Highly efficient photoinitiation in the cerium(III)-catalyzed aqueous autoxidation of sulfur(IV). An example of comprehensive evaluation of photoinduced chain reactions

Article abstract of DOI:10.1021/ja0439120

The photoinitiated and cerium(III)-catalyzed aqueous reaction between sulfite ion and oxygen has been studied in a diode-array spectrophotometer using the same light beam for excitation and detection. Cerium(III) is identified as the photoactive absorbing species, and the production of cerium(IV) initiates a radical chain reaction. To interpret all the experimental findings, a simple scheme is proposed, in which the additional chain carriers are sulfite ion radical (SO₃^-.), sulfate ion radical (SO₄ ^-.), and peroxomonosulfate ion radical (SO₅^-.). The overall rate of oxidation is proportional to the square root of the light intensity per unit volume, which is readily interpreted by the second-order termination reaction of the proposed scheme. It is also shown that the reaction proceeds for an extended period of time in the dark following illumination, and a quantitative analysis is presented for this phase as well. The postulated model predicts that cerium(III) should have a cocatalytic or synergistic effect on the autoxidation of sulfite ion in the presence of other catalysts. This prediction was confirmed in the iron(III)-sulfite ion-oxygen system. The experimental method and the mathematical treatment used might be applicable to a wide range of photoinduced chain reactions.

Full text of DOI:10.1021/ja0439120

Published on Web 03/10/2005
Highly Efficient Photoinitiation in the Cerium(III)-Catalyzed
Aqueous Autoxidation of Sulfur(IV). An Example of
Comprehensive Evaluation of Photoinduced Chain Reacions
Ildik o´ Kerezsi, G a´ bor Lente, and Istv a´ n F a´ bi a´ n*
Contribution from the UniVersity of Debrecen, Department of Inorganic and Analytical
Chemistry, Debrecen 10, P.O.B. 21, H-4010, Hungary
Received October 6, 2004; E-mail: ifabian@delfin.unideb.hu
Abstract: The photoinitiated and cerium(III)-catalyzed aqueous reaction between sulfite ion and oxygen
has been studied in a diode-array spectrophotometer using the same light beam for excitation and detection.
Cerium(III) is identified as the photoactive absorbing species, and the production of cerium(IV) initiates a
radical chain reaction. To interpret all the experimental findings, a simple scheme is proposed, in which
-
•
-•
the additional chain carriers are sulfite ion radical (SO
3
), sulfate ion radical (SO
4
), and peroxomonosulfate
-
•
ion radical (SO
5
). The overall rate of oxidation is proportional to the square root of the light intensity per
unit volume, which is readily interpreted by the second-order termination reaction of the proposed scheme.
It is also shown that the reaction proceeds for an extended period of time in the dark following illumination,
and a quantitative analysis is presented for this phase as well. The postulated model predicts that cerium(III)
should have a cocatalytic or synergistic effect on the autoxidation of sulfite ion in the presence of other
catalysts. This prediction was confirmed in the iron(III)-sulfite ion-oxygen system. The experimental method
and the mathematical treatment used might be applicable to a wide range of photoinduced chain reactions.
decomposition are mainly responsible for the catalytic effect.14
Introduction
Since then, it has been shown that the sulfito complexes may
1
Catalytic autoxidation of sulfur(IV) has attracted considerable
interest because of its dominant role in acid rain formation and
importance in industrial desulfurization processes.2 The sulfite
ion-oxygen system has been used for hydroxylation, epoxida-
either trigger a radical-type chain reaction by generating the
-
•
SO3 radical or be part of a direct oxidation of sulfite ion to
sulfate ion. All of the postulated mechanisms share the same
feature that oxygen is involved only in secondary reaction steps
in the overall process.
-6
7-9
tion, and oxidative cleavage of DNA.
sulfite ion is also important in metallurgical technologies
The autoxidation of
1
0,11
While many of the metal-ion-catalyzed systems are reasonably
well understood now, gaining further mechanistic information
on the core autoxidation is often circuitous. First of all, the
concentration of dissolved oxygen cannot be controlled as
accurately as that of other reactants. The second problem is that
while spectroscopic observations are typically suitable for
monitoring the metal catalysts or the sulfito complexes, direct
information on the concentrations of oxygen or free sulfite ion
is not acquirable. Finally, the complexation of the catalyst with
sulfite ion is kinetically coupled with the autoxidation process,
and very often redox reactions also occur in the absence of
oxygen; e.g., the iron(III) complexes are probably the most
frequently used catalysts of the autoxidation, but they also
and food chemistry.12,13 Multivalent metal ions are known to
be very active catalysts of this reaction, and stoichiometric,
kinetic, and mechanistic aspects of several systems have been
studied intensively since the 1930s.2-38 B a¨ ckstr o¨ m postulated
that the formation of transition metal sulfito complexes and their
(
1) Throughout this work, we use the term “sulfite ion” in a general sense to
2-
refer collectively to SO
3
and all of its singly or doubly protonated forms.
Differentiation between these forms in the text is only made when it is
particularly important for clarity. As no evidence for the existence of
2 3 2 2
sulfurous acid, H SO , is known, we adopt the notation H O‚SO for
hydrated sulfur dioxide emphasizing that it is the doubly protonated
2
-
conjugate acid form of SO
3
.
(
(
(
(
2) Coichev, N.; van Eldik, R. J. Chem. Educ. 1994, 71, 767.
3) Brandt, C.; van Eldik, R. Chem. ReV. 1995, 95, 119 and references therein.
4) Moya, H. D.; Neves, E. A.; Coichev, N. J. Chem. Educ. 1999, 76, 930.
5) Pezza, H. R.; Lopes, C. F. F.; Su a´ rez-Iha, M. E. V.; Coichev, N. Quim.
NoVa 1999, 22, 529.
17-18,22,30,37-38
oxidize sulfite ion.
(
6) Csord a´ s, V.; F a´ bi a´ n, I. AdV. Inorg. Chem. 2003, 54, 395.
7) Muller, J. G.; Hickerson, R. P.; Perez, R. J.; Burrows, C. J. J. Am. Chem.
Soc. 1997, 119, 1501.
(
(14) B a¨ ckstr o¨ m, H. L. J. Z. Phys. Chem., Abt. B 1934, 25, 122.
(15) Anast, J. M.; Margerum, D. W. Inorg. Chem. 1981, 20, 2319.
