Continuum of outer- and inner-sphere mechanisms for organic electron transfer. Steric modulation of the precursor complex in paramagnetic (ion-radical) self-exchanges

Article abstract of DOI:10.1021/ja069149m

Transient 1:1 precursor complexes for intermolecular self-exchange between various organic electron donors (D) and their paramagnetic cation radicals (D^+.), as well as between different electron acceptors (A) paired with their anion radicals (A ^.), are spectrally (UV-NIR) observed and structurally (X-ray) identified as the cofacial (π-stacked) associates [D, D^+.] and [A^-.· A], respectively. Mulliken-Hush (two-state) analysis of their diagnostic intervalence bands affords the electronic coupling elements (H_OA), which together with the Marcus reorganization energies (λ) from the NIR spectral data are confirmed by molecular-orbital computations. The H_DA values are found to be a sensitive function of the bulky substituents surrounding the redox centers. As a result, the steric modulation of the donor/acceptor separation (r_DA) leads to distinctive electron-transfer rates between sterically hindered donors/acceptors and their more open (unsubstituted) parents. The latter is discussed in the context of a continuous series of outer- and inner-sphere mechanisms for organic electron-transfer processes in a manner originally formulated by Taube and co-workers for inorganic (coordination) donor/acceptor dyads-with conciliatory attention paid to traditional organic versus inorganic concepts.

Full text of DOI:10.1021/ja069149m

Published on Web 03/06/2007
Continuum of Outer- and Inner-Sphere Mechanisms for
Organic Electron Transfer. Steric Modulation of the Precursor
Complex in Paramagnetic (Ion-Radical) Self-Exchanges
Sergiy V. Rosokha and Jay K. Kochi*
Contribution from the Department of Chemistry, UniVersity of Houston, Houston, Texas 77204
Received December 20, 2006; E-mail: jkochi@uh.edu
Abstract: Transient 1:1 precursor complexes for intermolecular self-exchange between various organic
electron donors (D) and their paramagnetic cation radicals (D+•), as well as between different electron
acceptors (A) paired with their anion radicals (A-•), are spectrally (UV-NIR) observed and structurally
(X-ray) identified as the cofacial (π-stacked) associates [D, D+•] and [A-•, A], respectively. Mulliken-Hush
(two-state) analysis of their diagnostic intervalence bands affords the electronic coupling elements (HDA),
which together with the Marcus reorganization energies (λ) from the NIR spectral data are confirmed by
molecular-orbital computations. The HDA values are found to be a sensitive function of the bulky substituents
surrounding the redox centers. As a result, the steric modulation of the donor/acceptor separation (rDA
)
leads to distinctive electron-transfer rates between sterically hindered donors/acceptors and their more
open (unsubstituted) parents. The latter is discussed in the context of a continuous series of outer- and
inner-sphere mechanisms for organic electron-transfer processes in a manner originally formulated by Taube
and co-workers for inorganic (coordination) donor/acceptor dyadsswith conciliatory attention paid to
traditional organic versus inorganic concepts.
Chart 1
1. Introduction
H. Taube and co-workers1 more than 50 years ago conceived
electron-transfer processes of inorganic (coordination) com-
pounds in terms of two distinctive mechanistic categories based
on the nature of the rate-limiting transition states.2,3 In outer-
sphere electron transfer, the bimolecular transition state (TS)
is traversed with the separate coordination spheres of both the
electron donor (D) and the electron acceptor (A) essentially
intact,4 whereas, in the inner-sphere mechanism, the unimo-
lecular (collapsed) transition state typically results from the
mutual interpenetration of coordination spheres via a critical
bridging ligand (L),5 as schematically depicted in Chart 1 with
D ) M′L6+n and A ) ML6+n+1 representing a pair of octahedral
complexes.6
separation that is (more or less) akin to step (a) in microscopic
reverse. However, these rate processes are strongly divergent
when the electronic coupling element for the precursor complex
is quantitatively taken into account, with HDA j 200 cm-1 for
the outer-sphere pathway7 and substantially greater values
pertaining to inner-sphere electron transfer.8,9
The phenomenological kinetics of outer- and inner-sphere
electron transfers share a common pathway involving three basic
transformations: (a) the diffusive association of the donor/
acceptor pair to form the 1:1 precursor complex [D,A] followed
by (b) the rate-limiting intracomplex electron transfer to afford
the successor complex [D+•,A-•], and then (c) the diffusive
From a purely conceptual point of view, the outer-sphere
pathway is relatively more readily managed theoretically since
Marcus10 demonstrated how the electron-transfer rates can be
(5) (a) Haim, A. Prog. Inorg. Chem. 1983, 30, 273. (b) Haim, A. Acc. Chem.
Res. 1975, 8, 264. (c) Schwarz, C. L.; Endicott, J. F. Inorg. Chem. 1995,
34, 4572.
(6) (a) Generally speaking, a separate deligation step will precede the formation
of the bridged-activated complex unless the donor or acceptor is coordi-
natively unsaturated. (b) In Taube and Myers’ original study,1 the rapid
loss of an aquo ligand from the substitution-labile chromium(II) donor
occurs prior to the formation of the chloro-bridged precursor (activated)
complex with the chlorocobalt(III) acceptor.
(7) (a) Logan, J.; Newton, M. D. J. Chem. Phys. 1983, 78, 4086. (b) Rosso,
K. M.; Smith, D. M.; Dupuis, M. J. Phys. Chem. A 2004, 108, 5242.
(8) Compare the evaluation of HDA in various RuII(bridge)RuIII systems: (a)
Creutz, C.; Taube, H. J. Am. Chem. Soc. 1969, 91, 3988. (b) Creutz, C.
Prog. Inorg. Chem. 1983, 30, 1.
(1) (a) Taube, H.; Myers, H. J. Am. Chem. Soc. 1954, 76, 2103. (b) Taube,
H.; Myers, H. J.; Rich, R. L. J. Am. Chem. Soc. 1953, 75, 4118. (c) Taube,
H. Nobel Lecture: Angew. Chem., Int. Ed. Engl. 1984, 23, 329.
(2) (a) Taube, H. AdV. Inorg. Radiochem. 1959, 1, 1. (b) Taube, H. Electron-
Transfer Reactions of Complex Ions in Solution; Academic: New York,
1970. (c) Meyer, T. J.; Taube, H. In ComprehensiVe Coordination
Chemistry; Wilkinson, G., Guilard, R., McLafferty, J. A., Eds.; Pergamon:
London, 1987; p 331 ff.
(3) For example, also see: (a) Lippard, S. J. Prog. Inorg. Chem. 1983, 30, 1.
(b) Cannon, R. D. Electron Transfer Reactions; Butterworth: London, 1980.
(c) Astruc, D. Electron Transfer and Radical Processes in Transition-Metal
Chemistry; VCH: New York, 1995.
(4) For example, see: Reynolds, W. L.; Lumry, R. W. Mechanism of Electron
Transfer; Ronald Press: New York, 1966.
(9) See also: (a) Demadis, K. D.; Hartshorn, C. M.; Meyer, T. J. Chem. ReV.
2001, 101, 2655. (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.
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J. AM. CHEM. SOC. 2007, 129, 3683-3697
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A R T I C L E S
Rosokha and Kochi
predicted from the structural properties of the individual (intact)
donor and acceptor. However, the comparable simplicity cannot
be so easily invoked for the inner-sphere activated complex,
and the calculations of the inner-sphere electron-transfer rates
have been significantly more difficult, with one exception
involving the isolable donor-bridge-acceptor or mixed-valence
complex.8,9 Thus Hush11 and Sutin12 showed how the charac-
teristic intervalence (IV) absorption bands extant with various
donor/acceptor dyads can be applied to the evaluation of the
critical electronic coupling element (HDA) in the corresponding
mixed-valence complex for intramolecular electron transfer.
However, the evaluation of HDA for intermolecular electron
transfer can be complicated by slow (intervening) ligand
substitutions6 required for octahedral structures (see Chart 1).13
Notably, such rate-limiting steps are avoided entirely in inner-
sphere electron transfer with many organic donor/acceptor dyads
in which direct electronic coupling of the redox centers can
occur without “ligand” involvment.14,15 Therefore at this
juncture, let us bifurcate our brief historical summary and
exclude the outer-sphere pathway from further detailed consid-
eration because it has already been successfully dealt with in
extended scope, breadth, and prolonged depth.3,4,16,17 By way
of contrast, there are almost no quantitative studies of inner-
sphere electron transfer, which we simply attribute to the dearth
of experimental data on the nature of the inner-sphere (strongly
adiabatic) transition state for intermolecular electron transfer.18
Indeed, the latter is again understandable in a historical context
because quantitative studies of electron-transfer processes have
heretofore largely focused on inorganic octahedral (and related
high-coordination) complexes that do not particularly favor close
donor/acceptor encounters, largely for symmetry/steric reasons.14
When Mulliken19,20 first considered the intermolecular potentials
of diffusive interactions, he showed that many types of organic
(and main-group metal) donor/acceptor dyads easily form a wide
variety of intermolecular [1:1] complexes that can be readily
monitored quantitatively via their characteristic charge-transfer
(CT) absorption bands.20,21
Accordingly, we now focus on inner-sphere electron transfer
in two distinctly separate but strongly related classes of organic
donor/acceptor dyads. Here in Part 1, we quantitatively examine
the fast kinetics and (isergonic) energetics of electron-transfer
self-exchange (SE) specifically between planar π-donors (D)
and their oxidized cation radicals (D+•), as well as between
planar π-acceptors (A) and their reduced anion radicals (A-•),
i.e.,
D + D+• {kSE} D+• + D
(1a)
(1b)
A
-• + A {kSE} A + A-•
In eq 1, the paramagnetic 1:1 associates [D,D+•] and [A-•,A],
respectively, would represent the donor/acceptor precursor
complex relevant to the self-exchange process.22,23 As such, the
spectral observation and scrutiny of the Hush intervalence
absorption band together with the isolation and X-ray analysis
of [D,D+•] and [A-•,A] will then form the critical facet in the
inner-sphere electron-transfer pathway.24-28 In Part II,29 we
enlarge the structural diversity to encompass different organic
functionalities in electron-transfer cross-exchange as allowed
by Mulliken charge-transfer theory19-21 for diamagnetic (un-
charged) donor/acceptor dyads, i.e.,
(10) (a) Marcus, R. A. Discuss. Faraday Soc. 1960, 29, 21. (b) Marcus, R. A.
J. Phys. Chem. 1963, 67, 853. (c) Marcus, R. A. J. Chem. Phys. 1965, 43,
679. (d) Marcus, R. A. ReV. Mod. Phys. 1993, 65, 599. (e) Marcus, R. A.;
Sutin, N. Biochim. Biophys. Acta 1985, 811, 265.
(11) Hush, N. S. Prog. Inorg. Chem. 1967, 8, 391.
(12) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441.
