Donor-Acceptor (Electronic) Coupling in the Precursor Complex to Organic Electron Transfer: Intermolecular and Intramolecular Self-Exchange between Phenothiazine Redox Centers

Article abstract of DOI:10.1021/ja038746v

Intermolecular electron transfer (ET) between the free phenothiazine donor (PH) and its cation radical (PH^.+) proceeds via the [1:1] precursor complex (PH)₂^.+ which is transiently observed for the first time by its diagnostic (charge-resonance) absorption band in the near-IR region. Similar intervalence (optical) transitions are also observed in mixed-valence cation radicals with the generic representation: P(br)P ^.+, in which two phenothiazine redox centers are interlinked by p-phenylene, o-xylylene, and o-phenylene (br) bridges. Mulliken-Hush analysis of the intervalence (charge-resonance) bands afford reliable values of the electronic coupling element H_IV based on the separation parameters for (P/P^.+) centers estimated from some X-ray structures of the intermolecular (PH)₂^.+ and the intramolecular P(br)P ^.+ systems. The values of H_IV, together with the reorganization energies λ derived from the intervalence transitions, yield activation barriers ΔG_ET? and first-order rate constants k_ET for electron-transfer based on the Marcus-Hush (two-state) formalism. Such theoretically based values of the intrinsic barrier and ET rate constants agree with the experimental activation barrier (E _a) and the self-exchange rate constant (k_SE) independently determined by ESR line broadening measurements. This convergence validates the use of the two-state model to adequately evaluate the critical electronic coupling elements between (P/P^.+) redox centers in both (a) intermolecular ET via the precursor complex and (b) intramolecular ET within bridged mixed-valence cation radicals. Important to intermolecular ET mechanism is the intervention of the strongly coupled precursor complex since it leads to electron-transfer rates of self-exchange that are 2 orders of magnitude faster (and activation barrier that is substantially lower) than otherwise predicted solely on the basis of Marcus reorganization energy.

Full text of DOI:10.1021/ja038746v

Published on Web 01/20/2004
Donor-Acceptor (Electronic) Coupling in the
Precursor Complex to Organic Electron Transfer:
Intermolecular and Intramolecular Self-Exchange between
Phenothiazine Redox Centers
Duoli Sun, Sergiy V. Rosokha, and Jay K. Kochi*
Contribution from the Department of Chemistry, UniVersity of Houston,
Houston, Texas, 77204-5003
Received September 26, 2003; E-mail: jkochi@uh.edu
Abstract: Intermolecular electron transfer (ET) between the free phenothiazine donor (PH) and its cation
•+
radical (PH•+) proceeds via the [1:1] precursor complex (PH)2 which is transiently observed for the first
time by its diagnostic (charge-resonance) absorption band in the near-IR region. Similar intervalence (optical)
transitions are also observed in mixed-valence cation radicals with the generic representation: P(br)P•+
,
in which two phenothiazine redox centers are interlinked by p-phenylene, o-xylylene, and o-phenylene (br)
bridges. Mulliken-Hush analysis of the intervalence (charge-resonance) bands afford reliable values of
the electronic coupling element HIV based on the separation parameters for (P/P•+) centers estimated from
some X-ray structures of the intermolecular (PH)2 and the intramolecular P(br)P•+ systems. The values
•+
of HIV, together with the reorganization energies λ derived from the intervalence transitions, yield activation
q
barriers ∆GET and first-order rate constants kET for electron-transfer based on the Marcus-Hush (two-
state) formalism. Such theoretically based values of the intrinsic barrier and ET rate constants agree with
the experimental activation barrier (Ea) and the self-exchange rate constant (kSE) independently determined
by ESR line broadening measurements. This convergence validates the use of the two-state model to
adequately evaluate the critical electronic coupling elements between (P/P•+) redox centers in both (a)
intermolecular ET via the precursor complex and (b) intramolecular ET within bridged mixed-valence cation
radicals. Important to intermolecular ET mechanism is the intervention of the strongly coupled precursor
complex since it leads to electron-transfer rates of self-exchange that are 2 orders of magnitude faster
(and activation barrier that is substantially lower) than otherwise predicted solely on the basis of Marcus
reorganization energy.
Introduction
from stopped flow and EPR line broadening measurements
pertinent to paramagnetic redox centers. However, when the
Classical Marcus theory has been successfully applied to the
prediction of intrinsic (activation) barriers, i.e., reorganization
energies λ, of various self-exchange reactions and to electron-
transfer (ET) rates of cross-exchange reactions from knowledge
of the component self-exchanges, especially of transition-metal
(inorganic) redox processes.1-3 The subsequent extension of
Marcus theory to conventional organic and organometallic donor
and acceptor dyads was lately summarized by Eberson4 in the
ground-breaking and widely cited monograph, Electron-Transfer
Reactions in Organic Chemistry. At the crux of the theoretical
treatment is the evaluation of the intrinsic ET barrier for
experimental self-exchange rates that generally are obtained
quantitative applicability of classical Marcus theory was later
tested in a direct comparison of experimental and theoretical
activation barriers for organic self-exchange reactions, the cal-
culated barriers were actually found in many cases to be sig-
nificantly higher than otherwise expected.5 The possible origin
of such a discrepancy between theory and experiment was re-
cently traced by Nelsen and Pladziewicz6 to the inherent limi-
tation of classical Marcus theory to redox systems with restricted
values of the electronic coupling between the donor and acceptor
dyads, generally with the electronic coupling element (HDA) <
200 cm-1 2,7
.
According to Sutin,2,8 the generalized expression for the
Marcus activation barrier can be alternatively expressed as eq
1 to accommodate those redox systems with substantive values
(1) (a) Marcus, R. A. Angew. Chem., Int. Ed. Engl. 1993, 32, 1111. (b) Marcus,
R. A. Discuss. Faraday Soc. 1960, 29, 21. (c) Marcus, R. A. J. Phys. Chem.
1963, 67, 853. (d) Marcus, R. A. J. Chem. Phys. 1965, 43, 679. (e) Marcus,
R. A.; Sutin, N. Biochim. Biophys. Acta 1985, 811, 265.
(2) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441.
(3) (a) Newton, M. D. In Electron Transfer in Chemistry; Balzani, V., Ed.;
Wiley-VCH: New York, 2001; Vol. 1, p 3. (b) Astruc, D. Electron Transfer
and Radical Processes in Transition-Metal Chemistry; Wiley-VCH: New
York, 1995. (c) Cannon, R. D. Electron-Transfer Reactions; Butterworth:
London, 1980.
(4) Eberson, L. Electron-Transfer Reactions in Organic Chemistry; Springer-
Verlag: New York, 1987.
∆Gq ) (λ - 2HDA)2/4λ
(1)
of HDA, i.e., adiabatic (strongly coupled) systems. (As such, eq
(5) Eberson, L.; Shaik, S. S. J. Am. Chem. Soc. 1990, 112, 4484.
(6) Nelsen, S.; Pladziewicz, J. Acc. Chem. Res. 2002, 35, 247.
9
1388
J. AM. CHEM. SOC. 2004, 126, 1388-1401
10.1021/ja038746v CCC: $27.50 © 2004 American Chemical Society

Donor-Acceptor Coupling in Precursor Complex to ET
A R T I C L E S
1 attains the classical Marcus limit of ∆Gq ) λ/4 only when λ
. HDA.) Thus, the inclusion of HDA (initially) as a disposable
parameter by Nelsen and Pladziewicz6 of a large and diverse
number of experimentally measured cross-exchange reactions
led to consistently good correlations with theoretically evaluated
(self-consistent) sets of intrinsic barriers based on eq 1.
This important finding raises a number of interesting questions
about organic/organometallic electron-transfer processes. First,
what is the mechanistic significance of the electronic coupling
element when the composite term λ - 2HDA is notably less
than λ? Second, how do such substantial values of the electronic
coupling element experimentally impinge on the quantitative
evaluation of the effective activation barrier for intermolecular
ET? Critical to addressing these questions is the independent
experimental measurement of the electronic coupling element.
In this study, we focus on a single redox center, the phenothi-
azinyl group (P), because of the reversible oxidation of this
rather extended aromatic group to generate its persistent cation
radical (P•+) at the accessible potential of only E°ox ) 0.61 V
vs SCE.9,10 Our choice of the phenothiazinyl redox center in a
more general context relates to its extensive use in a variety of
intermolecular and intramolecular thermal and photochemical
redox processes primarily aimed at development and testing of
different aspects of electron-transfer theory,11 to its mimicking
biochemical (redox) processes,12 as well as to its bearing on
organic and organometallic material science.13
Chart 1
co-workers,14 but now with particular attention to the transient
appearance of diagnostic intervalence (charge resonance, CR)
absorption bands of the precursor complex heretofore unre-
ported. Intramolecular electron exchange between phenothiazinyl
redox centers is then identified in mixed-valence cation radicals
in which P and P•+ are interconnected by three types of molec-
ular bridges, viz. para-phenylene, ortho-xylylene, and ortho-
phenylene in the mixed-valence donors 1, 2, and 3 depicted in
Chart 2, and the direct relationship between intermolecular and
intramolecular electron exchange between these (P/P•+) centers
is made through the common observation of diagnostic inter-
valence absorption bands in their electronic spectra.
Chart 2
For intermolecular ET, we reexamine the electron-transfer
kinetics between the parent phenothiazine donor (PH) and its
cation radical (PH•+) as well as that of its N-methyl derivative
in Chart 1 that were originally delineated by Bard and
Results
I. Intermolecular ET Between Phenothiazine and Its
Cation Radical. A. Isolation and (UV-Vis/ESR) Charac-
terization of Pure Phenothiazine Cation Radical. Selective
oxidation of phenothiazine (PH) was readily carried out in
dichloromethane with 1 equiv of the (one-electron) oxidant tris-
(4-bromophenyl) aminium hexachloroantimonate15 to afford the
(7) (a) Such an upper limit of the electronic coupling element is rather arbitrary
since it depends on the reorganization energy. See: Nelsen, S. In Electron
Transfer in Chemistry, Balzani, V., Ed.; Wiley-VCH: New York, 2001;
Vol. 1, p 342. (b) As used here, HDA emphasizes the molecular-orbital
description of the electronic coupling element between the donor and
acceptor in the precursor complex, whereas the more conventional Hab is
based on the valence bond description of electronic coupling between the
initial and final (ET) diabatic states. Their theoretical equivalence has been
quantitatively demonstrated by Newton3a and underscores another example
of the never-ending rivalry between MO and VB treatments. See:
Hoffmann, R.; Shaik, S.; Hiberty, P. C. Acc. Chem. Res. 2003, 36, 750.
(8) (a) Brunschwig, B. S.; Sutin, N. In Electron Transfer in Chemistry, Balzani,
V., Ed.; Wiley-VCH: New York, 2001; Vol. 1, p 583. (b) Brunschwig, B.
S.; Sutin, N. Coord. ,Chem. ReV. 1999, 187, 233. (c) Sutin, N. AdV. Chem.
Phys. 1999, 106, 7. (d) Creutz, C.; Newton, M. D.; Sutin, N. J. Photochem.
Photobiol., A 1994, 82, 47.
-
pure cation radical PH•+ as the brown crystalline SbCl6 salt
(see Experimental Section).16 The red crystalline salt of the
corresponding N-methyl derivative PMe•+SbCl6- was prepared
by the same procedure.
The electronic spectrum of the phenothiazine cation radical
salt dissolved in dichloromethane is characterized by three
groups of bands: (a) local (UV) absorptions at 272 and 320
nm that are related to those at 255 and 316 nm in the parent
phenothiazine,17 (b) prominent (vis) bands at 437 and 519 nm
that are absent in the parent donor, and (c) weak (near-IR) bands
listed in Table 1, together with those of the N-methyl analogue
PMe•+. The resolved ESR spectrum of phenothiazine cation
radical (Figure S1, Supporting Information) was well-simulated
for this study using the hyperfine splitting constants established
earlier.18
(9) See Eberson in ref 4, p 44.
(10) Moreover, the sizable reorganization energy for this redox pair derives from
a significant configurational change of the tub-shaped P to the planar P•+
attendant upon one-electron oxidation. The latter also points to the
mechanistic advantage accrued in a more general context by the use of
“infinitely” variable organic structures for electron-transfer studies.
(11) (a) Chen, P.; Duesing, R.; Graff, D. K.; Meyer, T. J. J. Phys. Chem. 1991,
95, 5850. (b) Ohno, T.; Yoshimura, A.; Mataga, N. J. Phys. Chem. 1990,
94, 4871. (c) Pelizzetti, E.; Giordano, R. J. Chem. Soc., Dalton Trans. 1979,
1516. (d) Sorensen, S. P.; Bruning, W. H. J. Am. Chem. Soc. 1973, 95,
2445. (e) Nath, S.; Singh, A. K.; Palit, D. K.; Sapre, A. V.; Mittal, J. P. J.
Phys. Chem. A 2001, 105, 7151. (f) Daub, J.; Engl, R.; Kurzawa, J.; Miller,
S. E.; Schneider, S.; Stockmann, A.; Wasielewski, M. R. J. Phys. Chem. A
2001, 105, 5655. (g) Shimada, E.; Nagano, M.; Iwahashi, M.; Mori, Y.;
Sakaguchi, Y.; Hayashi, H. J. Phys. Chem. A 2001, 105, 2997. (h) Reid,
G. D.; Whittaker, D. J.; Day, M. A.; Creely, C. M.; Tuite, E. M.; Kelly, J.;
Beddard, G. S. J. Am. Chem. Soc. 2001, 123, 6953. (i) Larson, S. L.; Elliott,
C. M.; Kelley, D. F. Inorg. Chem. 1996, 35, 2070. (j) Larson, S. L.; Cooley,
L. F.; Elliott, C. M.; Kelley, D. F. J. Am. Chem. Soc. 1992, 114, 9504. (k)
Borowitz, P.; Herbich, J.; Kapturkiewicz, A.; Opallo, M.; Nowacki, J. Chem.
Phys. 1999, 249, 49. (l) Kramer, C. S.; Zeutler, K.; Mu¨ller, T. J. J.
Tetrahedron Lett. 2001, 49, 8619.
B. Concentration-Dependent ESR Line Broadening and
Self-Exchange Rates between Phenothiazine Donor and
Acceptor Couples. The incremental addition of free phenothi-
(14) Kowert, B. A.; Marcoux, B. A.; Bard, A. J. J. Am. Chem. Soc. 1972, 94,
5538.
(15) (a) Bell, F. A.; Ledwith, A.; Sherrington, D. C. J. Chem. Soc. C 1969,
2719. (b) Connelly, N. G.; Geiger, W. E. Chem. ReV. 1996, 96, 877.
(16) The rather large SbCl6- was consistently used as a relative noncoordinating
anion to minimize electrostatic effects of the counterion on PH•+ and PMe•+
in the ET and self-association processes.
(12) (a) Kawai, K.; Takada, T.; Tojo, S.; Majima, T. J. Am. Chem. Soc. 2003,
125, 6842. (b) Shen, Z.; Strauss, J.; Daub, J. Chem. Commun. 2002, 460.
(c) Koenig, B.; Pelka, M.; Zieg, H.; Ritter, T.; Bouas-Laurent, H.; Bonneau,
R.; Desvergne, J.-P. J. Am. Chem. Soc. 1999, 121, 1681.
(13) (a) Fungo, F.; Samson, A.; Bard, A. J. Chem. Mater. 2003, 15, 1264. (b)
Ehmann, A.; Gompper, R.; Hartmann, H.; Mueller, T. J. J.; Polborn, K.;
Schuetz, R. Angew. Chem., Int. Ed. Engl. 1994, 33, 572. (c) Margerum, L.
D.; Murray, R. W.; Meyer, T. J. J. Phys. Chem. A 1986, 90, 728.
(17) (a) Shine, H. J.; Mach, E. E. J. Org. Chem. 1965, 30, 2130. (b) Wagner,
E.; Filipek, S.; Kalinowski M. K. Monatsh. Chem. 1988, 119, 929.
(18) Lu, J.-M.; Chen, Y.; Wen, X.; Wu, L.-M.; Jia, X.; Liu, Y. C.; Liu, Z.-L. J.
Phys. Chem. A 1999, 103, 6998.
9
J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004 1389

