Photoinduced electron transfer from excited [tris(2,2'- bipyridine)ruthenium(II)]2+ to a series of anthraquinones with small positive or negative Gibbs energy of reaction. Marcus behavior and negative activation enthalpies

Article abstract of DOI:10.1039/a902486g

In the electron transfer (ET) quenching reactions of electronically excited *Ru(bpy)₃²⁺ in acetonitrile an increase of the rate constant k(q) is observed in the series of 2-methyl-, 1-chloro-, and 1-nitro-anthraquinone as quenchers. If alkali salts are used as supporting electrolytes the AQ·^- radical anions are found to form specific associates with the alkali cations. In the presence of non-associating tetraalkylammonium salts the system follows the predictions of Marcus theory. Numerical methods are developed which allow the determination of the rate constants of the conventional reaction scheme. This analysis shows that the quantum yield of free AQ*^- radical anion formation is governed by the interplay of forward, reverse and back ET. Negative activation enthalpies are found for the activation controlled quenching reactions. From the numerical analysis of the system of rate constants it is inferred that this phenomenon is due to the elementary ET step in the reaction sequence. We discuss the pre-equilibrium and elementary reaction models for reactions with negative activation enthalpy and present, to our knowledge, the first example of successful discrimination between them.

Full text of DOI:10.1039/a902486g

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Photoinduced electron transfer from excited
[tris(2,2º-bipyridine)ruthenium(II)]2‘ to a series of anthraquinones
with small positive or negative Gibbs energy of reaction. Marcus
behavior and negative activation enthalpies
Rudolf Frank, Gerhard Greiner and Hermann Rau
FG Physikalische Chemie, Institut f ur Chemie, Universitat Hohenheim, D-70593 Stuttgart,
Germany. E-mail: rau130=uni-hohenheim.de
Received 29th March 1999, Accepted 14th June 1999
In the electron transfer (ET) quenching reactions of electronically excited *Ru(bpy) 2` in acetonitrile an
3
increase of the rate constant k is observed in the series of 2-methyl-, 1-chloro-, and 1-nitro-anthraquinone as
q
quenchers. If alkali salts are used as supporting electrolytes the AQ~~ radical anions are found to form speciÐc
associates with the alkali cations. In the presence of non-associating tetraalkylammonium salts the system
follows the predictions of Marcus theory. Numerical methods are developed which allow the determination of
the rate constants of the conventional reaction scheme. This analysis shows that the quantum yield of free
AQ~~ radical anion formation is governed by the interplay of forward, reverse and back ET. Negative
activation enthalpies are found for the activation controlled quenching reactions. From the numerical analysis
of the system of rate constants it is inferred that this phenomenon is due to the elementary ET step in the
reaction sequence. We discuss the pre-equilibrium and elementary reaction models for reactions with negative
activation enthalpy and present, to our knowledge, the Ðrst example of successful discrimination between them.
glance no such e†ect was expected, as MAQ is not a charged
species. Moreover, for this quenching reaction we observed
negative enthalpies of activation, which is in agreement with
the Ðndings of Tazuke et al.7 and with Kapinus and Rau.9 In
order to Ðne-tune *G¡ we performed the quenching reaction
1
Introduction
According to empirical formulae, e.g. that of Rehm and
Weller,1 and according to Marcus theory2 the rate constants
k
of photoinduced electron transfer (ET) reactions are a
ET
function of the Gibbs energy of reaction *G¡ of the quenching
between MAQ and *Ru(bpy) 2` at various ionic strengths
3
process. The correlation between k and *G¡ has been well
and with di†erent electrolytes. In the course of that work it
ET
established by experiment. For years much e†ort has been
became clear that two e†ects contribute to the reaction: (i) the
expected change of *G¡ due to a variation of the ionic
strength, as observed with a tetraalkylammonium salt as a
supporting electrolyte and (ii) a change of *G¡ due to strong
association of the reaction product 2-methylanthraquinone
radical anion with alkali cations if alkali salts are used as sup-
porting electrolytes.
invested in the Ðnally successful search3 for the ““invertedÏÏ
*G¡ region predicted by Marcus.
In this work we concentrate on the region of nearly zero
Gibbs energy of ET. This case is interesting as the reverse ET
to the excited donor may become more relevant than the back
ET to the ground state species. Also, when approaching
*G¡ \ 0 a transition from electron transfer to charge transfer
may develop: ion pairs may be relevant at moderately and
highly negative *G¡ values, whereas exciplexes might be
formed at small *G¡ values.3c,4 However, we never found any
exciplex emission in our ET systems and thus assume electron
transfer. As we concentrate on purely kinetic considerations in
this work the nature of the Ðrst ET intermediate is not dis-
cussed in detail.
Compared to the vast data base gathered on the ln k vs.
q
*G¡ relation rather few experiments have been performed
testing the correlation between *G¡ and the quantum yield of
product formation in photoinduced electron transfer reac-
tions.4d,10 Therefore, we expand our previous work8 in this
paper (a) by the determination of the quantum yields of the
anthraquinone radical anions; to this end we determined the
absorption coefficients of the AQ~~ radical anions and devel-
oped a new method for the calculation of the concentration of
Numerous studies have been performed using the excited
state of the tris(2,2@-bipyridine)ruthenium(II) complex
excited Ru(bpy) 2` by the laser Ñash, (b) by determining the
3
(Ru(bpy) 2`), which can be quenched by oxidative and
values of all relevant rate constants in the kinetic system
3
reductive ET.5 In this project we work on ET in
(Scheme 1); to this end we employ a combination of a RungeÈ
Kutta procedure of solving the system of coupled di†erential
rate equations (which avoids any assumptions like k > k
*Ru(bpy) 2`Èanthraquinone systems with small values of
3
*G¡. The quenching reaction of *Ru(bpy) 2` by benzo- and
3
32
b
naphthoquinones has been the object of some reports.6,7a
etc.) and a least squares method and (c) by including 1-
chloroanthraquinone (ClAQ) and 1-nitroanthraquinone
(NAQ) as quenchers which due to their less negative redox
potentials have more negative *G¡ values of ET from
A part of our results on the quenching reaction of
*Ru(bpy) 2` by 2-methylanthraquinone (MAQ) has already
3
been published.8 We reported a kinetic salt e†ect on the rate
constant k of this oxidative quenching reaction. At a Ðrst
*Ru(bpy) 2` than MAQ.
q
3
Phys. Chem. Chem. Phys., 1999, 1, 3481È3490
3481

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Scheme 1
We Ðnd that, contrary to the results in other systems,4 for
these ET systems the Marcus electron transfer model is ade-
quate also in the region of *G¡ B 0, and that it is the elemen-
tary electron transfer reaction which is responsible for the
negative activation enthalpy, to our knowledge the Ðrst clear
evidence for this concept in photochemistry.
details of quenching and transient absorption procedures have
been described previously.8 In short: The quenching experi-
ments were performed in the dynamic mode with excitation at
460 nm with a combination of an EMG 101 excimer laser and
FL 2000 dye laser by Lambda Physik with solutions deoxy-
genated by argon Ñushing and thermostatted between 15 and
45 ¡C. For the evaluation a SternÈVolmer analysis was
employed. Transient spectra were taken with the same excita-
tion source 1.3 ls after the Ñash in a 90¡ arrangement with a
battery-powered 250 W projector lamp as a light source and
2
Experimental
2.1 Materials
photomultiplierÈmonochromatorÈoscilloscope
(Tektronix
MAQ and ClAQ from Fluka were recrystallized several times
from ethanol. NAQ was separated from the byproduct 2-
nitroanthraquinone and puriÐed by column chromatography
using Al O (Fluka Typ 507 C neutral, Aktivitatsstufe IV) and
11302) combination whose trace was digitized and evaluated
on a computer.
