Estimation of self-exchange electron transfer rate constants for organic compounds from stopped-flow studies

Article abstract of DOI:10.1021/ja970321j

Second-order rate constants k₁₂(obsd) measured at 25 °C in acetonitrile by stopped-flow for 47 electron transfer (ET) reactions among ten tetraalkylhydrazines, four ferrocene derivatives, and three p- phenylenediamine derivatives are discussed. Marcus's adiabatic cross rate formula k₁₂(calcd) = (k₁₁ k₂₂ k₁₂f₁₂)(1/2) , Inf₁₂ = (In K₁₂)(2/4) ln(k₁₁k₂₂/Z²) works well to correlate these data. When all k₁₂(obsd) values are simultaneously fitted to this relationship, best-fit self-exchange rate constants, k(ii)(fit), are obtained that allow remarkably accurate calculation of k₁₂(obsd); k₁₂(obsd)lk₁₂'(calcd) is in the range of 0.55-1.94 for all 47 reactions. The average ΔΔG(ii)≠ between observed activation free energy and that calculated using k(ii)(fit) is 0.13 kcal/mol. Simulations using Jortner vibronic coupling theory to calculate k₁₂ using parameters which produce the wide range of k(ii) values observed predict that Marcus's formula should be followed even when V is as low as 0.1 kcal/mol, in the weakly nonadiabatic region. Tetracyclohexyl-hydrazine has a higher k(ii) than tetraisopropylhydrazine by a factor of ca. 10. Replacing the dimethylamino groups of tetramethyl-p-phenylenediamine by 9- azabicyclo[3.3.1]nonyl groups has little effect on k(ii), demonstrating that conformations which have high intermolecular aromatic ring overlap are not necessary for large ET rate constants. Replacing a γ CH₂ group of a 9- azabicyclo[3.3.1]nonyl group by a carbonyl group lowers k(ii) by a factor of 17 for the doubly substituted hydrazine and by considerably less for the doubly substituted p-phenylenediamine.

Full text of DOI:10.1021/ja970321j

5900
J. Am. Chem. Soc. 1997, 119, 5900-5907
Estimation of Self-Exchange Electron Transfer Rate Constants
for Organic Compounds from Stopped-Flow Studies
Stephen F. Nelsen,*,† Michael T. Ramm,† Rustem F. Ismagilov,† Mark A. Nagy,†
Dwight A. Trieber, II,† Douglas R. Powell,† Xi Chen,‡ Jamie J. Gengler,‡
Qinling Qu,‡ Jennifer L. Brandt,‡ and Jack R. Pladziewicz*,‡
Contribution from the Department of Chemistry, UniVersity of Wisconsin,
Madison, Wisconsin 53706-1396, and Department of Chemistry,
UniVersity of Wisconsin, Eau Claire, Wisconsin 54702
ReceiVed January 30, 1997X
Abstract: Second-order rate constants k12(obsd) measured at 25 °C in acetonitrile by stopped-flow for 47 electron
transfer (ET) reactions among ten tetraalkylhydrazines, four ferrocene derivatives, and three p-phenylenediamine
derivatives are discussed. Marcus’s adiabatic cross rate formula k12(calcd) ) (k11 k22 k12 f12)1/2, ln f12 ) (ln K12)2/4
ln(k11k22/Z2) works well to correlate these data. When all k12(obsd) values are simultaneously fitted to this relationship,
best-fit self-exchange rate constants, kii(fit), are obtained that allow remarkably accurate calculation of k12(obsd);
k12(obsd)/k12′(calcd) is in the range of 0.55-1.94 for all 47 reactions. The average ∆∆Gijq between observed activation
free energy and that calculated using kii(fit) is 0.13 kcal/mol. Simulations using Jortner vibronic coupling theory to
calculate k12 using parameters which produce the wide range of kii values observed predict that Marcus’s formula
should be followed even when V is as low as 0.1 kcal/mol, in the weakly nonadiabatic region. Tetracyclohexyl-
hydrazine has a higher kii than tetraisopropylhydrazine by a factor of ca. 10. Replacing the dimethylamino groups
of tetramethyl-p-phenylenediamine by 9-azabicyclo[3.3.1]nonyl groups has little effect on kii, demonstrating that
conformations which have high intermolecular aromatic ring overlap are not necessary for large ET rate constants.
Replacing a γ CH2 group of a 9-azabicyclo[3.3.1]nonyl group by a carbonyl group lowers kii by a factor of 17 for
the doubly substituted hydrazine and by considerably less for the doubly substituted p-phenylenediamine.
Introduction
Scheme 1
Three previous studies of intermolecular electron transfer (ET)
reactions involving hydrazines using stopped-flow measurements
of rate constants have been reported.1-3 In the work discussed
here a purified, isolable cation radical dissolved in acetonitrile
containing 0.1 M tetrabutylammonium perchlorate is injected
into a stopped-flow cell along with a neutral compound of lower
formal redox potential (E°′) in the same solvent, and the change
in absorbance resulting from the ET reaction which ensues is
followed as a function of time. A series of experiments varying
the concentrations, carried out under pseudo-first-order condi-
tions if possible, is used to determine the second-order rate
constant, k12(obsd), for the reaction. Ten of the compounds
employed, shown in Scheme 1 except for FeCp′2, have had
their self-exchange rate constants, kii(self), independently mea-
sured under self-exchange conditions. They include N,N,N′,N′-
tetramethyl-p-phenylenediamine (TMPD), three methylated
ferrocenes, and six tetraalkylhydrazines. Table 1 summarizes
the kii(self) values and formal oxidation potentials (E°′) mea-
sured by cyclic voltammetry. The total range of kii(self) values
q
is a factor of 5 × 1011 (15.9 kcal/mol spread in ∆Gii (self)) and
the equilibrium constants (K12), for the reactions studied range
from 1 to 2 × 1013 (∆G° ) 0 to -18.2 kcal/mol). These
reactions therefore provide stringent tests for the general utility
of the Marcus cross rate equation (eq 1).4
k12(calcd) ) (k11k22K12 f12)1/2
where
† University of WisconsinsMadison.
(1a)
(1b)
‡ University of WisconsinsEau Claire.
X Abstract published in AdVance ACS Abstracts, June 1, 1997.
(1) Nelsen, S. F.; Wang, Y.; Ramm, M. T.; Accola, M. A.; Pladziewicz,
J. R. J. Phys. Chem. 1992, 96, 10654.
ln f12 ) (ln K12)2/4 ln(k11k22/Z11Z22)
(2) Nelsen, S. F.; Chen, L.-J; Ramm, M. T.; Voy, G. T.; Accola, M. A.;
Seehafer, T.; Sabelko, J.; Pladziewicz; J. R. J. Org. Chem. 1996, 61, 1405.
(3) Nelsen, S. F.; Ismagilov, R. F.; Chen, L. J.; Brandt, J. L.; Chen, X.;
Pladziewicz, J. R. J. Am. Chem. Soc. 1996, 118, 1555.