A R T I C L E S
Kochi
Table 1. Electronic Spectra (in the NIR region) of Cation Radicals
(CR) and Dication (DC) of Phenothioazine-Based Mixed-Valence
Donors and Their Mononuclear Modelsa
Figure 1. Spectral changes attendant upon the addition of neutral
phenothiazine to the dichloromethane solution of its cation radical.
Concentrations: PH•+ ) 2 mM, PH (from bottom to top) ) 0, 9, 18 27,
47, 58, 72, 92 mM. Inset: Gaussian deconvolution (dashed line) of the
NIR band.
a
b
In dichloromethane. Determined by digital deconvolution of spec-
trum.
azine donor (PH) to a dichloromethane solution of its cation
radical (PH•+) resulted in the progressive change in the ESR
line widths as previously reported by Bard and co-workers14 to
derive from intermolecular ET between (PH/PH•+) dyads, in
which the initial broadening due to slow exchange evolves (upon
subsequent narrowing) to approach the fast-exchange limit
(Figure S2). Following the earlier kinetic studies, we determined
the second-order rate constant in the fast-exchange limit from
the line width dependence on the phenothiazine concentration
in dichloromethane solution19 (Figure S3) as kSE ) 5 × 109
M-1 s-1 for the (PH/PH•+) couple and as kSE ) 1.3 × 109 M-1
s-1 for the (PMe/PMe•+) couple at 25 °C (see Experimental
Section).20 The effective activation barrier of Ea ) 2.2 kcal
mol-1 and pre-exponential factor log A ) 11.3 were found for
the (PH/PH•+) self-exchange from the temperature dependence
of kSE (Figure S4).
C. Intervalence (Optical) Transition and the Intermo-
lecular Association of Phenothiazine and Its Cation Radical.
Various mixtures of phenothiazine and phenothiazine cation
radical in dichloromethane were characterized by the consistent
appearance of a new (unique) absorption band in the near-IR
region at 1600 nm under conditions in which neither pure donor
(PH) nor pure cation radical (PH•+) showed any absorption,
even at high concentrations and low temperatures (vida supra).
By contrast, the intensity of the NIR absorption band increased
linearly with the concentration of added phenothiazine at a
constant (low) concentration of the phenothiazine cation radical
(Figure 1), and the new NIR band increased monotonically as
the temperature of the (PH/PH•+) solution was progressively
lowered. Moreover, computer simulation of the near-IR band
confirmed its Gaussian band shape (Figure 1, inset). Such
behavior of the extremely red-shifted band with very broad and
weak absorbance was reminiscent of the CR transition in the
dimer cation radical or paramagnetic pimer derived from the
intermolecular association of various aromatic donors with their
own cation radical,21-23 which in the case of phenothiazine was
represented by the reversible equilibrium:
KPC
PH + PH•+
{
}
(2)
•+
[PH, PH ]
“pimer”
Quantitative analysis of the spectral changes was successfully
carried out by the Benesi-Hildebrand methodology,24 i.e.,
[PH•+]/APC ) 1/ꢀPC + 1/(KPCꢀPC[PH]), where APC is the
absorbance and ꢀPC is the molar extinction coefficient of the
NIR band of the paramagnetic pimer at the monitoring
wavelength, and [PH•+] and [PH] were the initial concentrations
of the phenothiazine cation radical and the parent donor,
respectively. The plot of [PH•+]/Apc versus reciprocal concentra-
tion of added [PH] was linear, and the least-squares fit produced
a correlation coefficient of greater than 0.999. The values of
the association constant of KPC ) 5 M-1 and extinction
(21) For previous examples of intermolecular π-association of various cation
radicals, see: (a) Lewis, L. C.; Singer, L. S. Chem. Phys. 1965, 43, 2712.
(b) Howarth, O. W.; Fraenkel, G. K. J. Am. Chem. Soc. 1966, 88, 4514.
(c) Howarth, O. W.; Fraenkel, G. K. J. Chem. Phys. 1970, 52, 6258. (d)
Badger, B.; Brocklehurst, B. Nature 1968, 219, 263. (e) Badger, B.;
Brocklehurst, B.; Dudley, R. Chem. Phys. Lett. 1967, 1, 122. (f) Badger,
B.; Brocklehurst, B. Trans. Faraday Soc. 1969, 65, 2582. (g) Badger, B.;
Brocklehurst, B. Trans. Faraday Soc. 1969, 65, 2588. (h) Badger, B.;
Brocklehurst, B. Trans. Faraday Soc. 1970, 66, 2939. (i) Meot-Ner, M.;
Hamlet, P.; Hunter, E. P.; Field, F. H. J. Am. Chem. Soc. 1978, 100, 5466.
(j) Meot-Ner, M. J. Phys. Chem. 1980, 84, 2724. (k) Meot-Ner, M.; El-
Shall, M. S. J. Am. Chem. Soc. 1986, 108, 4386. (l) All attempts to prepare
the corresponding anionic dimers in solution have been unsuccessful
heretofore. (m) Since the cationic and anionic dimers are both derived from
π-donor/acceptor pairs, they are hereinafter referred to interchangeably
(generically) as “π-mers” or precursor complexes (the designation “dimer”
is reserved for the dicationic (D2)2+ complexes23).
(22) For the spectral and structural characterization of such cation radical “π-
mers”, see: (a) Le Magueres, P.; Lindeman, S.; Kochi, J. K. J. Chem.
Soc., Perkin Trans 2, 2001, 1180. (b) Kochi, J. K.; Rathore, R.; Le
Magueres, P. J. Org. Chem. 2000, 65, 6826 and references therein. (c)
Charge resonance as employed here derives from Badger, Brocklehurst et
al.21d-g to describe the NIR absorption bands associated with the transient
cationic pimers of various aromatic donors.
(19) Note that in this study, dichloromethane was the solvent of choice because
of the expanded temperature range accessible for the kinetic studies as well
as the enhanced solubility and stability of the various phenothiazine cation
radical salts examined in this study.
(20) In acetonitrile solution, self-exchange rate constants of kSE ) 6.7 × 109
(23) For the formation of the cation radical dimer (PH)22+ at low temperature,
see Figure S6.
and 2.2 × 109 M-1 s-1 were determined for PH/PH•+ and PMe/PMe•+
,
respectively, by Bard et al.14
(24) Benesi, H. A.; Hildebrand, J. H. J. Am. Chem. Soc. 1949, 71, 2703.
9
1390 J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004