2
3
toluene or dichloromethane as an eluent. Acetonitrile from
Roth ““Fur die DNA SyntheseÏÏ was used as a solvent.
3
The kinetic model
A concise introduction into the kinetics of photoinduced elec-
tron transfer reactions (ET) and the Marcus theory is given by
Bolton and Archer.11 For our systems we have to discriminate
between ET systems in solutions with supporting electrolytes
that may or may not associate with the anthraquinone radical
anion produced by ET.
2.2 Electrochemical measurements
The redox potentials of the AQs at di†erent ionic strengths
and with di†erent supporting electrolytes were determined by
means of cyclic voltammetry as reported.8 The absorption
coefficients of the AQ~~ radical anions were determined in
optically transparent thin layer electrochemical cells (OTTL).
The absorbance in the 330 nm region of the AQs themselves
served as an internal standard for quantitative evaluation of
the formation of their reduction products. In short, the
OTTLs were constructed from two microscope slides, one
with a transparent, conductive indium-tin-oxide (ITO) layer
separated by etching in two areas which were contacted as
cathode and anode. The two slides were kept at 0.1 mm dis-
tance by a TeÑon spacer with two circular (1.5 cm diameter)
holes connected by a 1 mm wide channel (a pattern like a pair
of spectacles). Thus circular cathode and anode areas were
separated and could be observed separately. For monitoring
the absorption spectra of the radical anions the electrochemi-
cal cells were mounted into an HP 8452 A diode array spec-
trophotometer. The absorption coefficients of the AQs, which
serve as internal standards in the electrochemical experiments,
were determined by means of a Cary 4E spectrophotometer.
3.1 Et NClO as a non-associating supporting electrolyte
4
4
We will use reaction Scheme 1, which is commonly accepted.
Scheme 1 deÐnes the rate constants and intermediate species.
k
, k , k and k
represent di†usion controlled pro-
12 21 34
back
cesses. These rate constants can be calculated8,12,13 and are
given in Table 1. The radii of Ru(bpy) 2` and Ru(bpy) 3`
3
3
have been taken to be equal (0.71 nm)7c and those of all the
AQs and AQ~~s have also been taken to be equal (0.38 nm14).
The dependence of viscosity on Et NClO concentration is
4
4
taken to be the same as that for a NaClO solution.8 k , k
4
and k represent activation controlled steps and three inde-
b
23 32
pendent experiments are necessary for their determination.
The Ðrst one is the determination of the macroscopic rate
constant of the quenching reaction k which is related to the
q
rate constants of the di†erent reaction steps.
k
k
(k ] k
)
12 23 b
34
] k (k ] k ) ] k (k ] k )
k \
(1)
q
2.3 Spectroscopic measurements
k
k
21 32
21 b
34
23 b
34
Absorption spectra were taken by means of ZEISS DMR10,
Cary 4E and HP 8452 A spectrophotometers, emission spectra
with a Perkin Elmer LS50 Ñuorimeter. The experimental
k is determined directly from SternÈVolmer plots.
q
The second piece of information comes from the determi-
nation of the ratio k /k \ K \ e~*G2¡3@RT which is avail-
23 32
23
Table 1 Di†usion controlled rate constants which were used in the various calculation procedures
c(salt)/mol l~1
k
a/109 l mol~1 s~1
12
k
a/109 s~1
21
k
b/109 s~1
34
k
b/109 l mol~1 s~1
back,diff
0.1
0.2
0.3
0.4
0.5
19.4
18.3
17.1
16.1
15.2
6.04
5.66
5.31
5.02
4.73
1.82
2.53
2.86
3.03
3.09
19.3
18.1
16.95
16.0
15.1
A detailed description of the calculation procedures is given in ref. 7a and in ref. 13.b
3482
Phys. Chem. Chem. Phys., 1999, 1, 3481È3490

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able from the value of *G¡ . This, in turn, can be obtained
investigated in this work. In the quenching systems which
contain alkali salts as supporting electrolytes we observe spe-
ciÐc salt e†ects which we attribute to association of the AQ~~
anions with the alkali cations.8 We will discuss the problem of
association in the course of the quenching reaction in a later
section (5.2).
23
from electrochemical half-wave potentials E 1,8,15 according
1@2
to
*G¡ \ F[E (D`/D) [ E (A/A~)] [ E (*D) ] w [ w
23
1@2
1@2
00
p
r
(2)
where E is the energy of the donorÏs excited state. w is zero
as the AQs are neutral species and
00
r
4
Results
4.1 Redox potentials, association constants, and Gibbs
energies of reactions
z z e2 N
1
D A 0
A
]
A
w \
(2a)
(2b)
p
4ne e(r ] r ) 1 ] (r ] r )c
0
D
D
A
The redox potential data of ClAQ and NAQ as determined by
di†erential pulse polarography at various salt concentrations
are shown in Fig. 1, the data of MAQ are of the same type,
but lower by 120 to 140 mV.8 The redox potentials measured
in this study are within the range of the published ones,18 they
can be reproduced within less than 20 mV. These variations
may be due to traces of oxygen and water in the acetonitrile
used.
A
2N e2 J ] 1000
B
A 0
c \
e e k T
0
B
J is the ionic strength.
The third piece of experimental evidence is the quantum
yield / of the production of separated AQ~~ radical anions
which is deÐned as the ratio of c(AQ~~) /c(*Ru(bpy) 2`)¡.16
max
3
c(AQ~~)
is the maximum concentration of free AQ~~ rad-
Fig. 1 outlines two factors which inÑuence E : a small
max
1@2
icals observed by transient absorption approximately 1.3 ls
shift which is due to a change in concentration of the support-
after the laser Ñash. c(*Ru(bpy) 2`)¡ is the initial concentra-
ing electrolyte (attributed to the inÑuence of ionic strength on
the activity coefficients) and a large shift which is due to the
nature of the supporting electrolyte. This latter is rationalized
by an association of the alkali cations with the AQ~~ anions.
The association constant can be calculated from19
3
tion of *Ru(bpy) 2`, for its determination we developed a
3
convenient new method using the time proÐle of the laser irra-
diance, its Ñash energy and the absorption coefficients of
Ru(bpy) 2`.17 This method takes into account ground state
depletion and, if necessary, excited state absorption (which,
3
(e*E@25.6 [ 1)
however, proved unimportant in the present case. The
quantum yield is also a function of all the rate constants,
but, contrary to eqn. (1) there is no simple algebraic connec-
tion between / and the rate constants. Only in the case that
the reverse ET is slow (k > k ), as in rather exergonic ET
K
\
(4)
ass
c
salt
where *E is in mV. The association constants are high and
dependent on ionic strength as shown in the inset of Fig. 1 for
Na`/ClAQ~~. The observed decrease may be due to the use of
concentrations in eqn. (4) instead of activities. For
32
23
reactions, the quantum yield of radical anions is
Na`/NAQ~~ the value of K is 7650 at J \ 0.1 and 2260 for
k c
k
ass
q Q
1/q ] k c
q Q
34
] k
/ \
]
(3)
J \ 0.5 mol l~1. A value for K of Na`/ClAQ~~ (at J \ 0.1
ass
k
0
34
b
mol l~1) of 4150 in the literature19 is for DMF solution and is
in good agreement.
Three points should be emphasized: (a) The association of
alkali and AQ~~ ions is not a purely electrostatic one; associ-
ation constants calculated according to the Fuoss treatment20
c
being the quencher concentration. This equation yields k ,
as k can be calculated.10 But when k cannot be neglected
compared to k , as we Ðnd for the systems in this work, then
Q
b
34
32
23
relation (3) does not hold and an extensive analysis of the rate
constants is necessary.
