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CV OFFICE OF NAVAL RESEARCH Contract N00014-86-K-0556 Technical Report No. 78
Solvent Relaxation in Thermal Electron-Transfer Reactions:
0
Some Comparisons with Real-Time Measurements of Solvation Dynamics
by
OWN-l!'
G. E. McManis and M. J. Weaver
tM
'LfCT
Prepared for Publication
FE2Q98
in
S
Chem. Phys. Lett.
¢Am
Purdue University Department of Chemistry West Lafayette, Indiana
1988
February 17,
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Relaxation in Thermal Electron-Transfer/Reactions: Measurements of Solvation Dynamics/
SSolvent
Some Comparisons with Real-Time
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19 ABSTRC
*The
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solvent relaxation, electron transfer, timefresolved fluorescence
SUB.GROUP
(Continue on rev'erse if necessary and identify by biock number)
role of solvent dielectric relaxation on the barrier-crossing dynamics for outersphere electron transfer (ET), as evaluated from the solvent-dependent kinetics of metallocene self-exchange reactions, is compared with recent real-time measurements of polar solvation dynamics obtained from time-dependent fluorescence Stokes shifts (TDFS) for suitable chargetransfer excited states. While the solvent-dependent kinetics obtained in some aprotic media are consistent with the TDFS measurements, the barrier-crossing dynamics in several associated and/or highly polar liquids are indicative of much faster relaxation than inferred from TDFS. The possible nature, and implications, of these rapid modes are discussed.
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A KI,.
Solvent Relaxation in Thermal Electron-Transfer Reactions: Some Comparisons with Real-Time Measurements of Solvation Dynamics
George E. McManis and Michael J. Weaver Department of Chemistry Purdue University West Lafayette, Indiana
47907, U.S.A.
.1k
S+
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to Chemical Physics Ltes Lette
pSubmitted
.
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+ +
+,.
t,
t*+.
ABSTRACT
The dynamics
from the solvent dielectric relaxation evaluated barrier-crossing (ET),onasthe transfer electron for outer-sphere role
.
of
solvent-dependent
kinetics
of
compared with recent real-time
metallocene
self-exchange
measurements
of polar solvation dynamics
reactions,
is
obtained from time-dependent fluorescence Stokes shifts (TDFS) for suitabl& charge-transfer
excited
states.
While
the
solvent-dependent
kinetics
obtained in some aprotic media are consistent with the TDFS measurements, the barrier-crossing dynamics in several
associated and/or highly polar
liquids are indicative of much faster relaxation than inferred from TDFS. The possible nature, and implications, of these rapid modes are discussed.
I
Although the important role of the solvent medium in determining the free-energy barrier, recognized, I recently
its
been
AG*,
influence
treated
characteristics distortions),
,
(such as
upon
the
By
processes
has
long been
barrier-crossing dynamics
has
only
and subsequently afforded detailed
utilizing
probe
reactions
having
suitable
a small barrier contribution from intramolecular
and by taking proper account of the variation in AG* with the
solvent, kinetic
data
for electron-exchange
approximate
information
frequency,
',
corresponding
electron-transfer
theoretically, 2
scrutiny. 3
experimental
for
upon
on
the
the
dependence
solvent
solvent-dependent
reactions can yield at
of
properties. 4
frequencies
the
least
barrier-crossing
Comparison
predicted
from
with
the
conventional
dielectric continuum treatments yields reasonable agreement in some cases,3 although some substantial deviations between the experimental and predicted frequencies have come to light. 3 d ,4 b~c Concurrent
with
(yet
independent
of)
these
activities,
real-time
measurements of the dynamics of dipolar solvation have been undertaken by utilizing time-dependent fluorescence Stokes shifts (TDFS) for chromophores forming suitable charge-transfer excited these
measurements
(> 10 ps) down
to
in some ca.
been
restricted
to
"8
While the majority of
relatively
recent studies have examined solvent
0. 2 ps.and
relaxation times, dielectric
have
states. 5
Comparisons
between
rs, and the longitudinal times,
continuum
model
indicate
that
long
timescales
relaxation times
the experimental
TDFS
rL, predicted from the
typically
rs
rL,
although
6 multiexponential decay behavior is commonly observed. -8
Prompted in part by these experimental studies, increasing attention is
being
~~,--Z
focused
on
the
manner
and
extent
to
which
solvent
relaxation
%.