D + A {kCE} D+• + A-•
(2)
2. Results
(13) (a) The vast majority of quantitative electron-transfer studies of inorganic
coordination compounds have been carried out with octahedral complexes,
especially when compared to those with a lower metal coordination number,
such as linear, square planar, square pyramidal, etc. For the necessity of
the separate substitution step, see: Kochi, J. K.; Powers, J. W. J. Am. Chem.
Soc. 1970, 92, 137. (b) We anticipate that inorganic electron-transfer
reactions with coordinatively unsaturated metal (coordination) donors and
acceptors with square planar coordination, etc., will reveal intermolecular
charge-transfer bands. (c) See: Kochi, J. K. Angew. Chem., Int. Ed. Engl.
1988, 27, 1227.
(14) (a) The best organic electron donors and acceptors are generally substitution-
stable and contain planar (aromatic and olefinic) redox centers that are
sterically favorable for intermolecular π-interactions. (b) By comparison,
intermolecular interactions are less favorable with quasi-spherical (octa-
hedral) systems. For example, see: (b) Veya, P.; Kochi, J. K. J. Organomet.
Chem. 1995, 488, C4. (c) Le Magueres, P.; Hubig, S. M.; Lindeman, S.
V.; Veya, P.; Kochi, J. K. J. Am. Chem. Soc. 2000, 122, 10073. (d) Masnovi,
J. M.; Huffman, J. C.; Kochi, J. K. Hilinski, E. F.; Rentzepis, P. M. Chem.
Phys. Lett. 1984, 106, 20.
(15) (a) Mulliken, R. S. J. Am. Chem. Soc. 1952, 74, 811. (b) Kochi, J. K.
ComprehensiVe Organic Synthesis; Trost, B. M., Fleming, I., Ley, S. V.,
Eds.; Pergamon: New York, 1991; Vol. 7, p 849ff. (c) Rathore, R.; Kochi,
J. K. AdV. Phys. Org. Chem. 2000, 35, 193. (d) The earlier monograph by
Eberson, L. entitled: Electron Transfer in Organic Chemistry (Springer:
London, 1987) is unnecessarily restrictive because all redox processes are
uniformly (and unjustifiably) treated by the classical Marcus (outer-sphere)
formalism.
(16) (a) Marcus, R. A. Angew. Chem., Int. Ed. Engl. 1993, 32, 1111. (b) Chou,
M.; Creutz, C.; Sutin, N. J. Am. Chem. Soc. 1977, 99, 5615. (c) Bixon,
M.; Jortner, J. AdV. Chem. Phys. 1999, 106, 35.
The prime requirement for the quantitative analysis of organic
self-exchange dynamics is the availability of crystallographically
(X-ray) well-defined salts of the ion-radicals D+• and A-• so
that their kinetic behavior is relatively unaffected by their
counterions when these pure salts are dissolved in aprotic
organic solvents to minimize (strong) solvation effects. Ac-
cordingly, all the cation radicals for eq 1a (Table 1) were
(19) Mulliken, R. S. J. Phys. Chem. 1952, 56, 801.
(20) Mulliken, R. S.; Person, W. B. Molecular Complexes. Wiley: N.Y. 1969.
(21) (a) Foster, R. Organic Charge-Transfer Complexes; Academic Press: New
York, 1969. (b) Andrews, L. J.; Keefer, R. M. Molecular Complexes in
Organic Chemistry; Holden-Day: San Francisco, CA, 1964.
(22) Rosokha, S. V.; Kochi, J. K. J. Am. Chem. Soc. 2007, 129, 828.
(23) (a) Ganesan, V.; Rosokha, S. V; Kochi, J. K. J. Am. Chem. Soc. 2003,
125, 2559. (b) Sun, D.; Rosokha, S. V.; Kochi, J. K. J. Am. Chem. Soc.
2004, 126, 1388.
(24) (a) Historically, the electronic transitions associated with such [D, D+•
]
complexes of aromatic π-donors and their cation radicals have been referred
to as charge-resonance absorptions.25-27 (b) The corresponding intervalence
absorption of [A-•, A] complexes have been recently observed and identified
for olefinic and quinonoid π-acceptors and their associated anion radicals.23a,28
(25) (a) Badger, B.; Brocklehurst, B. Nature 1968, 219, 263. (b) Badger, B.;
Brocklehurst, B. Trans. Faraday Soc. 1969, 65, 2582; 1970, 66, 2939.
(26) (a) Lewis, I. C.; Singer, I. C. Chem. Phys. 1965, 43, 2712. (b) Howarth,
O. W.; Fraenkel, G. K. J. Am. Chem. Soc. 1966, 88, 4514.
(27) (a) Fritz, H. P.; Gebauer, H.; Friedrich, P.; Ecker, P.; Artes, R.; Schubert,
V. Z. Naturforsch. 1978, 336, 498. (b) Chi, X.; Itkis, M. E.; Reed, R. W.;
Oakley, R. T.; Cordes, A. W.; Haddon, R. C. J. Phys. Chem. B 2002, 106,
8278.
(17) (a) Gray, H. B.; Winkler, J. R. In Electron Transfer in Chemistry, Vol. III:
Biological Systems; Balzani, V., Ed.; Wiley-VCH: New York, 2001. (b)
Piotrowiak, P. In Electron Transfer in Chemistry, Vol. I: Principle and
Theories; Balzani, V., Ed.; Wiley-VCH: New York, 2001 (c) Mattay, J.
In Electron Transfer in Chemistry, Vol. II. Organic Molecules; Balzani,
V., Ed.; Wiley-VCH: New York, 2001. (d) Fukuzumi, S. Org. Biomol.
Chem. 2003, 1, 609.
(18) Strictly speaking, the substitution-stable Creutz/Taube mixed-valence
complex8a is a suitable electronic but a limited (kinetics) model for a
precursor complex in intermolecular (diffusive) electron-transfer processes.
(28) (a) Rosokha, S. V.; Lu, J.-M.; Newton, M. D.; Kochi, J. K. J. Am. Chem.
Soc. 2005, 127, 7411. (b) Rosokha, S. V. Newton, M. D.; Head-Gordon,
M.; Kochi, J. K. Chem. Phys. 2006, 326, 117.
(29) Sun, D.-L.; Rosokha, S. V.; Kochi, J. K. J. Phys. Chem B 2007. In press
(Sutin issue).
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Outer-/Inner-Sphere Mechanisms for Organic ET
A R T I C L E S
Table 1. Redox Potentials of Donors and Acceptors and the Spectral Characteristics of Their Cation and Anion Radicals
a In CH2Cl2, at 295 K. b In parentheses -log ꢀ for the most intense band. c Oxidation wave split at low temperature.
prepared as the closo-dodecamethylcarboranate (CB-) salts
depicted in Chart 2, in which the negative charge is known to
be extensively delocalized over the large quasi-spherical anion
to allow only separated ion pairs (SIP) to be formed in solution
and in the crystalline solid state.30 Likewise, all anion radicals
for eq 1b were prepared as SIP salts of the ligated potassium
counterion K(L)+, wherein the three-dimensional L ) [2,2,2]
cryptand completely encapsulates the alkali-metal cation suf-
ficient to isolate it from the anion radicals in Table 1.31,32
2.1. Preparation and Characterization of Ion-Radical Salts
of Electron Donors and Acceptors. The electronic coupling
(31) Lu, J. M.; Rosokha, S. V.; Lindeman, S. V.; Neretin, I. S.; Kochi, J. K. J.
Am. Chem. Soc. 2005, 127, 1797.
(32) Lu, J. M.; Rosokha, S. V.; Neretin, I. S.; Kochi, J. K. J. Am. Chem. Soc.
2006, 128, 16708.
(30) (a) Sun, D.-L.; Rosokha, S. V.; Kochi, J. K. Angew. Chem. 2005, 44, 5133.
(b) Rosokha, S. V.; Neretin, I. S.; Sun, D.-L.; Kochi, J. K. J. Am. Chem.
Soc. 2006, 128, 9394.
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A R T I C L E S
Rosokha and Kochi
Figure 1. Molecular structures of sterically open and hindered (closed) cation radicals: (A) TMPD+• vs (B) TPPD+•; (C) PTZ+• vs (D) PrPTZ+•; (E)
DMB+• vs (F) DBB+• [note that (B) to (F) are taken from X-ray structures of the corresponding D+•CB- salts and (A) taken from TMPD+•TCNE-•29].
Chart 2
ordinating (moderately polar) dichloromethane to lessen solvent
effects, and (iii) minimum counterion interaction for the cation
radicals to exist as separate ions with minimal ion-pairing
effects. Likewise, crystalline anion-radical salts of the electron
acceptor in Table 1 were prepared as the potassium cation totally
encased within the cavity of a three-dimensional polyether ligand
by potassium-mirror reduction in the presence of [2,2,2]cryptand
in THF solutions. In all cases, the pure salts were easily
separated in nearly quantitative yield by the addition of hexane,
and their purities established by spectral titration were found
to be >98%.
effects on the electron-transfer self-exchange of various cation
and anion radicals were based on the donor and acceptor systems
illustrated in Table 1. This donor and acceptor array included
The remote introduction of bulky tert-butyl (tBu) or isopropyl
(iPr) substituents into the organic donors caused only a relatively
minor perturbation of either the redox potential or the spectral
(UV-vis) characteristics of the redox core, as illustrated by the
comparison of the entries for phenylenediamine (3b vs 3a),
phenothiazine (4c vs 4b), and quinol ether (5b vs 5a) in Table
1. In each case, the basic structural changes established by X-ray
crystallographic analysis of crystalline salts (see Experimental
Section) from the one-electron oxidation of the sterically
hindered donor (Figure 1) are quite similar to those found in
the parent (planar) donors. For example, the oxidation of
tetramethyl-p-phenylendiamine (TMPD) to its cation radical
leads to (i) shortening of the Car-N bond from 1.41 to 1.36 Å,
(ii) significant quinonoid distortion of the aromatic ring so that
the essentially equivalent (C-C) bonds of 1.40 Å become
significantly different (1.42 and 1.36 Å), and (iii) planarization
of the amino group becomes essentially complete, so that the
sum of the internal C-N-C angles are 359.6° in the cation
radical. Similarly, the oxidation of the tetra-isopropyl-substituted
analogue (TPPD) leads to similar changes, i.e., (i) the shortening
of the Car-N bond from 1.42 to 1.36 Å; (ii) quinonoid distortion
of the aromatic ring so that the nearly equivalent aromatic bonds
(∼1.40 Å) in the neutral donor become nonequivalent (1.42 and
1.36 Å);37 and (iii) the planarization of the amino group, so
aromatic as well as olefinic systems that are open for intermo-
lecular interactions as well as those containing the same (redox)
core but sterically hindered with bulky substituents.33 All
electron donors and acceptors were characterized in dichlo-
romethane solution by reversible cyclic voltammograms, the E°
values of which are included in the third column. Of particular
interest is the aromatic donor OMB which exhibited an unusual
splitting of the anodic wave at low temperatures (see Figure
S1 in Supporting Information); the mechanistic implication of
this unusual behavior will be discussed below.