Donor-Acceptor Coupling in Precursor Complex to ET
A R T I C L E S
Table 2. Selected Geometric Parameters for the Neutral
Phenothiazine Donors and Their Cation Radicalsa
a
b
c
d
Rb
âc
γ
PHd
1.763
1.708
1.391
1.399
1.399
1.405
1.399
1.384
1.392
1.398
1.391
1.390
1.367
1.368
1.385
1.376
1.388
1.397
1.387
1.379
1.387
1.388
1.399
1.379
1.377
1.379
1.389
1.396
1.413
1.401
1.413
1.415
158.5
175.7
170.1
177.2
164.2
154.4
154.4 87.7
171.8 90.0
146.6 47/87 52/11
140.0 48.2 54.8
PH•+e
(PH)32+PHf 1.737
1.733
1.749
1.771
1.754
1.737
1.762
1.767
2+
Figure 2. (A) Crystal structure representation of the unit cell of (PH)3
-
2+
(PH) (PF6)2 showing the triplex (PH)3 and separate neutral donor. (B)
1
2+
Side view perspective of the triplex (PH)3
.
1•+g
2
coefficient of ꢀPC ) 760 M-1 cm-1 were obtained for eq 2 from
the slope and intercept (see Experimental Section). It is
noteworthy that the spectral behavior of the N-methyl analogue
was different, and no new absorption band was observed in
the NIR region upon incremental additions of N-methylphe-
nothiazine to the solution of PMe•+, even to high molar ratios
and at low (down to -80 °C) temperatures. We thus con-
cluded that the analogous (PMe/PMe•+) association was highly
limited, and the paramagnetic pimer was too weak to be detected
relative to that of the (PH/PH•+) association under the same
conditions.
2•+h
(1.720) (1.405) (1.369) (1.389) (165.3) (84.4) (8.7)
22+i
3
1.713
1.754
1.407
1.389
1.369
1.382
1.389
1.409
173.0 81/82 35/17
157.2 91.6
a Bond length in Å, angles in degrees, average bond lengths are presented
if aromatic ring in phenothiazine moieties are nonidentical. For complete
characterization, see Table S1 in the Supporting Information. b Dihedral
angle between the planes of side aromatic rings along the N-S axis. c Di-
hedral angle between the planes of phenothiazine and the bridging aromatic
ring. d From ref 26a. e From ref 26b. f Structural data for four independent
phenothiazine molecules; see text. g As SbF6- salt. h As CB11(CH3)12- salt.
In parentheses, the second phenothiazine center. i As SbCl6 salt.
II. Isolation and X-ray Structure of the Transient Precur-
sor Complex in Intermolecular ET. A. Isolation as a
Crystalline [1:1] Complex. Treatment of the pure phenothiazine
is appropriately described as an intermolecular (ternary) π-com-
plex of phenothiazine and two cation radicals (for details, see
the Experimental Section). As such, the triplex27 represents a
close structural analogue of the paramagnetic pimer28 in inter-
molecular self-exchange of phenothiazine donor/acceptor dyads
as described in eq 2.
III. Intramolecular ET between Bridged (P/P•+) Centers
in Mixed-Valence Cation Radicals. A. Synthesis of Bridged
Phenothiazine Donors and Their Mononuclear Models. The
phenothiazine mixed-valence donor 2 (2′) and its mononuclear
model 4 (see Table 3) were prepared from the lithium salt of
phenothiazine and the corresponding benzyl bromide in THF
at room temperature. The bridged donors 1 and 3 as well as
their mononuclear model 5 (Table 3) were synthesized by the
Ullman coupling of phenothiazine with the corresponding
iodobenzene derivatives at 220 °C, as described in the Experi-
mental Section.
cation radical salt PH•+PF6 with 4-fold phenothiazine donor
-
in 1,2-dichloroethane solution showed the diagnostic interval-
ence band at 1600 nm, the same as that shown in Figure 1.
Careful layering of this solution with n-hexane and refrigera-
tion at -30 °C for 2 weeks afforded well-formed dark brown
prisms, with the overall stoichiometric [1:1] composition of
(PH+PF6-)(PH). Indeed, the solid-state electronic spectrum of
this crystalline complex (in KBr pellet) bore a strong resem-
blance to the corresponding solution spectrum in Figure 1, with
the minor exception that the weak intervalence band in the
NIR region was slightly red-shifted (Figure S5), consistent
with previous comparisons of solid-state and solution spec-
tra.25 In an effort to isolate other crystalline salts of the tran-
sient intermolecular complex, we also prepared pure phenothi-
-
azine cation radical salts of SbCl6 and BF4-, but their
B. Electrochemical Generation of Mixed-Valence Cation
Radicals. Selective (one-electron) oxidations of the various
analogous treatment with free phenothiazine donor merely led
to microcrystalline powders unsuitable for X-ray crystallographic
analysis.
(27) For other comparative studies of 2:1 and 1:1 pimeric structures, see: (a)
Le Magueres, P.; Lindeman, S. V.; Kochi, J. K. Org. Lett. 2000, 2, 3567.
(b) We conclude from the bond distance changes and the opening of the
dihedral angle R that the effective charge on the central phenothiazine in
the triplex is roughly +1.0 and the asymmetric distribution is +0.7 and
+0.3 on the terminal phenothiazines (see Table 2, entries 3-5).
(28) (a) Note that the strong similarity of the solid-state spectrum in Figure S5
and the NIR band of the precursor complex in solution (Figure 1) supports
such a suggestion. (b) The 3.3 Å separation is similar to those published
previously for different complexes between cation and anion radicals and
their neutral precursor (e.g., in the 1:1 pimer of octamethylanthracene, which
is isoelectronic with phenothiazine).26b The planar moieties within such
associates lie atop one another (or somewhat shifted) with the interplanar
separation of 3.3 ( 0.3 Å which does not essentially depend on the
stoichiometric composition of the particular complex (1:1, 1:2, 2:1, etc).41
(c) In the [1:1] charge-transfer complexes between phenothiazine and
7,7,8,8-tetracyanoquinedimethane28d or 1,3,5-trinitrobenzene,28e the donor
and acceptor moieties also lie atop each other at the interplanar distance of
about 3.4 Å. (d) Toupet, L.; Carl, N. Acta Crystallogr., C 1995, 51, 249.
(e) Fritchie, C. J., Jr. J. Chem. Soc. A 1969, 1328.
B. X-ray Crystallography of the [1:1] Complex. The
ORTEP diagram of the unit cell in Figure 2 (left) shows that
phenothiazine exists in two discrete forms as (a) the molecular
triplex dication (PH)32+ and (b) the uncharged donor PH in the
equimolar ratio to constitute the overall [1:1] stoichiometry in
the crystalline sample. The bond lengths and angles (Table 2)
in the uncharged PH unit are identical to those of the free tub-
shaped donor determined independently.26 The stacked triplex
shown in Figure 2 (right) consists of cofacial (planar) phenothi-
azine units separated by a single distance of dD ) 3.3 Å, and it
(25) Lu¨, J.-M.; Rosokha, S. V.; Kochi, J. K. J. Am. Chem. Soc. 2003, 125, 12161.
(26) (a) McDowell, J. J. H. Acta Crystallogr., Sect. B 1976, 32, 5. (b) Uchida,
T.; Ito, M.; Kozawa, K. Bull. Chem. Soc. Jpn. 1983, 56, 577.
9
J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004 1391

A R T I C L E S
Kochi
Table 3. Oxidation Potentials of Mixed-Valence and Mononuclear
mixed-valence cation radical (relative to the dication plus donor)
with ∆E ) 3.3, 4.0, and 8.0 kcal/mol for 1•+, 2•+, and 3•+,
respectively.31 To explore the effects of this electronic interaction
on the spectral and structural properties of organic mixed-
valence systems, the bridged cation radicals were isolated as
crystalline salts (where possible) or prepared in situ (see
Experimental Section), and their spectral (UV-vis-NIR/ESR)
and structural (X-ray crystallography) properties examined are
as follows.
Donorsa
C. Intervalence Transitions in Mixed-Valence Cation
Radicals. The electronic spectra of the bridged (mixed-val-
ence) cation radicals 1•+, 2•+, and 3•+ were all characterized
by the presence of new (low-energy) absorption bands that
were singularly absent in the corresponding UV-vis spectra
of either (a) the mononuclear (model) cation radicals 4•+ and
5•+ or (b) the bridged dications 12+, 22+, and 33+, as listed in
Table 1.
a From reversible cyclic voltammograms measured at V ) 2 V s-1 in
dichloromethane. In parentheses: number of electrons transferred.
In the o-phenylene-bridged cation radical 3•+, the dis-
tinctive low-energy band shown in Figure 4A was cleanly
separated from the local bands and red-shifted to the NIR region
to closely approximate the intervalence charge-resonance band
at 1600 nm of the transient paramagnetic pimer observed in
the intermolecular association of phenothiazine with its cation
radical as illustrated in Figure 4A (see Experimental Section
for details). By comparison, the intervalence absorption band
of the p-phenylene-bridged cation radical 1•+ was significantly
blue-shifted to 910 nm and overlapped the local bands listed in
Table 1. However, the digital deconvolution of the vis-NIR
envelope via concentration variations (as described in the
Experimental Section) revealed the Gaussian-shaped compo-
nent shown in Figure 4B (inset) and listed in Table 1. Like-
wise, the intervalence band in the o-xylylene-bridged cation
radical 2•+ suffered more or less the same blue-shift, and the
successful deconvolution of the vis-NIR band envelope re-
vealed the diagnostic absorption band at 943 nm, as described
in Figure S6.
D. Intramolecular ET Rates in Mixed-Valence Cation
Radicals. The ESR spectrum of the phenothiazine redox center
(P•+) was characterized by three major lines corresponding to
the principal nitrogen hyperfine splitting further (partially) split
by aromatic hydrogens. The values of the hyperfine splitting
for the mononuclear models 4•+ and 5•+ identified in Table 4,
as well as the ESR line widths, were singularly unchanged in
dichloromethane solutions with the variation of temperature. On
the other hand, the mixed-valence cation radicals 1•+, 2•+, and
3•+ showed two distinctive behavioral patterns as the temper-
ature of the dichloromethane solution was progressively raised
from -90 to 30 °C in the following way:
D.1. Temperature-Dependent ESR Line Broadening in
Mixed-Valence Cation Radicals 1•+ and 2•+. Figure 5 (top)
shows the well-resolved ESR spectrum at -30 °C of the
p-phenylene-bridged cation radical 1•+, which underwent general
line broadening upon warming (+30 °C) and resulted in the
partial obliteration of the hydrogen hyperfine splittings, as
illustrated by the computer-simulated spectra in Figure 5 (right).
Figure 3. Initial positive scan cyclic voltammograms of the mixed-valence
donors 1, 2, and 3 including the ferrocene internal standard at 0.5 V.
phenothiazine donors in Table 3 to the relevant cation radi-
cals were initially examined by cyclic voltammetry. The phe-
nothiazine-containing donors 1, 2, and 3 (Figure 3) each
showed the initial (one-electron) oxidation to the mixed-valence
cation radical followed by a second (well-resolved) oxidation
to the dication as described in eq 3, where (br) represents the
molecular bridges illustrated in Chart 2, so that the potential
E2
{
P(br)P {E
\
1}P (br)P•+
} P(br)P2+
(3)
splitting ∆E ) E2 - E1 represents the energetics of the
disproportionation equilibrium (∆Gdisp ) - RT ln Kdisp) be-
tween the mixed-valence cation radical and the mixed-valence
dication.29,30 Accordingly, ∆E ) ∆Gdisp/F is a thermodynamic
quantity that can be directly related to the stabilization of the
electronic interaction between the (P/P•+) redox centers in the
(29) (a) Creutz, C. Prog. Inorg. Chem. 1983, 30, 1. (b) Evans, C. E. B.; Naklicki,
M. L.; Rezvani, A. R.; White, C. A.; Kondratiev, V. V.; Crutchley, R. J.
J. Am. Chem. Soc. 1998, 120, 13096.
(30) (a) Lindeman, S. V.; Rosokha; S. V.; Sun, D.-L.; Kochi, J. K. J. Am. Chem.
Soc. 2002, 124, 843. (b) Rosokha S. V.; Sun, D.-L.; Kochi, J. K. J. Phys.
Chem. A 2002, 106, 2283.
(31) See also Table 6, column 7.
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1392 J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004