The f12 value approaches 1 as K12 approaches 1, and is >0.1
S0002-7863(97)00321-1 CCC: $14.00 © 1997 American Chemical Society

Self-Exchange Electron Transfer Rate Constants
J. Am. Chem. Soc., Vol. 119, No. 25, 1997 5901
Table 1. E°′, Self-Exchange ET Values Measured by Homogeneous Exchange, and Those Estimated from Cross Reactions for Compounds
Employed in this Work
a
compound
E°′ (V vs SCE)
kii(self) (M-1 s-1
)
∆Giiq (self)
Hydrazines
11.63
11.88
12.56
12.87
13.57
12.9
rxnsb
kii(fit) (M-1 s-1
)
∆Giiq (fit)
∆∆G‡ (fit - self)c
21/210/+
22/u220/+
22/u230/+
21/u220/+
22/220/+
33N)2
+0.01d
-0.241d
-0.298e
+0.058d
-0.53g
-0.01d
+0.22i
+0.45i
+0.26j
+0.26k
1.85(6) × 104 [S]d
1.21(10) × 104 [S]d
3.84(11) × 103 [S]f
2.29(9) × 103 [S]d
∼700 (dec) [S]g
4
4
3
7
2
8
8
7
13
14
2.9 × 103
1.7 × 103
2.5 × 103
9.2 × 102
1.1 × 102
6.9 × 102
2.4 × 102
4.0 × 101
2.3 × 10-2
2.4 × 10-3
12.7
13.1
12.8
13.4
14.4
13.6
14.2
15.3
19.7
21.0
1.1
1.2
0.2
0.5
1.1
0.7 (est)
2.2 × 103(est) [S]d,h
k33NN33
k33N)2
cHx2N)2
0/+
iPr2N)2
3.0(3) × 10-3 [E]j,l
20.90
0.1
Ferrocenes
7.27
8.00
0/+
FeCp*2
-0.109d
+0.124d
+0.281d
+0.395d
2.9 × 107 [F]d,m
6
6
1
1
1.0 × 107
9.9 × 106
1.5 × 107
7.1 × 106
7.9
7.9
7.7
8.1
0.6
-0.1
FeCp*Cp0/+
8.5 × 106 [F]d
0/+
FeCp′2
FeCp2
0/+
8.1 × 106 [F]d
1.47 × 109 [P]n
8.03
0.1
1.5
PD-Derivatives
4.95
TMPD0/+
33)2PD
k33)2PD
+0.12d
+0.02i
+0.29i
4
3
3
1.2 × 108
1.8 × 108
4.0 × 107
6.4
6.2
7.1
a The method used for measurement of kii(self) is abbreviated in brackets: [S] ) slow exchange rate region NMR line-broadening measurements,
[E] ) equilibration rate measured on the laboratory time scale using 2H and 1H NMR to determine concentrations of deuterium-labeled and unlabeled
neutral compound, [F] ) fast exchange rate region NMR line-broadening measurements, [P] ) fast exchange region ESR line broadening
measurements. b Number of reactions studied having this compound as a component (Table 2). c ∆G‡(fit) - ∆G‡(self). d Reference 2. e Wang, Y.
University of Wisconsin, 1993. f Nelsen, S. F.; Wang, Y. J. Org. Chem. 1994, 59, 1655. g Nelsen, S. F.; Blackstock, S. C.; Kim, Y. J. Am. Chem.
Soc. 1987, 109, 677. h Estimated from the value measured in CH2Cl2. i Nelsen, S. F.; Kessel, C. R.; Grezzo, L. A.; Steffek, D. J. J. Am. Chem. Soc.
1980, 102, 5482. j Determined in this work. k Reference 8. l Reference 3. m Yang, E. S.; Chan, M.-S.; Wahl, A. C. J. Phys. Chem. 1980, 84, 3094
(reports a smaller rate constant than we used; see ref 1). n Reference 10.
Scheme 2
do not have an independently measured kii(self), we were
interested in extracting the most effective estimates of kii for
all of the compounds, assuming the overall accuracy of eq 1.
This was achieved by rearranging eq 1 in the form ln(kii) +
ln(kjj) ) Aij and doing a least squares analysis to obtain the
self-exchange rate constants kii(fit) that best fit the entire data
set.6 These kii(fit) values are given in Table 1 and used with
eq 1 to calculate the expected cross reaction rate constant
k12′(calcd) shown for all of the reactions in Table 2. Since it is
known from the 13 reactions of compounds with known kii-
(self) that eq 1 generally overestimates k12, we did not “fix”
the kii values for the “known” compounds, because this would
have resulted in the entire discrepancy between k12(calcd) and
k12(obsd) being transferred to the compounds with unknown
kii(self). Equation 1 is very good at calculating k12 using the
best fit kii(fit) values, as indicated by the ratio k12(obsd)/k12′-
(calcd) shown in the second-to-last column of Table 2. The
total range of k12 ratios observed is 0.55-1.94, corresponding
for most, but not all, of the reactions studied here. We employ
preexponential factors Z11 ) Z22 ) 1 × 1011 M-1 s-1, as has
been traditional. Equation 1 is followed surprisingly well by
these reactions,1-3 encouraging us to use stopped-flow inter-
molecular ET studies to estimate kii values for compounds for
which measurement under self-exchange conditions is not
possible, and the six compounds shown in Scheme 2 are
considered in this work. Their formal potentials are also shown
in Table 1.
q
q
to |∆∆Gij | differences of e0.40 kcal/mol and average |∆∆Gij |
of 0.13 kcal/mol (for comparison, the maximum and average
∆∆G12q(obsd) from the errors quoted for k12(obsd) are 0.12 and
0.04 kcal/mol). Twelve of the reactions studied (involving 24
q
components), exhibit |∆∆Gij | g 0.2 kcal/mol. Of the 24
components involved in these reactions with larger deviations,
six were phenylenediamine (PD)-derivatives (of the 10 PD-
derivative components in reactions studied, 60% of the data set
Stopped-Flow Kinetic Results and Data Treatment
involving these components), three components were FeCp*
2
Table 2 summarizes the 47 reactions considered here. Entries
1-13 are between pairs for which kii(self) for both components
are known (see Table 2). For these 13 reactions it is possible
to use eq 1 to calculate the cross reaction rate constant,
k12(calcd), and these are listed in Table 2. This approach leads
to k12(calcd) being higher than k12(obsd). In considering the
remaining 34 reactions, where one or both of the components
(50%), eight involved the hydrazines having a twist angle about
the NN bond (θ, ≈ 90°), iPr2N)2 and cHx2N)2 (30%), five were
the θ ≈ 180° 33N)2-derivatives (22%), and 2 were the θ ≈ 0°
hydrazines (10%). We have not discerned a way of accurately
q
predicting which reactions will show unusually large |∆∆Gij |
values. As noted previously with much less data,3 varying
Z11Z22 in eq 1b has only small effects on the fit of eq 1 to
experimental data.7
(4) Marcus, R. A.; Sutin, N. Inorg. Chem. 1975, 14, 213.
(5) For reviews of ET rate theory and applications, see: (a) Marcus, R.
A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265. (b) Sutin, N. Prog.
Inorg. Chem. 1983, 30, 441. (c) Sutin, N. Acc. Chem. Res. 1982, 15, 275.
(6) Pladziewicz, J. R.; Espenson, J. H. J. Am. Chem. Soc. 1973, 95, 56.

5902 J. Am. Chem. Soc., Vol. 119, No. 25, 1997
Table 2. Summary of Reactions Studied
Nelson et al.