(16) Hobson, D. B.; Richardson, P. J.; Robinson, P. J.; Hewitt, E. A.; Smith, I.
Ind. Eng. Chem. Res. 1987, 26, 1818.
(17) Kraft, J.; van Eldik, R. Atmos. EnViron. 1989, 23, 2709.
(18) Kraft, J.; van Eldik, R. J. Chem. Soc., Chem. Commun. 1989, 790.
(19) van Eldik, R.; Coichev, N.; Bal Reddy, K.; Gerhard, A. Ber. Bunsen-Ges.
Phys. Chem. 1992, 96, 478.
(20) Timpe, O.; Schl o¨ gl, R. Ber. Bunsen-Ges. Phys. Chem. 1993, 97, 1076.
(21) Berglund, J.; Fronaeus, S.; Elding, L. I. Inorg. Chem. 1993, 32, 4527.
(22) Brandt, C.; F a´ bi a´ n, I.; van Eldik, R. Inorg. Chem. 1994, 33, 687 and
references therein.
(
8) Lepentsiotis, V.; Domagala, J.; Grgi c´ , I.; van Eldik, R.; Muller, J. G.;
Burrows, C. J. Inorg. Chem. 1999, 38, 3500.
9) Wietzerbin, K.; Muller, J. G.; Jameton, R. A.; Pratviel, G.; Bernadou, J.;
Meunier, B.; Burrows, C. J. Inorg. Chem. 1999, 38, 4123.
(
(
10) Tiwari, B. L.; Kolbe, J.; Hayden, H. W., Jr. Metall. Trans. B 1979, 10,
6
07.
(
(
(
11) Cho, E. H. Metall. Trans. B 1986, 17, 745.
12) Wedziha, B. L.; Lamikanra, O. Food Chem. 1987, 23, 193.
13) McFeeters, R. F.; Barrangou, L. M.; Barish, A. O.; Morrison, S. S. J. Agric.
Food Chem. 2004, 52, 4554.
10.1021/ja0439120 CCC: $30.25 © 2005 American Chemical Society
J. AM. CHEM. SOC. 2005, 127, 4785-4793
9
4785

A R T I C L E S
Kerezsi et al.
In this paper, we describe an exceptional case where the
Instrumentation. UV-vis spectra were recorded on a HP-8543
diode-array or a Perkin-Elmer Lambda 2S scanning spectrophotometer.
A YSI 5100 dissolved oxygen meter and a YSI model 5239 probe with
YSI 5906 membrane cap were used for measuring the concentration
of dissolved oxygen in aqueous solutions. Two different lamps were
used in some of the photochemical experiments: an AvaLight DHS
(Avantes) and a high-power quartz lamp (Medicor, Hungary). Quantita-
tive kinetic measurements on the photochemical reaction were per-
formed on the HP-8543 diode-array instrument using the method and
3+
mechanism of the photoinitiated and Ce -catalyzed autoxidation
of sulfite ion could be explored in detail. Equation 1 defines
the stoichiometry and the rate of the overall process:
-
+
2
H O‚SO + O ) 2HSO + 2H
2
2
2
4
d[H O‚SO ]
d[O2]
1
2
2
2
V )
) -
(1)
4
2
dt
dt
general operating procedures described in an earlier publication.
A
built-in Hewlett-Packard 89090A Peltier thermostat was used to
maintain constant temperature (10.0 ( 0.1 or 25.0 ( 0.1 °C). The
solutions were kept homogeneous during the photochemical experiments
using the built-in magnetic stirrer of the standard cell compartment of
the HP-8543 instrument. A 3-mm stirring rod was used inside standard
quartz cuvettes (optical path length: 1.000 cm). The geometry of the
setup was carefully tested, and it was made sure that the stirring rod
never disrupted the light beam. The light source was calibrated by both
This system offers several unique advantages, making it
possible to draw unambiguous conclusions regarding the mech-
anism. First of all, complex formation or direct redox reactions
3+
do not occur between Ce and sulfite ions, and consequently
there is no interference from such processes. Second, the
concentration change of sulfite ion can be followed directly by
UV-vis spectroscopy. Third, the autoxidation is zeroth-order
with respect to dissolved oxygen, circumventing the problem
of less accurate control over its concentration. Fourth, due to
the photoinitiated nature of the reaction, it can be started and
ceased by turning illumination on and off, respectively.
A further point of interest in the present study is the
43
ferrioxalate actinometry and reproducing observations on the known
42
photoreaction of 2,6-dichloro-1,4-benzoquinone. Some additional
kinetic measurements on thermal reactions were performed with an
Applied Photophysics DX-17 MV sequential stopped-flow apparatus
using a 1 cm optical path length.
Results and Discussion
4+
39-41
widespread analytical use of the Ce -sulfite ion reaction.
Although quite a few methods have been developed based on
this process, no attention has been directed toward possible
interference from dissolved oxygen or light. Further on, in a
few cases the interpretation of the chemical principles of the
analysis is clearly incoherent and without ground.
Preliminary Observations. Sulfite ion and oxygen do not
react in the absence of catalysts in acidic aqueous solutions,
3
,5,36,44
3+
even at elevated temperatures.
We confirmed that Ce
has a catalytic effect on reaction 1 in our earlier high-temperature
study on the effect of dissolved oxygen on the aqueous redox
4
4
reactions of dithionate ion. This phenomenon was rather
unexpected, as the only previous related record known to us is
Experimental Section
4
+
Materials. All chemicals used in this study were of analytical reagent
a remark about possible effect of Ce on the autoxidation of
sulfite ion in a study connected to seawater chemistry.16 We
found that the catalytic process can be studied in a straightfor-
ward manner at room temperature.
grade and purchased from commercial sources. CeCl
and Ce(SO ‚4H O (Reanal) were used without further purification to
prepare stock solutions. The concentration of the Ce stock solution
was determined by complexometric titration with Na EDTA solution
at pH between 5 and 6 using xylenolorange indicator. The concentration
3
2
‚6H O (Aldrich)
4
)
2
2
3
+
2
3+
In preliminary studies on the Ce -sulfite ion-oxygen
system, the same experiments were carried out in a conventional
double beam and a HP-8453 diode-array spectrophotometer.
