
is estimated to be K ) 0.9 M-1. See: Eigen, M. Z. Phys. Chem. N. F.
(Frankfurt am Main) 1954, 1, 176.
was previously identified as the encounter complex [Q*,
ArH],12,13 i.e.
Scheme 1
KEC
kET
[Q*, ArH]
encounter
complex
Q* + ArH y z
y z Q•-, ArH•+
(2)
kET
Thus, the limiting value of kobs at high donor concentrations

Electron-Transfer Mechanisms with PhotoactiVated Quinones
J. Am. Chem. Soc., Vol. 121, No. 8, 1999 1691
Figure 2. Rehm-Weller treatment of the free-energy (∆GET) depen-
dence of the second-order quenching rate constants (k2) in acetonitrile
(b) and dichloromethane (0) solution. The solid line represents the
best fit of the data points according to eqs 6 and 7 with ∆GqET(0) )
0.15 eV.
Figure 3. Bell-shaped free-energy (∆GET) dependence of the formation
constant KEC for the encounter complex [Q*, ArH] in acetonitrile (0),
dichloromethane (b), chloroform (9), and carbon tetrachloride (O),
partially based on the data in ref 41.
C. Interdependence of k2, KEC, and kET. At low arene
concentrations, eq 323 simplified to a linear correlation between
kobs and [ArH] to reveal the direct relationship between k2 (in
eq 1) and KEC and kET (in eq 2), i.e.
a mild increase of less than 1 order of magnitude over the entire
exergonic region (-1.5 eV < ∆GET < 0 eV). This driving-
force dependence was similar to that observed previously for
the electron-transfer quenching of various aromatic donors and
acceptors in the excited singlet state.1-4 Despite the fact that
our experimental conditions (i.e., triplet quenching and equi-
librium constants KEC . 1) were significantly different from
those for fluorescence-quenching experiments, we arbitrarily
fitted our data to eq 6 (as illustrated in Figure 2), to probe the
kobs ) KECkET[ArH] ) k2[ArH]
(4)
Thus, the second-order rate constants k2 for electron transfer
from ArH to Q* could be obtained from either the initial slope
of the pseudo-first-order plot (see inset to Figure 1A) or the
slope of the double-reciprocal plot (see Figure 1B) as the product
K
ECkET (compare columns 4 and 7 in Table 1). In other words,
k2 ) (2 × 1010)/{1 + 0.25[exp(∆GET/RT) +
exp(∆GqET/RT)]} M-1 s-1 (6)
the second-order rate constant k2 in eq 2 represented a composite
quantity, the components of which we examined independently
in terms of their driving-force dependence as follows.
II. Driving-Force (∆GET) Dependence of k2, KEC, and kET
for the Electron-Transfer Quenching of Photoexcited Quino-
nes by Polymethylbenzenes. To study the driving-force
dependence of the electron-transfer quenching of Q* by ArH
in eqs 1 and 2, the free-energy change (∆GET) was calculated
general applicability of the Rehm-Weller relationship.1,2 In eq
6, k2 is the second-order (electron-transfer) rate constant and
∆GET and ∆GqET are the free-energy change and the activation
enthalpy of the electron transfer, respectively. The activation
enthalpy ∆Gq was taken as a monotonic function of ∆GET
ET
according to eq 5, where E0 is the oxidation potential of the
according to the standard Rehm-Weller formulation,1,2 i.e.
ox
∆GET ) E0ox - E*red + constant
(5)
∆GqET ) {(∆GET/2)2 + (∆GqET(0))2}1/2 + ∆GET/2 (7)
where ∆GqET(0) is the activation enthalpy at ∆GET ) 0. Since
there was no substantial difference in the absolute values of k2
and its driving-force dependence for the two solvents in Table
1, all the experimental data could be simulated with a single
Rehm-Weller parameter, ∆GqET(0) ) 0.15 eV (see the solid
line in Figure 2).27
polymethylbenzene donor (ArH) and E*red is the reduction
potential of the photoactivated quinone (Q*) in Chart 1.25
A. Driving-Force Dependence of the Rate Constant k2. The
second-order rate constants k2 in Table 1 varied over 4 orders
of magnitude from the most endergonic electron-transfer couple
(CX*/MES) to the most exergonic couple (DDQ*/HMB).