q
k12(obsd)
k12(calcd)
k12′(calcd)
k12(obsd)/
k12′(calcd)
∆∆Gij
a
b
entry
reductant
oxidant
(M-1 s-1
)
(M-1 s-1
)
(M-1 s-1
)
(kcal/mol)c
+
1d
2
22/u22
22/u23
FeCp*2
"
21/u22
"
FeCp*Cp
TMPD
21/21
21/u22
22/22
22/u22
22/u23
33)2PD
33N)2
k33NN33
iPr2N)2
iPr2N)2
TMPD
33)2PD
FeCp*Cp
FeCp*2
21/u22
22/22
22/u22
22/u23
33N)2
k33NN33
cHx2N)2
22/u22
33N)2
FeCp*2
"
2.3(2) × 106
5.7(3) × 106
1.35(23) × 106
7.6(5) × 104
6.3(13) × 106
3.5(5) × 105
1.6(1) × 103
1.2(1) × 104
2.6(2) × 102
5.5(2) × 101
3.2(2) × 105
1.1(1) × 104
3.1(1) × 104
4.9(6) × 104
1.1(2) × 102
1.7(2) × 100
1.35(5) × 101
7.7(4) × 102
2.1(1) × 104
8.6(3) × 104
6.2(1) × 103
4.0(1) × 105
2.5(1) × 102
5.4(6) × 105
3.6(2) × 104
1.21(5) × 105
7.8(3) × 102
5.5(2) × 100
3.8(2) × 101
6.3(3) × 104
2.0(2) × 106
1.2(1) × 106
1.1(1) × 106
5.9(2) × 105
2.09(5) × 103
1.13(5) × 104
3.4(1) × 104
1.17(6) × 106
3.5(4) × 105
2.2(1) × 105
8.3(2) × 105
3.8(2) × 103
5.3(2) × 106
4.8(2) × 104
1.17(13) × 10-2
1.02(3) × 103
4.4(2) × 105
6.8 × 106
1.0 × 107
5.5 × 106
2.1 × 106
7.5 × 106
4.9 × 106
2.1 × 103
2.9 × 104
7.6 × 102
1.1 × 102
6.9 × 105
4.0 × 104
5.3 × 104
1.5 × 106
5.0 × 106
2.1 × 106
1.1 × 105
6.3 × 106
3.3 × 105
2.0 × 103
7.4 × 103
2.7 × 102
6.5 × 101
2.5 × 105
1.3 × 104
3.8 × 104
5.2 × 104
1.9 × 102
1.6 × 100
1.1 × 101
5.5 × 102
2.3 × 104
1.6 × 105
6.1 × 103
3.3 × 105
2.0 × 102
6.9 × 105
3.9 × 104
1.1 × 105
5.7 × 102
5.0 × 100
3.3 × 101
7.3 × 104
3.2 × 106
6.2 × 106
1.0 × 106
5.5 × 105
2.1 × 103
9.5 × 103
4.0 × 104
1.1 × 106
3.0 × 105
1.9 × 105
7.0 × 105
6.7 × 103
5.9 × 106
4.8 × 104
7.4 × 10-3
1.7 × 103
3.7 × 105
1.5
1.1
0.6
0.7
1.0
1.0
0.8
1.6
1.0
0.8
1.3
0.8
0.8
0.9
0.6
1.0
1.2
1.4
0.9
0.5
1.0
1.2
1.3
0.8
0.9
1.1
1.4
1.1
1.1
0.9
0.6
1.9
1.1
1.1
1.0
1.2
0.9
1.1
1.2
1.2
1.2
0.6
0.9
1.0
1.6
0.6
1.2
-0.2
-0.1
0.3
0.2
0.0
-0.0
0.1
-0.3
0.0
0.1
-0.1
0.1
0.1
0.0
3d
21/u22+
+
4e,f
5d
iPr2N)2
FeCp′2
+
6d
FeCp*Cp+
+
7e,f
8e,f
9e
iPr2N)2
"
"
"
"
"
"
"
10
11e
12e
13
14
15e
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33g
34
35e
36
37
38
39
40
41
42
43
44
45
46
47
"
"
0.3
-0.0
-0.1
-0.2
0.0
0.3
0.0
-0.1
-0.1
0.1
k33N)2
k33)2PD+
+
cHx2N)2
"
"
"
"
"
"
"
"
"
0.0
-0.0
-0.2
-0.0
-0.1
0.1
+
k33N)2
+
33N)2
TMPD+
0.3
"
"
33)2PD+
FeCp*Cp+
-0.4g
-0.06
-0.0
0.0
+
FeCp*2
33N)2
21/u22
21/21
TMPD
FeCp*Cp
21/u22
21/21
k33NN33
FeCp*Cp
FeCp2
iPr2N)2
cHx2N)2
k33NN33
33N)2
21/21+
k33NN33+
-0.1
0.1
-0.0
-0.1
-0.1
-0.1
0.3
0.1
0.0
-0.3
0.3
"
"
"
+
k33N)2
"
"
"
"
+
cHx2N)2
k33)2PD+
k33)2PD+
-0.1
a k12(calcd) is calculated using eq 1 and kii(self) from Table 1, for reactions for which kii(self) is known for both reactants. k12′(calcd) is calculated
b
q
q
using the best fit kii(fit) values from Table 1. c ∆Gij (obsd) - ∆Gij (calcd) for k12′(calcd). d From ref 1. e From ref 3. f There is an error in the k12
reported in ref 3; this is the correct value. g From ref 2.
0/+
Determination of kii(self) for iPr2N)2
group substituted as CH(CD3)2 (see Experimental Section). The
NMR signals of the paramagnetic radical cations do not occur
in the region examined, and electron exchange is slow on the
NMR time scale. Labeled iPr2N)2-d6 shows a narrow doublet
(J ) ca. 1 Hz) in its 2H NMR, which decreases to half its initial
intensity after complete equilibration with 1 equiv of neutral,
unlabeled material. The ion concentrations of the solutions used
in the NMR measurements were 0.05-0.06 M, while the
stopped-flow reactions were conducted in 0.1 M tetrabutylam-
monium perchlorate at far smaller radical ion concentrations.
We could not use 0.1 M perchlorate because of the insolubility
of the hydrazine radical cation perchlorates, but carried out one
run in acetonitrile containing 0.1 M tetrabutylammonium
tetrafluoroborate and obtained the same rate constant, supporting
the assumption that ion-pairing does not significantly affect kii
measurements in acetonitrile. Although the change in relative
The small kii value obtained for iPr2N)2 in stopped-flow
experiments encouraged us to use direct measurement of kii(self)
by mixing deuterium-labeled neutral hydrazine with unlabeled
radical cation.3 We employed material having a single isopropyl
(7) The total error in solving the simultaneous equations drops very
slightly if Z is lowered and reaches a minimum when all Z values are fixed
at 2 × 109. This improves the fit of kii(fit) to kii(self) for the hydrazines
[principally because 22/22, which has the lowest E°′ and hence the largest
K12 values and smallest f12 values, has a lower k12(fit) than k12(self)], but
makes the fit worse for the ferrocenes. If Z11Z22 ) (Z11 + Z22)2/4 is used
with Zii values chosen by compound class, raising Zii for the ferrocenes
from the 2 × 109 M-1 s-1 which fits the hydrazines best to 2 × 1010 M-1
s-1 slightly improves the fit, but not significantly. Lowering Zii for PD-
derivatives continuously improves the total fit all the way down to Zii(PD)
) 2 × 103 M-1 s-1 and also raises kii(fit) toward kii(self) but hardly affects
anything but the PD-derivative numbers, and there is certainly no physical
justification for this effect, which we believe only occurs because of the
large scatter for the k12 values for reactions involving PD-derivatives. We
conclude that introducing additional fitting parameters by letting Zii values
vary does not significantly help eq 1 fit better, and we see no justification
for doing it.
1
intensity is smaller, use of H NMR for analysis gives better
data because of improved signal-to-noise and smaller acquisition
times, which allow the collection of more data points. The rate

Self-Exchange Electron Transfer Rate Constants
J. Am. Chem. Soc., Vol. 119, No. 25, 1997 5903
Table 3. Experimental Rate Constant for the Self-Exchange ET
Reaction of iPr2N)2
Although the neutral species have similar geometries, optical
spectra of the radical cations reveal a significant difference
+
+
T (°C)a
kii(self) M-1 s-1
between iPr2N)2 and cHx2N)2 in solution. Crystalline
iPr2N)2+ TsO-‚CH3CN is only twisted 8° about its NN bond.8
Its UV spectrum has a single broad maximum at 282 nm (ꢀ )
3200 M-1 s-1) in acetonitrile, assigned as the π f π* transition.9
expt
signal used
1
2H
2H
2H
1H
25.9
25.9
25.1
25.6
0.0034
0.0029
0.0034b
0.0031
2
3b
4
+
cHx2N)2 shows maxima at 276 (ꢀ ) 2400) nm and 386 (ꢀ )
a Spectrometer probe set at 298 K; temperatures listed are indepen-
dently measured using a methanol thermometer (see Experimental
Section). b In acetonitrile containing 0.1 M tetrabutylammonium tet-
1900) nm, suggesting that two forms are present, one with a
nearly untwisted NN bond and another having significantly
greater NN twist, presumably because of different nonbonded
interactions between the cyclohexyl groups. Twisting at the
NN bond is known to increase λmax by decreasing the π,π*
energy gap, both from calculations and the increase observed
in λmax as methyl groups are replaced by bulky tert-butyl
groups: Me2NNMe2+, λmax ) 303 nm; tBuMeNNMe2+, λmax
) 331 nm; tBuMeN)2+, λmax ) 414 nm.9 Distinctly different
cHx2N)2+ crystals are obtained with different counterions. The
tetrakis[m,m′-bis(trifluoromethyl)phenyl]boron salt gives color-
less crystals which X-ray crystallography shows are nearly or
completely untwisted about the NN bond and have the cyclo-
hexyl groups in the same io,io N-C rotamer as that found for
2
rafluoroborate. The other experiments used acetonitrile for H and
1
acetonitrile-d3 for H NMR detection.