Measurable progress of sulfite ion decay was observed only
with the latter instrument. The main difference in the experi-
ments is that the double-beam unit scans the spectrum with a
low intensity monochromatic light beam, whereas the diode-
array spectrophotometer irradiates the sample with a relatively
high energy undispersed light in the 190-1100 nm spectral
region. The observations confirm that illumination of the
samples with sufficient light intensity is essential in the Ce(III)-
catalyzed autoxidation of sulfite ion and the reaction can be
driven even by the light source of a standard photometer.
The photochemical nature of the process is demonstrated in
Figure 1. In this case, the variation in the concentration of
dissolved oxygen was followed in a solution containing sulfite
4+
of the Ce stock solution was determined by iodometric titration. Fresh
sodium sulfite stock solutions were prepared from Na (Reanal)
2 2 5
S O
every day. Doubly deionized and ultrafiltered water from a Millipore
Q system was used to prepare the stock solutions and samples. All
experiments were carried out at high and constant acid concentration
(sulfuric or perchloric acid), and additional salt was not used to adjust
the ionic strength.
(
(
(
23) Berglund, J.; Elding, L. I. Atmos. EnViron. 1995, 29, 1379.
24) Connick, R. E.; Zhang, Y. X. Inorg. Chem. 1996, 35, 4613.
25) Ermakov, A. N.; Proskrebyshev, G. A.; Stoliarov, S. I. J. Phys. Chem.
1
996, 100, 3557.
26) Ermakov, A. N.; Proskrebyshev, G. A.; Purmal, A. P. Kinet. Catal. 1997,
8, 325.
27) Travina, O. A.; Kozlov, Y. N.; Purmal, A. P.; Travin, S. O. Kinet. Catal.
(
(
3
1
997, 38, 242.
(
28) Fronaeus, S.; Berglund, J.; Elding, L. I. Inorg. Chem. 1998, 37, 4939.
29) Grgi c´ , I.; Dov zˇ an, A.; Ber cˇ i cˇ , G.; Hudnik, V. J. Atmos. Chem. 1998, 29,
(
3
15.
3
+
(
(
(
(
30) Brandt, C.; van Eldik, R. Transition Met. Chem. 1998, 23, 667.
31) Grgi c´ , I.; Pozni c´ , M.; Bizjak, M. J. Atmos. Chem. 1999, 33, 89.
32) Pezza, H. R.; Coichev, N. J. Coord. Chem. 1999, 47, 107.
33) Martins, C. R.; Cabral Neto, C. A.; Alves, J. J. F.; Andrade, J. B. J. Braz.
Chem. Soc. 1999, 10, 453.
ion and Ce . A steady decay in the oxygen concentration was
observed as long as the light source of a commercially available
Avantes fiber optic spectrophotometer was illuminating the
solution. When the light source was turned off, the concentration
change was reversed. The experiment was run in an open
reactor, and thus the slight increase in the concentration occurred
because of the dissolution of oxygen from ambient air. Similar
(34) Wolf, A.; Deutsch, F.; Hoffmann, P.; Ortner, H. M. J. Atmos. Chem. 2000,
3
7, 125.
(
(
(
35) Betterton, E. A.; Anderson, D. J. J. Atmos. Chem. 2001, 40, 171.
36) Ermakov, A. N.; Purmal, A. P. Kinet. Catal. 2001, 42, 479.
37) Lente, G. Ph.D. Thesis, University of Debrecen, Hungary, 2001. Available
free of charge via the Internet at http://www.unideb.hu/∼lenteg/index.html
38) Lente, G.; F a´ bi a´ n, I. J. Chem. Soc., Dalton Trans. 2002, 778.
39) Takeuchi, K.; Ibusuki, T. Anal. Chim. Acta 1985, 174, 359.
40) Koukli, I. I.; Sarantonis, E. G.; Calokerinos, A. C. Anal. Lett. 1990, 23,
(
(
(
(42) Lente, G.; Espenson, J. H. J. Photochem. Photobiol., A 2004, 163, 249.
(43) Hatchard, C. G.; Parker, C. A. Proc. R. Soc. London, Ser. A 1956, 235,
518.
1
167.
(41) Aly, F. A.; Alarfaj, N. A.; Alwarthan, A. A. Talanta 2001, 52, 715.
(44) Lente, G.; F a´ bi a´ n, I. Inorg. Chem. 2004, 43, 4019.
4786 J. AM. CHEM. SOC.
9
VOL. 127, NO. 13, 2005

Ce(III)-Catalyzed Aqueous Autoxidation of S(IV)
A R T I C L E S
Figure 1. Effect of light on the dissolved oxygen concentration in the
3
+
presence of sulfite ion and Ce . (A) Start of illumination. (B) End of
Figure 2. Kinetic traces measured in a diode-array instrument during the
photoinitiated autoxidation of sulfite ion. [Ce ] ) 0.50 mM; [S(IV)] )
3
+
illumination. [Ce ] ) 0.50 mM; [S(IV)] ) 1.00 mM; [H2SO4] ) 0.10 M;
3+
T ) 25 °C.
1
.00 mM; [O2] ) 0.19 mM (a, b), 0.22 mM (c); [H2SO4] ) 0.10 M; path
3
length 1.000 cm; V ) 3.00 cm ; T ) 25.0 °C; ti ) 5 s; td ) 0 s (a), 5 s (b),
15 s (c); λ ) 276 nm.
effects were not observed in the absence of either Ce3+ or sulfite
ion. The same conclusions were drawn when a quartz lamp was
used instead of the less intense light beam of the spectropho-
tometer (Figure S1 in Supporting Information). The loss of
oxygen was so rapid in this case that reliable kinetic measure-
ments were not possible because of the relatively slow response
time of the oxygen electrode.45
the sulfite ion-oxygen-Ce3 system, we found no obvious way
+
to decide which reactant is the photoactive species.
However, an experiment reported in our earlier study on the
3+
oxidation of dithionate ion conclusively shows that Ce is the
4
4
active absorbing species. In this experiment (shown in Figure
in ref 39 and in Figure S3 in the Supporting Information),
5
Stoichiometric studies were also carried out. The dissolved
oxygen content of a freshly prepared acidic solution containing
the slow disproportionation of dithionate ion produced sulfite
ion, which was in turn oxidized by dissolved oxygen in a
Ce(III)-catalyzed process. The observed kinetic curves and
repetitive spectra showed that no sulfite ion accumulated in any
detectable concentration until all oxygen was consumed. During
3+
Ce and sulfite ion was measured, and then the quartz lamp
was used to drive the reaction until the concentration of
dissolved oxygen dropped to zero. The sulfite concentration of
this sample was determined by measuring its UV-vis spectrum
immediately. It should be noted that H2O‚SO2 is the predominant
form of sulfite ion in the entire pH range of the present study
pKa1 ) 1.74 at 25.0 °C in 1.0 M NaClO4) and it has a UV
absorption band centered around 276 nm.
showed that the stoichiometry of the reaction corresponds to
eq 1 within experimental error.