Figure 2 demonstrates that the rate constants did not increase
linearly with the exergonicity of the electron transfer, but a sharp
increase over more than 3 orders of magnitude was observed
in the endergonic region (0 eV < ∆GET < 0.5 eV) followed by
B. Driving-Force Dependence of KEC. Figure 3 illustrates
the driving-force dependence of the formation constant KEC for
the encounter complexes [Q*, ArH] in eq 2. Thus, a bell-shaped
correlation between KEC and ∆GET was obtained in dichlo-
romethane (filled circles) with a maximum value of KEC ) 67
M-1 at ∆GET ) 0 eV. Importantly, KEC values close to unity
(25) (a) The reduction potential of the photoactivated quinones (E*red
)
is calculated as the sum of the triplet energy of the quinone (ET = 2.2
eV)26 and the reduction potential of the quinone in its ground state.25b,c See
also ref 2. (b) Mann, C. K.; Barnes, K. K. Electrochemical Reactions in
Non-Aqueous Systems; Dekker: New York, 1970. (c) Peover, J. E. J. Chem.
Soc. 1962, 4540. (d) For the oxidation potentials of the polymethylbenzenes
in Chart 1, see: Howell, J. O.; Goncalvez, J. M.; Amatore, C.; Klasinc, L.;
Wightman, R. M.; Kochi, J. K. J. Am. Chem. Soc. 1984, 106, 3968. (e)
The Coulombic work term (e2/ꢀR) is assumed to be constant for all donor/
acceptor combinations employed in this study.
(26) (a) Shcheglova, N. A.; Shigorin, D. N.; Yakobson, G. G. Y.;
Tushishvili, L. Sh. Russ. J. Phys. Chem. 1969, 43, 1112. (b) Trommsdorff,
H. P.; Sahy, P.; Kahane-Paillous, J. Spectrochim. Acta 1970, 26A, 1135.
(c) Herre, W.; Weis, P. Spectrochim. Acta 1973, 29A, 203.
were obtained in the endergonic free-energy region (∆GET
>
0.3 eV) and in the exergonic region (∆GET < -0.1 eV). A
similar bell-shaped correlation was observed previously in
chloroform (filled squares) and carbon tetrachloride (open
(27) To achieve a satisfactory overlap between the experimental data
and the Rehm-Weller simulations, all the experimental ∆GET values of
Table 1 are shifted by R ) -0.25 eV. For a theoretical explanation of the
shift parameter R in triplet-quenching experiments, see: Tamura, S.-I.;
Kikuchi, K.; Kokubun, H.; Usui, Y. Z. Phys. Chem. N. F. (Wiesbaden)
1978, 111, 7.

1692 J. Am. Chem. Soc., Vol. 121, No. 8, 1999
Hubig and Kochi
description of the intermediate donor/acceptor complex. Thus,
neither the purely diffusional encounters prior to electron transfer
as implied by Rehm and Weller1,2 nor the alternative exciplex
formation by “gradual electron shift” as invoked by Kuzmin et
al.11 matches our description of the encounter complex, which
is best described as the excited-state counterpart of (ground-
state) electron donor-acceptor (or charge-transfer) com-
plexes.30 This encounter complex is the critical intermediate prior
to electron transfer. Accordingly, any free-energy (or driving-
force) consideration of the resulting two-step electron transfer
(see eq 2) must include three kinetics parameters, viz., k2, KEC
,
and kET. As such, we now analyze their mechanistic relevance
as follows.