Donor-Acceptor Coupling in Precursor Complex to ET
A R T I C L E S
Figure 4. Spectral changes in the NIR region attendant upon the addition of oxidant to the solution of ortho-phenylene-bridged phenothiazines 3
(A)and its para-phenylene-bridged analogue 1 (B). Concentrations: (A) 3 ) 2 mM; oxidant (from bottom to top at 800 nm) 0, 0.4, 0.8, 1.2, 1.6,
2.0, 2.4, 2.8, 3.2, 3.6, 4.0, 4.4, 5.0 mM. (B) 1 ) 2 mM, oxidant (from bottom to top at 800 nm) 0, 0.4, 0.8, 1.2, 1.6, 2.0, 2.6, 3.2, 3.8 mM. Note that
the low-energy NIR absorption grows until oxidant to 1 (or 3) ratio is less than 1:1 (solid lines) and decreases when concentration of the oxidant is
higher than that of 1 (or 3) (dashed lines). Insets: Gaussian deconvolution (dashed lines) of the mixed-valence cation radical spectra NIR range (thick, solid
lines).
Table 4. ESR Spectral Parameters of the Mixed-Valence Cation
Radicals and Their Mononuclear Models
hyperfine splitting constants (G)a
cation
radical
b
N
H
H (aromatic)
PH•+f
PMe•+f
1•+
6.55(1)
7.66(1)
7.04(1)
7.04(1)
3.52(2)
7.04(1)
7.04(1)
7.42(1)c
7.31(3)d
2.59(2), 1.25(2), 0.48(4)
2.17(2), 1.02(2), 0.70(2), 0.28(2)
1.41(6), 0.70(2)
1.99(2), 1.02(4), 0.28(2)
1.00(4), 0.50(8), 0.20(4)
1.99(2), 1.02(4), 0.28(2)
2.2(2), 0.90(2), 0.35(4)
2•+
3.84(2)e
3.84(2)e
3•+
4•+
5•+
a
b
In parentheses: number of splitting nuclei. As indicated in footnotes
c
d
e
f
2
c-e. HN. HCH
.
HCH
.
From ref 18.
3
Figure 5 also includes the first-order rate constants (kET) for
intramolecular electron exchange in eq 4 of the mixed-valence
cation radical 1•+ that is typically obtained from the fit of the
experimental ESR spectrum to that calculated with the aid of
the ESR-EXN program.32
Similarly, the ESR spectrum of the ortho-xylylene-bridged
cation radical 2•+ (see Chart 2) was readily simulated at low
temperature with essentially the same hyperfine splittings
pertinent to the ESR spectrum of its mononuclear model 4•+
(Table 4 and Figure S7), but upon warming only the ESR
spectrum of the mixed-valence cation radical 2•+ showed
noticeable linebroadening (Figure S8). The latter was assigned
Figure 5. Temperature-dependent ESR line broadening of the mixed-
valence cation radical 1•+ (left) in comparison with the computer-simulated
spectra (right) based on first-order electron exchange.
(32) (a) Heinzer, J. Quantum Chemistry Program Exchange 209, as modified
by Petillo, P. A. and Ismagilov, R. F. We thank Prof. S. F. Nelsen for
providing us with a copy of this program. (b) The limited line broadening
and rather small changes in kET over the 120° temperature range in
dichloromethane in Figure 5 was not substantially changed in 1,2-
dichloroethane at its higher temperature limit (kET ) 4 × 109 s-1 at +60
°C). Thus, we were unable to attain the requisite temperatures (and enhanced
rates of kET ≈ 1 × 108 s-1) at which the diagnostic alternating line width
effects would be observed in the dynamic simulation of the ESR spectra,
as we previously showed in a related mixed-valence system.36 We thank a
reviewer for pointing out the desirability for such an experimental
verification.
to dynamic electron exchange, and the fits of the experimental
spectra with those calculated with the aid of the ESR-EXN
program32 afforded the first-order rate constants for intramo-
lecular ET in eq 5 as kET ) 2 × 107 s-1 at +30 °C and kET
e
2 × 106 s-1 at -60 °C.
9
J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004 1393

A R T I C L E S
Kochi
D.2. Temperature-Independent but “Doubled” ESR Spec-
trum of 3•+. The ESR spectrum of ortho-phenylene-bridged
cation radical 3•+ consisted of five major lines (Figure 6, left),
corresponding to hyperfine splitting by 2 equiv nitrogen nuclei,
but otherwise with no resolved proton splittings. Computer
simulation shown in Figure 6 (right) verified the spectral
assignment derived from twice the number of nitrogen splittings
with roughly half the coupling constants relative to those found
in the mononuclear model 5•+ and in the mixed-valence cation
radical 1•+ and 2•+ (Table 4). Such an increased number and
decreased splittings of hyperfine lines were characteristic of
other dimer cation radicals in which either the unpaired electron
is completely delocalized over both redox centers or electron
exchange in eq 6 is too fast to be resolved on the ESR time
scale with half-life τESR < 10-9 s,33 i.e.,
Figure 6. Comparison of the experimental (left) and computer-simulated
(right) ESR spectra of the mixed-valence cation radical 3•+ of the ortho-
phenylene-bridged donor.
redox centers to θ ) 172°, which is the same as that in PH•+.
There are also significant changes in the N-C, S-C, and C-C
bond lengths accompanying the oxidation of the mixed-valence
donor 1 to its cation radical (Table 2) to suggest a significant
contribution from resonance structures A and B pertinent to the
pair of partially oxidized phenothiazine moieties shown below.35
Moreover, the latter must be immeasurably fast even at -80
°C since the ESR spectrum was singularly unchanged as the
solution was allowed to warm incrementally over a 110° range
to ambient temperature.
D.3. Comparative ESR Behavior of Mixed-Valence Dicat-
ions. The bridged-dependent intermolecular interaction between
phenothiazinyl redox centers was also shown in the ESR
characteristics of the mixed-valence dications 12+, 22+, and 32+
.
Furthermore, it is important to note that both the mixed-
valence donor 1 as well as its cation radical 1•+ possess
crystallographic centers of symmetry so that the redox centers
(P/P) and (P/P•+) are pairwise equivalent. In particular, the
results in Table 2 are consistent with partial (positive) charge
that is equally distributed between both phenothiazine redox
centers in the mixed-valence cation radical 1•+, in accord with
the dynamic equilibrium in eq 3.35a
B. Structures of o-Xylylene-Bridged Mixed-Valence Sys-
tems. Mixed-valence systems such as 2 that incorporate the
ortho-xylylene bridge are conformationally flexible36 and often
not readily crystallized. Nonetheless, we were able to examine
the parent donor 2, its cation radical 2•+, and its dication 22+ as
single crystals suitable for X-ray. The structures of 2, 2•+, and
22+ show the same trend in bond length and angle changes as
those described for the p-phenylene-bridged analogues in Table
2. The ORTEP diagram of the mixed-valence donor 2 in Figure
8A presents the conformation with partial overlap of the two
(tub-shaped) phenothiazine redox centers (resulting from dif-
ferent rotations about the pair of methylene bonds; Table 2)
and center-to-center separation of dD ≈ 5.2 Å. One-electron
oxidation to the mixed-valence cation radical results in the
planarization of only one phenothiazine center (the other
maintaining its tub shape), but otherwise, 2•+ retains the overall
conformation of parent donor, as shown in Figure 8B. Two-
Thus, the ESR parameters for the p-phenylene- and o-xylylene-
bridged dications (Figure S11) were essentially the same as those
in the corresponding mixed-valence cation radicals 1•+ and 2•+,
to reveal 12+ and 22+ as de facto dication diradicals with (more
or less) weakly interacting (P•+/P) centers.34 By strong contrast,
the o-phenylene-bridged dication 32+ was ESR silent, to reveal
3
2+ as a diamagnetic dication25 with strongly spin-coupled (P•+/
P•+) centers reminiscent of the strong electronic interaction
between (P/P•+) centers necessary to describe the ultrafast
electron exchange in 3•+ (eq 6).
IV. Structure Analysis of Mixed-Valence Donors and
Cation Radicals. A. X-ray Structure Analyses of para-
Phenylene-Bridged Systems. The ORTEP diagram of the
mixed-valence donor 1 in Figure 7A shows the two (tub-shaped)
para-phenothiazinyl substituents to be arranged mutually per-
pendicular to the plane of the connecting phenylene bridge so
that 1,4-substitution leads to nearly coplanar phenothiazine redox
centers. Upon one-electron oxidation, the mixed-valence cation
radical 1•+ retains the same overall conformation, as shown in
Figure 7B. In the neutral donor, the phenothiazine redox centers
are both folded along the S-N axis with the dihedral angle of
θ ) 154°, which is the same as that found in the free
phenothiazine donor itself. Oxidation to the cation radical 1•+
results in the significant planarization of both phenothiazine
(33) (a) Gerson, F.; Kaupp, G.; Ohya-Nishiguchi, H. Angew. Chem., Int. Ed.
Engl. 1977, 16, 657. (b) Wartin, A. R.; Valenzuela, J.; Staab, H. A.;
Neugebauer, F. A. Eur. J. Org. Chem. 1998, 139, 9. (c) Lau, W.; Kochi,
J. K. J. Org. Chem. 1986, 51, 1801.
(35) (a) The equivalency of two phenothiazines in the X-ray structure of 1•+
may also result from the crystallographic disorder of P•+/P redox centers.
(b) For a discussion of this crystallographic point as it applies to a related
aromatic redox center, see Le Magueres, P. et al. in ref 22a and Lindeman
et al. in ref 30a.
(34) (a) This conclusion accords with that of Okada et al.34b who described 12+
as a triplet (ground-state) dication diradical (or as a nearly degenerate
singlet/triplet ground state).34b (b) Okada, K.; Imakura, T.; Oda, M.; Murai,
H. J. Am. Chem. Soc. 1996, 118, 3047.
(36) Sun, D.-L.; Rosokha, S. V.; Lindeman, S. V.; Kochi, J. K. J. Am. Chem.
Soc, 2003, 125, 15950.
9
1394 J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004

Donor-Acceptor Coupling in Precursor Complex to ET
A R T I C L E S
Figure 7. Molecular structures of the para-phenylene-bridged mixed-valence donor (A) and its cation radical (B) showing the same pair of tub/tub-shaped
-
phenothiazine redox centers in 1, but planar/planar in 1•+ (as SbCl6 salt).
Figure 8. Equivalent conformations of the ortho-xylylene-bridged mixed-valence donor (A) and its corresponding cation radical (B) showing roughly the
-
same cofacial disposition of the phenothiazine redox centers which are both tub/tub-shaped in 2, but planar/tub in 2•+ (as CB11(CH3)12 salt).
electron oxidation to the dication 22+ is accompanied by a
sizable rotational change to a more trans-like conformation
(Figure S12) with two (planar) phenothiazines more or less
coplanar in the manner reminiscent of that in the p-phenylene
analogue 1 established in Figure 7A. The changes in the in-
ternal geometries of the phenothiazinyl centers accompanying
two-electron oxidation to 22+ were similar to those in Table 2
for the p-phenylene-bridged pair (vide supra). Such struc-
tural changes indicate that the dication 22+ consists of a pair
of discrete (equivalent) phenothiazinyl redox centers that are
rather weakly interacting in accord with the ESR analysis (vide
supra).
C. X-ray Structure of the o-Phenylene-Bridged Donor. The
structurally rigid mixed-valence donor 3 was obtained as a single
crystal, and the ORTEP diagram (Figure S9) identifies the pairs
of cofacial phenothiazine centers separated by a (center-to-
center) distance of dD ) 3.3 Å (Table 2) that slightly deviates
from a parallel arrangement by a dihedral angle of θ ) 40°.
Although we were able to isolate both the mixed-valence cation
radical 3•+ and the dication 32+ as microcrystalline powders,
we were unable to grow single crystals suitable for X-ray
crystallographic analysis.
are represented by phenothiazine (PH) and phenothiazine cation
radical (PH•+), respectively. The corresponding first-order
process (to obviate diffusion) is then represented in this study
by mixed-valence systems P(br)P•+ in which a pair of phe-
nothiazine redox centers are interlinked by the variety of
molecular bridges (br) illustrated in Chart 2. We now find that
the direct mechanistic interrelationship between intermolecular
and intramolecular ET is made via diagnostic transient (optical)
changes, as follows.
I. Common Observation of Intervalence Absorptions in
Both Intermolecular and Intramolecular ET. The consistent
appearance of the new (unique) absorption band in various (PH/
PH•+) mixtures in Figure 1 arises from the intervalence transition
in the transient [1:1] complex or “pimer” that is spontaneously
formed by the intermolecular association according to eq 2. Such
a near-IR band has been previously associated with charge-
resonance transition of cofacially oriented aromatic donor/
acceptor dyads21,22 which are structurally represented in this
phenothiazine study by the ORTEP diagram in Figure 2.
The interconnection of phenothiazine (P/P•+) redox centers
represented by mixed-valence cation radicals 1•+, 2•+, and 3•+
in Table 1 also results in diagnostic near-IR absorption bands
that strongly depend on the nature of the molecular bridge. To
relate these intramolecular intervalence absorption bands with
the charge-resonance absorption of the intermolecular (pimer)
intermediate, let us first describe how the latter plays a critical
kinetics role in the mechanism of intermolecular ET.
Discussion
Intermolecular ET is observed as overall second-order kinetics
of freely diffusing electron donors and acceptors, which in the
case of the simple self-exchange process pertinent to this study
9
J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004 1395