3+
the whole course of this reaction, Ce is the only absorbing
species present; therefore light absorption by sulfite ion is not
3+
necessary for driving the reaction, and Ce must be the
(
photoactive species. As will be shown in the next sections, this
conclusion is also consistent with the results obtained here
because quantitative evaluation of all kinetic observations is
37,38
These studies
3+
possible assuming that Ce is the only photoactive reactant.
When the photoinitiation is carried out in the diode-array
spectrophotometer, the spectrum of the solution can be recorded
simultaneously. A recently introduced method uses the same
Experiments with Continuous Illumination. Photochemical
kinetic experiments can be performed with a diode-array
spectrophotometer in different ways. Essentially, the variants
differ in the illumination time of the sample during the
measurement of a single spectrum and in the duration of dark
periods between recording two consecutive spectra, when the
illuminating light is excluded by closing the shutter of the
photometer. The lengths of the illumination and dark periods
are given by ti and td, respectively. Thus, the duration of a full
cycle, tc, is given by tc ) ti + td. The simplest experiment is
when the sample is continuously illuminated after triggering
4
2
light beam to drive and analyze the photochemical reaction.
This technique has remarkable potential for extending quantita-
tive kinetic measurements on photochemical reactions. Typical
3+
kinetic traces measured in the Ce -sulfite ion system at 276
nm are shown in Figure 2. These experiments afforded quantita-
tive information about the process and will be discussed in detail
in the next sections.
Identification of the Photoactive Species. Only UV light is
absorbed by the components of the Ce(III)-sulfite ion system
because H2O‚SO2 and Ce3 have absorptions in the 195-300
nm range (Figure S2 in Supporting Information). An analysis
of the spectra recorded during the kinetic experiments proved
the reaction, i.e., t ) 0. Typical kinetic traces recorded using
d
+
this concept are shown in Figure 2. The reaction becomes slower
by increasing the length of the dark periods because the same
amount of light illuminates the sample over a longer period of
time. However, the rate does not decrease proportionally to the
cycle time. This clearly indicates that thermal reactions during
the dark periods also contribute to the overall process.
4+
that no detectable amounts of Ce , which has strong absorption
4
4
at around 320 nm, formed during the reaction at any time.
Under the conditions of the kinetic studies, both H2O‚SO2
3
+
and Ce contribute significantly to the overall absorbance,
although the relative values are different at different wave-
lengths. Consequently, both of them can in principle be
photoactive species. Based on the measurements carried out in
The photochemical use of diode-array instruments also affords
a way to determine quantum yields after careful calibration.42
The quantum yield of oxygen loss relative to the number of
3
+
photons absorbed by Ce in the fastest experiment shown in
Figure 2 (with td ) 0 s) was determined to be 76 ( 6. This
unequivocally indicates some kind of chain mechanism in which
(45) Macc a` , C. Anal. Chim. Acta 2004, 512, 183.
J. AM. CHEM. SOC.
9
VOL. 127, NO. 13, 2005 4787

A R T I C L E S
Kerezsi et al.
the role of light is only to initiate the chain but not to maintain
its propagation. In addition, the detected kinetic traces and rates
were also dependent on temperature (Figure S4 in Supporting
Information) indicating that the overall process involves thermal
reactions before or in the rate-determining step.
As shown in Figure 2, the measured kinetic traces are straight
lines; i.e., the rate did not depend on the time elapsed within a
kinetic run. The ratio of the initial concentrations of sulfite ion
and oxygen was reasonably close to the stoichiometric 2:1, so
one can conclude that the reaction is zeroth-order with respect
to both dissolved oxygen and sulfite ion. The same conclusion
was drawn from experiments with different initial concentrations
of the reactants. At 276 nm, the molar absorbances of H2O‚
3
+
SO2 and Ce were measured in independent experiments
Figure 3. Reaction rates as a function of sample volume. [Ce3+] ) 0.50
mM; [S(IV)] ) 1.00 mM; [H SO ] ) 0.10 M; T ) 25.0 °C.
2 4
(
Figure S2 in Supporting Information). The concentration of
3+
Ce does not change during the process, so the decrease in
absorbance is entirely due to the loss of H2O‚SO2. Consequently,
the rates of absorbance change could readily be converted into
the rate of reaction 1 by using the molar absorbance of H2O‚
-
1
-1
SO2 (364 M cm ) and considering the stoichiometry.
As already pointed out, V did not depend on the concentrations
of sulfite ion or oxygen and it was also independent of the ionic
strength and the pH in the studied region 0.1-1.0 (Figure S5
in Supporting Information). However, the rate depended on the
3+
intensity of light and the concentration of the photoinitiator Ce .
The intensity of the driving light cannot be changed directly
as the diode-array spectrophotometer has a fixed and carefully
stabilized light source. However, it is well-known that the rate
of a photochemical reaction is proportional to the intensity of
46
absorbed light per unit volume. Perhaps, the most convenient
way is to use the closely related quantity of absorbed photon
3+
Figure 4. Reaction rates as a function of Ce concentration. [S(IV)] )
4
2
3
count per unit volume in the evaluation of the results, which
is basically the part of the photon flow of the light beam (i.e.
1.00 mM; [H2SO4] ) 0.10 M; V ) 3.00 cm ; T ) 25.0 °C.
The dependence of the reaction rate on the Ce3 concentration
+
4
7
number of photons) absorbed by the photoactive species. The
absorbed photon count per unit volume (NV) can be calculated
from the known absorption spectra and concentrations of the
components and the emission properties of the carefully
calibrated light source42 and can be changed readily by varying
the volume of the sample irradiated. In the restricted space of
a 1 cm standard cuvette the accessible working volume range
is fairly limited, but a change by a factor of about 2 can still be
achieved, which is suitable for drawing basic conclusions. The
results are shown in Figure 3, where the logarithm of the rate
is plotted against the logarithm of sample volume. The points
define a straight line with some scatter, and the slope is -0.49
is somewhat more complex because NV itself is dependent on
3
+
the concentration of Ce (kinetic traces are shown in Figure
3
+
S6 in Supporting Information). A direct plot of V vs [Ce ]
shows some upward curvature, which is between linear and
parabolic (Figure 4, left axis). However, NV can be calculated
3
+
0.5
for each Ce concentration, and the quantity V/NV shows
3+
linear dependence on [Ce ] (Figure 4, right axis). This confirms
the following overall rate equation:
3+
0.5
V
V ) k [Ce ]N
(2)
2
The value k2 ) 30 ( 1 M-0.5 s-0.5 was determined by
(
0.06. Thus, the reaction is 0.5 order with respect to NV. This
multivariate least-squares fitting of all relevant measured data.