I. Driving-Force Dependence of k2 and Mechanistic
Significance of the Rehm-Weller Correlation. First, we note
that the driving-force dependence of the second-order rate
constant (k2) for electron-transfer quenching of photoexcited
quinones by polymethylbenzenes can be satisfactorily accom-
modated by the Rehm-Weller correlation in Figure 2.1,2
Furthermore, the only parameter that defines the shape of the
driving-force dependence of k2 in the Rehm-Weller formulation
(see eqs 6 and 7) is the activation enthalpy ∆GqET(0), which
establishes both the position and the steepness of the falloff of
k2 in the endergonic region, whereas the plateau of k2,max = 2
× 1010 M-1 s-1 in the exergonic region corresponds to the
diffusional limit of the rate constant in bimolecular reactions.31
For the electron-transfer quenching of photoexcited quinones,
the best fit of the steep falloff of k2 in the endergonic ∆GET
range yields a reasonable value for the activation enthalpy of
∆GqET(0) ) 0.15 eV.1-4
According to Rehm and Weller, a good agreement between
the experimental quenching data and the free-energy correlation
in eq 6 points to an outer-sphere electron-transfer mechanism,
which must not involve the intermediate formation of excited
charge-transfer complexes.1 However, such a mechanistic
conclusion applied to the quenching of the excited quinones is
in striking contrast to the experimental findings in this study,
viz., the observation of strong encounter complexes which
exhibit substantial (charge-transfer) bonding between the poly-
methylbenzene donor and the quinone acceptor moieties.12 In
Figure 4. Normal free-energy (∆GET) dependence of the intrinsic rate
constant (kET) for electron transfer within the encounter complex in
dichloromethane.
circles),12 and the data points obtainable in acetonitrile28 seem
to follow the same trend (open squares).
C. Driving-Force Dependence of kET. Figure 4 shows the
driving-force (∆GET) dependence of the intrinsic rate constant
kET for the electron transfer within the encounter complex of
polymethylbenzenes and photoexcited quinones in dichlo-
romethane. The kET values increased over 2 orders of magnitude
in a sigmoidal function from the most endergonic electron-
transfer couple (CX*/MES) with ∆GET ) 0.49 eV to the iser-
gonic couple (CX*/HMB) with ∆GET ) 0 eV. In the exergonic
region (∆GET < 0), the kET values were somewhat scattered
around an (apparent) plateau value of kmax = 108 s-1 29
.
Discussion
The interaction of photoexcited quinones (Q*) with polym-
ethylbenzenes (ArH) in acetonitrile leads to the formation of
quinone anion radicals (Q•-) and polymethylbenzene cation
radicals (ArH•+) with unit efficiency (see eq 1),12 and thus
represents a typical bimolecular electron-transfer quenching
process.21 Accordingly, current electron-transfer theories1,2,5-7
predict the second-order rate constant (k2) in eq 1 to show a
(30) (a) Our definition more closely matches Mataga’s and Turro’s
description of an exciplex (see ref 23c and Figure 2 in ref 3f, respectively).
Unfortunately, the clear picture of excited charge-transfer complexes has
been “blurred” over the years,13 and we thus prefer the less ambiguous
term “encounter complex”, which is experimentally characterizable by its
intrinsic absorption band ascribed to charge-transfer transitions.8,12 Similar
to ground-state EDA complexes, the formation constants and the degree of
charge transfer may vary dramatically with the donor/acceptor properties,
the solvent, and also steric effects.12,41 Whether or not they can be observed
spectroscopically will mainly depend on their lifetimes and thus on the rate
of the subsequent electron transfer. Thus, for diffusion-controlled electron
transfers in the highly exergonic free-energy region, encounter complexes
with very short lifetimes (i.e., KEC , 1) comparable to contact charge-
transfer complexes (Tamres; et al. In Molecular Complexes; Foster, R. F.,
Ed.; Academic Press: New York, 1979; Vol. 2, p 352) are expected. As
such, our operational definition of the encounter complex can be directly
verified by experiment (such as time-resolved absorption spectroscopy) and
has theoretical underpinnings based on Mulliken theory.15 (b) As a
consequence of this description of the encounter complex, its decay pathway
by electron transfer is straightforwardly given by a simple mechanism in
Scheme 1 (eq 2) and the kinetics readily described by three parameters,
characteristic dependence on the free-energy change (∆GET
)
associated with the electron transfer from ArH to Q*. On the
other hand, time-resolved spectroscopic studies12 reveal the
electron transfer from the polymethylbenzene to the photoexcited
quinone to proceed via an encounter complex13 with a rather
high formation constant KEC. As a result, the kinetics of this
electron-transfer quenching is more adequately described by a
two-step mechanism as depicted in eq 2, which implies three
parameters, viz., KEC and the intrinsic rate constants kET and
k-ET of the electron transfer within the intermediate complex.