Crystalline cation-radical salts of the electron donors were
prepared by direct one-electron oxidation with stoichiometric
amounts of the closo-dodecamethylcarboranyl radical (CB•),34
nitrosonium salt (NO+SbCl6-),35 or simply pentachloroanti-
mony36 to produce large (encumbered) counter anions. The
availability of such crystalline salts allowed the following: (i)
high kinetic stability (persistency) of the cation radical sufficient
for accurate measurements, (ii) good solubility in the nonco-
(33) For steric effects on the diffusive (charge-transfer) association of organic
and organometallic electron donor/acceptor dyads, see: (a) Wong, C. L.;
Kochi, J. K. J. Am. Chem. Soc. 1979, 101, 5593. (b) Fukuzumi, S.; Wong,
C. L.; Kochi, J. K. J. Am. Chem. Soc. 1980, 102, 2928. (c) Hubig, S. M.;
Rathore, R.; Kochi, J. K. J. Am. Chem. Soc. 1999, 121, 610. (d) Rathore,
R.; Lindeman, S. V.; Kochi, J. K. J. Am. Chem. Soc. 1997, 119, 9393.
(34) King, B. T.; Noll, B. C.; McKinley, A. J.; Michl, J. J. Am. Chem. Soc.
1996, 118, 10902.
(35) (a) Rathore, R.; Kochi, J. K. Acta Chem. Scand. 1998, 52, 114. (b) Rosokha,
S. V.; Kochi, J. K. J. Am. Chem. Soc. 2001, 123, 8985.
(36) Rathore, R.; Kumar, A. S.; Lindeman, S. V.; Kochi, J. K. J. Org. Chem.
1998, 63, 5847.
(37) (a) For quantitative (structural) evaluations of the quinonoidal distortion
of benzenoid rings upon one-electron oxidation and reduction, see the
Pauling-based bond-length/bond-order analysis: (b) Lindeman, S. V.;
Rosokha, S. V.; Sun, D.; Kochi, J. K. J. Am. Chem. Soc. 2002, 124, 843
and Lu J. M., et al. in ref 32.
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A R T I C L E S
that the sum of the C-N-C angles increases from 341.2° in
the neutral donor to 359.8° in the cation radical.
rowed in the final fast-exchange limit (see Figure S2 for
representative examples). Such well-known linebroadening
effects resulted from the intermolecular electron-transfer self-
exchange as described by eqs 1a and 1b (vide supra). Thus
following the earlier studies,43 we determined the second-order
rate constants (see Experimental Section for details) based on
the line width variation with changing concentrations of the
diamagnetic parent, and the self-exchange values of kSE are
included in Table 2 for the parent cation radicals and anion
radicals as well as their sterically hindered derivatives.44
Structural changes upon oxidation of the sterically hindered
phenothiazine and dimethoxybenzene donors, PrPTZ and DBB,
are also comparable to those in the unhindered parents: PTZ
and DMB, respectively. Thus, the oxidation of phenothiazine
results in (i) the shortening of the S-C bond from 1.76 to 1.71
Å in PTZ and from 1.77 to 1.73 Å in PrPTZ; (ii) shortening
of N-C bonds from 1.40 Å to 1.38 Å in PTZ and from 1.42 Å
to 1.40 Å in PrPTZ; and (iii) planarization, so the angle between
aromatic planes increases from 158° to 176° in PTZ and from
140° to 158° in PrPTZ. In the dimethoxybenzenes, one-electron
oxidation leads to (i) the shortening of the Car-O bonds (1.38
Å) in the neutral donor to 1.32 Å in the cation radical, (ii) the
quinonoidal distortion of the benzene ring consisting of es-
sentially equivalent bonds (∼1.39 Å) in the neutral donor to
inequivalent bonds of 1.44/1.36 Å in the cation radicals, and
(iii) the coplanarization of the methoxy group with respect to
the aromatic plane.38
The results in Table 2 revealed four salient structural facets
of the ion-radical kinetics for the self-exchange process. First,
limiting second-order rates that were uniformly close to the fast-
exchange limit of kSE ≈ (3-5) × 109 M-1 s-1 in Table 2 were
attained by all the unsubsituted (“open”) cation and anion
radicals. Second, the activation energies for ET self-exchange
of the open ion radicals as evaluated from the linear dependence
of ln kSE with inverse temperature lay in the range Ea ≈ 1-3
kcal mol-1 that is generally in accord with the diffusion barrier
of Ediff ≈ 2.5 kcal mol-1 45
. Third, of the various donor/acceptor
Spectral, electrochemical, and structural data thus indicate
that the thermodynamics of the redox processes, as well as the
geometric changes upon oxidation, and spectral properties of
ion radicals of hindered systems are close to those of planar
species that are sterically “open” for π-interactions. Let us now
compare how such π-interactions affect the dynamics of
electron-transfer self-exchange.
systems described in Table 1, the octamethylbiphenylene (OMB/
OMB+•) dyad was unique in that the temperature dependence
of the second-order rate constant ln kSE with T-1 was distinctly
nonlinear. Most revealingly, when solutions of OMB+• with
added OMB were progressively cooled, the EPR spectra showed
the appearance of additional hyperfine lines so that, at the lowest
temperature of -90 °C, the EPR spectrum simply consisted of
doubled lines with halved hyperfine splittings that were
diagnostic of the completely delocalized dimeric species:
(OMB)2+• structurally (X-ray) identified earlier.41a Fourth, their
sterically hindered (“closed”) analogues with tert-butyl or
isopropyl substituents were consistently slower by several orders
of magnitude in comparison with their more “open” parents.
As such, the clear distinction between the self-exchange kinetics
of the open versus the sterically hindered ion radicals caused
us to closely examine the intermolecular interaction with their
diamagnetic parents in greater detail, as follows.
2.2. EPR Studies of Ion Radicals and the Electron-
Transfer (ET) Kinetics of the Self-Exchange Processes.
Dissolution of the pure ion-radical salts (Table 1) in dichlo-
romethane at room temperature formed the basis of our quan-
titative rate measurements since earlier studies principally by
Weissman and co-workers39 defined the self-exchange kinetics
via their diagnostic EPR linebroadening behavior. Indeed, our
measurements based on the isolation of pure ion-radical salts
(see Experimental Section) consistently afforded well-resolved
EPR spectra, the hyperfine splitting constants of which were
basically within the experimental errors.40,41 Most importantly,
the incremental addition of either the neutral donor (D) to the
cation radical (D+•) or the neutral acceptor (A) to the anion
radical (A-•) generally led to the same characteristic progressive
linebroadening (slow-exchange limit) observed earlier.42 As a
result, the further addition of the diamagnetic parent induced
the collapse of the resolved EPR spectrum of the ion radical
into a single broad envelope which then characteristically nar-
2.3. Spontaneous Association of Ion Radicals with their
Diamagnetic Parents. Formation of Transient 1:1 Com-
plexes. The facile association of ion radicals with their
diamagnetic parents was experimentally observed spectroscopi-
cally as intermolecular 1:1 associates, hereinafter referred to as
transient complexes (TCs).22,23 For example, dichloromethane
solutions of all the ion radicals in Table 1 were characterized
by intense absorptions in the UV-vis spectral region, but the
colored solutions were completely transparent in the near-IR
region between 1000 and 3000 nm. On the other hand, when
the diamagnetic parent was added, a new absorption band could
be detected immediately in the NIR region (Figure 2), typically
at λmax ) 1900 nm with the extinction coefficient ꢀmax ) 1700
(38) Rathore, R.; Kochi, J. K. J. Org. Chem. 1995, 60, 4399.
(39) (a) Ward, R. L.; Weissman, S. I. J. Am. Chem. Soc. 1957, 79, 2086. (b)
Phillips, W. D.; Rowell, J. C.; Weissman, S. I. J. Chem. Phys. 1960, 33,
626.
(40) For example, the values of the EPR hyperfine splittings of the cation radicals
41a
are (in G): 4.5 (12H) for OMB+•
;
5.45 (2H), 3.34 (12H), and 1.67
(12H) for OMA+• 41a
7.15 (2N) and 1.9 (4H) for TPPD+• 41b
for DMD+• 41c 1.23 (4H) for TTF+• 41d
;
7.05 (2N), 2.0 (4H), and 6.8(12H) for TMPD+• 41b
4.37 (6H), 3.12(6H), and 0.48 (2H)
etc.
;
;
;
;
(41) (a) Kochi, J. K.; Rathore, R.; Le Magueres, P. J. Org. Chem. 2000, 65,
6826. (b) Grampp, G.; Kelterer, A.-M.; Landgraf, S.; Sacher, M.; Nietham-
mer, D.; Telo, J. P.; Dias, R. M. B.; Vieira, A. J. S. C. Monatsh. Chem.
2005, 136, 519. (c) Forbes, W. F.; Sullivan, P. D. J. Phys. Chem. 1968,
48, 1411. (d) Khodorkovsky, V.; Shapiro, L.; Krief, P.; Shames, A.; Mabon,
G.; Gorgues A.; Giffard, M. Chem. Commun. 2001, 2736.
(42) Note that the rate constants for electron-transfer self-exchange for most of
the ion radicals from Table 1 are available in the literature.23b,43 However,
the reported values were generally obtained with ion radicals prepared in
situ in various solvents and with different counterions. Accordingly, to
exclude solvent and counterion effects, we have remeasured all the rate
constants using consistently pure ion-radical salts with bulky counterions
in the same noncoordinating solvent, i.e., the moderately polar dichlo-
romethane.
(43) (a) Kowert, B. A.; Marcoux, B. A.; Bard, A. J. J. Am. Chem. Soc. 1972,
94, 5538. (b) Grampp, G. Spectrochim. Acta 1998, A54, 2349. (c) Grampp,
G.; Jaenicke, W. Ber. Bunsen. Phys. Chem. 1991, 95, 904. (d) Jurgen, D.;
Pedersen, S.; Pedersen, J. A.; Lund, H. Acta Chem. Scand. 1997, 51, 767.
(e) Eberson, L. AdV. Phys. Org. Chem. 1982, 18, 79. (f) Grampp, G.; Harrer,
W.; Hetz, G. Ber. Buns. Phys. Chem. 1990, 94, 1343.
(44) The self-exchange kinetics of the sterically hindered ion radicals were more
difficult to measure, and thus the values of kSE were somewhat less accurate
owing to the more complex hfs patterns with overlapping lines (slow
exchange limit). Moreover, the relatively slow second-order rate constants
of these closed ion radicals prevented their approach to the fast exchange
limit (see details in the Experimental Section).
(45) Calvert, J. G.; Pitts, J. N. Photochemistry; Wiley: New York, 1966; p
627.