Experiments with Intermittent Dark Periods. Measure-
ments were carried out by opening and closing the shutter in
the light beam for controlled periods. Detailed experiments were
carried out to study the reaction with interrupted illumination
again indicates a chain mechanism and also strongly suggests
that the terminating step is second-order with respect to the chain
4
6
carriers.
In a more general sense, we note that studying the intensity
dependence through changing the volume in photochemical
reactions is a very advantageous technique when polychromatic
light is used as a driving force. If a series of filters were to be
used for the same purpose, they would almost surely change
the spectral properties of the driving light, whereas changing
the volume leaves the spectral distribution of intensities
unaltered.
3+
3
under standard conditions ([Ce ] ) 0.50 mM; V ) 3.00 cm ;
T ) 25.0 °C) at which the constant reaction rate upon continuous
-6
-1
illumination was V0 ) (2.3 ( 0.1) × 10 M s . As shown by
the two slower traces in Figure 2 (the curves with td ) 5 and
15 s), kinetic traces were zeroth-order with interrupted illumina-
tion as well.
Because the reaction rate is constant during exposure to light
of constant intensity, one would expect that the progress of the
reaction is proportional to the time of illumination. As a test, a
series of experiments were carried out where ti and tc were
(
46) Atkins, P. W.; de Paula, J. Physical Chemistry, 7th ed.; Oxford University
Press: Oxford, 2002; pp 924-936.
(
47) Verhoeven, J. W. Pure Appl. Chem. 1996, 68, 2223.
4788 J. AM. CHEM. SOC.
9
VOL. 127, NO. 13, 2005

Ce(III)-Catalyzed Aqueous Autoxidation of S(IV)
A R T I C L E S
This line of reasoning also demonstrates that the average
reaction rate V measured in an experiment with interrupted
illumination carries information on the progress of the reactions
in the dark periods. First, the fraction of the overall reaction
occurring in the dark, Q, is defined
V ti
Vtc
0
Q ) 1 -
(3)
Furthermore, the amount of oxygen consumed in the dark period,
n, can be calculated as
n ) Vt - V t
(4)
c
0 i
Figures 6, 7, and 8 show how Q and n depend on ti and td.
The fact that the reaction still persists somewhat after the
end of the illumination is readily interpreted by noting that a
chain reaction does not stop immediately after ceasing the
initiation. The concentration of the reactive intermediates can
only decrease in some time through the termination step(s).
-
6
-3
Although this time is often very short (10 -10 s) in chain
reactions, there is no reason to think that it cannot be longer
occasionally.
In general, two fundamentally different chain terminations
4
6
can be operative. The termination reaction is first-order with
respect to the chain carriers when they react with scavengers
being present in relatively large concentrations, while recom-
bination steps yield second-order kinetics.
The instantaneous reaction rate, Vd, as a function of time in
the dark period can be given for first-order and second-order
termination, respectively:
Figure 5. Calculated reaction rate as a function of time during experiments
3
+
with intermittent dark periods. [Ce ] ) 0.50 mM; [S(IV)] ) 1.00 mM;
3
[
)
H2SO4] ) 0.10 M; V ) 3.00 cm ; T ) 25.0 °C; ti ) td ) 2 s (a); ti ) td
5 s (b); dotted lines, average rates.
changed simultaneously in such a manner that their ratio was
kept constant. In other words, the average amount of photons
absorbed during a longer period of reaction time was constant.
It would clearly be expected that the average reaction rate
measured in such a series of experiments remains unchanged.
However, this is not the case, the average reaction rate decreased
as ti increased in this series (Figure S7 in Supporting Informa-
tion).
Another related unexpected observation was that the quantum
yield depended not only on the volume of the samples and the
concentration of Ce3+ but also on the length and distribution of
the dark periods. The highest quantum yield measured in our
experiments with long dark periods (td) and short illumination
times (ti) exceeded 500. These observations can only be
interpreted again by assuming that the reaction persists for some
time in the dark periods following illumination.
1st
-k5t
Vd ) V0e
(5)
(6)
V0
+ k6t
2
d
nd
V
)
1
In these formulas, V0 is the rate under illumination, k5 is a
pseudo first-order rate constant, k6 is the product of a pseudo
second-order rate constant and the steady-state concentration
of the recombining chain carrier at the end of the illumination
period. This concentration is the same for each kinetic run as
long as the reactant concentrations and illuminating light
intensities are the same.
From eqs 5 and 6, n can readily be calculated by integrating
Vd over the time period from 0 to td:
In fact, the analysis of data (vide infra) showed that the
instantaneous reaction rate changes as depicted in the examples
of Figure 5, where curve a (ti ) 2 s, td ) 2 s) and curve b (ti
V0
k5
td
1
st
1st
n
)
)
∫
(7)
(8)
0
)
5 s, td ) 5 s) have the same ti/td ratio but exhibit different
average rates. At this point, it should be explained why the
detected kinetic traces remain zeroth-order despite the varying
instantaneous reaction rates in the dark. The reaction remains
undetected in the dark period because the spectrophotometer
cannot measure without light. The loss of sulfite ion in the dark
period is detected during the next illumination phase. Therefore,
the difference between two successive observation points is
characteristic of the progress of the reaction in a complete cycle
V0
td
2
nd
2nd
n
∫
Vd dt ) ln(1 + k6td)
0
k6
From eqs 7 and 8, the value of Q can also be calculated:
1 - e-k5td)
(
1
st
Q
)
)
(9)
-
k6td
k5ti + (1 - e
)
(Figure S8 in Supporting Information). The overall progress of
ln(1 + k6td)
2
nd
the reaction is the same in every cycle, so the detected kinetic
trace remains zeroth-order.