In order to solve the problem without any assumptions we
Ðrst varied the values of k and k in the vicinity of the start-
23
b
values from eqn. (1) and deter-
ing data, calculated the k
q, calc
mined the square of the deviation from the experimental
value, (k
[ k
)2. As starting values k was taken from
q, exp
q, calc
23
k \ k
k
/(k ] k ) which follows from eqn. (1) under the
q
12 23 21
23
b
assumption of k > (k ] k ) and k was taken from eqn. (3)
32
34
b
which holds under the condition k > k . With the same set
32
23
of rate constants we solved the system of di†erential equations
of Scheme 1 by numerical integration (RungeÈKutta). These
calculations yield values of c(AQ~~)
and the square of the
deviation of [c(AQ~~) [ c(AQ~~) ]2 is determined. That
calc
exp
calc
pair of rate constants k
and k which minimizes both
23
b
squares of deviation is considered to be the correct one.
For doing these calculations we must know k
. It was
back
determined in separate experiments. But, as the concentration
of the free ions is of the order of 10~6 mol l~1 and as we are
looking to the Ðrst 1 to 2 ls of the reaction only, the inÑuence
of k
on the results vanishes. Thus all the rate constants for
back
Scheme 1 are available.
Fig. 1 Half-wave potentials of Rubpy, ClAQ, and NAQ in acetoni-
trile solution vs. NHE. É É É É L É É É É Rubpy3`/*Rubpy2`. È = È
ClAQ/ClAQ~~ in the presence of Et NClO , ---- = ---- in the pres-
3.2 Associating supporting electrolytes
The experiments were performed in acetonitrile solution with
deÐned ionic strength as only then the electrochemical values
of *G¡ can be used for reliable calculations. Reliable values
are important in the vicinity of *G¡ B 0, the region which is
4
4
ence of NaClO . È + È NAQ/NAQ~~, in the presence of
4
Et NClO , ---- + ---- in the presence of NaClO . The inset shows
4
4
4
the dependence of the association constant between ClAQ~~ and Na`
as a function of the ionic strength.
Phys. Chem. Chem. Phys., 1999, 1, 3481È3490
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Table 2 *G¡ (salt) values: Gibbs energy of the forward ET of the various combinations of *RubpyÈAQ in the presence of di†erent salts; *G¡
23
b
values in square brackets: Gibbs energy of the back ET starting from the Cl back to the ground state molecules
AQ
c(salt)/mol l~1
*G¡ (Et NClO ); [*G¡]/kJ mol l~1
23
*G¡ (NaClO ); [*G¡]/kJ mol~1
*G¡ (LiCLO ); [*G¡]/kJ mol~1
4
4
b
23
4
b
23
4
b
MAQ
measured
0.48
e†ectivea
measured
[12.55
[14.34
[16.22
[19.63
e†ectivea
0.1
0.2
0.3
0.5
9.44 [[212.2]
7.63 [[210.2]
8.22 [[210.8]
5.65 [[208.3]
3.92 [[206.5]
1.24 [[203.9]
5.96 [[208.6]
4.23 [[206.9]
[3.69
[5.32
2.88 [[205.5]
0.75 [[203.4]
ClAQ
NAQ
measured
[14.28
e†ectivea
0.1
0.2
0.3
0.5
2.12 [[204.7]
0.29 [[202.9]
1.89 [[202.3]
[0.676 [[201.9]
[2.22 [[200.4]
[17.27
[19.59
[1.13 [[199.3]
[3.31 [[197.1]
measured
[24.90
[26.89
[29.25
e†ectivea
0.1
0.25
0.5
[15.83 [[186.6]
[17.53
[15.83 [[186.6]
[15.83
[19.11
[15.83 [[186.6]
a See text, Section 4.3.1.2 and Fig. 5.
are of the order of 2 to 4 in acetonitrile. It is neither a purely
covalent one as in protonation where the Ðrst and second
reduction potentials in contrast to the case of Na` interaction
coincide. (b) The electrochemical results are valid for equi-
librium conditions and may not be valid for transient species.
(c) The tetraalkylammonium ion does not associate with
AQ~~ radical anions.19 We can conÐrm this from the match-
ing of the transient absorption spectra of the AQ~~ radical
ions in ET-quenching experiments in salt-free solutions and
solutions which contain Et NClO .
4
4
The Gibbs energies of reaction of the ET step (*G¡ ) were
23
calculated according to eqn. (2), they are compiled in Table 2.
For non-associating Et NClO these Gibbs energies of reac-
4
4
tion of the forward ET are positive in the case of MAQ, close
to zero for ClAQ and decrease to considerably negative values
in the case of NAQ. The Gibbs energies of the ET reaction in
the presence of alkali as calculated according to eqn. (2) are
much lower than the ones in the presence of Et NClO . But
4
4
note that the electrochemically determined redox potentials
correspond to reaction conditions in which the equilibrium
state between free and complexed AQ~~ radical anions is
reached. This equilibrium may not be established in ET quen-
ching experiments.
Fig. 2 Spectra of the various NAQ species which are formed during
the electrochemical reduction of NAQ in optically transparent thin
layer cells. For details see text.
Table 3 Absorption coefficients of the anthraquinone radical anions and of their associates with alkali cations in AN and DMF
Species
j
/nm and (e/cm~1 l mol~1) in acetonitrile
j
/nm and (e/cm~1 l mol~1) in DMF
max
max
AQ~~
534 to 544 (8 500 to 12 000)30,32,41h43
553 to 556 (11 200 to 14 300)33,44,45
530 (9 320)33
AQ~~É É ÉLi`
MAQ~~
539 (10 312)
515 (9 540b)
505a (8 750b)
564 (11 360)
552 (11 070)
MAQ~~É É ÉNa`
MAQ~~É É ÉLi`
ClAQ~~
539 (10 245)
528 (9 390)
575 (11 385)
565 to 570 (10 800)30
ClAQ~~É É ÉNa`
ClAQ~~É É ÉLi`
NAQ~~
540a (9 650b)
567 (9 670)
552 (9 290)
560 (9 030)
556 (7 420)
548 (7 380)
535a (6 060b)
NAQ~~É É ÉNa`
a The corresponding spectra cannot be observed in OTTLs but in laser Ñash transient absorbance measurements only. b Estimated values. For
details see text, section 4.2.2.
3484
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Fig. 3 Normalized transient absorption spectra from laser Ñash
experiments. Spectrum of ClAQ~~: È = È in the presence of
Et NClO , ---- = ---- in the presence of NaClO . Spectrum of
Fig. 5 Rate constants of the quenching reaction of *Ru(bpy)2` by
3
4
4
4
ClAQ corrected for viscosity e†ects as a function of the Gibbs energy
NAQ~~: È + È in the presence of Et NClO , ---+ --- in the pres-
4
4
of reaction *G¡ . È = È in the presence of Et NClO , - --= --- in
ence of NaClO .
23
4
4
4
the presence of NaClO . eff*G¡ see Section 5.2.
4
23
Tables 2 also include *G¡ values. These values are highly
4.2.1 Et NClO
as
a
supporting electrolyte. With
b
4
4
negative, the back ET is in the Marcus inverted region, there-
Et NClO in acetonitrile (AN) or in DMF the spectra of the
4
4
fore the corresponding kinetic constants k are expected to
AQ~~ are almost identical. In Fig. 2 the spectra of NAQ and
b
decrease if *G¡ becomes increasingly more negative. Data for
its electrochemically reduced species are shown.
b
k will be given in section 4.3.