Table 4. Comparison of Geometries at Nitrogen for Crystal
Structures Reported Here
d(NN)
(Å)
Rav(N)
(deg)
twist
compound
θ(NN) (deg)a
iPr2N)2, major
iPr2N)2, minor
cHx2N)2, at N1
cHx2N)2, at N2
k33)2PD+
1.394(4)
1.399(5)
1.389(7)
115.8(3)
115.8(5)
116.7(5)
116.6(5)
119.9(2)
108.4(2)
108.0(1)
88.8(5)
85.6(8)
-87.1(6)
-87.9(6)
1.0(4)c
180
1.361(3)b
1.504(3)
1.505(3)
k33N)2
+
iPr2N)2 (see Chart 1 of ref. 8 for illustrations of the N-C
d
33N)2
180
-
rotamers possible). The SbF6 salt gives red crystals which
a Calculated from the heavy atom positions, assuming the lone pairs
bisect the CNC angles in a projection down the NN bond. b N-CAr
distance. c Nitrogen lone pair, aryl p orbital twist. d Nelsen, S. F.;
Hollinsed, W. C.; Kessel, C. R.; Calabrese, J. C. J. Am. Chem. Soc.
1978, 100, 7876.
are clearly strongly twisted (θ ca. 45°) and not in the N-C
io,io rotamer but in approximately C2 rotomers (possibly ii,oo;
all C2 rotamers are calculated to be significantly twisted).
Dissolving the colorless crystals produces reddish solutions
immediately, as expected because N-C rotation is rapid on the
laboratory time scale (a barrier of 11 kcal/mol has been
determined for iPr2N)2+).8 The crystal structures will be
reported separately following analysis; we have not yet found
proper disorder models for these complex crystals.
constant obtained using 1H NMR is indistinguishable from those
2
using H NMR. The kii(self) values obtained in these experi-
ments are summarized in Table 3.
-
The crystal structure of k33)2PD+PF6 establishes that the
Crystal Structures
nitrogens are planar and that the nitrogen lone pairs are lined
up with the aromatic ring p orbitals (see Table 4); therefore,
the cation is a close structural analogue of TMPD+, but has
considerably enlarged alkyl groups. The carbonyl groups are
anti. The crystal structure of k33N)2 also has the carbonyl
groups anti, θ ) 180° by symmetry in the crystal (as does
33N)2), and d(NN) and Rav within experimental error of those
for 33N)2 (see Table 4).
Although we previously reported the X-ray structures of two
salts of iPr2N)2+,8 we were unable to obtain a structure of the
neutral compound. Due to its globular shape, low molecular
weight, and the absence of polar groups on the periphery of
the molecule, iPr2N)2 has a low melting point (42-44 °C) and
is quite volatile. Its crystals are very soft and deform at room
temperature, and obtaining the crystal structure required all
manipulations to be done at -20 °C. Sublimation gives nice-
looking, but badly twinned, crystals which did not produce a
structure we could solve. iPr2N)2 is very soluble in several
common organic solvents (probably on the order of 1g/mL),
but only ca. 15 mg/mL in acetonitrile. Vapor diffusion of
acetonitrile into a toluene solution at -25 °C gave crystals which
were twinned and disordered, with two conformers present. It
was possible to use data from one domain of a twin and to
model the disorder. Some constraints had to be put on the
disorder, so the accuracy of the bond lengths and angles is not
very high; however, it was possible to determine that θ for
iPr2N)2 is near 90° (see Table 4). The nitrogens are equivalent
by symmetry, and the parameters for the major and minor
conformations are similar. Crystal twinning resulted in an even
poorer structure being obtained for cHx2N)2. In the monoclinic
unit cell obtained (P21/n), dimensions a and c differ by only
1.3%, preventing formation of a single crystal. There is no
symmetry element relating the two nitrogens, and therefore their
parameters are different (Table 4). In summary, θ is close to
90° for both neutral hydrazines and the Rav(N) values are similar
but imprecisely determined. Similar pyramidalities at nitrogen,
defined using the average of the bond angles at nitrogen, Rav(N),
and θ values have been reported8 for 33NN(iPr)2 and its 3-keto
analogue.
Discussion: Applicability of Equation 1 to the Reactions
Studied
It has puzzled us that the classical Marcus theory (eq 1),
correlates our k12(obsd) values so well, because it employs a
constant preexponential factor, ignores tunneling effects, and
assumes that only the total vertical free energy barrier λ and
exoergicity determine the ET rate constant. The more modern
vibronic coupling theory has four fundamental parameters
determining the rate constant: a classical vertical barrier
component λs, a quantum-mechanically-treated component λV,
an energy for the average frequency coupled to the electron
transfer hνV, and the electronic coupling matrix element V. The
compounds studied clearly have a large range for λV (argued to
be vanishingly small for ferrocenes and unusually large for
hydrazines) and hνV (usually assumed to be e300 cm-1 for
ferrocenes but as high as 1668 cm-1 for TMPD),10 making it
seem unlikely that eq 1 would predict k12 quantitatively for cross
reactions among them. Nevertheless, eq 1 works well. We have
therefore carried out model vibronic coupling theory calculations
(9) Nelsen, S. F.; Blackstock, S. C.; Yumibe, N. P.; Frigo, T. B.;
Carpenter, J. E.; Weinhold, F. J. Am. Chem. Soc. 1985, 107, 143.
(10) (a) Grampp, G.; Jaenicke, W. Ber. Bunsen-Ges. Phys. Chem. 1984,
88, 325. (b) Grampp, G.; Jaenicke, W. Ibid. 1984, 88, 335. (c) Grampp,
G.; Jaenicke, W. Ibid. 1991, 95, 904.
(8) Nelsen, S. F.; Chen, L. J.; Powell, D. R.; Neugebauer, F. A. J. Am.
Chem. Soc. 1995, 117, 11434.

5904 J. Am. Chem. Soc., Vol. 119, No. 25, 1997
Table 5. Model Parameters for ET Used in Calculations
Nelson et al.
b
c
d
typea
Vb
λsb
λV
λb
hνV
kii
HY
FE
PD
0.1
0.1
0.1
10
10
10
40
15
10
50
25
20
800
300
1500
8.86 × 103
1.12 × 107
7.66 × 108
a Parameters mimicking: HY ) hydrazine, FE ) ferrocene, PD )
p-phenylenediamine. b Unit: kcal/mol. c Unit: cm-1
assuming Keq ) 1 for preassociation.
. ,
d Unit M-1 s-1
using Jortner’s double-sum Franck-Condon factor (eq 2),11
which is applicable to reactions of any size of V, where S )
λV/hνV, to see what behavior would be expected using more
modern theory. We inserted Keq ) 1 M-1 for precursor complex
k12(Jor) ) Keq[4π2/h]V2FCV,w(g)
(2a)
FCV,w(g) )
(4πλskBT)-1/2
[
V exp(-VhνV/RT)]-1
w F(V,w) ×
∑V∑
∑
exp(-VhνV/RT)exp[-(λs+ {w - V}hνV + ∆G°)2/4λsRT]
(2b)
Figure 1. Comparison of calculated effects of exoergicity upon ∆Gq
for ET for the HY,HY+, FE,FE+, and PD,PD+ model parameters. Solid
line: Marcus (eq 1, Z11 ) Z22 ) 1011 M-1 s-1) prediction. Broken
lines: Jortner (eq 2) prediction. Squares: V ) 0.1 kcal/mol. Tri-
angles: V ) 0.5 kcal/mol. Diamonds: V ) 1.0 kcal/mol. Circles: V
) 0.02 kcal/mol, shown only for PD,PD+.