Q
(10)
k t + ln(1 + k t )
6 i
6 d
J. AM. CHEM. SOC.
9
VOL. 127, NO. 13, 2005 4789

A R T I C L E S
Kerezsi et al.
Figure 8. Amount of oxygen consumed in the dark period (n) as a function
of length of the dark periods (td) during experiments with intermittent dark
periods. Solid line: best fit to the second-order termination model (eq 8).
Figure 6. Fraction of the reaction occurring in the dark (Q) as a function
of illumination time (ti) during experiments with intermittent dark periods.
3+
3
+
[Ce ] ) 0.50 mM; [S(IV)] ) 1.00 mM; [H2SO4] ) 0.10 M; V ) 3.00
Solid line: best fit to eq 9 or 10. [Ce ] ) 0.50 mM; [S(IV)] ) 1.00 mM;
3
3
cm ; T ) 25.0 °C. Several different integration times shown: ti ) 5 s (9),
[
H2SO4] ) 0.10 M; V ) 3.00 cm ; T ) 25.0 °C; td ) 90 s.
2
s (b), 1 s (2).
Therefore the general method and the equations are directly
applicable to all photoinitiated chain reactions.
Suggested Mechanism. The autoxidation of sulfite ion is
3
+
driven by light absorbed by Ce , and the corresponding
photochemical steps need to be crucial in triggering the overall
3
+
reaction. Aqueous Ce is known to participate in several
photochemical processes which produce highly reactive inter-
4
8
mediates. Each of these species is expected to be capable of
generating the chain carriers via direct reactions with sulfite
ion. First, we postulate a kinetic model with the simplest
initiation sequence (eqs 11-16). An alternative model with
different initiation steps will be discussed briefly in a subsequent
part of the paper.
3
+
+
4+
Figure 7. Fraction of the reaction occurring in the dark (Q) as a function
of length of the dark periods (td) during experiments with intermittent dark
periods. Solid line: best fit to the second-order termination model (eq 10).
Ce + H + hV ) Ce + 0.5 H2
V ) R N
(11)
(12)
(13)
(14)
(15)
(16)
1
1
11 V
3+
Dotted line: best fit to the first-order termination model (eq 9). [Ce ] )
3
Ce4+ + H O‚SO ) SO + Ce + 2H
-•
3+
+
0
2
.50 mM; [S(IV)] ) 1.00 mM; [H2SO4] ) 0.10 M; V ) 3.00 cm ; T )
5.0 °C; ti ) 1 s (a), 2 s (b), 5 s (c).
2
2
3
4
+
V ) k [Ce ][H O‚SO ]
1
2
12
2
2
Figure 6 shows the experimental value of Q as a function of
SO3-• + O ) SO
-•
ti with td kept constant. Both eqs 9 and 10 fit equally well (solid
line) to the measured points in this graph because the equations
are parametrically the same if td is kept constant. The successful
fit confirms the explanation that the thermal reaction proceeds
for an extended period of time in the dark because of the
relatively slow termination step.
Figure 7 depicts the results from three sets of experiments
where td was varied at constant ti (ti ) 1, 2, and 5 s were used).
The solid lines represent the best fit to eq 10 (second-order),
whereas the dotted lines are the best fits to eq 9 (first-order).
The second-order fit is clearly superior to the first-order fit in
each case, which suggests that the termination is second-order,
in agreement with the conclusion drawn earlier based on the
2
5
V ) k [SO •][O2]
-
1
3
13
3
-
•
-•
-
+
SO
+ H
O‚SO
) SO
+ HSO
+ H
5
2
2
4
4
-
•
V ) k [SO ][H O‚SO ]
14
14
5
2
2
SO4-• + Ce + H ) Ce + HSO4
3+
+
4+
-
-•
3+
V ) k [SO ][Ce ]
1
5
15
4
SO4-• + SO4 ) S O
-•
2-
2
8
-
• 2
0
.5 order with respect to NV.
V ) k [SO
]
1
6
16
4
Figure 8 shows how n depends on td. Only the second-order
fit is shown in the graph. The fit is acceptable, and it is also
It should be noted that R11 is fully equivalent to the quantum
efficiency of reaction 11, and k12-k16 are second-order rate
4
7
clear that n is independent of ti as predicted by eq 8. A numerical
-1
constants of bimolecular steps.
Photochemical excitation of Ce yields Ce and hydrogen
in aqueous solution. However, the Ce formed cannot usually
analysis of the data set gave k6 ) 1.9 ( 0.3 s for the conditions
given.
3
+
4+
4
+
At this point, it should be noted that the quantitative
considerations presented in this section and eqs 3-10 are not
dependent on the actual chemistry of the system studied.
(
48) Shilov, V. P.; Yusov, A. B. High Energy Chem. 1999, 33, 242 and
references therein.
4790 J. AM. CHEM. SOC.
9
VOL. 127, NO. 13, 2005

Ce(III)-Catalyzed Aqueous Autoxidation of S(IV)
A R T I C L E S
3
+ 48
be detected as it oxidizes water and reproduces Ce . This
reaction occurs spontaneously even without light, but light
equal under steady-state conditions if the chain is reasonably
long:
4
8
accelerates it; i.e., the net result is photochemical splitting of
water in the absence of any other reagents. It is well documented
that this process occurs, albeit not particularly efficiently, in
R N ) 2 × k [SO -•]
2
ss
(17)
11
V
16
4
In this equation, [SO4-•]ss is the steady-state concentration of
the sulfate ion radical, which can be expressed as follows:
3
+
49
aqueous Ce solutions upon UV illumination.
The oxidation of water by Ce4 probably becomes inferior
+
compared to other reactions in the presence of a reducing agent
R N
11 V
40
SO4-•] )
such as sulfite ion. In agreement with earlier literature results,
our stopped-flow experiments confirmed that Ce4+ oxidizes
sulfite ion quite rapidly. The usual time scale of this process is
[
(18)
ss
x
2k16
The rate of every chain propagation step is equal, and this rate
is also identical to the overall rate of the chain reaction:
5
-20 ms in 0.1 M H2SO4, and increasing the pH further
accelerates the reaction so that it goes to completion within the
dead time of the stopped-flow instrument. Thus, Ce4 needs to
be present at very low steady-state concentration levels and is
considered to be one of the chain carriers. It should be added
that competing reactions of Ce4 with other reactants are not
feasible in this system.