A R T I C L E S
Kochi
Table 5. Comparison of Experimental (from ESR data) and
Calculated Intramolecular Electron-Transfer Rate Constant in
Mixed-Valence Cation Radicals and Intermolecular Self-Exchange
Table 6. Estimation of the Electronic Coupling Elements in
Organic (Mixed-Valence) Cation Radicals and Cation Radical
Pimer via Mulliken-Hush Formalism (from the Intervalence Band)
and Cyclic Voltammetry Data
∆G*,a kcal/mol
kΕΤ (+30 °C), s -1
a
b
b
c
rDA
νIV
∆νIV
ꢀ
H
∆E
V
H
TD
IV
MVCR
λ, kcal/mol
theora
exptlc
theorb
exptld
MVCR
Å
103 cm-1 103 cm-1 103 M-1 cm-1 103 cm-1
103 cm-1
•+
(PH)2
1•+
17
30
31
16
2.5
6.4
6.3
1.2
2.6
7.2
7.2
1.2 × 1010e
0.5 × 1010f
2 × 107
2 × 107
>109
•+
(PH)2
1•+
3.3
8.6
5.2
3.3
5.8
10.3
10.6
5.6
2.5
3.2
4.8
3.0
0.76
0.86
0.36
2.5
0.66
0.40
0.53
1.28
3 × 107
0.17
0.14
0.34
2.66
2.45
2.77
2•+
3 × 107
2•+
3•+
1.3 × 1011
3•+
a From ∆G* ) (λ - 2HIV)2/(4λ) based on λ ) νIV and HIV from Table
a Separation between the centers of phenothiazinyl moieties. b Bandwidth
at half-height. c Calculated with Mulliken-Hush expression (eq 8). d Cal-
culated from F∆E ) ∆Gdisp ) 2H2/λ
6. b From kET
)
1012 exp(-∆G*theor/RT), unless otherwise noted.
c Estimated from temperature dependence of experimental rate constant,
(2 kcal/mol. d From ESR line broadening. e Diffusion-corrected second-
order rate constant of self-exchange kse calculated from 1/kse ) 1/kdiff
+
1/(KPCkET) at 25 °C. f Second-order rate constant of self-exchange evaluated
from concentration-dependent ESR line broadening at 25 °C.
heights, respectively (in cm-1), of the absorption band, ꢀ is the
molar extinction coefficient at the absorption maximum (in M-1
cm-1), and rDA is the effective ET distance (in Å). An important
point in such an analysis of the phenothiazine redox dyad is
the proper choice of the separation parameter rDA, in other
words, the structural characterization of the intermolecular pimer
II. The Mechanism of Intermolecular ET via the Precur-
sor Complex of Phenothiazine Redox Dyads. The generalized
(self-exchange) kinetics between an aromatic donor and its
cation radical must include the generic precursor complex,2,37
and such an ET mechanism for phenothiazine oxidation-
reduction is represented by:
•+
(PH)2 in eq 2. In the absence of the X-ray structure of the
[1:1] precursor complex, we based our analysis on the triplex
shown in Figure 2 as the isolable close relative since it is the
crystallizable (equimolar) form out of solution. Although the
triplex includes a single neutral donor with a pair of cation
radicals, the initial step in the formation of this [2:1] complex
is preceded by a prior [1:1] association, and we take half of the
triplex to be a reasonable approximation for rDA ) 3.3 Å as the
cofacial separation of (P/P•+) redox centers in the precursor
complex.28,41
Utilization of eq 8 with the spectral characteristics of the near-
IR absorption band in Figure 1 and the separation distance of
rDA ) 3.3 Å leads to the value of HDA ) 6.6 × 102 cm-1 for
the electronic coupling element within the precursor complex
for the (PH/PH•+ ) self-exchange (Table 6).42
KPC
ket
9
PH•+ + PH
8 [PH•+, PH]
8 [PH, PH•+] a PH + PH•+
(7)
where KPC is the intermolecular association constant of the
precursor complex and ket is the first-order exchange rate within
the precursor complex, herein described as the pimer. The
independent evaluations of the association constant as KPC ) 5
M-1 (see eq 2), together with the first-order rate constant
theoretically evaluated from the intervalence band as ket ) 1.4
× 1010 s-1 (vide infra), lead to the second-order rate constant
for intermolecular ET as kSE(theor) ) 1.2 × 1010 M-1 s-1 38
.
The corresponding experimental second-order rate constant
kSE(exptl) obtained directly from the ESR line broadening
experiments is also included in Table 5 (column 6). It is thus
noteworthy that the theoretical prediction (column 5) based on
the generalized mechanism for intermolecular ET according to
eq 7 is within acceptable limits of the experimental results.
III. Electronic Coupling in the Precursor Complex (Pimer).
The transient character of the precursor complex in intermo-
lecular ET largely precludes a direct (structural) examination
of the electronic coupling element HDA that is required for
quantitative evaluation of the activation barrier according to eq
1. Thus, let us now turn to the charge-resonance absorption band
at 1600 nm that is observed in the intermolecular pimer (Figure
1) and simply relate it to the analogous absorptions in mixed-
valence systems (Figure 4). Using the Mulliken formalism,39
IV. Evaluation of the Electronic Coupling Element in
Mixed-Valence Systems. A. The para-Phenylene-Bridged
Cation Radical 1•+. The application of the Mulliken-Hush
formalism (eq 8) to the mixed-valence system 1•+ in Table 6
follows from the earlier studies of Nelsen, Lambert, and co-
workers43,44 who employed the same structurally rigid para-
(40) (a) Hush, N. S. Z. Electrochem. 1957, 61, 734. (b) Hush, N. S. Trans.
Faraday Soc. 1961, 57, 557. (c) Hush, N. S. Prog. Inorg. Chem. 1967, 8,
391. (d) Hush, N. S. Electrochim. Acta 1968, 13, 1005.
(41) (a) Note that previous studies showed that the separation dD in [2:1]
complexes is close to that in the corresponding [1:1] associations.41c,d (b)
Strictly speaking, in extended (organic) redox systems, the separation
parameter in eq 8 is difficult to evaluate precisely for two principal
reasons: (i) the “distance” refers to the separation between two hypothetical
(diabatic) states3a,41e and (ii) the “charge” is highly diffuse. In this study,
we utilize the experimentally accessible X-ray structures to approximate
the distance between centroids, which in the case of phenothiazines is
arbitrarily chosen to lie between N/S atoms. In an ongoing collaboration
with M. D. Newton, preliminary results indicate that the calculated values
Hush showed that the electronic coupling element (HDA
)
•+
between redox centers in mixed-valence complexes can be
estimated directly from the intervalence absorption bands as:40
of rDA in the pimer (PH)2 is close to that based on X-ray studies. (c)
Hanson, A. W. Acta Crystallogr. 1968, B24, 773. (d) Fritchie, C. J.; Arthur,
P., Jr. Acta Crystallogr. 1966, 21, 139. (e) See also: Nelsen, S. F.; Newton,
M. D. J. Phys. Chem. 2000, 104, 10023.
HIV ) 0.0206(νmax∆ν1/2ꢀ)1/2/rDA
(8)
(42) The two-state model for ET is based on orthogonal initial and final diabatic
states. The extent to which there is orbital overlap between cofacial redox
centers violates this restriction, but only strictly speaking. What is not yet
known is the degree to which even a modicum of orbital overlap completely
violates the applicability of the two-state model, and it thus remains to be
seen (by further studies such as this) as to how far this restriction can be
further tested with other (orbital) combinations.
(43) (a) Nelsen, S. F.; Adamus, J.; Wolff, J. J. J. Am. Chem. Soc. 1994, 116,
1589. (b) Nelsen, S. F.; Trieber, D. A.; Wolff, J. J.; Powell, D. R.; Rogers-
Crowley, S. J. Am. Chem. Soc. 1997, 119, 6873. (c) Nelsen, S. F.; Ramm,
M. T.; Wolff, J. J.; Powell, D. R. J. Am. Chem. Soc. 1997, 119, 6863. (d)
Nelsen, S. F.; Ismagilov, R. F.; Powell, D. R. J. Am. Chem. Soc. 1997,
119, 10213.
where νmax and ∆ν1/2 are the maximum and full-width at half-
(37) Ganesan, V.; Rosokha, S. V.; Kochi, J. K. J. Am. Chem. Soc. 2003, 125,
2559.
(38) For the detailed description of intermolecular ET kinetics, see the following
discussion.
(39) (a) Mulliken, R. S. J. Am. Chem. Soc. 1952, 74, 811. (b) Mulliken, R. S.
J. Phys. Chem. 1952, 56, 801. (c) Mulliken, R. S.; Person, W. B. Molecular
Complexes; Wiley: New York, 1969.
9
1396 J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004