F(v,w) )
exp(-S)V!w![ {(-1)V+w-rS(V+w-r)/2}/{r!(V - r)! ×
∑
r
(w - r)!}]2 (2c)
formation into the expression for k12(Jor) to get the units correct
becomes strongly negative for PD,PD+, suggesting to us that
the reactions studied here are unlikely to be this strongly
nonadiabatic since we do not see the predicted effect of k12(obsd)
deviating more from eq 1 behavior as ∆G° becomes more
negative. Because λV for the PD,PD+ model almost completely
disappears at λs ) 8 kcal/mol and V ) 0.02 kcal/mol, we were
forced to use this λs value. Note that when these parameters,
PD,PD+ ET is in the inverted region when ∆G° < -6 kcal/
mol, where k12(Jor) starts to decrease with increasing exoergicity.
Most of our experimental data are for compounds with very
different ET parameters (λV and hνV). We believe it is clear
that the λ values should be averaged, thus λV12 ) (λV1 + λV2)/2
(and λ12 ) (λ1 + λ2)/2). The most reasonable method of
averaging for the hνV values is to use the root of the weighted
squares sum for the two compounds (eq 3), which is how the
averaging is carried out to calculate the average hνV mode from
the contributions of all of the modes of a single compound.5
for intermolecular ET reactions. Values for Keq above 0.3 M-1
have been argued to be correct for TMPD0/+ 10,12
To simplify
.
our considerations, λs was fixed at 10 kcal/mol, which is close
to the experimental value obtained from solvent effects on
kii(self) for bis-N,N′-bicyclic hydrazines.13 We chose model
parameter sets HY, FE, and PD (HY representing hydrazine,
FE ferrocene, and PD phenylenedimine parameters), assigning
hνV values of 800, 300, and 1500 cm-1, respectively, and
choosing λV values to make kii(Jor), the k12(Jor) value at ∆G°
) 0, have values of ca. 9 × 103, 1 × 107, and 8 × 108 M-1
s-1, respectively, in rough agreement with the experimental kii
values for these three classes of compounds (see Table 5). We
first consider what happens when the driving force increases
for two compounds having the other ET parameters the same.
Figure 1 shows a graphical comparison of the changes in
k12(calcd) from eq 1 (Z11 ) Z22 ) 1011), in behavior using kii )
kii(Jor) at ∆G° ) 0, and in k12(Jor) as exoergicity increases for
these models for four V values ranging from 0.02 kcal/mol (in
the clearly non-adiabatic region) to 1.0 kcal/mol (in the nearly
adiabatic region). Also shown for the HY,HY+ model reaction
is a dotted line with a slope of -1/2, which is the behavior
expected if f12 ) 1 in eq 1. We note that use of the traditional
Z11 ) Z22 ) 1011 value causes the adiabatic prediction of eq 1
to lie slightly below the V g 0.1 kcal/mol curves for the
HY,HY+ model set and slightly above such curves for the
FE,FE+ model set and to track the PD,PD+ models set closely
for the V ) 0.1 kcal/mol curve. The differences using the two
approaches are too small to be detected in our experimental
data when V is g 0.1 kcal/mol, except for the PD model when
∆G° becomes <-8 kcal/mol and V is >0.1 kcal/mol (where
k12 is too large to be experimentally measured anyway). The
calculated V ) 0.02 kcal/mol differences are larger as ∆G°
hνV12
)
[{(λV1)/(λV1+λV2)}(hνV1)2 + {(λV2)/(λV1+λV2)}(hνV2)2]1/2 (3)
As shown in Table 6, both for calculated HY,FE+ and HY,PD+
reactions, even better agreement between k12′(calcd) and k12(Jor)
is obtained. The maximum difference between the two calcula-
tions is about 25% out to ∆G° ) -11.5 kcal/mol, which
corresponds to ∆∆Gq estimates using eqs 1 and eq 2 being under
0.2 kcal/mol. Surprisingly to us, the effects of large differences
in tunneling efficiency are not calculated to detectably affect
k12; just knowing kii values and ∆G° appears to be sufficient to
determine k12 reasonably well even in the modestly nonadiabatic
region. We believe that these calculations rationalize the
observed rate data and demonstrate that, despite the assumptions
made in its derivation, eq 1 is indeed expected to be adequate
for extracting kii values from experimental data, even when the
λV and hνV parameters for reaction partners differ greatly and
when the reactions are not strongly adiabatic.
(11) (a) Ulstrup, J.; Jortner, J. J. Chem. Phys. 1975, 63, 4358. (b) Jortner,
J.; Bixon, M. J. Chem. Phys. 1988, 88, 167. (c) Cortes, J.; Heitele, H.;
Jortner, J. J. Phys. Chem. 1994, 98, 2527.
(12) The size of Keq for electron transfer reactions in general remains
unknown. Since we are interested here in the effect of driving force on k12,
any value could be chosen. If Keq varied widely in real reactions, eq 1,
which does not consider it, would work less well.
Discussion: kii(fit) Values
All of the kii(fit) values derived from the cross reaction rate
constants (k12(obsd)), are smaller than the independently deter-
(13) Table 1, footnote f.

Self-Exchange Electron Transfer Rate Constants
J. Am. Chem. Soc., Vol. 119, No. 25, 1997 5905
Table 6. Comparison of Marcus and Jortner Calculated k12 (Keq
for preassociation ) 1) as a Function of Driving Force for
Reactions Where the Components Have Different ET Parameters
The kii(fit) value for cHx2N)2 is ca. 10 times that for iPr2N)2
(∆∆Gii ) -1.3 kcal/mol). One factor predicted to make kii
larger for cHx2N)2 than for iPr2N)2 is a smaller λs. Using the
touching spheres approximation for modeling, the transition state
in Marcus’s dielectric continuum formula for estimation of λs5
(eq 4) predicts a smaller λs for the larger compound cHx2N)2.
q
Marcus
k12
Jortner
k12
Jortner/Marcus
ratio
∆G°
∆∆G‡
HY,FE+a
3.52 × 105
2.22 × 106
1.18 × 107
5.39 × 107
2.10 × 108
7.07 × 108
0
3.15 × 105
2.05 × 106
1.14 × 107
5.51 × 107
2.29 × 108
8.17 × 108
1.12
1.08
1.03
0.98
0.92
0.86
-0.07
-0.05
-0.02
+0.01
+0.05
+0.09
λs(kcal/mol) ) 332.1 (2rav)-1γ
(4)
-2.31
-4.61
-6.92
-9.22
-11.53
Use of the molecular volumes occupied in the crystal for
iPr2N)2 and cHx2N)2 342.56 and 558.15 Å3, respectively, yields
rav of 4.34 and 5.11 Å from the relationship V ) (4/3)π(rav)3,
HY,PD+b
3.33 × 106
1.97 × 107
9.65 × 107
3.83 × 108
1.26 × 109
3.51 × 109
q
2.60 × 106
1.67 × 107
8.92 × 107
3.99 × 108
1.49 × 109
4.65 × 109
1.24
1.18
1.08
0.96
0.85
0.75
-0.13
-0.10
-0.05
+0.02
+0.10
+0.17
an expected additional contribution of 0.76 kcal/mol to ∆Gii
0
-2.31
-4.61
-6.92
-9.22
-11.53
for iPr2N)2, or an increase in kii of cHx2N)2 by a factor of 3.6.