This electron-transfer mechanism differs significantly from that
of Rehm and Weller1,2 and from that of Kuzmin11 in the
(28) In acetonitrile, significant curvature in the kinetics plot such as that
in Figure 1A is only obtained for ∆GET > 0.2 eV, which allowed us to
reliably extract values for KEC and kET using the reciprocal evaluation in
eq 3. The lack of sufficient curvature in the kinetics plots for ∆GET < 0.2
eV is not likely to be caused by low KEC values since no strong solvent
dependence of KEC is evident in Table 1 (see also ref 12), but it arises from
the plateau values of kobs which severely exceeded the time resolution of
the 10-ns laser pulse (kET . 108 s-1). See also ref 12.
K
EC, kET, and k-ET. [Note that k-ET = 0 is omitted in eq 3.] By contrast,
the fate of the long-lived exciplex according to Kuzmin11 is related to the
experimental observation of ion radicals. When ion radicals are not observed,
the exciplex decays directly to the ground state (without the completion of
the electron transfer and the intervention of ion radicals). Alternatively,
the observation of ion radicals is attributed to ionic dissociation of the
exciplex which necessitates complete electron transfer similar to that in
Scheme 1.
(29) Since in the driving-force region of the plateau (-0.1 eV < ∆GET
< 0 eV) the electron-transfer quenching rate constants (k2 ≈ 109 M-1 s-1
;
see Table 1) are clearly below the diffusion limits, the value of kET = 108
s-1 is most likely not the fastest intrinsic electron-transfer rate constant
and may be exceeded substantially in diffusion-controlled electron transfers
at highly exergonic driving forces.
(31) Moore, J. W.; Pearson, R. G. Kinetics and Mechanism, 2nd ed.;
Wiley: New York, 1981; p 239f.

Electron-Transfer Mechanisms with PhotoactiVated Quinones
J. Am. Chem. Soc., Vol. 121, No. 8, 1999 1693
fact, the presence of such charge-transfer complexes as excited
intermediates implies that the concept of outer-sphere electron
transfer is not applicable to the quenching reactions of quinones.
Thus, the above-delineated (contradictory) conclusions on the
electron-transfer mechanism demonstrate that free-energy cor-
relations of quenching rate constants that are arbitrarily fitted
to the Rehm-Weller equation do not provide any evidence to
either rule out the formation of intermediate excited complexes
or to draw any other conclusions about the degree of bonding
in the electron-transfer transition state.
exhibit independent and different driving-force dependencies
(see Figures 3 and 4), the interpretation of the driving-force
dependence of k2 must be highly ambiguous, particularly in the
endergonic region. The endergonic and slightly exergonic
regions, however, are the most relevant free-energy regions since
they cover the significant changes in k2 which are simulated by
the Rehm-Weller formulation. As a consequence, ∆GqET(0)
values or the related reorganization energies that are formally
extracted from Rehm-Weller simulations lose thermodynamic
significance.