As far as information about absorption spectra of AQ~~
radical anions and AQ2~ di-anions is available in the liter-
ature the spectra of this work agree well with reported ones.22
This also holds for the absorption coefficients of the AQ~~
radical anions compiled in Table 3.22 No changes of the
absorbance are observed in the anodic part of the cell, the
absorption coefficients of the AQ~~ cation radicals which may
be produced in our OTTLs, are reported to be very low.23
In the presence of Et NClO in electrochemical reduction
experiments of all AQs the formation of new absorption
bands in the 550 nm and 400 nm region is observed during
the Ðrst part of the reduction. This spectrum consequently is
assigned to the AQ~~ radical anion.
In the laser Ñash experiments the transient absorption
spectra of the AQ~~ species can be observed in salt-free solu-
tions and in the presence of Et NClO (Fig. 3). These tran-
b
4.2 Absorption coefficients of the AQ~— radical anions and
absorption spectra of transients in the quenching experiments
The absorption coefficients of the AQ~~ radical anions were
determined by electrochemical reduction in optically transpar-
ent thin layer cells (OTTL). The results are compiled in Table
3.21
In the electrochemical experiments the various reduced
species of the AQs are formed in a consecutive way.
4
4
4
4
sient spectra in both solutions are identical and equal to the
spectra of the AQ~~ species in the electrochemical reduction
experiments.
4.2.2 Alkali perchlorates as supporting electrolytes. In AN
the reduced AQ species appear to be not stable on the electro-
chemical time scale if alkali perchlorates are used as support-
ing electrolytes. In contrast, in DMF only a shift of the
absorbance maxima to shorter wavelengths and a decrease of
the absorption coefficients compared to those in the presence
of Et NClO is observed, but the general structure of the
4
4
spectra during electro-chemical reduction is preserved. Obvi-
ously the associates are stabilized by DMF, which is a strong-
er solvating agent than AN.24 We have not taken e†orts to
analyze this in detail. In order to obtain absorption coeffi-
cients of the AQ~~. . . Na`/Li` species in AN we assumed that
the relative decrease of the coefficients is the same in AN and
DMF. The data designated as estimated values in Table 3 are
calculated according to this assumption.
Contrary to the situation in electrochemical reduction, the
absorption spectra of AQ~~É É ÉNa` and AQ~~É É ÉLi` species in
AN can be observed in the laser Ñash experiments. The tran-
sient absorption spectra with ClAQ and NAQ are shown in
Fig. 4 Rate constants of the quenching reaction of *Ru(bpy)2` by
3
AQs corrected for viscosity e†ects: È … È MAQ in the presence of
Et NClO , --- … --- MAQ in the presence of NaClO , É É É É … É É É É
4
4
4
MAQ in the presence of LiClO , L MAQ in the presence of
4
Mg(ClO ) ; È = È ClAQ in the presence of Et NClO , ---= ---
ClAQ in the presence of NaClO ; È + È NAQ in the presence of
4 2
4
4
4
Et NClO , ---- + ---- NAQ in the presence of NAClO .
4
4
4
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Table 4 Rate constants calculated by the iterative procedure outlined in Section 3
AQ
c(salt)/mol l~1
k /109 l mol~1 s~1
k
/109 s~1
23
k
/109 s~1
32
/(%)
k
/109 l mol~1 s~1
k /109 s~1
q
back
b
MAQ
Without salt
0.0
0.12
(0.037)
125
Et NClO
0.1
0.3
0.5
4
4
0.22
0.4
0.5
0.0815
0.134
0.166
3.66
1.49
0.915
2.8
4.34
5.09
69.6
68.7
62.6
18.8
24.8
25.1
NaClO
0.1
0.3
4
0.32
0.74
1.03
0.107
0.242
0.346
2.32
0.772
0.470
1.64
2.6
2.61
91.5
82.6
62.7
43.5
61.4
74.0
0.5
LiClO
4
0.1
0.2
0.3
0.5
0.29
0.45
0.6
0.100
0.148
0.198
0.307
2.76
1.45
0.959
0.511
2.39
3.38
3.97
4.00
63.3
90.0
76.0
48.1
26.0
32.5
35.0
46.3
0.92
ClAQ
Without salt
0.0
1.2
0.35
1.53
16.3
Et NClO
0.1
0.2
0.3
4
4
2.35
2.7
2.9
0.90
0.103
1.11
1.19
2.14
1.15
0.849
0.486
5.95
6.88
7.75
8.10
11.0
9.94
8.84
7.89
24.4
29.6
29.6
30.6
0.5
3.0
NaClO
0.1
0.3
4
2.4
3.0
3.3
0.883
1.15
1.33
1.89
0.73
0.350
7.3
8.04
7.14
20.8
14.0
11.5
19.0
28.2
35.4
0.5
NAQ
Without salt
0.0
6.45
5.85
(2.89)
2.60
Et NClO
4
4
0.1
4.38 ] 10~3
5.2
5.8
9.4
7.2
30.8
27.9
NaClO
0.1
0.5
4
6.28
4.73
2.88
3.33
4.84 ] 10~3
5.59 ] 10~3
Fig. 3, those with MAQ are in Fig. 3 of ref. 8. In the presence
trolled value. k varies between 0.12 ] 109 l mol~1 s~1
q
of NaClO the absorbance maxima are observed at shorter
without salt and 0.5 ] 109 and 1.0 ] 109 1 mol~1 s~1 at
4
wavelengths compared to the ones in the presence of
c(Et NClO ) \ 0.5 mol l~1 and c(NaClO ) \ 0.5 mol l~1,
4
4
4
Et NClO and this shift is larger with MAQ and ClAQ than
respectively, thus showing a relative increase by a factor of up
4
4
with NAQ.
to 8. In the case of ClAQ higher values of k are observed, the
q
relative increase of k is less pronounced, only a factor of 2.5
q
4.3 Quenching experiments
results and the di†erence between the e†ect of Et NClO and
4
4
4.3.1 Rate constants. In Fig. 4 the quenching rate con-
NaClO almost disappears. In the case of NAQ the value of
4
stants k , corrected for viscosity changes due to varying elec-
k approaches the limit of di†usion control and no inÑuence
q
q
trolyte content, are given as
a
function of the salt
of the ionic strength or of alkali ions is observed.
concentration.25 In the case of MAQ the k values are rela-
*G¡ is dependent on salt concentration (Table 2). In Fig. 5
q
23
tively small, of the order of 1% to 5% of the di†usion con-
ln k g of ClAQ is shown as a function of *G¡ , MAQ and
q r
23
Table 5 Activation parameters determined from ln(k /T ) vs. 1/T plots
q
Substance, salt,
c(salt)/mol l~1
*HE/kJ mol~1
*SE/J K~1 mol~1
[137 ^ 15
*GE/kJ mol~1
27.6 ^ 9.2
MAQ, Without salt
[13.1 ^ 4.6
MAQ, Et NClO
4
4
0.1
0.5
[17.6 ^ 1.0
[16.5 ^ 1.0
[142 ^ 2
[134 ^ 2
25.3 ^ 1.2
23.6 ^ 1.8
MAQ, NaClO
0.5
4
[6.7 ^ 1.6
[0.3 ^ 0.7
[9.8 ^ 1.2
[11.3 ^ 1.7
[95 ^ 5
[75 ^ 24
[108 ^ 4
[102 ^ 6
21.7 ^ 2.1
22.0 ^ 1.5
22.5 ^ 2.4
19.1 ^ 3.3
MAQ, LiClO
0.5
MAQ, Mg(ClO )
4
4 2
0.5
ClAQ, Et NClO
4
4
0.1
ClAQ, NaClO
0.1
4
[12.4 ^ 1.0
[5.4 ^ 0.6
[106 ^ 3
[80.5 ^ 2
19.3 ^ 1.9
18.6 ^ 1.2
0.5
NAQ, Et NClO
4
4
0.1
6.3 ^ 1.1
[36.5 ^ 3.6
17.2 ^ 2.2
NAQ, NaClO
0.1
0.5
4
3.8 ^ 0.8
7.9 ^ 1.0
[44.5 ^ 2.6
[39 ^ 3.5
17.2 ^ 1.6
20.0 ^ 2.0
3486
Phys. Chem. Chem. Phys., 1999, 1, 3481È3490

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NAQ show an analogous behavior. When the kind of electro-
lyte is changed from Et NClO to NaClO the Gibbs energy
4
4
4
of reaction *G¡ (calculated according to eqn. (2) from the
23
redox potentials) becomes more negative, but only a minor
(Table 4, MAQ up to 100%) increase of k is observed.
q
4.3.2 Activation parameters. The activation parameters of
the quenching reaction of some reaction systems were deter-
mined from Eyring plots (ln k /T vs. 1/T ), using the experi-
q
mental k data. For an activation controlled reaction the
q
temperature dependence is determined by that of k . The
23
results are compiled in Table 5.