9
J. AM. CHEM. SOC. VOL. 129, NO. 12, 2007 3687

A R T I C L E S
Rosokha and Kochi
Table 2. Rates Constants and Effective Activation Energies of the Electron-Transfer Self-Exchange Reaction of Ion Radicalsa
a Measured in CH2Cl2 at 295 K, with CB- or K(L) + counterions, unless noted otherwise. b Measured with SbCl6- counterion. c From ref 46. d From ref
+
22. e From ref 28b. f NBu4 counterion. g Doubled EPR spectrum at low temperature.41a
M-1 cm-1 for the phenothiazine cation radical.46,47 The intensity
of the new NIR absorption increased upon further additions of
the diamagnetic parent, and it also showed significant enhance-
ment as the temperature was lowered (Figure S4 in the
Supporting Information). Considerable differences in the NIR-
absorption intensity were apparent with various ion-radical pairs.
For example, the octamethylbiphenylene system (OMB/OMB+•)
showed intense NIR bands at λmax ) 1850 nm,41a whereas the
tetramethyl-p-phenylenediamine pair (TMPD/TMPD+•) af-
forded only a weak but quite distinct absorption in NIR region
(λmax ) 1050 nm) at the same concentrations (Figure S3 in the
Supporting Information). Comparable spectral data are tabulated
in Table 3 (columns 3 and 4) for the transient complexes of all
the open cation- and anion radicals. However, detailed
comparisons confirmed that the sterically hindered (closed) pairs
showed no evidence for complex formation since their parent/
ion-radical mixtures were completely transparent in the NIR
region between 1000 and 3000 nm, even at the highest attainable
concentrations and at very low temperatures.
(46) See Sun D.-L., et al. in ref 23b.
(47) Note that similar NIR absorption bands were observed in other solvents,
such as acetonitrile, acetone, THF, etc. The solvent dependence of such
systems will be reported later in detail.
Quantitative analysis of the absorption intensity with changing
concentrations of the parent/ion-radical combinations followed
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3688 J. AM. CHEM. SOC. VOL. 129, NO. 12, 2007

Outer-/Inner-Sphere Mechanisms for Organic ET
A R T I C L E S
Table 3. Thermodynamics of Ion-Radical Associations with Their
Parent (eqs 3 and 4) and Spectral Characteristics (NIR
+•
-•a
Intervalence Band) of the Dimeric Species: D2 or A2
transient
complex
λmax
(nm)
ꢀmax
(M-1 cm-
Kπ
−∆Hπ
(kcal/mol)
−∆Sπ
(eu)
1
1
)
(M-
)
+•
1a
2
(OMB)2+•
1850
2430
1050
c
1900
c
c
1850
c
2115
1515
1406
2200
5700
5000
1150
350
60
2.5b
5.7b
1.3b
2b
12b
4b
(OMA)2
+•
3a
3b
4a
4b
4c
5a
5b
6
(TMPD)2
0.1
+•
(TPPD)2
+•
(PTZ)2
1700
3
2.4b
4b
+•
(MePTZ)2
+•
(PrPTZ)2
+•
(DMB)2
530
0.9b
3.2b
10b
+•
(DBB)2+•
(TTF)2
5000
1000
3000
3200
6
5.5
3.4
3.2
3.3
16
8.5
6
-•
7
(TCNE)2
4.5
11
5
-•
8
(DDQ)2
-•
9
(TCNQ)2
7
a Measured in CH2Cl2 at 295 K, with CB-• or K(L) + counterions, unless
-
noted otherwise. b With SbCl6 c TC not observed (see text).
Figure 2. Typical spectral changes in NIR range attendant upon addition
of neutral parents to their ion radicals in dichloromethane (l ) 1 mm, 22
°C). (A) 2.1 mM OMA+•CB and (from bottom to top) 0, 0.7, 1.0, 1.5, 2.0,
3.0, 4.0 mM OMA. (B) 5.5 mM of K(L)+DDQ-• and 0, 1.6, 3.0, 4.6, 6.0,
8.0 mM of DDQ.
the pattern established earlier for the formation of cationic as
well as the anionic complexes according to eqs 3 and 4,
respectively,
Kπ
{
D + D+•
} [D, D+•]
(3)
(4)
Kπ
Figure 3. (A) Crystal lattice of the dimeric units formed by two partially
charged DDQ moieties with hydrogens and solvent molecules omitted for
A
-• + A { } [A-•, A]
\
clarity. (B) Details of the transient complex (TC) of DDQ and DDQ-•
.
for which typical intensity changes of the NIR absorption bands
are illustrated in Figure 2. The equilibrium constant (Kπ) for
complex formation derived from the concentration dependence
studies are included in column 5 of Table 3 (see Experimental
Section for details). The linear dependence of ln Kπ with inverse
temperature (see inset Figure S3) afforded the thermodynamic
parameters ∆Hπ and ∆Sπ which are listed in columns 6 and 7
(Table 3).
carefully overlaid with hexane, and the mixture was allowed to
stand undisturbed for several weeks, whereupon it deposited
dark brown crystals, the X-ray crystallographic analysis of which
revealed the triclinic unit cell to contain three independent DDQ
forms, hereinafter referred to as A, B, and C and paired with
the completely encapsulated potassium counterion K(15-crown-
+
5)2 shown in Figure 3A. Forms A and B constitute a pair of
2.4. Isolation and X-ray Structure of the Ion-Radical
Transient Complex. Dissolution of the crystalline potassium
salt of the dichlorodicyanoquinone anion radical (K+DDQ-•)43
in dichloromethane was accomplished by the addition of the
polyether ligand (benzo-15-crown-5) and was followed by the
addition of equimolar amounts of the parent acceptor (DDQ).
This dark green solution was simply cooled to -65 °C and
quite similar centrosymmetric dimeric units shown in Figure
3B, in which the DDQ moieties lie parallel to each other at the
close interplanar separation of rπ ) 2.95 Å (in form A) and
2.97 Å (in form B). In the crystal lattice, these dimeric units
are interchangeable with the bis-ligated potassium counterion,
as illustrated in Figure 3A. The third (more isolated) form C
consists of the monomeric DDQ unit that is separately arranged
9
J. AM. CHEM. SOC. VOL. 129, NO. 12, 2007 3689

A R T I C L E S
Rosokha and Kochi
between the stacks formed by interchanging dimeric units and
[K(15crown5)2]+.
Such a comprehensive analysis of the solid-state data leads
us to conclude that the paramagnetic (mixed-valence) complexes
-•
+•
such as (DDQ)2 and (TTF)2 share structural features in
To determine the distribution of the overall negative (-1)
charge between the DDQ moieties, they were analyzed in
comparison with those of the parent DDQ and its separated
anion radical DDQ-•. Such an analysis indicated that the
geometry of the separate species C is essentially that of the
neutral acceptor (see Table S2 in the Supporting Information).
On the other hand, both A and B forms show elongated CdO
and CdC double bonds and with the CsC single bond shortened
relative to that in the neutral acceptor. [The latter corresponds
to an increase of the electron density in the LUMO.] Moreover,
quantitative analysis similar to that in other benzoquinone
systems examined earlier48 (see Supporting Information for
details) indicated that each DDQ moiety in species A and B
bears one-half a negative charge to verify the overall (-1)
charge on each of the dimeric units. Most important for the
present study is the fact that geometries of these dimeric DDQ
units show the following: (i) the interplanar π-separations of
2.97 and 2.95 Å which are quite similar to those observed in
several diamagnetic dianionic dimers of DDQ and its dianionic
triplex associates;23a and (ii) the lateral shifts of ∼1.8 Å parallel
and ∼0.4 Å perpendicular to the O-O axis, as also observed
in other associates.49
2-
common with their diamagnetic (dimer) analogues, (DDQ)2
49 and (TTF)22+ 22 and that the latter can be gainfully employed,
,
especially when the former structure is experimentally unavail-
able (vide infra). The interplanar π-separation within the cofacial
(1:1) array which is measurably less than their van der Waals
radii, but subject to some lateral excursion, points to a rather
shallow potential minimum or multiple, close-lying minima22
to indicate that the same mutual arrangement of the ion radical
with its neutral parent is also likely to coexist in solution. In
such a case, we conclude that the cofacial arrangement and
interplanar separation extant in the transient complex (TC)
represent a reasonable approximation of the precursor complex
(PC) in the electron-transfer self-exchanges of interest in this
study.
2.5. Electronic Structures of the Transient Complexes. The
well-defined electronic transitions in the NIR spectral region
that characterize the ion-radical complexes in Table 3 allow
the application of Mulliken-Hush (two-state) methodology55
to establish values of the electronic coupling element (HDA) and
the reorganization energy (λ) for electron transfer within these
1:1 cation-radical and anion-radical associates, i.e.,
The unit cell shown in Figure 3A clearly demonstrates the
existence of discrete dimeric units of the DDQ moiety in the
crystalline complex. As such, its cofacial or face-to-face (slightly
slipped) π-stacking at the interplanar separation of rπ ≈ 3 Å is
strongly related to those of analogous ion-radical assemblies
observed with octamethylbiphenylene,50 tetracyanoquinodimeth-
ane,51 and tetrathiafulvalene,22 in which the dimeric units
(OMB)2+•, (TCNQ)2-•, and (TTF)2+• have also been structur-
ally characterized, but in less cleanly differentiated units. We
also note that the crystallographic literature contains structural
data of the other ion-radical salts listed in Table 1, but as other
types of intermolecular associates that include dicationic and
dianionic dimers as well as mixed-valence triads, pentads, and
higher aggregates.52 It is thus noteworthy that they are uniformly
characterized by a common structural motif consisting of the
parallel (cofacial) π-arrangements of planar entities (lying atop
each other but somewhat shifted laterally) at interplanar separa-
tions that lie in a rather narrow range of rπ ≈ 3.0-3.3 Å, which
is notably 0.2-0.5 Å shorter than the sum of their van der Waals
radii.53 Furthermore, no pertinent structural distinction can be
made between the paramagnetic (ion-radical) complexes estab-
lished in this and other related systems from those of the
diamagnetic (dimer) dications and dianions in the same family
of ion radicals.22,23
[D, D+•] {ET} [D+•, D] and [A-•, A] {ET
\ \
} [A, A-•] (5)
However, such an analysis requires the prior assignment of both
ion-radical complexes to either a localized (Class II) or
delocalized (Class III) category within the Robin-Day clas-
sification.56 Thus, in localized mixed-valence complexes, the
reorganization energy is equal to the intervalence transition
energy, i.e., νIV ) λi + λs (where λi is the vibrational and the
λs is solvent component of the reorganization energy), and it is
solvent-dependent. The electronic coupling in such systems can
be evaluated as55
HDA ) 0.0206(νIV ∆ν1/2 ꢀIV)1/2/rDA
(6)
where νIV and ∆ν1/2 are the spectral maximum and full width
at half-maximum (cm-1) of the electronic (intervalence) band,
ꢀIV is its extinction coefficient (M-1 cm-1), and rDA is the
separation (Å) between the (donor/acceptor) redox centers. On
the other hand, in the delocalized complexes the electronic
coupling is evaluated directly from the energy of the intervalence
transition as νIV ) 2HDA, and it is essentially solVent-
independent.