Donor-Acceptor Coupling in Precursor Complex to ET
A R T I C L E S
phenylene bridge in various mixed-valence cation radicals with
redox centers derived from different N-centered donors, and our
later study of intramolecular electron exchange between ben-
zenoid redox centers mirrored the earlier results.30,36 Such
impressive agreements thus serve as the first step in a test of
the Mulliken-Hush two-state model to correctly predict the
electronic coupling element in the mixed-valence cation radical
1•+ containing a pair of (more or less) planar phenothiazine
redox centers. As such, the characteristics of the NIR absorption
band in Table 1 (third entry), together with the separation
parameter of rDA ) 8.6 Å obtained from X-ray crystallographic
data, leads to the value of HDA ) 4.0 × 102 cm-1 from eq 8
based on the assignment of the p-phenylene-bridged cation
radical 1•+ to the Class II category of Robin-Day mixed-valence
systems.45,46 The latter classification also allows the reorganiza-
tion energy (λ) to be directly evaluated from the intervalence
absorption band, i.e., νIV ) λ, as listed in Table 6 (third column).
electronic interaction between (P/P•+) redox centers results in
the resonance stabilization of the mixed-valence state that is
inherent to the driving force for the disproportionation equilib-
rium,29 e.g.: the free-energy change of which is given by ∆Gdisp
Kdisp
P(br)P•+ + P(br)P•+
8 P(br)P2+ + P(br)P
(9)
) F∆E1/2, where ∆E1/2 ) E1/2(2) - E1/2(1) as described in eq
3. Although the free energy of disproportionation ∆Gdisp is
determined as the sum of several factors, the contribution from
the resonance stabilization of the mixed-valence cation radical
is generally the major component.51 As such, the electronic
coupling element can be evaluated thermodynamically from the
reversible oxidation data as8 HTD ) (λ∆Gdisp/2)1/2, and the values
of the electronic coupling element obtained from the cyclic
voltammetric measurements in Figure 3 are listed in Table 6
(column 8) for the mixed-valence cation radicals 1•+, 2•+, and
3•+. Although such a thermodynamics analysis represents the
upper limit to the effective electronic coupling element,51,52 the
significant discrepancies between the CV-based values of HTD
(column 8) and the spectral-based values of HIV (column 6)
raise a question as to the applicability of the Mulliken-Hush
(two-state) formalism to reliably predict the electronic coupling
element from the intervalence absorption bands in mixed-valence
cation radicals (1•+, 2•+, and 3•+) and in the intermolecular pimer
B. The ortho-Xylylene-Bridged Cation Radical 2•+. The
conformationally flexible mixed-valence cation radical 2•+ has
the potential to juxtapose the pair of (P/P•+) redox centers in
the cofacial arrangement akin to that extant in the intermolecular
pimer shown in Figure 2.47 However, the extended and distinctly
nonplanar phenothiazine at one redox center is apparently too
large to accommodate such an intimate (face-to-face) arrange-
ment of both (P/P•+) redox centers, and a compromise is struck
in the stable conformational structure shown in Figure 8B, in
which a separation distance of rDA ) 5.2 Å is evaluated.48 This,
together with the analogous application of Mulliken-Hush
formalism in eq 7 to the intervalence absorption band of 2•+ in
Table 1 (fifth entry), leads to HDA ) 5.3 × 102 cm-1 for
electronic coupling element and the reorganization energy of λ
(PH)2 .
•+ 53 Accordingly, we now turn to the earlier approach of
Newton, Nelsen, and co-workers,54 who addressed this funda-
mental problem by the direct comparison of the predicted rates
of intermolecular ET based on HIV from the Mulliken-Hush
treatment with the experimental rates obtained independently,
as follows.
) 10.6 × 103 cm-1
.
V. Testing the Two-State Model for Intramolecular and
Intermolecular ET between Phenothiazine Redox Centers.
A. Intramolecular ET in Mixed-Valence Cation Radicals.
The intramolecular rate constant can be evaluated within the
Marcus-Hush formalism as:2
C. The ortho-Phenylene-Bridged Cation Radical 3•+. The
direct attachment of the redox centers to an o-phenylene bridge
as in the structurally rigid mixed-valence cation radical 3•+
juxtaposes the (P/P•+) centers at a separation distance of rDA
) 3.3 Å (with a tilt of θ ) 40°).49 Together with the highly
red-shifted intervalence absorption band to 1700 nm (Table 1),
the application of Hush eq 850 leads to HDA ) 1.28 × 103 cm-1
for the electronic coupling element and the reorganization energy
of λ ) 5.6 × 103 cm-1 that is surprisingly close to that of the
intermolecular pimer (see Table 5 column 2).
kET ) κνn exp(-∆G*/RT)
(10)
where κ is the electronic transmission coefficient, νn is the
nuclear vibration frequency related to ET, and ∆G* is the
activation free energy for ET. When the electronic coupling is
D. Alternative (Thermodynamics) Estimation of the Elec-
tronic Coupling Element. The electronic interaction between
a pair of redox centers in a mixed-valence systems can be
alternatively estimated by an electrochemical method. Thus, the
(50) (a) Although 3•+ may appear to be delocalized on the ESR time scale of τ
≈ 10-9 s, we tentatively conclude that it falls into the Robin-Day Class II
category based on the solvent dependence of the intervalence band as seen
by the blue-shift with increasing solvent polarity as described in Table S1.
(b) A reviewer has suggested that the intervalence bandwidth of 3•+ (∆ν1/2
) 3.0 × 103 cm-1) is less than the theoretically predicted values for Class
1/2
(44) (a) Lambert, C.; Noll, G. J. Am. Chem. Soc. 1999, 121, 8434. (b) Holzapfel,
M.; Lambert, C.; Selinka, C.; Stalke, D. J. Chem. Soc., Perkin Trans. 2
2002, 1553.
II,40 i.e., ∆ν1/2 ) (2300νIV
)
) 3600 cm-1. However, a discrepancy of
600 cm-1 is not uncommon (see: Elliot et al. in ref 54). (c) Even if this
were so, our basic conclusions would remain unchanged since the electronic
coupling element for Class III would be roughly twice as large (i.e., HIV
) hνIV/2 ) 2.8 × 103 cm-1), and the reorganization energy would be less
(not greater) than the maximum values listed in Tables 5 and 6.
(51) Note that HTD evaluated from the electrochemical data is expected to
represent an upper limit to the intrinsic electronic coupling element because
of the neglect of the other energy terms.36,52
(45) The value of rDA as estimated from molecular structure of 1•+ is very close
to the distance between the spin centers in dication diradical 12+ as
determined by Okada et al.34b from its ESR (triplet) spectrum.
(46) (a) The mixed-valence cation radical 1•+ is assigned to the Robin-Day Class
II category46b based on the ESR characteristics showing electron localization
of the unpaired electron on a single phenothiazine redox center, and the
same applies to the o-xylylene-bridged cation radical 2•+. Furthermore, the
values of HAD < λ/2 in Table 6 support the assignment of these systems
to Class II. (b) Robin, M. B.; Day, P. AdV. Inorg. Chem. Radiochem. 1967,
10, 247.
(52) A reviewer has also indicated that the correlation between ∆Gdisp and Hab
is generally weaker for the organic intervalence compounds with aromatic
redox centers (due to small solvation difference between dication and cation)
than for the usual mixed-valence coordination compounds.
(47) For such a syn conformation in the analogous o-xylylene-bridged cation
radical with benzenoid redox centers, see Sun, D.-L. et al. in ref 36.
(48) It is important to note that the configuration of the two phenothiazine centers
in 2, 2•+, and 22+ systematically change from tub/tub, tub/planar, and planar/
planar, respectively. See text for the mechanistic implications of such
structural changes in the phenothiazine redox centers.
(53) Since the MHS (two-state) model requires the diabatic states to be
orthogonal,2,8 the orbital overlap that may exist in pimer (PH)2•+ and mixed-
valence cation radical 2•+ and 3•+ may necessitate some correction of the
parameters obtained via eq 8.
(54) For previous examples of the application of such a test, see: Elliot, C. M.;
Derr, D. L.; Matyushov, D. V.; Newton, M. D. J. Am. Chem. Soc. 1998,
120, 11714, and Nelsen and co-workers in ref 43.
(49) Compare with the ORTEP structure in Figure S10.
9
J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004 1397

A R T I C L E S
Kochi
energy in Table 5 is ∆GET ) 2.5 kcal mol-1. This value
compares quite favorably with the experimentally measured
values of the activation barrier Ea ) 2.2 kcal mol-1 obtained
from the temperature-dependent ESR line widths.58
q
sufficiently strong, as given in Table 6, κ can be taken as unity
(i.e., adiabatic ET), and the activation barrier is given by
Marcus-Hush eq 1. The theoretically predicted activation free
energies ∆G*(theor) evaluated in this manner from the reor-
ganization energy (λ) and the electron coupling element (HIV)
in Table 5 show consistently reasonable agreements with the
experimental values derived from the temperature dependence
of the ET rate constant evaluated by ESR (line broadening)
measurements as ∆G*(exptl) in column 4. The same reasonable
agreement is also observed in Table 5 (columns 5 and 6)
VI. Electronic Effects of Strong Donor-Acceptor Coup-
ling on Intermolecular and Intramolecular ET. Direct com-
parison of theoretically predicted and experimental values of
activation barriers and ET rates between (P/P•+) centers
indicates that Marcus-Hush eq 1, together with the two-state
Mulliken-Hush eq 8, provides a suitable description of
intermolecular and intramolecular ET rates when strong elec-
between the predicted rate constant kET(theor) that is based on
55
∆G*(theor) with νn ) 1012 s-1
and the experimental rate
•+
tronic couplings in the intermolecular pimer (PH)2 and the
mixed-valence cation radicals P(br)P•+ are taken into account.
It is particularly noteworthy that the electronic couplings ob-
tained from the intervalence (optical) transitions in Table 6 thus
appear to be meaningful and reasonably accurate for (P/P•+)
interactions in the intermolecular pimer and in the mixed-val-
ence cation radical. If so, we now inquire as to what kind of
mechanistic insight may be gained from an inquiry into the ET
parameters listed in Table 6. For example, the values of the
electronic coupling element evaluated by the Mulliken-Hush
constant kET derived from ESR line-broadening measurements
for both 1•+ and 2•+. We take this convergence to constitute a
valid test for the reliable evaluation of the electronic coupling
element via the Mulliken-Hush analysis of the intervalence
absorption band.56 Since the proximal arrangement of P/P•+ in
the o-xylylene-bridged cation radical 2•+ is reminiscent of that
extant in the intermolecular pimer taken in Figure 2, let us also
apply the Mulliken-Hush analysis to this transient intermediate
as it applies to the precursor complex in intermolecular ET.
B. Intermolecular ET via the Precursor Complex. The
direct observation of the charge-resonance (NIR) band in the
intermolecular association of the free phenothiazine donor (PH)
and its cation radical (PH•+) in Figure 1 leads (based on
Mulliken-Hush analysis) to the electronic coupling element HIV
) 6.6 × 102 cm-1 and the other parameters listed in Table 6
(entry 1) for the pimeric precursor complex (PH)2•+. Applying
the Marcus-Hush methodology presented in eq 8, we evaluated
the intramolecular electron exchange within the precursor
complex as ket ) 1.4 × 1010 s-1. According to the mechanistic
pathway in Scheme 1 (eq 7), the theoretically predicted second-
order rate constant for phenothiazine self-exchange includes the
precursor complex and is given by k2 ) KPCket ) 7 × 1010
M-1 s-1, when KPC ) 5 M-1, as evaluated in eq 2. Since this
self-exchange is close to the diffusion-controlled limit, explicit
correction for diffusion must be taken into account as kSE(theor)
) k2kdiff/(k2 + kdiff) ) 1.2 × 1010 M-1 s-1, where kdiff ) 1.5 ×
1010 M-1 s-1 in dichloromethane at 25 °C.57 This theoretically
predicted value of second-order rate constant for the self-
exchange is included in Table 5 (column 5) and compares
favorably with the experimental rate constant of kSE(exptl) )
0.5 × 1010 M-1 s-1 in column 6, especially if due cognizance
is taken of the uncertainty in our evaluation of the preexponential
factor.55
•+
procedure for the intermolecular pimer (PH)2 is comparable
to that in the o-xylylene-bridged cation radical 2•+, but the ET
reorganization energy is substantially lower than that for 2•+.
Such a divergence may be related to the somewhat different
arrangement of phenothiazine moieties in (PH)2•+ in comparison
with that presented in Chart 2, and the strong electronic coupling
of the cofacial (P/P•+) redox centers in the intermolecular pimer
(see Figure 2) may arise from incomplete solvation and resultant
decrease in the outer-sphere reorganization energy.59 By contrast,
such a solvent restriction is less unfavorable in the partially
overlapped (P/P•+) centers in 2•+, and the larger interplanar
separation could result in increased solvation of the mixed-
valence cation radical relative to that in the “tight” intermo-
lecular pimer. Such a tentative suggestion is also supported by
a comparison of the p-phenylene-bridged cation radical 1•+ and
the o-phenylene-bridged analogue 3•+, since the (P/P•+) redox
centers in 1•+ are significantly separated and lead to values of
HIV and λ that are similar to those in 2•+. On the other hand,
q
(58) The activation free energy ∆GEFF measured from the temperature
q
q
dependence of the self-exchange rate constant is: ∆GEFF ) ∆HEFF
-
q
R∆SEFF ) 1.5 + 2.7 ) 4.2 kcal/mol at 295 K. This effective value is
determined as the sum of the free energy of activation of ET (∆GETq),
precursor complex formation (∆GPC ) -RT lnKPC), and a term related to
the temperature dependence of diffusion ∆Gdiffq (since reactions are close
q
q
to the diffusion-controlled limit). That is, ∆GEFF ) ∆GET + ∆GPC
+
)
∆Gdiffq. From the experimentally determined: ∆GEFF ) 4.2 and ∆GPC
q
To circumvent any ambiguity in νn, the theoretical prediction
can be alternatively tested by the direct comparison of the
activation energies. Thus, the theoretical barrier predicted in
eq 1 from the electronic coupling element and the reorganization
-0.9, and taking into account the activation energy related to diffusion
(which is: ∆Gdiff ≈ 2-3 kcal/mol58b), the experimental barrier for ET
q
q
q
q
can be estimated as: ∆GET (exptl) ) ∆GEFF - ∆GPC - Gdiff ) 4.2 -
(-0.9) - 2.5 ) 2.6 kcal/mol, which agrees reasonably with the theoretical
prediction from the Mulliken-Hush analysis: ∆GETq(theor) ) 2.5 kcal/
mol. Note, however, that such a close coincidence may be somewhat
fortuitous, since the accurate comparison requires the more rigorous estimate
of diffusion effects. (b) Calvert, J. G.; Pitts, J. N., Jr. Photochemistry;
Wiley: New York, 1966; p 627.
(55) Since the electron-transfer self-exchange of organic cation radicals involve
numerous molecular (∼500-3000 cm-1) and solvent (∼10-100 cm-1
)
vibrational modes, the pre-exponential factor νn ) (Σνi2λi/Σλi)1/2, as
described by Sutin,2 is difficult to rigorously calculate from the available
data. Thus, for this study, we have simply taken νn to be uniformly 1012
s-1, the same value as previously used for the description of ET in
phenylene-bridged organic mixed-valence cation radicals30 and in the
kinetics evaluation of the intermolecular anion radical self-exchange.37
(56) The ability of the two-state model to utilize the intervalence absorption
bands to correctly predict the electron-transfer rates of mixed-valence cation
radicals 1•+-3•+ and (PH•+/PH) self-exchange underscores its utilitarian
value for further use provided that due cognizance is presently taken of
the rigorous definitions of the separation parameter and the pre-exponential
factor for reliable computations of the Mulliken-Hush electronic coupling
element.
(59) In classical Marcus theory, reactants are surrounded by solvent that are
rearranged to accommodate ET. The solvent (outer-sphere) reorganization
is: λout ) e2(1/Dop - 1/Ds)(1/2a1 + 1/2a2 - 1/r), where e is the charge
transferred, Dop and Ds are the optical and static dielectric constants of
medium, a1 and a2 are the radii of reactants, and r is the distance between
them (as such, the decrease of r results in the diminution of solvent
reorganization). It should be noted, however, that this relationship (or its
modification, taking into account nonspherical shapes of the reactants) is
(strictly speaking) valid only if: r > (a1 + a2). Thus, it cannot be applied
quantitatively to the pimer in which two phenothiazine moieties are
positioned parallel at an interplanar separation less than their molecular
size. As a result, the pimer is best considered as a dipole within the solvent
sphere, and the redox process within such a pimer will require substantially
less solvent reorganization.
(57) Grampp, G.; Jaenicke, W. Ber. Bunsen-Ges. Phys. Chem. 1991, 95, 904.
9
1398 J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004