The most striking information in Table 5 is that in the case
of MAQ and ClAQ negative enthalpies of activation are
observed. The positive activation parameters for NAQ charac-
terize the viscosity e†ect as the quenching reaction with NAQ
is close to di†usion control. In our systems negative enthalpies
and energies of activation occur only if *G¡ is positive or
23
slightly negative.
Fig. 6 Rate constants of the forward (k ) and backward (k ) elec-
5
Discussion
23
b
tron transfer of MAQ as a function of the e†ective Gibbs energy of
reaction.
5.1 The system with Et NClO as a supporting electrolyte
4
4
With the entries in Tables 1 and 4 all the rate constants are
available. The back ET reaction to the ground state is far in
associating electrolyte and deÐne an e†ective eff*G¡ as shown
the inverted region (Table 2), k is still high. However, high
23
b
in Fig. 5. The values in Fig. 6 characterized by open symbols
values of k are not unusual.3c A feature which is important
b
have been determined with these eff*G¡ .
for the assessment of negative activation enthalpies (vide infra)
23
However, the independence of ET and association seems
is that the values of k and, of course, of (k ] k ) are higher
b
b
34
not to be complete. The k values for the same concentrations
than those of k . In Table 4 this is clearly visible, note that
q
32
of complexing and non-complexing electrolytes vary up to
for ClAQ the results of the iterative solution of the set of rate
100% (Table 2). If we determine the rate constants with
equations are close to those arrived at with the assumption
eff*G¡ for the quenching systems in associating electrolytes
k
> (k ] k ), which, as mentioned, was used for selecting
23
32
b
34
by the procedure outlined above we inevitably Ðnd larger k
the starting values for the iteration.
23
values than those for non-complexing tetraalkylammonium
If we compare the values of k and k with Et NClO as a
23
b
4
4
salt. On the other hand, if we plug the k value obtained for
supporting electrolyte (Table 4) as a function of *G¡ and *G¡
23
23
b
quenching in the presence of Et NClO into the calculation
(Table 2), respectively, we realize that with decreasing *G¡ an
4
4
23
the program does not Ðnd a solution to the double minimum
problem. These pieces of evidence indicate that there is some
inÑuence of alkali ions directly on ET.
increase of k , but with decreasing *G¡ a decrease of k is
23
b
b
observed. This indicates in a qualitative way that Marcus
behavior is followed. The counter-movement of these ET rate
constants is prima facie evident from the fact that the quantum
5.3 Negative activation enthalpies
yields of AQ formation do not follow the increase of k when
*G¡ is decreased by the choice of di†erent ionic strengths or
quenchers. The increase of k must be partially compensated
by an increase of k . According to the Marcus equation the
data for MAQ and ClAQ are Ðtted to (because of the narrow
span of *G¡ not very accurate) parabolas (Figs. 6 and 5).
23
23
One of the most outstanding features of the ET system investi-
gated here is the negative temperature e†ect on emission
quenching. This is observed only for MAQ and ClAQ which
show activation controlled quenching at positive or slightly
23
b
23
negative *G¡ values. The use of the RungeÈKutta procedure
23
for solving the set of di†erential rate equations provides, to
5.2 The system with associating alkali perchlorates as
supporting electrolytes
the best of our knowledge, for the Ðrst time all the rate con-
stants of Scheme 1 and the assessment of their relative magni-
tudes justiÐes a deeper rooted discussion of the problem of
negative activation.
The *G¡ data are calculated from E
obtained in equilibrium electrochemical experiments accord-
values which are
23
1@2
ing to eqn. (2). When the k values in the presence of NaClO
It is common knowledge that chemical reactions are accel-
erated on heating. This is rationalized by the concept of an
activation barrier and expressed in the Arrhenius (5) and
Eyring (6) equations
q
4
values are plotted vs. these *G¡ (Fig. 5) they are not on the
23
Marcus parabola represented by the plot for Et NClO , but
4
4
about an order of magnitude smaller. However, the series of
points for di†erent NaClO concentrations can also be Ðtted
by a parabola.
4
k \ A e~Ea@RT
(5)
As pointed out in Section 4.1 the association constant of
alkali cations and AQ~~ radical anions is determined from the
di†erence of the redox potentials of the AQs in complexing
and non-complexing supporting electrolytes. In the Ñash
experiments the AQ~~ radical anion is created in the ET step,
so prima facie ET and association are di†erent processes. It is
therefore conjectured that in laser Ñash experiments the redox
potentials of the non-associating electrolytes should be used
also for the quenching reaction in solutions containing associ-
k T
h
k T
h
e~*GE@RT \
e*SE@R e~*HE@RT
(6)
B
B
k \
There are, however, reports on a small number of reactions
which are decelerated on heating. Formally, this requires
negative activation energies or enthalpies in eqns. (5) or (6).
Among these reactions are gas phase reactions26 and reactions
in solution9,27h33 of very di†erent types: some DielsÈAlder
reactions,27 radical reactions,28 proton29 and electron transfer
reactions,7h9,15a,30,31 addition of carbenes32 to oleÐns and
others.33 Some theoretical papers have appeared.34
ating electrolytes. Therefore, we project the k data for associ-
q
ating electrolytes on the Marcus parabola of the non-
Phys. Chem. Chem. Phys., 1999, 1, 3481È3490
3487

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Negative temperature e†ects on reaction rates have been
rationalized by the postulate of a kinetic intermediate XY
according to
under steady state conditions of dc /dt \ 0 to be
XY
k k
1 2
~1
k \
(11)
k
] k
2
k1
k2
X ] Y E8F XY ÈÈÈ Z
(7)
Steady state conditions may be reached if either the equi-
k~1
librium is established (i.e. k > k ) or if the rate constant k
2
~1
2
which is engaged in two competitive reactions (k
and k ).
is much larger than k . In the frame of the Arrhenius treat-
~1
2
~1
There is no doubt that this may be a good explanation when
the existence of the intermediate is experimentally proven, e.g.
by (transient) absorption or exciplex emission or a scavenging
reaction. However, negative activation energies sometimes are
considered as compelling evidence for the existence of an
intermediate27,28a even if no other piece of evidence exists.