We have already noted that, in some systems (e.g., DMB+•/
DMB), the energies of the intervalence bands are notably higher
in more polar solvents (such as DMF, acetonitrile, and acetone)
than those measured in the less polar dichloromethane, whereas
(48) See Lu, J. M., et al. in ref 32.
(49) (a) Yan, Y.-K.; Mingos, M. P.; Muller, T. E.; Williams, T. E.; Kurmoo,
M. J. Chem. Soc., Dalton Trans 1995, 2509. (b) Marzotto, A.; Clemente,
D. A.; Pasimeri, L. J. Crystallogr. Spectrosc. Res. 1988, 18, 545.
(50) Le Magueres, P.; Lindeman, S.; Kochi, J. K. J. Chem. Soc., Perkin Trans.
2 2001, 1180.
+•
in some cases such as (OMB)2 the NIR transitions are
practically solVent-independent. We accordingly assigned the
first group of ion-radical complexes to Robin-Day Class II, and
the second to Class III in Table 4. Importantly, such an
assignment is supported by ab initio computations of the
electronic coupling and reorganization energies in various
(51) (a) Goldstein, P.; Seff, K.; Trueblood, K. N. Acta Crystallogr. 1968, B24,
778. (b) Hanson, A. W. Acta Crystallgr. 1968, B24, 773. (c) Kobayashi,
H. Bull. Chem. Soc. Jpn. 1974, 47, 1346.
(52) Soos, Z. G.; Klein, D. J. In Molecular Association; Foster, R., Ed.; Academic
Press: New York, 1975; Vol. 1.
(53) (a) The measurable contraction of the interplanar separation beyond their
van der Waals radii53b is taken to represent the inner-sphere character of
the intermolecular interaction as spectrally revealed by the charge-transfer
transition. For a discussion of this important point, see Rathore, et al. in
ref 33d. (b) Bondi, A. J. Phys. Chem. 1964, 68, 441.
(55) (a) Creutz, C.; Newton, M. D.; Sutin, N. J. Photochem. Photobiol. A: Chem.
1994, 82, 47. (b) Brunschwig, B. S.; Sutin, N. In Electron Transfer in
Chemistry; Balzani, V., Ed.; Wiley: New York, 2001; Vol. 2, p 583.
(56) Robin, M. B.; Day, P. AdV. Inorg. Chem. Radiochem. 1967, 10, 247.
(54) See Rosokha, S. V., et al. in ref 22.
9
3690 J. AM. CHEM. SOC. VOL. 129, NO. 12, 2007

Outer-/Inner-Sphere Mechanisms for Organic ET
A R T I C L E S
Table 5. Computeda Reorganization Energies and Coupling
Table 4. Mulliken-Hush Analysis of the Electronic Interaction
within the Transient π-Complex
Elements for the Mixed-Valence Ion-Radical Complexes in
Comparison with Experimentalb (Spectral) Values
ion-radical
νIV
,
HDA,
a
expt b
λcalcd
(103 cm-
λexpt
(103 cm-
HDA
HDA
1
1
π
-complex
Class
rπ, Å
103 cm-
103 cm-
transient
complex
1
1
1
1
)
)
(103 cm-
)
(103 cm-
)
+•
1
2
3a
4a
5a
6
7
8
9
(OMB)2+•
III
III
II
II
II
II
II
II/III
II/III
3.2
3.3
3.1
3.2
3.2
3.4
3.0
2.9
3.2
5.4
4.1
9.5
5.3
5.4
4.7
7.2
7.1
4.6
2.7a
+•
(OMA)2
2.1a
1.7b
1.1b
0.7b
1.6b
1.1b
1
2
3a
5a
6
(OMB)2+•
4.0 (6.2)
2.5 (4.9)
5.7 (10.5)
5.8
4.4
4.4 (6.6)
5.5 (9.4)
-
-
2.3 (3.2)
- (3.3)
2.6 (3.7)
2.5
3.6
4.2 (7.2)
3.4 (4.8)
2.7
2.1
1.7
0.7
1.6
1.1
+•
(OMA)2
(TMPD)2
+•
+•
(TMPD)2
9.5
5.4
4.7
6.6
7.1
(PTZ)2
(DMB)2
(TTF)2
+•
+•
(DMB)2
(TTF)2
+•c
+•
-•d
-•
7
8
(TCNE)2
(TCNE)2
-•
-•
(DDQ)2
3.6a (1.8)b
2.3a (1.4)b
(DDQ)2
3.6 (1.8)
-•
(TCNQ)2
a B3LYP calculation and the Hartree-Fock calculation in parentheses.
b See Table 4. c From ref 22. d From ref 28b.
a HDA ) νIV/2. b From eq 6.
complexes (vide infra). Additionally, this assignment is con-
sistent with the larger formation constants of Class III com-
plexes, and this is confirmed by the observation of the “doubled”
combinations of the localized molecular orbitals of the mono-
mers, as described earlier.59 Thus in the cation-radical complex,
the electronic coupling element was calculated as one-half of
the energy difference between the HOMO and HOMO-1
(resulting from the pairwise splitting of the HOMO orbital of
the parent donor) in the neutral closed-shell dimer. Likewise,
in the anion-radical complex, HDA was calculated as one-half
of the energy difference between the LUMO + 1 and LUMO
(resulting from orbital splitting of the acceptor LUMO in the
corresponding neutral dimer).60 The computed values (see
Experimental Section and the Supporting Information for details)
are listed in Table 5.
ESR spectrum of the (OMB)2 π-complex (vide supra).41a
+•
For Class II complexes, we thus calculated the electronic
coupling element HDA from eq 6 based on the spectral
characteristics of the NIR band using the separation parameter
(rπ) taken from solid-state data, and the reorganization energy
was equated to the energy of NIR transition. For Class III
complexes, the coupling energy was determined directly from
the intervalence transition as HDA ) νIV/2. The data are
presented in the last column of Table 4.
Since the corresponding spectral data for the ion-radical
complexes of the sterically hindered analogues were experi-
mentally unavailable owing to the very limited magnitude of
their formation constant (Kπ in Table 3) sufficient to allow their
isolation, we next turned to several quantum-mechanical
methods to compute estimates of the electron-transfer parameters
λ and HDA. Before proceeding further, however, it was necessary
to evaluate the reliability of the theoretical methods by first
comparing the computed values of λ and HDA with the
corresponding experiment-based values obtained from the
spectral data and eq 6 as follows.
2.6. Computations of the Reorganization (λ) and Elec-
tronic Coupling (HDA) Energies. 2.6.1. Reorganization En-
ergy. The intramolecular component (λi) was calculated as the
energy difference between the initial diabatic state with the
electron located on the donor (with reactants in their relaxed
geometries) and the final diabatic state (with the same nuclear
geometry but the electron transferred to the acceptor)57 see
Experimental Section for details. The solvent reorganization
energy (λo) for electron transfer within the ion-radical complex
was based on the solvent cavity of radii ao with an internal
dielectric constant of ꢀin ) 2 immersed in medium with static
and optical dielectric constants ꢀs and ꢀo, respectively, using
the Kirkwood solvation model.28,58 The estimated values of the
reorganization energies are listed in Table 5 for several ion-
radical complexes in dichloromethane (for computational details
of λi and λo, see the Experimental Section and Supporting
Information).
The comparative values of the computed reorganization
energy (λ) and coupling element (HDA) in Table 5 based on
solid-state structures of the ion-radical complexes led us to
several important conclusions. First, the results of the DFT
calculations of the electronic coupling elements for Class III
π-complexes agree well with those obtained from spectral data
based on Hab ) νIV/2 [note the experimental reorganization
energies are unavailable for these types of ion-radical π-com-
plexes]. Second, for Class II complexes, the experimental
reorganization energies from the intervalence transition energy
lie between the values obtained with the Hartree-Fock and the
DFT-computed intramolecular reorganization component λi.
However, the computed coupling elements are notably higher
than those derived from the experimental (spectral) energies.
The probable origin of such a discrepancy was discussed earlier,
and it lies in either the uncertainty of the separation parameter
61-63
rπ
or the labile nature of the ion-radical complex in
solution,64 or both. Such ambiguities notwithstanding, we
conclude that the molecular-orbital computations are in reason-
able agreement with the experimental (spectral) data, certainly
sufficient to provide theoretical insight into the electronic
coupling elements of the sterically hindered ion-radical com-
plexes in the following way.
While bulky substituents generally prevent the close approach
of sterically hindered moieties, the molecular modeling (MM)
studies indicate that a pair of di-tert-butyl-substituted dimethoxy-
benzene (see DBB in Table 1) moieties can approach each other
(59) Newton, M. D. Chem. ReV. 1991, 91, 767.
2.6.2. Electronic Coupling Element. Theoretical evaluations
of HDA for the ion-radical complexes were based on the energy
splitting resulting from the symmetric and antisymmetric
(60) Huang, J.-S.; Kertesz, M. J. Chem. Phys. 2005, 122, 234707.
(61) As noted recently,62 the proper values of rDA for the Mulliken-Hush
equation may be significantly lower than that based on the geometric
separation (rπ) of the redox centers, which implies that the correct coupling
element may be up to 50% higher than that calculated from the crystal-
lographic data.63
(57) (a) Nelsen, S. F.; Blackstock, S. C.; Kim, Y. J. Am. Chem. Soc. 1987, 109,
677. (b) Perng, B.-C.; Newton, M. D.; Raineri, F. O.; Friedman, H. L. J.
Chem. Phys. 1996, 104, 7153.
(58) Vener, M. V.; Ioffe, N. T.; Cheprakov, A. V.; Mairanovsky, V. G. J.
Electroanal. Chem. 1994, 370, 33.
(62) (a) Newton, M. D. In Electron Transfer in Chemistry; Balzani, V., Ed.;
Wiley-VCH, New York, 2001; Vol. 1, p 3 ff. (b) Nelsen, S. F.; Newton,
M. D. J. Phys. Chem. A 2000, 104, 10023.
(63) See the discussion by Rosokha et al. in ref 22.
9
J. AM. CHEM. SOC. VOL. 129, NO. 12, 2007 3691

A R T I C L E S
Chart 3
Rosokha and Kochi
nism for the self-exchange processes in eqs 1 and 2, since they
all pertain to identical experimental conditions of concentrations,
temperatures, and solvents.
3.1. Generalized Formulation of the Electron-Transfer
Kinetics for Ion-Radical Self-Exchanges. The direct melding
of the second-order kinetics for eqs 1a and 1b with the
equilibrium complex formation in eqs 3 and 4 leads to the
composite mechanistic formulation in Scheme 1 which is equally
applicable to cation radicals as well as to anion radicals as
described in eqs 7 and 8, respectively.