This estimated difference in λs accounts for about half of the
difference obtained from the cross rate studies, suggesting that
some factor in addition to a difference in λs is lowering ∆G‡
for cHx2N)2 relative to iPr2N)2. The X-ray crystal structures
show that both neutral hydrazines are in θ near 90° conforma-
tions. The presence of a more twisted solution conformation
for cHx2N)2+ than for iPr2N)2+ from comparison of their optical
spectra suggests that the larger kii for the former compound may
well result from a smaller λV value, because λV is expected to
decrease as the difference in twist between the neutral and cation
oxidation states decreases.
a Using λs12 ) 10, λV12 ) 27.5, V ) 0.1 kcal/mol, hνV12 ) 700 cm-1
b Using λs12 ) 10, λV12 ) 25, V ) 0.1 kcal/mol, hνV12 ) 981 cm-1
.
.
We shall consider 9,9′-bis-9-azabicyclo[3.3.1]nonane (33N)2)
and its derivatives next. We succeeded in measuring kii(self)
in methylene chloride at 8.7(5) × 103 M-1 s-1,2 but were unable
to measure it in acetonitrile due to low solubility. The
kii(CD2Cl2)/kii(CD3CN) ratios were about 5 for 22/u220/+ and
21/u220/+, allowing us to estimate kii(self,CD3CN) for 33N)2
to be 2.2 × 103 M-1 s-1,2 which produces kii(self)/kii(fit) ) 3.2
(∆∆Giiq ) -0.68 kcal/mol), comparable in agreement to those
for directly measured compounds. 33N)2 has a 180° lone pair/
lone pair twist angle (θ) in both neutral and radical cation
oxidation states and, probably as a direct result, exhibits much
faster ET than its θ ≈ 90° analogue, iPr2N)2. The X-ray average
radius of 33N)2, at 4.371 Å, is only 0.7% larger than that of
iPr2N)2, so λs differences ought to be small. The smaller
geometry change for 33N)2 should result in a smaller λV value,
and the difference in ∆Gq values of 7.43 kcal/mol would require
a difference in λV of 29.7 kcal/mol if only λV differed. The
nitrogens of iPr2N)2 are significantly less pyramidal than those
of 33N)2, which would tend to lower λV for iPr2N)2 relative to
that for 33N)2; the θ difference is clearly more important.
The mono- and bis-γ-keto compounds k33NN33 and k33N)2
have geometries at their nitrogens and molecular volumes very
similar to those of 33N)2, and we fully expected that all three
would have similar kii values and that the only effect upon k12
values using them would be their significant difference in redox
potentials, corresponding to a 10.1 kcal/mol more exoergic
reaction for oxidation of the same compound by k33N)2+ than
by 33N)2+. As shown in Table 1, however, bis-γ-keto substitu-
tion lowers kii(fit) by a factor of 17, corresponding to an increase
in ∆Giiq of 1.7 kcal/mol. It appears to us that the change in kii
is unlikely to be caused by changes in λV, λs, or hνV for these
very similar compounds. We suggest that the most likely origins
for the rate decrease upon replacement of CH2 by CdO γ to
nitrogen are a decrease in V or in equilibrium constant for
precursor complex formation. It seems reasonable to us that
the “hole” would avoid the electron-withdrawing carbonyl
group, which might lower V by reducing the fraction of relative
orientations which have better electronic overlap.
‡
‡
Figure 2. Correlation between ∆Gii (fit) and ∆Gii (self) from Table
1.
mined homogeneous kii(self) values except for FeCp*Cp0/+
,
where the kii(self)/kii(fit) ratio is 0.85. Similar deviations are
observed for transition metal coordination compound examples
(ref. 5b, p 468), so there appears to be a detectable contribution
to k12 which is not accounted for properly by eq 1. It is more
meaningful to examine activation free energy differences
because they are linearly related and may be directly compared.
Figure 2 shows a plot of ∆Gii (fit) vs ∆Gii (self). The regression
line shown corresponds to ∆Gii (fit) ) 0.974∆Gii (self) + 0.93,
and the average deviation of ∆Gii (fit) from this line is 0.45
kcal/mol. The differences [∆Gii (self) - ∆Gii (fit)] are shown
in the last column of Table 1; the average difference is 0.66
kcal/mol. These two ways of summarizing the data illustrate
the small, systematic nature of the deviations of experiment and
theory. Four different kinds of experiments were used to obtain
the kii(self) values in Table 1, which span a factor of 4.9 ×
1011. The cross rate studies use the same kind of experiment
to cover the entire range, since k12 is sensitive to ∆G°, and the
accuracy of the ∆G° measurements from electrochemistry does
not significantly depend upon its size. The kii(fit) values
obtained by simultaneously fitting all cross reaction data to eq
1 are very effective at predicting k12(obsd) and are reasonably
close to, but somewhat lower than, kii(self) values.
q
q
q
q
q
q
q
Replacing the dimethylamino groups of TMPD by 9-
azabicyclo[3.3.1]nonyl groups in 33)2PD appears to have little
effect on kii: kii(fit,33)2PD)/kii(fit,TMPD) ) 1.46. Even the
order of reactivity is in doubt, since obtaining a rate ratio greater

5906 J. Am. Chem. Soc., Vol. 119, No. 25, 1997
Nelson et al.
than 1 depends entirely on having entry 32, 33N)2,33)2PD+, in
the data set. Elimination of this reaction (i.e., optimization of
the remaining 46 reactions) drops the ratio to 0.68.14 The
important point is that 33)2PD and TMPD have nearly the same
kii value. This is surprising in terms of literature discussion of
the probable transition state for TMPD self-ET.10,15 Methylated
PD+ salts crystallize with the aromatic rings in parallel stacks
having ring interplanar distances in the range of 3.1-3.7 Å.16
The stacks are strongly tilted for TMPD+, placing the CAr-N
atom of one unit roughly above the N atom on the adjacent
unit, and Grampp and Jaenicke used 5.46 Å ring centers distance
with parallel ring planes in modeling the TMPD0/+ transition
state.10a,c Rauhut and Clark15 found the ring centers distance
to be an exceptionally “soft” parameter in calculations of the
energy of both PD encounter complexes and transition states
for self-ET, noting that the energy increases <0.5 kcal/mol for
D2 symmetry parent [PD,PD]+ ET transition states between 3.55
and 4.95 Å when the rings are parallel. They also noted that
calculated V decreases sharply as the ring planes move apart.
Thus, it has been considered that the transition states for ET
which will lead to rapid ET in PD-derivatives are those which
have the rings parallel and the π systems overlapping, as they
do in crystals, to maximize V. We think it is significant that
33)2PD has about as large a kii as TMPD, because its large
alkyl groups preclude significant aryl ring overlap. Crystalline
and to be a maximum when the orbital energies are the same.
Changes in overlap may be accounted for well by the averaging
used, but cross reactions will have different orbital energies,
which we expect to tend to make V12 smaller than (V11V22)1/2
.
This would be expected to make the kii(fit) values smaller than
the kii(self) values as observed, because the self-exchange
reactions would not suffer from the orbital energy mismatch
effect, and might be expected to have larger V values. We note
that the largest deviation of kii(fit) from kii(self) occurs for
TMPD, an unhindered aromatic system which might be able
to achieve a larger Vii in its self-exchange reaction than in
reactions with any of the hydrazines or ferrocenes used in this
work.