Highly speculative structures have been invented for these
intermediates like hydrogen bonded radicals with adjacent
radical sites,28b n- complexes of radicals,29 or di†erent confor-
mations of catenanes.33f These intermediates by chemical
intuition should be very unstable and this, of course is the
reason for their evasiveness. However, if these intermediates
are short-lived they should disturb heavily or destroy the
equilibrium, thus causing an erosion of the basis of the kinetic
““pre-equilibriumÏÏ model. There seems to be the need for an
alternative.
ment (5) these two limiting cases are
““pre-equilibriumÏÏ: k > k
:
2
~1
k k
1 2
A A
1 2
e~*Ea(k1)~Ea(k~1)`Ea(k2)+@RT
~1
k \
\
k
A
~1
A A
]
1 2
\
e~**H `Ea(k2)+@RT
(12)
(13)
A
~1
““elementary reactionÏÏ: k ? k
:
2
~1
k \ k \ A e~Ea(k1)@RT
1
1
There are thousands of reactions which proceed according to
scheme (7). What is the special feature of the few ones which
have negative temperature e†ects? In the pre-equilibrium case
the e†ective activation energy of the disappearance of X or Y
may be negative if *H¡ is negative and larger in absolute
value than E (k ). (Eqn. (12) and Fig. 7). This means that E (k )
In order to rationalize the zero and small negative activa-
tion enthalpies observed in the oxidation of hydrated Fe2` by
Ru(II) polypyridine complexes by Braddock and Meyer,30b
Marcus and Sutin34c,d,g have pointed out that the Marcus
parabolas represent free enthalpy vs. polarization and that for
the temperature dependence the formulae of thermodynamics
can be used.35
a 2
a 2
must be smaller than E (k ). Again this type of potential
a ~1
energy surface is abundant. However, in order to keep the
condition of k > k the preexponential factor A(k ) has to
2
~1
~1
be larger than A(k ), and this case is rare. As the magnitude of
2
the preexponential factor is tied to the activation entropy and
thus in most cases to the reaction entropy, a large increase in
L(*G*/T )
entropy of the back reaction k
token, a large decrease of the reaction entropy in the forward
is required or, at the same
*H* \ [T 2
*S* \ [
(8)
(9)
~1
LT
reaction (k ) of the equilibrium is required.
L*G*
LT
1
If *H¡ is very negative the entropy e†ect in the pre-
exponential factors A(k ) and A(k ) is no longer expected to
1
~1
compensate for the di†erence in activation energies E (k
a ~1
and E (k ) to maintain the condition k > k , and thus the
a 2 ~1
elementary reaction case is reached with E B E (k ). Simple
)
For cross reactions, like the ones of Braddock and Meyer, the
activation enthalpy *H* consists of two terms which may
have opposite signs and thus may become negative. Eqn.
(10)34g shows the concert of reaction enthalpy *H¡ and reac-
tion entropy *S¡. It is evident that *H* may become negative
if the reaction entropy is highly negative.
2
a
a 1
simulations conÐrm this scheme. Note that in this Arrhenius
treatment a trajectory on the potential energy surface is used
as a reaction coordinate and that all elementary reactions in
eqn. (7) have positive activation energies.
(j ] *H¡)2 (T *S¡)2
In EyringÏs (and MarcusÏ) treatment the reaction coordinate
R of an elementary reaction is deÐned as a trajectory on the
surface of the free enthalpy G, and the transition state is at the
saddle point conÐguration, i.e. at the locus of the reaction
coordinate with maximum free enthalpy.37 Thus *GE is
always positive, when the reactants are stable chemical
species. As G(R) \ H(R) [ T S(R) the G surface is connected
*H* \
[
(10)
4j
4j
In eqn. (10) j is the reorganization energy.2 Marcus and Sutin
demonstrated also a quantum chemical approach.34c Negative
activation enthalpies may evolve if the spacing of quantum
states of the product state of an elementary reaction is wider
than that of the reactants accompanied by a lesser reactivity
of the more energetic states of the activated complex. This
also corresponds to a negative reaction entropy.
After not being able to Ðnd a stable n-complex as an inter-
mediate in halocarbene addition to an oleÐne by calculation36
Houk and Rodan considered the free enthalpy, the enthalpy
and the entropy surfaces of an elementary reaction34b in order
to rationalize the negative temperature e†ect observed in these
reactions. These ideas allow one to abandon the must of pos-
tulating an intermediate, but obviously they have not been
generally considered in the newer work. Indeed we ourselves
came across HoukÏs paper34b only in the preparation of a
publication on the same concept. We are going to compare
the ““pre-equilibriumÏÏ and ““elementary reactionÏÏ models in
the light of the results for the *Ru(bpy) 2`/AQ system. Eqn.
3
]
(7) is in essence included in Scheme 1 (PC
ground state).
CI ] FI and
^
Both models for rationalization of negative activation ener-
gies can be considered as limiting cases of the reaction scheme
(7). The rate constant of disappearance of X may be calculated
Fig. 7 Arrhenius reaction diagram for reactions with negative reac-
tion enthalpy *H¡ leading to negative activation energies for
X ] Y ] Z.
3488
Phys. Chem. Chem. Phys., 1999, 1, 3481È3490

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tron transfer states, potential energy curves of continuous
charge transfer with continuously established solvent reaction.
Scheme 1 is based on the Marcus assumption of vanishing
coupling of the locally excited and electron transfer states, of
potential energy curves with non-relaxed solvent polarization
and of a well deÐned complete electron transfer step. This
gives justiÐcation to treat the precursor and successor com-
plexes as individual species. We could not detect any exciplex
emission in the Ru(bpy) 2`Èanthraquinone systems which
3
means that radiationless deactivation and dissociation to free
ions of a possible exciplex would be so fast that the elemen-
tary reaction case is a better description of the system.
6
Conclusion
In this work we show how all the rate constants of the con-
ventional ET Scheme 1 can be determined. These data are
evidence for the concept of negative activation enthalpy in an
elementary reaction in the excited state. Thus a reaction with
negative activation enthalpy may but need not proceed via an
intermediate species. Added salts inÑuence the rate constants
and quantum yields of free radical ions in an ET system.
Alkali ions associate with the anthraquinone radical anions
Fig. 8 Schematic diagram demonstrating the possibility for negative
activation enthalpy for an ““ exchange reaction ÏÏ (*G¡ \ 0). G(R) is
taken arbitrarily as parabolic, T S(R) is arbitrarily linear. Note that for
less negative reaction entropy *HE is positive.
and seem to inÑuence the ET from excited Ru(bpy) 2` to
3
anthraquinones directly.
with two others, the H and the S (or T S) surfaces. Fig. 8 is a
demonstration for the special case of *G¡ \ 0 which is close
to our system, consequently *H¡ \ T *S¡. For G(R) a para-
bolic form is assumed and T S(R) is taken to be a linear func-
tion of the reaction coordinate, a situation close to the one
treated by Sutin and Marcus in ref. 34g. In this case H(R) and
G(R) are very di†erent and the maximum of H is far from the
conÐguration of the transition state of the maximum of G. At
this conÐguration H is lower than the enthalpy of the reac-
tants, consequently *H* is negative.
Acknowledgements
The support of the Fonds der Chemischen Industrie, Frank-
furt, is gratefully acknowledged. We thank Prof. Dr. U.
Steiner and Prof. Dr. E. Kapinus for helpful discussions.
References
1
(a) D. Rehm and A. Weller, Ber. Bunsen-Ges. Phys. Chem., 1969,
73, 834; (b) D. Rehm and A. Weller, Isr. J. Chem., 1970, 8, 259.
(a) R.A. Marcus, J. Chem. Phys., 1956, 24, 966; (b) R. A. Marcus,
Annu. Rev. Phys. Chem., 1964, 15, 155; (c) R. A. Marcus, Angew.
Chem., 1993, 105, 1161.
(a) L. J Calcaterra, G. L. Closs and J. R. Miller, J. Am. Chem.
Soc., 1983, 105, 670; (b) G. L. Closs, L. T. Calcaterra, N. J. Green,
K. W. PenÐeld and J. R. Miller, J. Phys. Chem., 1986, 90, 3673; (c)
I. R. Gould, D. Ege, J. E. Moser and S. Farid, J. Am. Chem. Soc.,
1990, 112, 4290.