+
d[O2]
-
) V ) V ) V ) V
11
(19)
1
1
11
11
dt
+
Combining eqs 15, 18, and 19 eliminates the steady-state
concentration of the sulfate ion radical and gives the following
rate equation:
Cerium(IV) is a typical one-electron oxidant, and as such its
3
+
reaction with H2O‚SO2 is expected to produce Ce and the
-
•
sulfite ion radical (SO3 ), which is another chain carrier. The
d[O2]
R11
3+
0.5
-
•
-
) k15
[Ce ]NV
(20)
reaction of SO3 with H2O‚SO2 would lead to no net chemical
dt
x
2k16
-
•
3+
change, and the reaction between SO3 and Ce would be
the exact reverse of eq 12 and therefore thermodynamically
This formula is in agreement with the experimentally found rate
law given in eq 2 with
-
•
unfavorable. Thus, SO3 is most likely to react only with O2
(
eq 13). This reaction was frequently postulated in elaborated
0.5
3,5,22
mechanisms for sulfite ion autoxidation.
k
2
) k15 × R11 × (2k16)-0.5
(21)
The product of eq 13 is the highly reactive peroxomonosulfate
-
•
According to the rate law for the termination step (eq 16),
the concentration of the sulfate ion radical will fall to zero in
the dark period following the usual second-order decay kinetics:
ion radical, SO5 , which is a strong oxidant. Its reaction with
3
+
4+
Ce would produce two highly reactive species, Ce and the
2-
peroxomonosulfate ion SO5 , and lead to a branching in the
chain. Such an effect (branching in the chain) is clearly not
supported by the experimental data, and the oxidation of Ce
by SO5 was excluded from the kinetic model. An alternative
step is the reaction of SO5 with H2O‚SO2 which produces a
sulfate ion and a sulfate ion radical (SO4 ) in a simple oxygen-
transfer process. This particular elementary step was also
considered in earlier mechanistic studies on the autoxidation
of sulfite ion.2 Sulfate ion radical is thus the fourth chain carrier
SO4-•]
[
3
+
SO4-•] )
ss
[
(22)
-
•
-
•
1 + 2k [SO ] t
16 4 ss
-
•
-•
Comparing eqs 6 and 21 gives
k ) 2k [SO -•]
ss
(23)
6
16
4
2
In summary, the scheme given in reactions 11-16 provides
coherent interpretation for all the experimental observations.
Further Mechanistic Points. It should be noted that the
values of the rate constants k12-k16 could not be determined
directly from the measurements. However, it is possible to find
estimates for the important rate constants using plausible
chemical considerations.
It is clear that k16 is a second-order rate constant and cannot
be larger than the diffusion controlled limit of 10
fact, the recombination rate constant of the sulfate ion radical
was estimated in an earlier work to be
3+
-•
which may either react with H2O‚SO2 or Ce to produce SO3
4
+
or Ce , respectively. The chain would be completed with the
formation of both of these two species. However, mathematical
analysis showed that the inclusion of the reaction between sulfate
ion radical and H2O‚SO2 would clearly predict significant
sulfite-ion dependence of the overall rate of the autoxidation.
Experimentally no such dependence was observed, and therefore
only the reaction of sulfate ion radical with Ce is included in
the final model. It should be noted that SO4 has a crucial role
in the model, because its recombination reaction with another
3+
1
0
-1 -1
M
s . In
-
•
5
1
-
•
SO4 (eq 16) is assumed to be the termination step.
k ) 4.4 × 10 M s-1
8
-1
(24)
The rate equation was obtained on the basis of the kinetic
1
6
5
0
model (eqs 11-16) using the long chain approximation. It
should be emphasized that this way of derivation is mathemati-
cally equivalent to simply setting steady-state approximations
for all of the reactive intermediates in the system, only less
tedious algebraically. The main assumption is that the rates of
chain carrier formation in initiation and termination should be
Combining eqs 23 and 24 gives
[SO
-•]ss ) 2.2 × 10-9
M
(25)
(26)
4
Combining eqs 17 and 23 gives a value for R11:
R ) 0.15
1
1
(
(
49) Heidt, L. J.; McMillan, A. F. Science 1953, 117, 75.
50) Espenson, J. H. Chemical Kinetics and Reaction Mechanisms, 2nd ed.;
McGraw-Hill: New York, 1995; pp 181-189.
This is not an unreasonable quantum efficiency for reaction 11.48
J. AM. CHEM. SOC.
9
VOL. 127, NO. 13, 2005 4791

A R T I C L E S
Kerezsi et al.
Finally, from eq 21 one can deduct
k ) 2.3 × 10 M s-1
6
-1
(27)
15
It should be noted that the sulfate ion radical was reported to
react with water in a reaction giving a hydroxyl radical and
-1 52
hydrogen sulfate ion with a first-order rate constant of 440 s .
SO4-• + H O ) OH + HSO
•
-
4
(28)
2
This reaction could in principle compete with reaction 15
under the concentration range of this study. However, it is also
well-known that the sulfate ion radical can be favorably
produced by the reaction of hydroxyl radical and hydrogen
sulfate ion in sulfuric acid.53 This is the exact reverse of reaction
4
+
Figure 9. Kinetic traces measured in the reaction of sulfite ion and Ce
3
0. Since sulfuric acid was used in the present study, the
in the presence and absence of oxygen. [Ce4 ] ) 0.20 mM; [S(IV)] ) 0.20
mM; [O2] ) 0.20 mM (a), 0 (b); [H2SO4] ) 0.10 M; path length 1.000 cm;
T ) 25.0 °C; λ ) 330 nm.
+
equilibrium of reaction 30 is probably shifted considerably to
the left and thus the formation of the hydroxyl radical is not
feasible.
One can also calculate the average chain length,50 r, for the
conditions used in the experiments with interrupted illumination:
to react rapidly (with a second-order rate constants of about
8
-1 -1
2+
2+
22,54
10 M s ) with Fe and Mn ions.
Appropriate kinetic
data are not available for direct comparison of the oxidation
rates of Ce and the other metal ions. However, the thermo-
dynamic driving force is considerably less for the oxidation of
3
+
3
+
V15
k [Ce ]
15
3
r ) V16
)
) 1.2 x 10
(29)
k [SO -•]
16
4
ss
3+
2+
2+
Ce than for that of Fe and Mn . This difference predicts
3
+
a much slower reaction with Ce if the oxidation occurs in an
outer-sphere complementary electron-transfer process. An ad-
ditional reaction path through an initial oxygen transfer step
followed by other processes can also be imagined in the
oxidation of Fe and Mn which may exist in various higher
oxidation states as oxo species. In contrast, such a reaction path
This expression also shows that the use of the long chain
approximation is justified.50
3+
According to previous studies on the photochemistry of Ce ,
it is possible that the leaving electron reacts with dissolved
2
+
2+
oxygen instead of water to form the superoxide ion in the
primary photochemical process.48
3
+
is unlikely to be operative with Ce and cannot enhance the
oxidation rate.