II. Driving-Force Dependence of KEC and Its Conse-
quences for the Rehm-Weller Correlation. We now turn to
the free-energy dependence of the formation constants KEC in
Figure 3, which follows a bell-shaped function with a maximum
at ∆GET ) 0. This remarkable driving-force dependence of KEC
can be readily explained on the basis of the electronic (charge-
transfer) description of the encounter complexes [Q*, ArH].32
Thus, the stability of the complex between photoexcited quinone
(Q*) and polymethylbenzene (ArH) depends on the degree of
mixing between the “local” excited state and the charge-transfer
excited state of the complex, viz., {Q*, ArH} T {Q•-, ArH•+},
which is optimized when the two states are at equal energy
levels. In fact, this condition is met for the [CX*/HMB] couple
Conclusions
Driving-Force Dependence of kET and Its Mechanistic
Significance. The intrinsic rate constants kET in Figure 4
represent the (first-order) rate constants for the electron transfer
within the initially formed encounter complex. These electron-
transfer rate constants are by definition not affected by the
preceding diffusional processes that establish the preequilibrium
in eq 2, and thus may be directly compared with rate constants
of other diffusion-free electron-transfer processes such as back
electron transfer in ion-radical pairs35,36 or intramolecular
electron transfer between a donor and an acceptor molecule
linked by a rigid spacer.37 A variety of such donor/acceptor
systems (in particular intramolecular donor-acceptor pairs37 and
solvent-separated ion-radical pairs36) have been successfully
used to verify the bell-shaped driving-force dependence for
electron-transfer rate constants predicted by Marcus theory.5
Thus, in the “normal” region the rate constants increase with
the exergonicity of the electron transfer until -∆GET equals
the reorganization energy (λ). Once the electron transfer
becomes more exergonic (-∆GET > λ), the rate constants
decrease in the “inverted” region. However, the rates of back
electron transfer (-ET) in contact ion-radical pairs do not
follow these predictions of Marcus theory. Instead, the rate
constants (ln k-ET) decrease linearly with decreasing free-energy
change over a rather wide exergonic driving-force region (-3.0
eV < ∆GET < -0.5 eV).35 Unfortunately, owing to the
experimental procedures for the generation of the ion-radical
pairs,38 the back electron transfer in contact ion-radical pairs
is restricted to the exergonic free-energy region. In contrast,
this study describes endergonic electron transfer between a
donor and an acceptor molecule which are in close (van der
Waals) contact.39 For such electron-transfer processes, the
since the energy of the charge-transfer state, viz., ECT
)
E0ox(HMB) - E0red(CX) ) 2.13 eV,33 closely matches the
energy of the photoexcited quinone, viz., ET(CX) = 2.2 eV,26
and consequently ∆GET ) E0ox - E0red - ET = 0. Accordingly,
the formation of strong encounter complexes is particularly
important for bimolecular electron-transfer reactions with free
energies close to zero (-0.1 eV < ∆GET < 0.3 eV), and KEC
values as high as 200 M-1 are in fact found in this free-energy
region.12 This finding has two important consequences for the
mechanistic basis of the Rehm-Weller formulation as follows.
First, the Rehm-Weller correlation is based on an outer-
sphere reaction scheme in which electron transfer occurs upon
a purely diffusive encounter between the donor and the
acceptor.1,2,5 Thus, for any donor/acceptor combination, the
equilibrium constant for the formation of the encounter complex
is assumed to be close to unity,24 which implies lifetimes of
the diffusive encounters of less than 100 ps.34a The data on KEC
and kET reported here (see Table 1) prove both assumptions in
their general form to be incorrect. Thus, the free-energy
correlation as formulated in eq 6 is not generally applicable
since it is not valid for strongly bound (long-lived) encounter
complexes.34b
(35) (a) Asahi, T.; Mataga, N. J. Phys. Chem. 1989, 93, 6575. (b) Asahi,
T.; Mataga, N.; Takahashi, Y.; Miyashi, T. Chem. Phys. Lett. 1990, 171,
309. (c) Asahi, T.; Mataga, N. J. Phys. Chem. 1991, 95, 1956. (d) Asahi,
T.; Ohkohchi, M.; Mataga, N. J. Phys. Chem. 1993, 97, 13132.
(36) (a) Mataga, N.; Asahi, T.; Kanda, Y.; Okada, T.; Kakitani, T. Chem.