%~%,P~~-
2 charge
attending
transfer may
picture. 6 d '9
continuum
from
differ
In
for
accounting
mechanisms
particular,
dielectric-
conventional
the
multiexponential relaxation have been identified,including the expectation that r > rL for solvent molecules nearby the solute as a consequence of diminished dipole interactions.6d,9 Given the current rapid evolution in both experimental and theoretical aspects of charge solvation dynamics, it is clearly of interest to compare these results and concepts with corresponding information on the dynamics In particular, there is a need to
of electron-transfer barrier crossing.
identify the components of the overall dielectric response having the most Such a comparison is considered
relevance to the barrier-crossing problem. here,,
utilizing
our
recent
data
on
metallocene self-exchange reactions. 4 c believe ,
that
its
significance
is
solvent-dependent kinetics
the
for
While necessarily preliminary, we heightened
by
the
emerging
new
perspectives of dynamical solvent effects in chemical reactivity.
Results and Discussion Unlike TDFS measurements of dielectric solvent relaxation, which are from
relatively directly
extracted evaluation
of
such
effects
in
the
time-dependent dynamics
of
Stokes
shifts,10
the
barrier
crossing
for
intermolecular electron transfer requires consideration of the influence of energetics
barrier
upon
the
observed
rate
constant,
kob.
A
useful
I formalism for this purpose is expressed as1 ,12
kob - K
where
K
is
the
equilibrium
9v
exp(-AG*/RT)
constant
for
(1)
forming
the
appropriate
I %5
3 internuclear geometry, and K., is the electronic transmission coefficient. We have recently employed this relation to extract solvent-dependent barrier-crossing frequencies, vP, from kob values obtained for metallocene self-exchange
reactions
technique.4c,13
These
using
the
reactions,
(Cp - cyclopentadienyl), pentamethyl-cyclopentadienyl),
proton
involving
nmr
line-broadening
cobalticenium-cobaltocene,
its decamethyl derivative, C' Co +/O
and
ferricenium-ferrocene,
several virtues for this purpose, as detailed earlier. 4
(C-
Cp2 Fe+/o,
have
These include the
presence of only small inner-shell (i.e. reactant intramolecular) barriers, small
or
negligible
work-term effects
upon
K.,
and
the
stability
and
0nonspecific solvation of the reactants in a variety of nonaqueous media.-[ The
estimation
of
absolute
Y.
values
for
such
electron-exchange
processes is hampered not only by uncertainties in Kp but, most critically, *P
in the AG* values. -*
However, relative v. values in different solvents can
be evaluated, at least approximately, since K
should be roughly constant
p
and there is good evidence be described
for
that the required solvent dependence of AG
self-exchange reactions by the
can
conventional dielectric
continuum formula 14 -..
&G:-
where
e
is
the
(e2 /4)(a-'
electronic
R')(,e-l
charge,
1)
(2)
a is the reactant radius,
R
internuclear distance (commonly presumed to equal 2a), and eop and
is
the are r
the optical and static dielectric constants, respectively.
*This 0
includes
measurements
of
optical
intervalence
transition
energies, Eop, in mixed-valence compounds, such as analogs of the metallocenes considered here, 15 in which the15 solvent-dependent E.p values ,16 vary approximately in accordance with Eq (2).
?-
4
%
The central issue here is the role of solvent dielectric relaxation in the
barrier-crossing
implies that ic.
frequency.