Scheme 1
crosswise to an effective interplanar separation of ∼5 Å without
significant atomic overlap (Chart 3).
Roughly the same separation also pertains in the laterally
shifted complex from tetraisopropyl-substituted p-phenylendi-
amine (TPPD). In order to estimate the values of the electronic
coupling elements of the sterically hindered complexes, we
computationally varied the interplanar separations (rπ) extant
in those derived from the sterically open parents. In all cases,
the increase in the interplanar separation resulted in an
exponential decrease in the HOMO splitting as typically depicted
in Figure 4.
Indeed, the generalized self-exchange mechanisms in Scheme
1 contain the important earmarks of the earliest theoretical
formulations of electron transfer,4 in which the diffusive
encounter (kdiff) of the donor/acceptor (redox) pair leads to the
1:1 precursor or encounter complex, [D,D+•] and [A-•,A],
followed by the rate-limiting electron transfer (kET) to afford
the successor complex [D+•,D] and [A,A-•], etc. It is thus his-
torically noteworthy that the earliest formulation of the diffusive
encounters of electron donor/acceptor pairs by Mulliken15a
identifies the electronic transition that characterizes the various
1:1 associates as charge transfer to encompass the HOMO-
LUMO gap. Since the related theoretical concept is involved
as the interValence transition in the Hush formulation,11 their
descriptions of the precursor complex must be considered
interchangeable,65 i.e., hνIV(Hush) ) hνCT (Mulliken), and the
preequilibrium steps in Scheme 1 are diffusion limited, as de-
scribed in (all) other electron-transfer theories. Under these
circumstances, the energy of the intervalence (charge-transfer)
transition within the transient complex (TC) can be directly
considered in the context of the activation barrier for adiabatic
electron transfer in the precursor complex (PC), in line with
the classical two-state model developed by Hush for mixed-
valence systems.11,55
Figure 4. Exponential dependence of the HOMO splittings on the
interplanar separation within (TMPD)2 (calculated at the B3LYP/6-31G*
level).
According to the calculations in Figure 4, the electronic-
coupling characteristics of HDA ≈ 100-300 cm-1 are to be
expected when the cofacial dyads are (artificially) arranged at
an interplanar separation of rπ ≈ 5-5.5 Å, and we have used
these estimates (together with the reorganization energy taken
from unhindered parents) in the kinetics analysis of the ET self-
exchange processes for the ion radicals presented in Table 1.
3.2. Steric Effects on the Potential-Energy Surfaces for
Ion-Radical Self-Exchange. Electron transfer occurring within
the precursor complex plays a crucial role for the overall kinetics
for Scheme 1. According to Sutin et al.,66 the adiabatic ground-
state (GS) and the excited-state (ES) energies for such a com-
plex are obtained via the interaction of the diabatic states at
each point (X) along the electron-transfer reaction coordinate
as
3. Discussion
The spectral detection, isolation, and X-ray structures of the
series of transient complexes in Figures 2 and 3 provide the
critical links to the elucidation of the electron-transfer mecha-
EGS,ES ) (HDD + HAA)/2 ( ((HDD - HAA)2 + 4HDA2)1/2/2
(9)
(64) The experimental numbers in Table 5 represent the averaged values over
a variety of mutual arrangements involving multiple local minima around
the basic structure, as discussed in ref 22. The most common example of
such a deviation is the lateral shift parallel or perpendicular to the main
axis, as well as mutually perpendicular arrangements. Earlier analysis of
tetrathiafulvalene dyads showed that several local maxima result from such
deviations, and a somewhat similar behavior can be expected for other
systems. For example, for TMPD the mutual arrangement atop each other
(as in its salt with the ClO4- counterion) is characterized by HDA ) 2.1 ×
103 cm-1, while the value of HDA ) 2.6 × 103 cm-1 pertains to the dyad
resulting from shifts by ∼1.8 Å parallel to the main axis. Likewise, the
crossed structure produces the rather small coupling of HDA ) 0.2 × 103
cm-1. In contrast, the lateral shift of dimethoxybenzene moieties leads to
a decrease of HDA, but in this case, the parallel and crossed structures are
where HDD ) λX2 and HAA ) ∆GET + λ(X - 1)2 represent the
energies of the initial and final diabatic states along the reaction
coordinate, and the coupling element HDA is assumed to be
(65) (a) See: Le Magueres et al. in ref 50 and references therein. (b) It should
be noted that, in Mulliken theory, the charge-transfer transitions in
intermolecular complexes are primarily considered in terms of the constitu-
ent donor/acceptor redox or ionization potentials, whereas, in Hush theory,
the intervalence transition in localized or bridged (intramolecular) mixed-
valence complexes are primarily related to the reorganization energies. Since
the ion-radical associates of interest in this study are intermolecular mixed-
valence complexes, we refer to the NIR optical transitions as charge transfer
or intervalence interchangeably to combine both features.
characterized by comparable values of HDA) (2.4 and 1.7) × 103 cm-1
,
respectively. The energy differences among such in-plane (librational)
excursions are expected to be minor in solution.28
(66) Brunschwig, B. S.; Sutin, N. Coord. Chem. ReV. 1999, 187, 233.
9
3692 J. AM. CHEM. SOC. VOL. 129, NO. 12, 2007

Outer-/Inner-Sphere Mechanisms for Organic ET
A R T I C L E S
Figure 5. Representative energy diagrams for electron transfer within ion-radical complexes: (a) sterically hindered [TPPD/TPPD]+• with Hab ) 250 cm-1
, λ/2; (b) sterically open [TMPD/TMPD]+• with Hab ) 1700 cm-1 < λ/2, and (c) in the sterically close [OMB/OMB]+• with Hab ) 2700 cm-1 > λ/2.
Table 6. Comparison of the Experimental and Calculated Rates
constant. Thus, the spectral (or computational) evaluation of
Constants for Electron-Transfer Self-Exchange of Organic Ion
the reorganization energies and coupling elements allows us to
calculate the energy surface for electron transfer within various
ion-radical complexes with ∆G° ) 0. Sutin’s development12,66
of the Marcus-Hush formulation10,11 specifically describes how
the electronic coupling element (HDA) directly affects the ET
transition state, as illustrated in the potential-energy diagrams
in Figure 5. In each case, the lightly dashed parabolic curves
portray the separate reactant (blue) and product (green) diabatic
surfaces, respectively, the electronic interaction of which leads
to the overall potential-energy surface for electron transfer
shown as the lower (heavy red) curves.
The sequence in Figure 5a-c represents typical examples of
the increasing interplay between the “intrinsic” barrier (λ) and
the “resonance” stabilization (HDA) of the transition state. In
particular, these are arbitrarily classified as three limiting energy
surfaces for electron transfer, which are designated as (a) Type
S with λ/2 . HDA, (b) Type M with λ/2 g HDA, and (c) Type
L with λ/2 e HDA. In practice, these three limiting types of the
free-energy profiles as illustrated in Figure 5 are found
experimentally for the TPPD/TPPD+•, TMPD/TMPD+•, and
OMB/OMB+• dyads in which the HDA values are small (250
cm-1), medial (1700-1), and large (2500 cm-1), respectively,
in comparison to λ; and this series also reflects the decreasing
trend in the steric hindrance extant between these donor/acceptor
moieties (vide supra).
3.3. Electron-Transfer Mechanisms for Ion-Radical Self-
Exchanges. The Mulliken-Hush delineation of the potential-
energy surfaces into the three distinctive categories, Type S,
M, and L, as depicted in Figure 5, necessitates the reevaluation
of the generalized mechanistic proposal for self-exchange, as
initially presented in Scheme 1 (eqs 7 and 8) in the following
way.
3.3.1. Energy-profile Type S encompasses the precursor
complex of sterically hindered ion radicals in which the
interplanar separation of rπ ≈ 5-6 Å is characterized by
electronic coupling elements of HDA ≈ 100-300 cm-1. Their
adiabatic (state) energies are likely to approximate those of the
diabatic states, with notable deviations being only observed at
Radicalsa
ion
∆
G*,b
k
SE (calcd),c
kSE (expt),
1
1
radical
(kcal/mol)
(109 M-1 s-
)
(109 M-1 s-
)
1a
2
OMB+•
OMA+•
TMPD+•
TPPD+•
PTZ+•
0
0
3.2
6.3
0.8
0.003
7.0
0.4
1.0.
0.3
7.5
10
2.4
2.5
2.3
0.01
4.7
0.3
1.5
0.1
2.7
4.3
2.5
3.3
3a
3b
4a
4c
5a
5b
6
7
8
9
2.9
6.2c
1.3
3.2c
2.2
3.3c
0.4
2.2
1.2
0.6
PrPTZ+•
DMB+•
DBB+•
TTF+•d
TCNE-•e
DDQ-•
TCNQ-•
7.5
7.5
a In CH2Cl2 at 295 °C. b With eq 11. c See Experimental Section for
calculation details. d Reference 22. e Reference 28b.
or around the transition state. No significant resonance stabiliza-
tion of the ground state of the precursor complex is evident,
and thus its formation constant is usually insufficient for
experimental detection. It should be stressed, however, that
although the coupling of ∼200 cm-1 has only a rather minor
effect on the transition energy in such a system, it is sufficient
to ensure adiabatic electron transfer and the electronic transmis-
sion factor for electron transfer will be close to unity, and the
second-order rate constants kSE for the bimolecular electron-
transfer processes in Scheme 1 can be described as
kSE ) Z exp(-∆G*/RT)
(10)
where Z ) 1011 M-1 s-1 is the collision frequency, and the
activation barrier (for ∆G° ) 0) is67
∆G* ) (λ - 2Hab)2/4λ
(11)
The application of eqs 10 and 11 using the reorganization
energies and coupling elements evaluated for the hindered donor/
acceptor dyads in Table 5 leads to the second-order rate
constants listed in Table 6 which are in reasonable agreement
with the experimental values.
3.3.2. Energy-profile Type M is characterized by coupling
elements for sterically “open” ion radicals that form mixed-
valence precursor complexes with interplanar separations of rπ
) 3.0-3.3 Å and the coupling elements of HDA ≈ 1000-3000
cm-1 which measurably alter the potential-energy surface for
the electron transfer within the precursor complex, as is
(67) (a) Note that the activation barrier and the calculated electron-transfer rates
are affected even by such relatively small values of HDA. For example, in
the p-phenylenediamine system with λ ) 9500 cm-1, the correction for
Hab ) 250 cm-1 leads to a 3-fold increase in rate. (b) We believe that, in
Type S systems, the electronic coupling between redox centers in organic
donor/acceptor dyads is sufficient for adiabatic electron transfer even for
the sterically hindered moieties. Compare: Nelsen, S. F.; Pladziewicz, J.