Phys. 1988, 127, 249. (b) Kikuchi, K.; Takahashi, Y.; Koike, K.;
Wakamatsu, K.; Ikeda, H.; Miyashi, T. Z. Phys. Chem. N. F. 1990, 167,
27. (c) Niwa, T.; Kikuchi, K.; Matsusita, N.; Hayashi, M.; Katagiri, T.;
Takahashi, Y.; Miyashi, T. J. Phys. Chem. 1993, 97, 11960. (d) Gould, I.
R.; Young, R. H.; Moody, R. E.; Farid, S. J. Phys. Chem. 1991, 95, 2068.
(e) Levin, P. P.; Pluzhnikov, P. F.; Kuzmin, V. A. Chem. Phys. 1989, 137,
331. (e) Levin, P. P.; Raghavan, P. K. N. Chem. Phys. Lett. 1991, 182,
663.
(37) (a) Miller, J. R.; Calcaterra, L. T.; Closs, G. L. J. Am. Chem. Soc.
1984, 106, 3047. (b) Closs, G. L.; Miller, J. R. Science 1988, 240, 440. (c)
Gunner, M. R.; Robertson, D. E.; Dutton, P. L. J. Phys. Chem. 1986, 90,
3783. (d) Gunner, M. R.; Dutton, P. L. J. Am. Chem. Soc. 1989, 111, 3400.
(38) Contact ion-radical pairs are generated by charge-transfer excitation
of electron donor/acceptor complexes which effects the spontaneous transfer
of an electron from the donor to the acceptor.35 This photoinduced charge-
separation process is strongly endergonic by nature, and thus the corre-
sponding charge recombination or back electron transfer is exergonic.
(39) The charge-transfer transitions in the absorption spectra of the
encounter complexes [Q*, ArH] point to a strong orbital overlap between
donor and acceptor molecule, which is achieved by close contact as observed
in the analogous ground-state EDA complexes. See: Rathore, R.; Lindeman,
S. V.; Kochi, J. K. J. Am. Chem. Soc. 1997, 119, 9393.
Second, we note that the second-order quenching rate constant
(k2) is a composite of KEC and kET as described in eq 4. Since
KEC deviates substantially from unity and both KEC and kET
(32) Weller, A. Reference 9.
(33) The reduction potential of CX is E0red ) -0.51 V12 and the oxidation
potential of HMB is E0 ) 1.62 V25d vs SCE.
ox
(34) (a) For example, a unit equilibrium constant for diffusive association
(kd) and dissociation (k-d), i.e., K ) kd/k-d ) 1, and a diffusion-controlled
rate constant kd ) 2 × 1010 M-1 s-1 for the association process result in a
dissociation constant of k-d ) 2 × 1010 s-1 which corresponds to a lifetime
of 50 ps for the encounter complex. See also: Marcus, R. A. Reference 5a.
(b) The high formation constants of the encounter complexes in this study
may be related to the long lifetimes of the excited (triplet) quinones which
allow multiple collisions with donors during their natural decay. However,
high formation constants (K ≈ 40 M-1) are also found for various excited
complexes in the singlet manifold10c,11a,34c (where the excited-state lifetimes
are orders of magnitude shorter than those of the triplet quinones), and
thus the relevance of the lifetimes is questionable. [Note that a direct
comparison of encounter complexes with singlet and triplet quinone is not
possible owing to the ultrashort lifetime (≈10 ps) of singlet excited
quinones. See: Hubig, S. M.; Bockman, T. M.; Kochi, J. K. J. Am. Chem.
Soc. 1997, 119, 2926.] (c) Nath, S.; Pal, H.; Palit, D. K.; Sapre, A. V.;
Mittal, J. P. J. Phys. Chem. A 1998, 102, 5822.