Discussion: Comparison with Transition Metal Complex
Cross Rate Studies
Wherland has reviewed outersphere ET reactions of metal
complexes in nonaqueous solvents.17 Macartney and co-workers
have studied many cross reactions of metal-centered systems
with +2/+3 charges in acetonitrile, where work terms are
presumably important, and all reactions were analyzed using
2+/3+
the form of eq 1 containing work terms.18 For Co(bpyO2)3
reactions with ten ML33+/2+ (M ) Fe and Os, L ) 2,2′-bipyridyl
and 9,10-phenanthroline derivatives), cross rate theory gave
kii(Co) values in the range of 0.8-2 M-1 s-1 18a
while for
,
-
33)2PD+PF6 has the ring stacks slightly less tilted than
3+/2+
2+/3+
Mn(urea)6
reactions with 17 ML3
(M ) Fe, Os, and
TMPD+, with an interplanar distance of 4.88 Å, 1.33 and 1.50
Å larger than for TMPD+ClO4- and -Br- respectively,16b and
a 6.69 Å ring centers distance. The only way that π-aryl-
overlapped transition states could be attained for 33)2PD would
be to fix the N,N axes perpendicular to avoid nonbonded
interaction. Restricting the ET to such a small subset of
approaches would be expected to cost entropy relative to
TMPD, where there is no such requirement, which would be
expected to lower kii. The large kii(fit) for 33)2PD indicates
that the π-overlapping “stacked” transition state for TMPD is
not as important a factor in determining kii as has been believed.
Bis-γ-keto substitution in going from 33)2PD to k33)2PD
lowers kii(fit) by a factor of 4.4 with the 47 reaction data set
(2.2 with the 46 reaction data set). This effect is significantly
smaller than for the 33N)2 hydrazines, which lack the p-
phenylene bridging group between the nitrogens, and seems
qualitatively consistent with the lowered V for regions near the
keto groups mentioned above, since regions near the keto groups
would block a smaller fraction of the molecule, but we do not
know how to quantitate such an idea.
The preexponential term of ET rate constants using vibronic
coupling theory contains V2 (see eq 2a); therefore, using eq 1
involves an implicit assumption that V12 ) (V11V22)1/2. With
the wide range of structures used, we expect Vii to vary
significantly; however, eq 1 correlates with k12(obsd) well, so
the assumption that V12 ) (V11V22)1/2 is apparently a rather good
approximation. The consistently slightly smaller kii(fit) than
kii(self) values might, however, be caused by somewhat different
V values for the two types of experiments. We expect V to be
affected both by orbital overlap and relative orbital energies
Ru), kii(Mn) varied by over a factor of 1400, from 6.2 × 10-3
to 4.4 × 10-6 M-1 s-1 18b
.
Futhermore, both the Co and Mn
complexes produce far larger kii values when Ni(macrocyclic
ligand)3+/2+ components are employed, kii(Co) values of 50-
600, and kii(Mn) values of 0.14-0.19 (using kii(Ni) values,
which are range from 1 to 6 × 103 M-1 s-1, obtained using
cross rate theory with other complexes).18c These reactions do
not follow cross rate theory very quantitatively at all, but how
important the work term corrections are in causing this result
remains unclear to us. Wherland and co-workers have studied
14 cross reactions between 0 and +1 states of cobalt clathro-
chelates with ferrocene derivatives19a and other cobalt
clathrochelates19b in acetonitrile. These reactions, which do not
involve work term corrections, follow eq 1 with great precision.19c
Summary and Conclusions
Equation 1 predicts k12 values with remarkable consistency,
q
with few discernable trends over a wide range of ∆G°, ∆Gii ,
and reactant structures. Cross reaction data allow estimates of
kii < 5 × 102 M-1 s-1, where kii(self) cannot be determined
(without labeling experiments, which require extremely small
values) because of insensitivity of both the ESR and NMR
spectra to electron exchange when it is so slow. Three principal
points of interest in the kii(fit) values obtained were found: (a)
(17) Wherland, S. Coord. Chem. ReV. 1993, 123, 169-99.
(18) (a) Macartney, D. H.; Mak, S. Can. J. Chem. 1992, 70, 39. (b)
Macartney, D. H. Inorg. Chim. Acta 1987, 127, 9. (c) Aquino, M. S.;
Foucher, D. A.; Macartney, D. H. Inorg. Chem. 1989, 28, 3357.
(19) (a) Borchardt, D.; Wherland, S. Inorg. Chem. 1986, 25, 901. (b)
Gribble, J.; Wherland, S. Inorg. Chem. 1989, 28, 2859. (c) When the least
q
squares fitting procedure is used, |∆∆Gij | averages to 0.05 kcal/mol. The
(14) That there is a problem is most easily seen by examining reaction
pairs having a common third component. Dividing the k12(obsd) values for
such cases allows direct calculation of the kii ratio for the other components.
kii(fit), M-1 s-1 values obtained are FeCp2 ) 9.18 × 106 and FeCp′2
)
6.74 × 106, and the values for five of the clathrochelates are similar to
those reported using input kii values for the ferrocenes.19a However,
examining this data set illustrates an important point about using the least
squares fitting procedure. The data set contains 10 components and 14
reactions, so few components appear in more than three cross reactions.
Because the two (BBu)2-containing examples were only reacted with
FeCp*2 and only one of all three of these components was run versus a
different component, this subset of reactions is underdetermined and the
least squares program cannot correctly determine the related kii(fit). For
the fitting approach employed here to be effective, it is essential that
sufficient data for each component is obtained to allow the independent
determination of each kii being fitted in the data set.
+
When this is done for 33)2PD and TMPD oxidation by iPr2N)2 and
cHx2)2+, the ratios are 0.50 and 0.51, but for the cation reduction by 33N)2,
q
0/+
the ratio is 14!. Deleting reaction 32 increases ∆Gii for 33N)2 by 0.14
kcal/mol and for 33)2PD0/+ by 0.45 kcal/mol, while all the other values
change by e0.05 kcal/mol. Deleting reaction 32 changes the relative rate
constants for 33N)20/+/k33NN330/+/k33N2 from 17.2:5.6:1 to 14.1:5.6:
0/+
1.
(15) Rauhut, M.; Clark, T. J. Am. Chem. Soc. 1993, 115, 9127.
(16) (a) Tanaka, J.; Mizuno, M. Bull. Chem. Soc. Jpn. 1969, 42, 1841.
(b) de Boer, J. L.; Vos, A. Acta Crystallogr. 1972, B28, 835.

Self-Exchange Electron Transfer Rate Constants
J. Am. Chem. Soc., Vol. 119, No. 25, 1997 5907
yellow solid: 1H NMR (CD3CN) δ 4.95 (m, 2H), 4.50 (m, 1H), 2.2-
1.15 (m, ∼30 H).
The kii(fit) are systematically lower than kii(self) by a small,
but significant, amount which we suggest might be caused by
a smaller V for cross than for self-ET reactions. (b) Hindering
the approach of the aromatic rings by replacing the Me2N
groups of TMPD by 33N groups in 33)2PD changes ∆Giiq very
little (0.3 kcal/mol or less); thus, close approach of the π faces
of the aromatic rings is not required for fast ET, as had been
suggested in the literature. (c) Bis-γ-keto substitution in going
Tetracyclohexylhydrazine, cHx2N)2 was prepared analogously to
iPr2N)2.8 A mixture of 270 mg of CuI, 36 mL of freshly distilled THF,
and 2 M cyclohexylmagnesium chloride (7 mL, 14 mmol) was stirred
at 0 °C under nitrogen, and tricyclohexyldiazenium hexafluorophosphate
(2.45 g, 5.8 mmol) was added in one portion. The mixture was allowed
to warm to room temperature and stir overnight, and then treated with
ammonium chloride (0.9 g) in water (40 mL) and extracted with 4 ×
160 mL portions of pentane. After the organic phase was dried with
magnesium sulfate, filtered, and concentrated, the residue was recrystal-
lized from toluene and acetonitrile to give the hydrazine as a white
solid, 0.933 g (2.6 mmol, 44%): mp 194-196 °C. 1H NMR (C6D6) δ
2.74 (tt, J ) 12, 3 Hz, 4H), 1.90 (br d, J ) 12 Hz, 8H), 1.78 (br d, J
) 13 Hz, 8H), 1.67-1.56 (m, 12H), 1.26 (qt, J ) 13, 3.5 Hz, 8H),
1.08 (qt, J ) 13, 3.5 Hz, 4H); 13C NMR (C6D6) δ 61.99, 34.80, 27.49,
26.68. Empirical formula was established by mass spectrometry: calcd
for C24H44N2 360.3505, obsd m/e 360.3486 (30.0%). The structure was
confirmed by X-ray crystallographic analysis.
q
from 33N to k33N rings raises ∆Gii (fit) by about 1.7 kcal/mol
in the hydrazine system 33N)2 and by about 1.0 kcal/mol in
the aromatic system 33)2PD; therefore, despite the fact that the
geometry at the nitrogens remains almost unaffected, the change
in barrier is more important than substantially increasing the
distance between the centers of the molecules in b.