While
be
minor
solvent
for
the
present
This contribution, however, is
metallocene
systems
component of AG* is relatively small, ca 10%. then, we can time, r
sensitivity
= I (i.e. reaction adiabaticity is achieved), 17 w
influenced by reactant vibrations. to
the
simply regard
vn
since
the
of
may be likely
inner-shell
Under these circumstances,
to be related to
the
effective
relaxation
I by
(3)
n--i
The
vn
comparison
between
transfer barrier
such
solvent-dependent
crossing and
r*f
corresponding TDFS
values
for
relaxation
electron-
times,
TS'
forms the objective here. At least for a Debye fluid (i.e. that having a single relaxation time, dielectric
D)
terms
of
type 4 a,
continuum treatments
one-dimensional
of the barrier-crossing dynamics
overdamped motion 2 ab
lead
to
relations
in
of the
7
(4)%
a-Kr
(f/CS)r 0 , with e.
dielectric loss spectra, by rL
-
frequency" dielectric constant.
Although the proportionality constant K in
Eq
(4) depends
somewhat
on AG
being the
as well as on the shape of
"infinite
the barrier
top,2b this dependence is relatively mild so that usually K is within ca twofold
of
unity
for
weak-overlap
electron
circumstances, then, we expect that r~f
i
exchange.
Under
these
%]
can be equated approximately with
,%
"%.
5 7
*
A
related
treatment
for
solvents
exhibiting
multiple
dielectric
relaxation yields the conclusion that r.ff is influenced disproportionately by the
faster relaxation mode(s),
so
often-predominant "slow" relaxation.2 c Debye solvents we might anticipate
this
dependent
situation,
it
electron-transfer
rLI,
where rLI
is the
On the other hand, at least for > T
that r.f
as a result of short-
f,as noted above. 9 a
range solvent contributions to Given
r.ff <
that
is
instructive
results
in
to
the
examine
light
of
the the
solventcontinuum
predictions as a preface to comparison with corresponding TDFS data. I
summarizes
rate
constants
for
self
ke,
exchange,
for
Table
+/0 Cp2 Co,
Cp2Co /0, and Cp2 Fe+/*
in fifteen solvents, expressed as rate ratios with
respect
in
to
those
k. /k..(ref).
The
extracted
from
reference
solvent
data
refs.
the
solvent"
for
the
cobaltocene
and
18,
respectively.
4c
is
"reference
somewhat
arbitrary,
and
dimethylsulfoxide,
ferrocene
couples
are
Although the choice of
dimethylsulfoxide was
selected
since it displays Debye-like dielectric loss behavior 1 9 and TDFS relaxation kinetics. 6 a
Listed
these
probes
in each solvent, again quoted as ratios
value
in DMSO,
alongside
are
ff/* ff(ref).
The
the
corresponding
latter were
?*ff
estimates
to respect
for
to the
obtained from the
rate
ratios by using (cf. Eq. (1)]: [off/r~fa(ref)]-
where
the
AG03
[k.*/k. 1 (ref)] exp([AG*-
estimates
were
obtained
AG
from
(ref)]/RT )
Eq.
(2)
(see
(5)
Table
I
footnotes).
This procedure therefore assumes that Kp (and x* 2 ) are solvent
independent
(vide supra).
While the absolute k.
values in each solvent
are markedly different for the three probe reactions
.
,m_ .
. .. ...
.= ,.
r
.
.
m>
...
. K.
..
..
E.. B..
. .
*.,
.
.^
. *.
...
(apparently due to
_
,
6 electronic
coupling
effects
on K
,113),
the
rate
and
relaxation
time
ratios are largely similar in a given solvent.
e 140%
,.
Also listed in Table I are the corresponding longitudinal relaxation time ratios,
rL/TL(ref),
obtained from dielectric loss
data.
Comparison
between the corresponding rvff/r ff(ref) and TL/TL(ref) values reveals that while these ratios are in reasonable agreement (within ca. twofold of each
V.
other) in a number of solvents, some substantial discrepancies are present.