1694 J. Am. Chem. Soc., Vol. 121, No. 8, 1999
Hubig and Kochi
driving-force dependence in Figure 4 clearly reveals a normal
grade) was stirred over concentrated H2SO4, washed with
aqueous bicarbonate, and distilled serially from P2O5 and from
CaH2 under an argon atmosphere. The synthesis and purification
of 2,5-dichloroxyloquinone was described previously.12
Kinetic Measurements. The laser flash experiments were
carried out using the third harmonic (355 nm) of a Q-switched
Nd:YAG laser (10 ns fwhm) and a kinetic spectrometer with a
time resolution of less than 10 ns as described earlier.12,43
General Procedure. Upon 355-nm laser excitation of the
quinone (ca. 5 mM) in acetonitrile or dichloromethane, the decay
of the triplet quinone (Q*) was observed at 500 nm in the
presence of varying concentrations (10-4 to 10-1 M) of
polymethylbenzene. The exponential decay was fitted to first-
order kinetics, and lifetimes close to the time domain of the
laser pulse were corrected by the (pythagorean) approximation
region; i.e., the rate constants increase with increasing driving
5-7
force -∆GET
.
Thus, we hope that the data presented here
will provide a new proving ground (a) to study the direct
(diffusion-free) electron transfer between donors and acceptors
in van der Waals contact39 over an endergonic as well as
(slightly) exergonic free-energy range and (b) to test recent
electron-transfer theories40 that are not limited to the outer-
sphere model, but consider significant bonding in the transition
state of bimolecular electron transfer. On the other hand, in a
separate study41 we will demonstrate how the complications in
the kinetics evaluation that are caused by the formation of
encounter complexes with strong charge-transfer bonding (as
described herein) can be circumvented by employing sterically
encumbered electron-transfer substrates.
τcorr ) (τ2
- τ2
) )
laser
1/2. The observed rate constants (kobs
meas
Experimental Section
were plotted against the arene concentration. The slope of the
linear (initial) portion of the pseudo-first-order plot yielded the
bimolecular rate constant k2 in Table 1 (see eq 1), and the
kinetics of the entire (curved) plot is evaluated on the basis of
eqs 2, 3, and 4. For the extracted KEC and kET values (see Table
1), we estimate error limits of (10-20% considering both the
inherent numerical errors of double-reciprocal evaluations and
the varying degree of curvature in the kinetics plots such as in
Figure 1A. For additional details of the experimental procedures
and the kinetics analysis, see Rathore et al. in ref 12.
Materials. Durene, pentamethylbenzene, hexamethylbenzene,
chloranil, and dichlorodicyanobenzoquinone were obtained from
Aldrich and purified by recrystallization from ethanol.42 Mesi-
tylene, p-xylene, and 1,2,4-trimethylbenzene (Aldrich) were
purified by distillation. Toluene (reagent grade) was distilled
from sodium and benzophenone under an argon atmosphere.
Acetonitrile (reagent grade) was stirred over KMnO4 and
subsequently distilled from P2O5. Dichloromethane (reagent
(40) (a) Tributsch, H.; Pohlmann, L. Science 1998, 279, 1891. (b)
Eberson, L.; Shaik, S. S. J. Am. Chem. Soc. 1990, 112, 4484. (c) Sastry, G.
N.; Shaik, S. S. J. Am. Chem. Soc. 1995, 117, 3290. (d) Reddy, A. C.;
Danovich, D.; Ioffe, A.; Shaik, S. S. J. Chem. Soc., Perkin Trans. 2 1995,
1525. (e) Shaik, S. S.; Danovich, D.; Sastry, G. N.; Ayala, P. Y.; Schlegel,
H. B. J. Am. Chem. Soc. 1997, 119, 9237. (f) Fukuzumi, S.; Wong, C. L.;
Kochi, J. K. J. Am. Chem. Soc. 1980, 102, 2928.
(41) Hubig, S. M.; Rathore, R.; Kochi, J. K. J. Am. Chem. Soc., in press.
(42) Perrin, D. D.; Armarego, W. L. F. Purification of Laboratory
Chemicals, 3rd ed.; Pergamon: Oxford, 1988.
Acknowledgment. We thank R. Rathore for providing the
dichloroxyloquinone, and the National Science Foundation and
the R. A. Welch foundation for financial support.
JA982710Z
(43) Bockman, T. M.; Karpinski, Z. J.; Sankararaman, S.; Kochi, J. K.
J. Am. Chem. Soc. 1992, 114, 1970.