3
+
4+
-•
Ce + O + hν ) Ce + O2
2
Qualitative Tests for the Validity of the Mechanism. The
mechanism proposed in the previous section has several
verifiable implications. Some of these predictions were tested
in this work.
V ) R N
30 V
(30)
30
Consequently, the initiation sequence may proceed via alterna-
tive or parallel steps. Superoxide ion is expected to oxidize
sulfite ion in a fast reaction:
4+
The first prediction is that the oxidation of sulfite ion by Ce ,
if carried out in the presence of dissolved oxygen, should
consume O2 as well. In other words, there must be some sort
of synergy between the two oxidative processes. This was
experimentally confirmed by three different methods. An
experiment with the oxygen measuring probe was carried out
O2-• + H O‚SO ) SO + H O
-•
4
(31)
2
2
2
Thus, the overall effect of the change in the initiation step is
that one photon would start two chains and not one. In the
limiting case, this would introduce a factor of 2 on the left side
of eq 17 and subsequent expressions, but the derivation remains
unaltered. Therefore, the main considerations are the same
regardless of whether the real initiation occurs in a specific
reaction or it is some sort of a linear combination of reactions
4+
where Ce was added to an air-equilibrated acidic sulfite ion
solutions (Figure S9). The loss in oxygen concentration was
quite rapid. In another experiment, the oxidation of sulfite ion
4+
by Ce was followed by measuring the absorbance decrease
at 330 nm in a stopped-flow instrument (Figure 9). In the
4+
presence of dissolved oxygen, less Ce was consumed than in
1
1 and 30.
4+
the presence of oxygen clearly implying that O2 rather than Ce
As noted earlier, the reaction of SO5-• with Ce3+ was not
considered in the final kinetic model primarily because it would
have introduced branching into the chain, whereas the experi-
mental data clearly indicate an unbranched chain reaction.
Strictly speaking, this implies only that SO5 reacts more
favorably with H2O‚SO2 than with Ce , which is usually
was the oxidizing agent for most of the sulfite ion present in
the solution. The third method was also a stopped-flow
experiment, but sulfite ion was used in small excess and the
absorbance was followed at 276 nm (Figure S10). More sulfite
ion was consumed when dissolved oxygen was present. All of
these observations are consistent with the implications of the
proposed model. These experiments also prove that the role of
oxygen is not negligible in the analytical methods based on the
-
•
3+
present at somewhat lower concentration levels. At first sight,
this finding is somewhat unexpected because SO5 is known
-
•
4
+
39-41
Ce -sulfite ion reaction.
(
(
(
51) Huie, R. E.; Clifton, C. L. Chem Phys. Lett. 1993, 205, 163.
52) Bao, Z. C.; Barker, J. R. J. Phys. Chem. 1996, 100, 9780.
53) Neta, P.; Huie, R. E.; Ross, A. B. J. Phys. Chem. Ref. Data 1988, 17,
(54) Berglund, J.; Elding, L. I.; Buxton, G. V.; Salmon, G. A. J. Chem. Soc.,
Faraday Trans. 1994, 90, 3309.
1
027.
4792 J. AM. CHEM. SOC.
9
VOL. 127, NO. 13, 2005

Ce(III)-Catalyzed Aqueous Autoxidation of S(IV)
A R T I C L E S
of oxygen loss.2
2,37-38
Kinetic traces recorded in the presence
3
+
and absence of Ce are shown in Figure 10. This experiment
was performed in a scanning spectrophotometer, where the only
light going through the sample is the weak monochromatic (360
3+
nm) analyzing beam, which is not absorbed by Ce . The
absorbing species at this wavelength are the iron(III)-sulfito
complexes. It is clearly seen that the presence of Ce3
accelerates the decomposition of the iron(III)-sulfito complexes
and therefore the rate of autoxidation of sulfite ion, which is in
agreement with the expectations based on the mechanism.
In conclusion, the results presented here clarify important
aspects of the autoxidation of sulfite ion and may be crucial in
exploring the detailed chemical background of the related
analytical procedures. The synergistic effects demonstrated here
offer the possibility of using Ce(III) as a cocatalyst in industrial
oxidations of sulfur species. Furthermore, the experimental
method and the mathematical treatment used in this paper for
the particular example of the autoxidation of sulfite ion are also
applicable to a much wider range of photoinitiated chain
reactions.
+
Figure 10. Kinetic traces measured in the sulfite ion-iron(III)-oxygen
3
+
3+
system in the presence and absence of Ce . [Fe ] ) 2.0 mM; [S(IV)] )
3
+
2
.0 mM; [Ce ] ) 0 (a), 0.20 mM (b); [H2SO4] ) 0.010 M; [O2] ) 0.20
mM; path length 1.000 cm; T ) 25.0 °C; λ ) 360 nm.
Another important implication of the proposed model is that
Ce3+ participates not only in photochemical initiation of the
chain reaction, but also in maintaining it. In many earlier studies
on catalytic autoxidation of sulfite ion, the postulated mecha-
Acknowledgment. This paper is dedicated to Prof. Ern_o
Br u¨ cher on his 70th birthday. The authors also thank the
Hungarian Research Fund for financial support under Grant
Numbers OTKA T042755 and M028244.
nisms involve the generation of sulfite ion radical in a chain
reaction.3
,5,22
Our kinetic model implies that Ce3+ has a
cocatalytic or synergistic effect in these systems because it can
increase the efficiency of the chains. This possible effect was
experimentally confirmed in the extensively studied iron(III)-
sulfite ion-oxygen system. A general feature of this system is
that iron(III)-sulfito complex(es) form in the beginning of the
reaction, the decomposition of which is dependent on the rate
Supporting Information Available: A figure showing the
spectra of Ce(III) and S(IV); nine figures demonstrating various
kinetic effects in the title reaction. This material is available
free of charge via the Internet at http://pubs.acs.org.
JA0439120
J. AM. CHEM. SOC.
9
VOL. 127, NO. 13, 2005 4793