Donor-Acceptor Coupling in Precursor Complex to ET
A R T I C L E S
the relative arrangement of (P/P•+) centers in the o-phenylene-
bridged cation radical 3•+ is structurally quite related to that in
the intermolecular pimer (PH)2•+, and these closely related
structures lead to intervalence absorption bands in the same NIR
region and essentially the same reorganization energies. How-
ever, the electronic coupling element in 3•+ is almost twice that
evaluated for the intermolecular pimer (PH)2•+, and such a
discrepancy in HIV may be related to the enhanced (electronic)
interconnection of (P/P•+) centers in 3•+ that is abetted via an
“unsaturated” bridge.
strongly bonded precursor complex plays a critical role in ET
kinetics. Thus, structural features of this intermolecular pimer,
together with strong donor-acceptor coupling, result (a) the
q
lowering of the classical Marcus activation barrier of ∆GET
)
λ/4 by an amount HIV dictated by eq 1 and (b) the lowering of
the reorganization energy relative to that predicted from the
analysis of separated redox centers. The consequent lowering
of the barrier for intermolecular ET differs dramatically to
approach the diffusion-controlled limit despite a large reorga-
nization energy that is either calculated theoretically or observed
in the corresponding mixed-valence cation radical. For the
mixed-valence cation radical to be an appropriate model for
intermolecular ET the connecting bridge should allow the redox
centers to adopt an appropriate face-to-face disposition without
the introduction of an extraneous electronic connectivity.30b The
latter in a more extended context will provide the structural basis
for the design of multicentered arrays consisting of substantially
more than two redox centers to effect facile ET among
polymolecular redox sites (i.e., electrical conductors, wires, etc.).
We hope that further studies of other organic redox centers and
different types of molecular bridges will provide more general
support and extensions of these conclusions.
Summary and Conclusion
Analyses of the spectral (UV-NIR, ESR) and structural (X-
ray crystallographic) data for the phenothiazine intermolecular
pimer (PH)2•+ and mixed-valence cation radicals 1•+, 2•+, and
3•+ yield considerable insight into the mechanism of intermo-
lecular (ET) self-exchange in the following ways.
First: The precursor complex identified as the intermolecular
pimer (PH)2•+ must be explicitly included in the redox kinetics
as described in Scheme 1 (eq 7). The Mulliken-Hush two-
state model allows the critical electronic coupling element HIV
and the Marcus reorganization energy λ to be evaluated via the
intervalence (charge-resonance) absorption band, and the ap-
plication of the Marcus-Hush eq 1 for the activation energy
leads to the theoretical prediction of the ET rate that is in accord
with that established experimentally via the temperature-
dependent ESR line broadenings. The strong electronic coupling
Experimental Section
Materials and Synthesis. Phenothiazine (Aldrich) was purified by
recrystallization from benzene. Iodobenzene, 1,4-diiodobenzene, and
N-methylphenothiazine (Aldrich) were used without further purification.
Dichloromethane, acetonitrile, chloroform, toluene, hexane, and tet-
rahydrofuran were purified according to published procedures.61 4,5-
Dimethyl-1,2-diiodobenzene was synthesized by iodination of o-xylene
with I2.62 1,2-Bis(bromomethyl)methylbenzene was prepared by bro-
momethylation of benzenes.63 Nitrosonium hexachloroantimonate was
prepared from SbCl5 and NOCl according to the literature procedure.64
For the synthesis of 1,2-bis(phenothiazinyl-N-tolyl)benzene, the mixture
of 398 mg (2 mmol) of phenothiazene and 10 mL of ethyl ether, 0.8
mL of 2.5 M n-butyllithium was added dropwise at room temperature
with being stirred.65 After 0.5 h, 132 mg (1 mmol) of 1,2-bis-
(bromomethyl)benzene in 5 mL of ethyl ether was added to the yellow
solution. The mixture was stirred at room temperature for 1 h, and the
precipitate was filtered and washed twice with 5 mL of ethyl ether. 2
(510 mg) was obtained (yield 66%) after recrystallization from
dichloromethane/ethanol. The mononuclear donor 4 was synthesized
in a similar manner with bromomethylbenzene. The attachment of the
phenothiazine moiety to various benzene derivatives was achieved by
the Ullmann arylation of phenothiazine with iodobenzenes.66 For
example, the mixture of phenothiazine (796 mg, 4 mmol), 1,4-
diiodobenzene (660 mg, 2 mmol), potassium carbonate (3 g), and copper
metal (100 mg) was heated at 220 °C for 3 days. After cooling, the
solid was extracted with 100 mL of dichloromethane three times. The
solvent was removed, and the residual was purified by chromatography
over silica gel with dichloromethane/hexane (1/9) as elute. Recrystal-
lization from dichloromethane/ethanol afforded 199 mg of 1 (20%).
The mixed-valence donor 3 and the mononuclear donor 5 were
synthesized by a similar procedure using 4,5-dimethyl-1,2-diiodoben-
zene and iodobenzene, respectively. All of the compounds prepared
in the intermolecular pimer with HIV ) 660 cm-1 results in
q
substantial lowering of the activation barrier from (a) ∆GET
)
4.2 kcal mol-1 (in the absence of pimer) and ET rates that are
rather slow on the ESR time-scale to (b) ∆GETq ) 2.1 kcal mol-1
and ET rates at the diffusion-controlled limit. In other words,
the intervention of the strongly coupled precursor complex
(PH)2 leads to ET rates of (PH/PH•+) self-exchange by two
•+
orders of magnitude faster than otherwise predicted solely from
the value of the reorganization energy alone.60a
Second: The intimate cofacial structure of the precursor
complex (PH)2•+ plays a critical role in increasing the magnitude
of the electronic coupling and lowering the reorganization
energy for the intermolecular ET,60b and mechanistic insight is
provided by the comparison of these ET parameters with those
independently evaluated for the mixed-valence cation radical
1•+, 2•+, and 3•+. Thus, the electronic coupling within the
•+
intermolecular pimer (PH)2 is comparable to that in the
o-xylylene-bridged cation radical 2•+, but there are substantial
differences in the reorganization energies that can be attributed
to difference in the outer-sphere reorganization energies arising
from slightly displaced (P/P•+) redox centers. On the other hand,
•+
the reorganization energy of the intermolecular pimer (PH)2
is akin to that in the o-phenylene-bridged cation radical 3•+ in
which (P/P•+) redox centers bear a close structural similarity,
but different electronic coupling owing to an additional bridge
connectivity.30b
1
were characterized by H NMR, 13C NMR, MS, melting points, and
Third: As a prototypical redox center, phenothiazine is
relevant to organic ET in general, especially insofar as the
(61) Perrin, D. D.; Armarego, W. L. F.; Perrin, D. R. Purification of Laboratory
Chemicals, 2nd ed.; Pergamon: New York, 1980.
(62) Hart, H.; Harada, K.; Du, C.-J. F. J. Org. Chem. 1985, 50, 3104.
(63) Za´vada, J.; Pa´nkova´, M.; Aenold, Z. Collect. Czech. Chem. Commun. 1976,
41, 1777.
(64) Kim, E. K.; Kochi, J. K. J. Am. Chem. Soc. 1991, 113, 4962.
(65) Clarke, D.; Gilbert, B. C.; Hanson, P.; Kirk, C. M. J. Chem. Soc., Perkin
Trans. 2 1978, 10, 1103 and references therein.
(66) Okada, K.; Imakura, T.; Oda, M.; Murai, H. J. Am. Chem. Soc. 1996, 118,
3047.
(60) (a) Note that the ET rate constant derived from classical Marcus theory [Z
exp(-λ/4RT)] is kET ) 8 × 107 M-1 s-1 when Z ) 1011 M-1 s-1 and λ )
17 kcal/mol. (b) The planarization of both phenothiazine redox centers in
the pimer indicates that part of the reorganization energy is already taken
up in the pre-equilibrium step prior to the electron-transfer step. Compare
with: Gwaltney, S. R.; Rosokha, S. V.; Head-Gordon, M.; Kochi, J. K. J.
Am. Chem. Soc. 2003, 125, 3273.
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J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004 1399