(a) I. R. Gould, R. H. Young, L. J. Mueller and S. Farid, J. Am.
Chem. Soc., 1994, 116, 8176; (b) I. R. Gould, R. H. Young, L. J.
Mueller, A. C. Albrecht and S. Farid, J. Am. Chem. Soc., 1994,
116, 8188; (c) I. R. Gould and S. Farid, Acc. Chem. Res., 1996, 29,
522; (d) M. G. Kuzmin, Pure Appl. Chem., 1993, 65, 1653; (e)
M. G. Kuzmin, J. Photochem. Photobiol. A: Chem., 1996, 102, 51;
(f) N. A. Sadovskii, M. G. Kuzmin, H. Gorner and K. Scha†ner,
Chem. Phys. L ett., 1998, 282, 456.
M. Z. Ho†mann, F. Bolletta, L. Moggiand and G. L. Hug, J.
Phys. Chem., Ref. Data, 1989, 18, 219.
(a) D. Plancherel, J. G. Vos and A. von Zelewski, J. Photochem.,
1987, 36, 267; (b) J. R. Darwent and K. Kalyanasundaram, J.
Chem. Soc., Faraday T rans. 2, 1981, 77, 373; (c) A Vlcek jr. and F.
Bolletta, Inorg. Chem. Acta, 1983, 76, L227.
(a) N. Kitamura, S. Okano and S. Tazuke, Chem. Phys. L ett.,
1982, 90, 13; (b) N. Kitamura, R. Obata, H.-B. Kim and S.
Tazuke, J. Phys. Chem., 1987, 91, 2033; (c) N. Kitamura, H.-B.
Kim, S. Okano and S. Tazuke, J. Phys. Chem., 1989, 93, 5750; (d)
H.-B. Kim, N. Kitamura, Y. Kawanishi and S. Tazuke, J. Phys.
Chem., 1989, 93, 5757; (e) N. Kitamura, R. Obata, H.-B. Kim and
S. Tazuke, J. Phys. Chem., 1989, 93, 5764.
Such large di†erences between G and H are observed only
when large entropy e†ects exist in the reaction. If in Fig. 8 the
reaction entropy and thus T *S¡ were less negative, *H*
might be positive as one can easily derive from this Ðgure. In
real reactions the form of the G, H and T S surfaces may di†er
widely from those of Fig. 8.38 For the vast majority of reac-
tions *G¡ D 0 and T S¡ is small compared with *H¡ (and T S
is not a linear function of the reaction coordinate). Then the G
and H surfaces are close and very similar in shape, the
maximum of the H surface is near the transition state conÐgu-
ration: *H* is positive.
2
3
4
The pre-equilibrium case is easily recognized if an interme-
diate species can be detected. If no intermediate can be seen a
numerical estimation of the conditions k ? k or k > k
2
~1
2
~1
is necessary in order to discriminate between the pre-
equilibrium and elementary reaction cases. In the
5
6
*Ru(bpy) 2`Èanthraquinone system the CI (Scheme 1) cannot
3
be seen. The numerical results demonstrate that k ] k
?
b
34
k
(corresponding to k ? k ) and thus in this system the
32
2
~1
negative activation enthalpy has to be attributed to the ele-
mentary reaction. To the best of our knowledge this is the Ðrst
example of an excited state reaction where this conclusion can
be based on experimental evidence.
7
Tazuke et al.7 have found very similar results in comparable
systems. They preferred the equilibrium explanation for the
interpretation of their Ðndings, however on the more conven-
tional argumentative basis. We believe that their systems also
are examples of elementary reactions with negative activation
enthalpies, but as the quantum yield measurement is missing
in their publication we cannot decide the question.
It has been argued4 that for ET reactions near *G¡ \ 0 a
reaction scheme like eqn. (7) should be used rather than reac-
tion Scheme 1 as in this energy region an exciplex interme-
diate should be formed directly in a bimolecular reaction from
the reactants. Exciplex formation according to eqn. (7)
requires considerable coupling of the locally excited and elec-
8
9
R. Frank and H. Rau, Recl. T rav. Chim. Pays.-Bas, 1995, 114,
556.
E. I. Kapinus and H. Rau, J. Phys. Chem., 1998, 102, 5569.
10 (a) T. Ohno, A. Yoshimura and N. Mataga, J. Phys. Chem., 1990,
94, 4871; (b) T. Kakitani, N. Matsuda, A. Yoshimori and N.
Mataga, Prog. React. Kinet., 1995, 20, 347; (c) N. Mataga, T.
Ashai, Y. Kanda, T. Okada and T. Kakitani, Chem. Phys., 1988,
127, 249.
11 J. R. Bolton, M. D. Archer, in Electron tranfer in inorganic,
organic and biological systems, Adv. Chem. Ser., ed. J. R. Bolton,
N. M. Mataga and P. G. McLendon, ACS, Washington, DC,
1991, vol. 228, p. 7.
Phys. Chem. Chem. Phys., 1999, 1, 3481È3490
3489

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12 (a) M. V. Smoluchowski, Z. Physik. Chem. (L eipzig), 1918, 92,
129; (b) P. Debye, T rans. Electrochem. Soc., 1942, 82, 265; (c) M.
Eigen, Z. Physik. Chem., (Wiesbaden), 1954, 1, 176.
Sauer and S. Gordon, J. Phys. Chem., 1979, 83, 1803; (g) D. D.
Davies, R. E. Huie and J. T. Herron, J. Chem. Phys., 1973, 59,
628; (h) J. Connor, A. VanRodselar, R. W. Fair and O. P.
Strausz, J. Am. Chem. Soc., 1971, 93, 560; (i) J. L. Jourdain, G.
Poulet and G. LeBras, J. Chem. Phys., 1982, 76, 5827; (k) M.
Meot-Ner (Mautner) and F. H. Field, J. Am. Chem. Soc., 1978,
100, 1356; (l) D. K. Sen Sharma and P. Kebarle, J. Am. Chem.
Soc., 1982, 104, 19; (m) R. Hiatt and S. W. Benson, J. Am. Chem.
Soc., 1972, 94, 6886.
13 C. Chiorboli, M. T. Indelli, M. A. Rampi-Scandola and F. Scan-
dola, J. Phys. Chem., 1988, 92, 156.
14 Estimated to be equal to that of methylviologen.15a
15 (a) C. R. Bock, J. A. Connor, A. R. Gutierrez, T. J. Meyer, D. G.
Whitten, B. P. Sullivan and J. K. Nagle, J. Am. Chem. Soc., 1979,
101, 4815; (b) W. E. Jones and M. A. Fox, J. Phys. Chem., 1994,
98, 5095.
16 As the quenching process is a bimolecular reaction this quantum
yield is not a characteristic property of the quencher or donor
but it is a function of the reaction conditions, especially of the
quencher concentration. With increasing quencher concentration
it approaches an upper limit. The quencher concentration in this
work is so high that this limit is reached.
27 V. D. Kiselev and J. G. Miller, J. Am. Chem. Soc., 1975, 97, 4036.
28 (a) O. Hammerich and V. D. Parker, Acta Chem. Scand. Ser. B,
1983, 37, 379; (b) J. B. Olson and T. H. Koch, J. Am. Chem. Soc.,
1986, 108, 756; (c) J. Wang, Ch. Doubleday, jr. and N. J. Turro, J.
Am. Chem. Soc., 1989, 111, 3692.
29 B. Reitstoen and V. D. Parker, J. Am. Chem. Soc., 1990, 112,
4968.