V
Most notably, the r f
values in methanol and ethanol are at least 50 fold This anomaly has been noted previously on
smaller than expected from r
the basis of related electrochemical exchange kinetics. 3 d '4 b similar discrepancies between the relative r
and r
Qualitatively
values are also seen
in Table I for propylene carbonate and especially N-methylformamide (NMF). The
TDFS
solvation
acetonitrile,
DMSO,
Castner et al. probe LDSthan
in
of four
nitrobenzene,
and
of
the solvents
methanol,
have
in
been
Table
I,
"
examined by
for timescales down to ca. 0.5 ps using the fluorescence
.6a
7 50
dynamics
DMSO
The
[i.e.
r.
value
rs/ts(ref)
in
acetonitrile
-
0.11,
in
is
about tenfold smaller
rough
accordance
with
the
corresponding rL ratio (Table I), even though rs is ca. 1.5-2 times rL 6a in good accordance with the corresponding r ff/r ff(ref)
This behavior is ratios in Table methanol,6a
I.
however,
corresponding r*f obtained
in
r ,/r
differ
significantly
data in Table I.
nitrobenzene,
smaller than r. with
The solvation dynamics observed in nitrobenzene and
with
the
=
solvent benzonitrile
2
predominant -
for nitrobenzene
(Table I).
that
expected
from
I
the
Biexponential relaxation behavior was
This yields rs/rs(ref)
ff(ref)
from
rs
value
being
4
fold
0.5 in this solvent, as compared and the
dielectrically
For methanol Castner et al.
similar
found that
*.-.* .4.4
~d'.
-
9
~,r..'-'
*~q~,%
1 .,%%%
*4*44
7 s/rs(ref)
1
relaxation
which
times
Indeed, the r
for
stands
in
marked
barrier-crossing,
contrast
to
the
r*ff/rff(ref)
corresponding
0.05
(Table I).
values are indicative of dielectric relaxation in methanol
that is at least as rapid as in acetonitrile, whereas the rs value in the latter solvent is around tenfold shorter than in the latter. 6a More striking differences between the barrier-crossing and real-time solvent relaxation behavior are exposed by examining some recent TDFS data obtained using %
Coumarin
153
the
multiexponential
decay
behavior was
values
were obtained in propylene
(N4P)
that
values.
are
These
markedly and
fluorescence probe. 6 b
(5-10
other
are
than
indicative
of
accordance with
the MSA
treatment
short-range relaxation time, with es.6b
6b-d
Although the
these measurements,
observed,
average
i
rs
(PC) and N-methylpropionamide
longer
7S/TLand the solvent dielectric constant, NMP under the conditions employed.
in
typically
carbonate
fold)
data
30 ps
to > ca.
restricted
laaintmsaewas and
as
Es'
the
corresponding
rL
a correlation between es = 75-300 in PC and
since
This behavior is qualitatively in
of Wolynes,9a which predicts
that
the
is longer than rL to an extent increasing
r.,
A difficulty, however, is
that the
likely concomitant changes
in c. and the solvent size can blur this prediction.
versus log
,
relative
to
DMSO as
The data
for
For comparison purposes, a plot of log (rff/L) r
r
and
listed
in
numbered
refer Table
1
the
relaxation times
I,
is
shown
according
to
the
in
Fig.
scheme
1.
in
Table
I.
are
seen
to
decrease
continuously
(and
solvents with progressively higher e. values.
,-p
'""51
In
those
.,.'iL-'i...%
%.%
q
-%
~%'
%
"%
in
each solvent contrast
- log es behavior noted in ref. 6b, the log (r/vL)
log (/ Fig.
to
where
roughly
to
is the
values in
linearly)
for
In particular, the solvents
'%
%
t%%
t"%
"-"%%°%
"•"%
","-
.
2-'•" S"..
.7-.
8 having the
highest dielectric constants,
respectively), yield also (.ff/%L)