R. Acc. Chem. Res. 2002, 35, 247.
9
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A R T I C L E S
Rosokha and Kochi
characteristic of Robin-Day Class II mixed-valence systems.56
Thus, even for dyads with relatively low ratios of HDA/λ, such
as TMPD+•/TMPD, the barrier for electron transfer is roughly
halved relative to those in weakly interacting systems with ∆G*
) λ/4. Moreover, the ground-state stabilization of such a system
enables this precursor complex to be observed in solution with
the aid of electronic (NIR) spectroscopy and its formation
constant to be calculated generally in the order of Kπ ≈ 0.1-1
M-1 in Table 3. It is also possible to calculate the overall rate
of the self-exchange process for the energy profile based on
the experimentally measured formation constant (Kπ) of the ion-
radical complex and the intramolecular rate constant (kET) given
as68
Notably, the experimental characteristics of the delocalized
complex near or beyond the Class II/III border are generally
similar to those of strongly coupled Class II systems. However,
the increased stability of an ion-radical complex such as OMB/
OMB+• (which is characterized by the formation constant of
Kπ ≈ 350 M-1) results in the appearance of principal new
features. First, such high equilibrium constants from the kinetics
point of view necessitates the rate constant for dissociation to
be explicitly taken into account, since dissociation can become
the rate-limiting step. Indeed, numerical calculations of the self-
exchange (see Experimental Section for details) result in rate
constants for self-exchange of OMB which are slower than those
determined for Robin-Day Class II systems discussed above.
Moreover, lowering the temperature can result in decreased rates
kET ) κelνn exp(-∆G*/RT)
(12)
+•
of (OMB)2 dissociation. Thus, the exchange rates between
the monomeric and dimeric paramagnetic species can even
become slow on the EPR time scale, such that two separate
EPR spectra can be simultaneously observed. At very low
temperatures, almost all the monomer is associated, and the pure
Notably, the kETKπ product for the “open” ion radicals described
in Table 1 (with the formation constant of the precursor complex
taken from Table 3) is close to, or even faster than, the
bimolecular diffusion rate, as evaluated by kdiff ) 1.5 × 1010
M-1 s-1 in CH2Cl2 at 295 K. Therefore, the self-exchange rate
constant kSE for the bimolecular electron-transfer process in
Scheme 1 must be recalculated from the standard steady-state
approximation,69 i.e.,
+•
spectrum of the dimeric (OMB)2 with a doubled number of
lines and halved splitting constants is observed in solutions
containing both OMB+• and OMB.70 Moreover, the high
equilibrium constants for such a π-complex formation is further
reflected in the unusual electrochemical behavior of OMB that
shows the oxidation wave to be split upon lowering the
temperature. Although quantitative modeling of the splitting is
beyond the scope of the current work, qualitatively it is related
to the fast (and significant) complex formation of the oxidized
species while the neutral donor is still available in solution at
the earliest stages (i.e., foot) of the CV wave. Indeed, the anodic
behavior of the dimeric (OMB)2+• is similar to the splitting of
the oxidation wave previously observed in mixed-valence
(bridged) systems.8b
1/kSEcalcd ) 2/kdiff + 1/KπkET
(13)
and these values of the second-order rate constant for the self-
exchange are included in Table 6.
Strongly coupled Class II complexes (such as those involving
TTF),22 with large ratios of HDA/λ, are characterized by higher
equilibrium constants in the range of Kπ ≈ 1-10 M-1. Most
importantly, the barriers for electron transfer within such ion-
radical complexes drop to almost zero, and they consequently
approach the Robin-Day Class II/Class III borderline. On the
3.4. Conciliation of Organic versus Inorganic Electron-
Transfer Mechanisms. The foregoing comprehensive descrip-
tion of organic electron-transfers contains a number of important
features in common with Taube’s seminal dichotomy into
separate outer-sphere and inner-sphere electron-transfer mech-
anisms based on the behavior of inorganic coordination com-
plexes, as follows in (i), (ii), and (iii) below.
-•
-•
other hand, such dyads as (DDQ)2 and (TCNQ)2 show
equilibrium constants in the same range, but the solvent
dependence of their NIR bands reveals their possible delocalized
nature. It thus appears that these precursor complexes also lie
close to the Class III/Class II border but more on the delocalized
side.
3.3.3. Energy-profile Type L includes ion-radical complexes
that lie beyond the Class II/III border. Owing to the large values
of HDA (relative to λ) resulting in the complete delocalization
of the electron in the Robin-Day Class III (ion-radical)
associates,71 the separate precursor and successor complexes in
the electron-transfer mechanism in Scheme 1 must be replaced
by a single intermediate as shown in Scheme 2. Thus, the overall
(i) The outer-sphere versus the Type S process for self-
exchange lie co-incident at one end of a mechanistic spectrum
since both of their loosely bound (degenerate) precursor and
successor complexes exhibit only weak electronic coupling with
HDA < 200 cm-1 characteristic for electron-transfer processes
of inorganic redox dyads which are adequately described by
Marcus (outer-sphere) theory.10
(ii) At the other mechanistic extremum, the classical (Taube)
inner-sphere mechanism and the Type L pathway both occupy
the other, strongly adiabatic limit in which the extensive
electronic couplings between donor/acceptor moieties with HDA
g 2700 cm-1 are enforced by direct ligand bridging and by
intimate (cofacial) juxtapositions, respectively.71
Scheme 2
self-exchange processes according to Scheme 2 are controlled
by (diffusive) association and dissociation of the π-complexes.
(68) Where κel is the electronic transmission coefficient (κel ≈ 1 for adiabatic
reaction) and νn is the nuclear vibration frequency.12,
66
If such mechanistic concepts of electron transfer are to have
any generality, they must equally accommodate the complete
spectrum of quantitative reactivities (including Type M) of both
organic and inorganic donors and acceptors, despite any intrinsic
structural differences among them.72 Accordingly, let us proceed
by extending Taube’s outer-sphere/inner-sphere terminology to
organic redox dyads. Since organic donors and acceptors are
(69) Newton, M.; Sutin, N. Ann. ReV. Phys. Chem. 1986, 35, 435.
(70) As such, the study of OMB provides the direct link between the earlier
separate ESR studies of the self-exchange process, on one hand, and the
electronic structure of the paramagnetic dimers, on the other hand.
(71) (a) For other examples of the unusual Type L potential-energy surfaces in
intermolecular electron-transfer processes, see: (b) Rosokha, S. V.; Kochi,
J. K. New J. Chem. 2002, 26, 851. (c) Rosokha, S. V.; Dibrov, S. M.;
Rosokha, T. Y.; Kochi, J. K. Photochem. Photobiol. Sci. 2006, 5, 914. (d)
See also ref 29.
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Outer-/Inner-Sphere Mechanisms for Organic ET
A R T I C L E S
not usually considered in terms of ligand-dependent “coordina-
tion spheres”, we propose an alternative allusion to “distance-
dependence” which is based on the effective van der Waals radii
of electron donors and acceptors.53 In this way, the bimolecular
interactions in outer-sphere processes are also viewed as those
that extend beyond their van der Waals separation, as denoted
by rOS in Chart 1. Equivalently, the inner-sphere interactions
are then those that are manifested in a measurable van der
Waals’ distortion owing to the close juxtaposition of donor/
acceptor dyads in the precursor complex, so that the inner-sphere
separation (rIS) in Chart 1 is substantially more intimate than
the outer-sphere separation (rOS).73
(iii) The medial Type M potential-energy surface, on this
basis, derives from the attractive electronic coupling (HDA) that
is sufficient to contract the donor/acceptor separation, with the
magnitude of rIS diagnostic of a localized (Class II) inner-sphere
precursor complex. Likewise, the Type L potential-energy
surface from a strongly coupled donor/acceptor dyad is described
as a delocalized (Class III) inner-sphere precursor complex.71
It is important to note that for both Type M and L systems
the spectroscopic observations of the intermolecular charge-
transfer or intervalence absorption bands are the experimental
harbinger of the inner-sphere interactions extant within the
precursor complexes because such HOMO f LUMO transitions
are absent (or very weak) when the donor/acceptor separations
lie beyond the van der Waals limit.53
a complete donor/acceptor delocalization diagnostic of Robin-
Day Class III. In this case, the separate precursor and successor
complexes are merged (Scheme 2) because the intermolecular
electron transfer accompanies the diffusive encounter of the
donor/acceptor dyad without any reorganization barrier.
4.1. Continuum of Outer-Sphere and Inner-Sphere Mech-
anisms for Ion-Radical Self-Exchanges. When viewed in this
way, there will be a continuous progression of precursor
complexes in which the electronic coupling element (HDA) is
strongly and easily modulated by the donor/acceptor separation
(rDA) and orientation, as affected by steric factors, solvation,
etc. This mechanistic picture is strongly dependent on the
Mulliken-Hush formulation of the diffusive intermolecular
intermediates, in which HDA values can continuously vary over
a range of donor/acceptor (redox) functionalities and (steric)
separations.
We believe that organic donors and acceptors are ideally
suited for quantitative studies of electron-transfer mechanisms
for several important reasons. Thus, organic redox groups such
as benzenoid and other aromatic systems as well as mono- and
polyolefinic centers are planar and offer open π-access which
is at the same time easily controlled, i.e., “tuned”, by remote
substitutents. Next, such electron donors and acceptors are, by
and large, substitution stable, and the complication and ambigu-
ity from extraneous pre-equilibrium processes can be circum-
vented. Most important, the electronic transitions that charac-
terize the critical precursor complex can usually be found in
accessible spectral regions for experimental (Mulliken-Hush)
and theoretical analysis.
4. Summary and Conclusions
The three limiting potential-energy surfaces described in
Figure 5 as Types S, M, and L, in a more general mechanistic
context, can be represented as an alternative, expanded version
of Taube’s seminal dichotomy into separate outer-sphere and
inner-sphere electron-transfer transition states. First, the outer-
sphere and Type S processes both occupy one end of a
mechanistic spectrum (Scheme 1) that pertains to nonadiabatic
or weakly adiabatic electronic transitions within the precursor
complex. Second, Type M processes represent a broad inter-
mediate range of inner-sphere mechanisms in which the
intermolecular separation (rDA ) rIS) between donor and
acceptor moieties is considerably contracted, lying closer than
the sum of their van der Waals radii, to form localized precursor
complexes which are alternatively described as belonging to
Robin-Day Class II. These transient donor/acceptor associates
are sufficiently bound to reveal intervalence electronic transitions
Finally, we hope that the “separation-based” measure of the
precursor complex (rDA ) rOS or rIS) will provide useful and
quantitative insights for the mechanistic evaluation of a variety
of other electron-transfer processes, especially as they apply to
hybrid organic/inorganic,15 metalloorganic,13c and biochemical17
redox dyads of increasing relevance in today’s diversified
applications.