17 R. Frank and H. Rau, EPA Newsletter, 1999, 65, 39.
18 (a) A. E. Brodsky, L. L. Gordienko and L. S. Degtiarev, Electro-
chim. Acta, 1968, 13, 1095; (b) M. E. Peover, J. Chem. Soc., 1962,
4540; (c) A. Aumuller and S. Hunig, L iebigs Ann. Chem., 1986,
165; (d) H. Shalev and D. H. Evans, J. Am. Chem. Soc., 1989, 111,
2667; (e) R. G. Compton, B. A. Coles, M. B. G. Pilkington and D.
Bethell, J. Chem. Soc., Faraday T rans., 1990, 86, 663; (f) K.
Umemoto, Chem. L ett., 1985, 1415; (g) J. Posdorfer, M. Olbrich-
Stock and R. N. Schindler, Z. Phys. Chem., N. F. Munchen 1991,
171, 33.
30 (a) N. Sutin and B. M. Gordon, J. Am. Chem. Soc., 1961, 83, 70;
(b) J. N. Braddock and T. J. Meyer, J. Am. Chem. Soc., 1973, 95,
3158; (c) J. L. Cramer and T. J. Meyer, Inorg. Chem., 1974, 13,
1250.
31 E. Baggott and M. J. Pilling, J. Chem. Soc., Faraday T rans 1,
1983, 79, 221.
32 (a) N. J. Turro, G. F. Lehr, J. A. Butcher, R. A. Moss and W.
Guo, J. Am. Chem. Soc., 1982, 104, 1754; (b) R. A. Moss, W.
Lawrynowicz, N. J. Turro, I. R. Gould and Y. Cha, J. Am. Chem.
Soc., 1986, 108, 7028
19 (a) I. Piljac, M. Tkalcec and B. Grabaric, Anal. Chem. 1975, 47,
1369; (b) V. D. Bezuglyi, L. V. Shkodina and T. A. Alekseeva,
Soviet Electrochemistry, 1984, 19, 1282; (c) M. E. Peover and J. D.
Davies, J. Electroanal. Chem., 1963, 6, 46; (d) R. L. Blankespoor,
D. L. Schutt, M. B. Tubergen and R. L. DeJong, J. Org. Chem.,
1987, 52, 2059; (e) S. Lazarov, A. Trifonov and J. Panajotov, Z.
Phys. Chem., 1965, 233, 49.
33 (a) S. R. L. Fernando, U. S. M. Maharoof, K. D. Deshayes, T. H.
Kinstle and M. T. Ogawa, J. Am. Chem. Soc., 1996, 118, 5783; (b)
H. A. Garrera, J. J. Cosa and C. M. Previtali, J. Photochem. Pho-
tobiol. A: Chem., 1991, 56, 267; (c) R. B. Murphy and W. F.
Libby, J. Am. Chem. Soc. 1977, 99, 39; (d) H. Werner, E. O.
Fischer, B. Heckl and C. G. Kreiter, J. Organomet. Chem., 1971,
28, 367; (e) T. Shimomura, K. J. Tolle, J. Smid and M. Scwarc, J.
Am. Chem. Soc., 1967, 84, 796; (f) A.-M. Albrecht-Gary, C.
Dietrich-Buchecker, Z. Saad and J.-P. Sauvage, J. Chem., Soc.,
Chem. Commun., 1992, 280.
20 C. Chiorboli, F. Scandola and H. Kisch, J. Phys. Chem., 1986, 90,
2211.
21 Reaction spectra are available as supplementary material.¤
22 (a) R. M. Wightman, J. R. Cockrell, R. W. Murray, J. N. Burnett
and S. B. Jones, J. Am. Chem. Soc., 1976, 90, 2526; (b) J. L.
Roberts jr., H. Sugimoto, W. C. Barrette jr., and D. T. Sawyer, J.
Am. Chem. Soc., 1985, 107, 4556.
23 J. Mayer and R. Kraslukianis, J. Chem. Soc., Faraday T rans.,
1991, 87, 2943.
24 (a) W. R. Fawcett and G. Liu, J. Phys. Chem., 1992, 96, 4231; (b)
P. Suppan, J. Photochem. Photobiol. A: Chem., 1990, 50, 293.
25 We have eliminated the change of viscosity due to increasing salt
34 (a) M. Mozurkewich and S. W. Benson, J. Phys. Chem., 1984, 88,
6429; (b) K. N. Houk, and N. G. Rodan, J. Am. Chem. Soc., 1984,
106, 4293; (c) R. A. Marcus and N. Sutin, Inorg. Chem., 1975, 14,
213; (d) R. A. Marcus, J. Electroanal. Chem., 1977, 82, 9; (e) W.
Stiller, R. Schmidt, E. Muller and N. V. Shokierev, Z. Phys.
Chem. (Munich), 1992, 162, 119; (f) Y. Chen, A. Rauk and E.
Tschuikow-Roux, J. Phys. Chem., 1991, 95, 9900; (g) R. A.
Marcus and N. Sutin, Comments Inorg. Chem., 1986, 5, 119.
35 Experimental quantities are usually indicated by the double-
dagger symbol. The relationships are *Gt \ *G* [ RT ln (hZ/
concentration by
a
multiplicative correction: g \ g/g \
r
0
1 1
kT ); *SE \ *S* ] R ln (hZ/kT ) [ R; *HE \ *H* [ RT .34c
1 ] 0.018 c1N@a2ClO4 ] 0.73 cNaClO4 . In eqn. (1) the di†usion con-
trolled rate constants are dependent on g, but also the activation
controlled ones if they represent adiabatic reactions with the lon-
gitudinal relaxation times in the pre-exponential factor. (See e.g.
D. F. Calef and P. G. Wolynes, J. Chem. Phys., 1983, 78, 430,
3387; E. M. Kosower and D. Huppert, Annu. Rev. Phys. Chem.,
1986, 37, 127; G. Grampp, W. Harrer and W. Jaenicke, J. Chem.
Soc., Faraday T rans., 1, 1987, 83, 161.)
2
2
36 K. N. Houk, N. G. Rodan and J. Mareda, J. Am. Chem. Soc.,
1984, 106, 4291.
37 This is a simpliÐcation, Marcus deÐnes an (N [ 1)-dimensional
hypersurface, the set of conÐgurations which separate the reac-
tant and product conÐgurations to be the transition state (R. A.
Marcus, in Investigation of Rates and Mechanisms of Reactions,
ed. E. S. Lewis, T echniques of Chemistry, vol. VI, Part 1, ed. A.
Weissberger, J. Wiley & Sons, New York, London, Sydney,
Toronto, 1974, pp. 13È46.
26 (a) W. Roth, T. Bastigkeit and S. Boerner, L iebigs Ann., 1996,
1313; (b) Wei, J. Chem. Eng. Sci., 1996, 51, 2995; (c) M. Mozuir-
kewich, J. J. Lamb and S. W. Benson, J. Phys. Chem., 1984, 88,
6435; (d) J. J. Lamb, M. Mozuirkewich and S. W. Benson, J.
Phys. Chem., 1984, 88, 6441; (e) A. Menon and N. Sathyamurthy,
J. Phys. Chem., 1981, 85, 1021; (f) R.-R.Lii, R. A. Gorse, jr., M. C.
38 The form of the surfaces is dependent on the speciÐc reaction.
Houk and Rodan34b have arbitrarily used Morse curves, we have
also used parabolas for G, H and T S as well as a Gaussian for G
and a parabola for T S: It seems that for all forms of the surfaces
the situation of negative activation enthalpy can be reached when
the reaction parameters are chosen suitably.
¤ Supplementary material (SUP 57584, 6 pp.) deposited with the
British Library. Details are available from the Editorial Office.
Paper 9/02486G
3490
Phys. Chem. Chem. Phys., 1999, 1, 3481È3490