Experimental Section
The preparations of most of the compounds used have been described
(see the footnotes to Table 1). Cross reaction rate constant were
obtained by analysis of absorbance vs time data obtained using either
an Applied Photophysics model SX17MV stopped-flow and data
analysis system or a Durrum Model D-110 stopped-flow interfaced with
On-Line-Instrument-Systems data aquisition and analysis software. The
reaction between cHx2N)2 and iPr2N)2 was so slow that absorbance
vs time data were obtained using a Hewlett-Packard 8452 diode array
spectrophotometer following manual mixing of reactants in a thermo-
stated cell. Data analysis for this reaction was done using Applied
Photophysics software supplied with the SX17MV spectrometer.
Reactant solution preparation and handling have been described.2
1,1-Dicyclohexylhydrazine. (Note: nitrosoamines are carcinogenic
and mutagenic.) A solution of 52.26 g (0.248 mol) of N-nitrosodicy-
clohexylamine in 220 mL dry THF was added over 1 h to a stirring
mixture of 16.93 g (0.445 mol) of LiAlH4 in 200 mL of dry THF, and
the mixture was refluxed overnight and stirred at room temperature an
additional day. The mixture was cooled in a dry ice-acetone bath
and worked up by slow addition of 15 mL of H2O followed by 120
mL of 20% NaOH. The aqueous layer was extracted with 2 × 150
mL of Et2O, and the combined organic layers were dried with
magnesium sulfate and concentrated to give 36.6 g of a colorless oil
which was Kugelrohr distilled at 80-85 °C (0.03 Torr) to give 35.51
g (0.181 mol, 73%) of 1,1-dicyclohexylhydrazine: 1H NMR (CDCl3)
δ 2.63 (br s, 2H), 2.45 (m, 2H), 1.78-1.6 (m, 10H), 1.25-0.9 (m,
10H); 13C NMR (CDCl3) δ 60.83 (CH), 29.18 (CH2), 26.20 (CH2),
25.61 (CH2). Empirical formula was established by mass spectrom-
etry: calcd for C12H24N2 196.19395, obsd m/e 196.1940 (57.9%).
Tricyclohexyhydrazine. A mixture of 1,1-dicyclohexylhydrazine
(12.06 g, 62 mmol), cyclohexanone (6.56 g, 67 mmol), 50 mL of
acetonitrile, and 0.3 mL of acetic acid was stirred for 30 min and treated
with NaBH3CN (4.20 g, 67 mmol), and an additional 50 mL of
acetonitrile was added by syringe, followed by 40 mL of methanol to
dissolve the white solid present. The reaction mixture was stirred and
refluxed, 0.15 mL of acetic acid was added every 15 min for 3 h, and
reflux was continued for 2 h. After the solution was cooled overnight,
the mixture was treated with 40 mL of 20% NaOH and extracted with
5 × 100 mL portions of pentane. After the extracts were dried over
magnesium sulfate, filtered, and concentrated, the yellow oil obtained
crystallized slowly. Recrystallization from methanol gave 6.81 g (24.5
mmol, 40%) of tricyclohexylhydrazine as a white solid: mp 60.5-61
Tetracyclohexylhydrazine Radical Cation Hexafluoroantimonate,
cHx2N)2+SbF6-. AgSbF6 (81.0 mg, 0.236 mmol) was weighed out in
a 50 mL Schlenk flask under nitrogen and dissolved in CH2Cl2 (3 mL).
Tetracyclohexylhydrazine (85.0 mg, 0.236 mmol) was added as a solid
resulting in a greenish-black solution. After 5 h of stirring, the mixture
was filtered through Celite and the filter was rinsed with CH2Cl2 (5
mL). The bright-red solution was evaporated to give a red solid that
was dissolved in minimum amount of CH2Cl2 (ca 3 mL). Precipitation
with ether afforded the product (119 mg, 84%). Recrystallization by
vapor diffusion of ether into a CH2Cl2 solution proceeded very quickly
and gave large but rather shapeless crystals, whereas recrystallization
by vapor diffusion of ether into acetonitrile solution proceeded much
slower, giving small but very well-developed prisms. The structure
of the radical cation was confirmed by X-ray crystallographic analysis
of a prism from CH3CN recrystallization.
1,4-Bis(3′-keto-9′-azabicyclo[3.3.1]non-9′-yl)benzenium Hexafluo-
-
rophosphate, k33)2PD+PF6
. A solution of NOPF6 (0.59 g, 3.35
mmol) in 10 mL of acetonitrile was added by cannula to the neutral
compound (Table 1, footnote k, 1.18 g, 3.35 mmol) in 50 mL of CH2Cl2,
under nitrogen, and the mixture was stirred overnight. The blue residue,
after solvent removal, was crystallized by vapor diffusion of ether into
acetonitrile, giving 0.55 g (1.3 mmol, 40%) of the salt, which was
characterized by obtaining an X-ray crystal structure.
Crystal structure data and refinement parameters for iPr2N)2,
cHx2N)2, k33)2PD+PF6-, and k33N)2 appear in the Supporting
Information.20
Acknowledgment. We thank the National Science Founda-
tion for partial financial support of this work under Grants CHE-
9504133 (J.R.P.) and -9417946 (S.F.N.). Acknowledgement
is also made to the donors of the Petroleum Research Fund,
administered by the ACS for partial support of the research
under grant ACS-PRF 29982-B4 (JRP). We thank Fred King
for assistance with Fortran programming.
1
°C; H NMR (C6D6) δ 2.70 (tt, J ) 10.3, 3.4 Hz, 1H), 2.58 (tt, J )
11.5, 3.4 Hz, 2H), 1.93 (br d, J ) 12.8, 2H), 1.83-1.70 (m, 10H),
1.57 (br d, J ) 12.3, 3H), 1.42 (qd, J ) 12.3, 2.5 Hz, 4H), 1.30-1.05
(m, 12 H); 13C NMR (C6D6) δ 61.09 (CH), 57.81 (CH), 33.00, 31.35,
27.05, 26.76, 26.68, 24.41. Empirical formula was established by mass
spectrometry: calcd for C18H34N2 278.2722, obsd m/e 278.2722
(28.0%).
Supporting Information Available: Experimental for de-
0/+
2
1
termination of ET rate constants for iPr2N)2 by H and H
-
NMR, and crystal data for iPr2N)2, cHx2N)2, k33)2PD+PF6
,
and k33N)2 (5 pages). See any current masthead page for
ordering and Internet access instructions.
Tricyclohexyldiazenium Hexafluorophosphate. A solution of
tricyclohexylhydrazine (1.95 g, 7 mmol) in 15 mL of freshly distilled
methylene chloride was added by cannula, over 10 min, to a solution
of NOPF6 (2.60 g, 14.8 mmol) in 10 mL of freshly distilled acetonitrile
stirring at -35 °C. After an additional 35 min of stirring, 270 mL of
ether was added by syringe, and the product was filtered and dried in
a stream of nitrogen, giving 2.45 g (5.8 mmol, 83%) of a greenish
JA970321J
(20) The authors have deposited atomic coordinates for these structures
with the Cambridge Crystallographic Data Centre. The coordinates can be
obtained, on request, from the Director, Cambridge Crystallographic Centre,
12 Union Road, Cambridge, CB2 1EZ, U.K.