A R T I C L E S
Kochi
elemental analysis, as follows. 1,2-Bis(phenothiazinyl-N-tolyl)benzene
(2): mp 218 °C dec; yield 66%. H NMR (CDCl3): δ 7.34 (m, 2H),
(local band) maxima at 780 and 880 nm continued to rise, but the
intensity of low-energy shoulders dropped, and a well-defined isosbestic
point was observed (Figure 3B). Finally, when the concentration of
the oxidant to bridged donor attained a 2:1 molar ratio (i.e., the oxidant
concentration equal to the concentration of phenothiazine redox centers
P), the spectral shape became quite close to that of mononuclear cation
radical 5•+ (Table 1). Such a spectral behavior indicated that the low-
energy component was related to the presence of both neutral and
cationic counterparts within the bridged species, i.e., it was the
intervalence transition. (The addition of the neutral donor 1 to the
solution of cation radical 1•+ did not alter the electronic spectrum in
the NIR range, which confirmed the intramolecular nature of the NIR
absorption.) Digital deconvolution of the NIR absorption into Gaussian
components led to the parameters (wavelength and ꢀ) of the intervalence
bands of 1•+ listed in Table 1. The mixed-valence donor 2 showed
essentially the same spectral behavior (Figure S5), and spectral
deconvolution of mixed-valence cation radical 2•+ (inset in Figure S5)
afforded spectral parameters in Table 1.
1
7.19 (m, 2H), 7.10 (d, J ) 8.4 Hz, 4H), 7.00 (m, 4H), 6.90 (m, 4H),
6.67 (d, J ) 8.4 Hz, 4H), 5.23 (s, 4H). 13C NMR (CDCl3): δ 144.1,
133.6, 129.2, 128.2, 127.2, 127.0, 123.7, 122.6, 121.3, 115.5, 50.5.
Anal. Calcd for C32H24N2S2: C, 76.80; H, 4.80. Found: C, 76.78; H,
4.89. 1,4-Bis(N-phenothiazinyl)benzene (1): mp 250 °C dec; yield 20%.
1H NMR (CDCl3): δ 7.51 (s, 4H), 7.14 (d, J ) 7.8 Hz, 4H), 7.00 (t,
J ) 7.2 Hz, 4H), 6.93 (t, J ) 7.2 Hz, 4H), 6.53 (d, J ) 7.8 Hz, 4H).
13C NMR (CDCl3): δ 143.0, 140.3, 130.3, 127.1, 126.9, 123.2, 122.7,
117.8. Anal. Calcd for C30H20N2S2: C, 76.27; H, 4.24. Found: C, 75.85;
H, 4.26. 1,2-Bis(N-phenothiazinyl)4,5-dimethylbenzene (3): mp 225
°C; yield 26%. 1H NMR (CDCl3): δ 7.53 (s, 2H), 6.75 (m, 4H), 6.53
(m, 8H), 6.11 (m, 4H), 2.49 (s, 6H). 13C NMR (CDCl3): δ 144.1, 140.2,
133.6, 129.0, 128.2, 127.1, 123.7, 122.6, 115.6, 16.5. Cyclic voltam-
metry was performed on a BAS 100A Electrochemical Analyzer as
described previously.30
Isolation of Cation Radical and Dication Salts. Addition of 1 equiv
NOSbCl6 (or NOPF6) to the phenothiazines PH and PMe, the mixed-
valence donors 1, 2, and 3, or the mononuclear models 4 and 5 in
dichloromethane at -40 °C produced dark red solutions of the cation
radicals. After removal of NO (gas), hexane was added, and the dark
red precipitate of the cation radical was filtered and washed with cold
hexane. Mixed-valence dications 1++, 2++, and 3++ were similarly
produced using 2:1 molar ratio of nitrosonium to the bridged donor.
The purities of all salts were determined by iodometric titration and
were found to be greater than 98%.67
The addition of the oxidant to 2 mM solution of 3 resulted in the
appearance of bands in the 700-900 nm range and a new band at
∼1700 nm (Figure 3A). The intensity of all of the NIR absorption bands
grew linearly with concentration of oxidant until the molar ratio of the
oxidant to that of the neutral donor approached 1:1. Further additions
of oxidant led to the gradual disappearance of the band at 1700 nm,
while the intensity of absorption in the 700-900 nm range continued
to grow (although the shape of the spectra changed significantly relative
to that of model cation radical 5•+; Figure 3A). Finally, when the
concentration of oxidant reached twice that of the initial concentration
of donor 3, the low-energy band at ∼1700 nm disappeared, and a single,
very intense band with maximum at 700 nm was observed in the 600-
900 nm spectral range. We thus assigned the absorption band at 1700
nm to the intervalence band of mixed-valence cation radical 3•+. (The
energy of this band was solvent-dependent (Table S1), whereas the
positions of the local bands were essentially invariant.) The intense
absorption band of dication 3++ at 700 nm was reminiscent of that
observed in phenothiazine dimer and was attributed to the strong
interaction of phenothiazine cation radical centers in the formation of
the diamagnetic dication.23,25
UV-vis-NIR spectroscopic measurements were carried out with a
Cary 500 UV-vis-NIR spectrometer. The pure, isolated salt of the
mononuclear or mixed-valence cation radicals (or dications) was
dissolved in dichloromethane in a Schlenk tube and transferred under
an argon atmosphere into the quartz spectroscopic cell (equipped with
a Teflon valve fitted with Viton O-rings). The samples of cation radical
salts (KBr pellets) for solid-state (UV-vis-NIR) absorption measure-
ments were prepared under an argon atmosphere in a glovebox.
UV-Vis-NIR Study of Phenothiazine Pimer Formation. The
phenothiazine donor PH and its cation radical PH•+ were characterized
in dichloromethane solution by intense absorption bands in the UV
region. The cation radical additionally showed absorption bands in the
visible region with major peaks at 437 and 519 nm and in NIR region
with peaks at 664, 729, and 820 nm (Table 1). (Note that cooling the
concentrated solution of cation radical PH•+ led to the appearance of
new absorption band at ∼700 nm because of the formation of cation
radical dimer (PH)22+ as illustrated in Figure S6.) When phenothiazine
PH was added to the solution of cation radical PH•+, a new (Gaussian)
band centered at 1600 nm appeared (Figure 1), consistent with the
dynamic association of the electron donor with its cation radical (i.e.,
pimer formation).37 From the absorbance dependence of this band on
the concentration of PH, the pimer formation constant and extinction
coefficient of new band were determined by the Benesi-Hildebrand
procedure (see text).
ESR measurements (from -90 to +30 °C) were performed on Bruker
ESP-300 X-band or Varian E-line Century 100 ESR spectrometer as
described.25,30 ESR spectra simulations (PEST WinSim program, V.
0.96, Public EPR Software Tools, National Institute of Environmental
Health Sciences) were carried out as described earlier.30 The intramo-
lecular ET rate constants kET within mixed-valence cation radical 1•+
,
2•+, and 3•+ were evaluated from the temperature-dependent line broad-
ening using dynamic ESR spectra simulations (ESR-EXN program) as
described previously.30,32 The intermolecular self-exchange rate con-
stants kSE (for PH•+/PH and PMe•+/PMe dyads in dichloromethane)
were determined from the dependence of cation radical ESR line widths
on concentration of parent donor in the fast-exchange limit.14 The ESR
spectrum of phenothiazine cation radical (Figure S1) changed dramatic-
ally upon addition of parent phenothiazine. Initially, the well-resolved
spectrum broadened to the four unresolved lines (Figure S2), and then
the incremental addition of phenothiazine gradually led to single broad
line. This broad line became narrower with the continuous addition of
the neutral donor, i.e., system approached the fast-exchange limit.
Following earlier studies,14 the electron self-exchange rate constant kSE
was calculated in fast-exchange limit from the slope of dependence of
line width (∆H) on the inverse concentration of the parent donor, 1/C
(Figure S3) as kSE ) 2.05 × 1073/slope, where 3 is the second moment
of the ESR spectrum.14 The same procedure was carried out at different
temperatures, and Arrhenius dependence of rate constants (Figure S4)
led to the activation energy Ea and pre-exponential factor (log A).
The spectral characteristics of mixed-valence cation radicals 1•+
3•+ in the UV-vis region were similar to those of their mononuclear
cation radicals 4•+ and 5•+ and phenothiazine cation radical PH•+
-
.
Spectral analysis of the mixed-valence cation radicals 1•+-3•+ via
oxidative titration of the parent donor with SbCl5 revealed the
intervalence bands, as follows. The addition of 0.5 mM oxidant to 2
mM solution of donor 1 resulted in the appearance of absorptions
corresponding to local bands of phenothiazine cation radical (maxima
at 680, 780, and 880) and an extra component as a shoulder around
900-1100 nm (Figures 3B). Increasing concentrations of the oxidant
led to a linear growth of intensity of all bands until concentration of
oxidant reached that of donor 1. With further additions of oxidant, the
X-ray Crystallography of the Cation Radicals. The intensity data
were collected with aid of a Siemens SMART Apex diffractometer
equipped with a CCD detector using Mo KR radiation (λ ) 0.71073
(67) Rathore, R.; Kumar, A. S.; Lindeman, S. V.; Kochi, J. K. J. Org. Chem.
1998, 63, 5847.
9
1400 J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004

Donor-Acceptor Coupling in Precursor Complex to ET
A R T I C L E S
Table 7. Crystallographic Data for Aromatic Donors and Their Cation Radicals
•+
•+
1
1 SbF 2CH Cl2
2
2 CB (CH ) - 2CH Cl2
3
(PH)32+PH (PF -
)
6 2
6
2
11
3 12
2
empirical formula
fw
cryst syst
space group
a, Å
C30H20N2S2
472.60
orthorhombic
Pbca
13.869(1)
8.0185(4)
20.090(1)
90
C32H24Cl4 F6 N2S2Sb
878.20
triclinic
C32H24N2S2
500.65
triclinic
C47H64B11 Cl4N2S2
981.83
monoclinic
P21/c
14.695(1)
23.991(1)
15.625(1)
90
110.95(1)
90
C32H24N2S2
500.65
tetragonal
I1/a
13.819(1)
13.819(1)
26.189(2)
90
C48H36F12 N4P2S4
1086.98
monoclinic
C2
19.303(1)
11.225(1)
20.546(1)
90
92.84(1)
90
4446.3(4)/4
1.624
P1h
P1h
7.782(1)
10.292(1)
10.450(1)
96.32(1)
99.68(1)
94.16(1)
816.5(1)/1
1.768
10.764(1)
12.195(1)
19.820(1)
107.86(1)
96.35(1)
95.02(1)
2440.6(1)/4
1.363
b, Å
c, Å
R, deg
â, deg
90
90
90
90
γ, deg
V, Å3/Z
2234.1(2)/4
1.405
24484/3685
3268
5144.5(4)/4
1.268
48067/12777
8571
5001.6(5)/8
1.330
27473/4238
3256
F
calcd, g/cm3
total/unique reflns
9002/5096
4484
0.035/0.082
26742/15165
12585
0.048/0.114
24530/7549
6455
0.061/0.152
data [I > 2σ(I)]
a
b
R1 /wR2
0.041/0.108
0.065/0.149
0.056/0.144
a
b
2
2
2
R1 ) ∑||Fo| - |Fc||/Σ |Fo|. wR2 ) {∑[w(Fo - Fc )2]/∑[w(Fo )2]}1/2
Å) at -150 °C unless otherwise specified. The structures were solved
by direct method and refined by full matrix least-squares procedure
with IBM Pentium and SGI O2 computers.68 The X-ray structure details
of compounds mentioned here are on deposit and can be obtained from
Cambridge Crystallographic Data Center, 12 Union Road, Cambridge,
CB2 1EZ U.K.
for help with some of the ESR spectral measurements, S. V.
Lindeman for crystallographic assistance, and the R. A. Welch
Foundation for financial support.
Supporting Information Available: Solvent dependence of
the intervalence band for the mixed-valence cation radical 3•+
(Table S1), selected bond lengths and angles from X-ray studies
of phenothiazine-based systems (Table S2), ESR spectra
(experiment and simulation) for the cation radical PH•+ (Figure
S1), concentration effects of the parent donor PH on line shape
of cation radical PH•+ ESR spectrum (Figure S2) and its line
width ∆H (Figure S3), Arrhenius dependence of the self-
exchange rate constant for PH•+/PH dyad (Figure S4), solid-
state spectrum of phenothiazine pimer (Figure S5), temperature
dependence of the electronic spectrum of concentrated solutions
of phenothiazine cation radical in dichloromethane (Figure S6),
spectral changes upon oxidative titration of the mixed-valence
donor 2 (Figure S7), ESR spectra (experiment and simulation)
for the mononuclear cation radical 5•+ (Figure S8), temperature-
dependent ESR spectra of mixed-valence cation radical 2•+ and
dynamic ESR simulation (Figure S9), ORTEP diagram for the
donor 3 from X-ray crystallography (Figure S10), ESR spectra
of dication diradicals 12+ and 22+ (Figure S11), and ORTEP
diagram of the dication salt 22+(SbCl6-)2 (Figure S12) (PDF,
CIF). This material is available free of charge via the Internet
at http://pubs.acs.org.
Single crystals of the neutral mixed-valence donors 1, 2, and 3 were
obtained by the slow evaporation of their solutions in dichloromethane/
ethanol mixture. To obtain single crystals of mixed-valence cation
radical 1•+, a solution of (2 mM) nitrosonium hexachloroantimonate
(NO•+SbCl-6) and donor 1 (2 mM) in dichloromethane (20 mL) was
prepared under an argon atmosphere at -30 °C. The solution was
carefully layered with toluene and placed in the cold bath (-60 °C).
After 7 days, the dark red single crystals were formed as the cation
radical salt (1•+ SbCl6-) suitable for X-ray crystallographic analysis.
The single crystals of the mixed-valence cation radical 2•+ were obtained
by the exposure of the neutral donor 2 (4 mmol) with 1 equiv of
decamethylcarbonyl radical in dichloromethane at 23 °C. Careful
layering of this solution with hexane followed by refrigeration at -65
°C for 2 weeks afforded dark red crystals of 2•+ CB11(CH3)12-. The
single crystals of the dication 22+(SbCl6-)2 were obtained by oxidation
of 2 with 2 equiv of tris(4-bromophenyl)aminium hexachloroantimonate
in dichloromethane, followed by crystallization as described earlier.
To obtain single crystals of phenothiazine pimer, the 4-fold excess of
phenothiazine donor was added to 1,2-dichloroethane solution of pure
phenothiazine cation radical salt PH•+PF6-. Careful layering of this
solution with n-hexane and refrigeration at -30 °C for 2 weeks afforded
well-formed dark brown prisms, with the overall stoichiometric [1:1]
composition (PH+PF6-)(PH). Crystallographic data for the pertinent
aromatic donor, their cation radicals, dications, and pimer are presented
in Table 7.
JA038746V
Acknowledgment. We thank Professor S. F. Nelsen for kindly
providing us with a copy of the ESR-EXN program, J. M. Lu
(68) Sheldrick, G. M. SHELXS-86, Program for Structure Solution; University
of Go¨ttingen: Go¨ttingen, Germany, 1986.
9
J. AM. CHEM. SOC. VOL. 126, NO. 5, 2004 1401