5. Experimental Section
5.1. Materials. Tetramethyl-p-phenylenediamine (TMPD), phe-
nothiazine (PTZ), N-methylphenothiazine (MePTZ), tetrathiafulvalene,
(TTF), dichlorodicyanobenzoquinone (DDQ), tetracyanoethylene
(TCNE), and tetracyanoquinodimethane (TCNQ) from commercial
sources were purified by sublimation in vacuo and/or by recrystallyza-
tion. Octamethylbiphenylene (OMB),41a octamethylanthracene (OMA),41a
tetra-isopropyl-p-phenylenediamine (TPPD),41b and dimethoxydimeth-
ylbenzene (DMB)72f were synthesized and identified according to the
literature procedures. Solvents were prepared and handled as described
in which Mulliken-Hush analysis leads to the reduced reor-
74
ganizational barriers by the amount: λ/4 - HDA
.
Third, the
Type L process and the delocalized inner-sphere mechanism
both occupy the other, strongly adiabatic limit sufficient to effect
earlier.23b Cation-radical salts D+•CB- and D+•SbCl6 were produced
-
in dichloromethane by oxidation of the donor with stoichiometric (1:
1) amounts of either dodecamethylcarboranyl radical CB• (prepared
(72) For example, inorganic donor/acceptor dyads are metallocentric, and electron
transfer is largely directed between single atomic centers. In contrast,
organic donor/acceptor dyads involve multiple (carbon) centers, and electron
transfer is consequently more diffusive. Moreover, ligands usually play
important roles in inorganic (coordination) donors and acceptors, whereas
the concept is alien to and essentially undefined in organic donors and
acceptors.
by oxidation of Cs+CB- with PbO2)34 or nitrosonium salt NO+SbCl6
-35
and precipitated with hexane. Anion-radical salts K+(cryptand) A-• were
prepared either by potassium-mirror reduction of the corresponding
electron acceptor in THF in the presence of a stoichiometric amount
of [2,2,2]cryptand31 or by addition of stoichiometric amounts of the
cryptand to the suspension of the potassium salt: K+A-• in dichlo-
romethane. The mixture was stirred until dissolution was complete
which was then followed by precipitation with hexane. Colorless single
crystals of the hindered donors (DBB, PrPTZ) were prepared by the
slow evaporation of their solution in dichloromethane at room tem-
perature. To prepare single crystals of the cation-radicals salts,
TPPD+•SbCl6-, DBB+•CB-, DMB+•CB-, PTZ+•CB-, PrPTZ+•CB-,
(73) (a) Under these circumstances, the molecular or atom-bridged activated
complex of Taube can be approximated as either a type M or L system in
which the bridged is considered virtual, as in the case of a mixed organic/
inorganic (distorted) redox dyad. See: (b) Fukuzumi, S., et al. in ref 33b.
(c) Kochi, J. K. Pure Appl. Chem. 1990, 52, 571. See also: (d) Kochi, J.
K. in ref 13c. (e) For the quantitative comparison of the electronic coupling
in the intramolecular (bridged) mixed-valence system relative to that in
the corresponding intermolecular cofacial (through-space) system, see: (f)
Sun, D. L.; Rosokha, S. V.; Lindeman, S. V.; Kochi, J. K. J. Am. Chem.
Soc. 2003, 125, 15950. Sun et al. in ref 23b.
(74) Marcus, R. A. J. Phys. Chem. 1992, 96, 1753.
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A R T I C L E S
Rosokha and Kochi
the salts were dissolved in dichloromethane, and the solutions were
overlaid with hexane at room temperature. The mixture was then slowly
cooled to -60 °C and kept at this temperature for several days. To
Accordingly, the second-order rate constants for the sterically open ion-
radicals OMB+•, OMA+•, DMB+•, DDQ-•, TCNQ-• (which were
characterized by relatively simple EPR spectra) were calculated as kSE
) 1.52 × 107 × ∆∆H/∆C/(1 - Pi), where ∆∆H/∆C represented the
slope of the width of the central line in the EPR spectrum on the
concentration of added neutral donor or acceptor, and (1 - Pi) is
exchange-probability correction. For the sterically hindered cation-
radicals TPPD+•, DBB+•, and PrPTZ+• (which are characterized by
complex EPR spectra), the line width variation with concentration of
added donor were evaluated via the EPR spectra simulations with the
WINSIM program.76 The self-exchange rate constants kSE(calcd) in
Table 6 for the TMPD+•, PTZ+•, DMB+•, DDQ-•, and TCNQ-• were
calculated via eq 13 with Kπ taken from Table 3; the first-order rate
constant kET calculated according to eq 12 (with a preexponential factor
-•
prepare single crystals of the (DDQ)2 complex, equimolar amounts
of the parent acceptor (DDQ) was added to the clear solution obtained
by the addition of 15-crown-5 polyether ligand (in 2:1 molar ratio) to
the suspension of the potassium salts K+DDQ-•. The solution was then
covered with hexane, cooled to -60 °C, and kept at this temperature
for several weeks. This resulted in the formation of dark brown crystals
of the (1:1) anionic π-complex as the bis-ligated potassium salt: K(15-
+
crown-5)2 (DDQ)2-•(DDQ).
5.2. X-ray Crystallography. The intensity data for the X-ray studies
were collected at -100 °C with a Bruker SMART Apex diffractometer
equipped with a CCD detector using Mo KR radiation (λ ) 0.710 73
Å). The structures were solved by direct methods and refined by a full
matrix least-squares procedure as described earlier.75 The crystal-
lographic data are presented in Table S1 in the Supporting Information.
5.3. Electrochemistry. Cyclic voltammetry (CV) and Osteryoung
square-wave voltammetry (OSWV) were performed on a BAS 100A
of 1012 s-1, as discussed earlier23). For the sterically hindered TPPD+•
,
PrPTZ+•, and DBB+•, the rate constants were calculated via eq 10
since experimental values of Kπ were not available. In these cases, the
activation barriers were calculated using HDA ) 200 cm-1 (as discussed
in text) and the reorganization energy was taken from the unhindered
(open) analogues. For OMB+• and OMA+•, the rate constants were
calculated by the numerical solution (with Mathematica program) of
the system of differential equations describing the process in eq 14, as
described earlier.28b In these calculations, the rate constants for complex
formation were taken as being equal to the diffusion rate constant, and
the rate constants of the complex dissociation were calculated as kdiss
) kdiff/Kπ.
Electrochemical Analyzer in dichloromethane with n-Bu4N+PF6 as
-
the supporting electrolyte, and ferrocenium salt with E° ) 0.475 V vs
SCE was added as the internal standard, as described previously.23
5.4. Spectral (UV-vis-NIR) Measurements. Electronic absorption
spectra were recorded on a Varian Cary 5 spectrometer in Teflon-capped
quartz cuvettes. Formation of the dimeric (D)2+• and (A)2-• was studied
under an argon atmosphere at room temperature (22 °C) in dichlo-
romethane. The measurement of the new NIR bands (in the 1000-
3000 nm range) was effected when the donor was added to the solution
of its cation radical or the acceptor was added to the solution of its
anion radical. The quantitative analysis of the intensities of the NIR
absorption bands with the aid of Benesi-Hildebrand or Drago
procedures as described earlier23a afforded the formation constants (Kπ)
and extinction coefficients (ꢀπ) of the 1:1 complexes. Since these
procedures were approximate, the Kπ and ꢀπ values were also evaluated
more precisely by the computer fitting (by Kπ and ꢀ variations) of the
experimental absorptions (measured in series of solutions with different
concentrations of the donor or the acceptor and their ion-cation radical
5.6. Computational Methodologies. The reorganization energy for
the electron transfer within the complexes was calculated as a sum of
the inner- and outer-sphere components. The intramolecular contribution
(λi) to the overall reorganization energy for electron transfer within
paramagnetic ion-radical dyads was calculated as the difference between
the initial diabatic state (with the electron located on the donor (D or
A-•) with reactants in their relaxed geometries) and the final diabatic
state (with the same nuclear geometry but the electron transferred to
the acceptor (D+• or A)).57 For example, in the case of cation-radical
complexes, λicalcd ) {Ec(rn) + En(rc)} - {En(rn) + Ec(rc)}, where rn
and rc are the optimized coordinates and En and Ec are the energies of
the neutral donor and its cationic counterpart. Accordingly, we first
optimized the geometry of the donor and the corresponding cation
radicals and determined their energies, En(rn) and Ec(rc) via Hartree-
Fock and DFT computations with the aid of Gaussian 98 (6-311G*
basis and B3LYP functional).77 Then the single-point calculation of
D+• in the geometry of the neutral D led to Ec(rn), and the neutral donor
in the geometry of the cation produced the values of En(rc). The energy
differences afforded the inner-sphere reorganization energies, listed in
Table S4 which also contains computational details as well as values
calculated via an analogous procedure for anion-radical complexes.
For calculations of the solvent reorganization energy, the ion-radical
π-complex was considered as a cavity of radii a0 with an internal
dielectric constant of ꢀin ) 2 immersed in a solvent with static and
+
salts). The exact expression A ) 0.5 × ꢀ × {(D0 + D0 + 1/Kπ) -
+
+
[(D0 + D0 + 1/Kπ)2 - 4 × D0 × D0
]
0.5} was employed, where D0
+
and D0 were the concentrations of the donor and the cation-radical
salt added. The same procedure was applied to the solutions of the
electron acceptors and their anion-radical salt. Subsequent measurements
of Kπ at different temperatures with the aid of a Dewar equipped with
quartz windows resulted in the enthalpy and entropy changes ∆Hπ and
∆Sπ for the formation of the π-complex.
5.5. EPR measurements were performed on a Bruker ESP-300
X-band spectrometer, and the hyperfine splitting constants were
determined by computer simulation of the ESR spectra of pure anion-
radical salts using the WinSim program.76 Kinetic parameters for
intermolecular electron-transfer self-exchange were determined from
the (general) line broadening of ion-radical spectra in the presence of
added (neutral) donor or acceptor.43 The self-exchange processes with
the PTZ+• and TMPD+• cation radicals were measured in dichlo-
romethane in the fast exchange limit, and their second-order rate
constants were calculated as kSE ) 2.05 × 107 × 3/(∆∆H/∆C), where
∆∆H/∆C represented the slope of the width of a single line in the
EPR spectrum on the concentration of added neutral donor or acceptor,
and the 3 is the second moment of the EPR spectra. With the other
ion radicals, the measurements were carried out in the slow exchange
limit (since the solubilities of the parent donors and acceptors in
dichloromethane were not sufficient to satisfy the criteria for the
measurements in the fast exchange limit, i.e., (3/4∆)1/2∆∆H < 0.2).
optical dielectric constants ꢀs ) 8.93 and ꢀo ) 2.028.43c The reorganiza-
calcd
tion energy λo
based on the Kirkwood solvation model is given
by28,58
λocalcd ) 1/2a0(1/ꢀin - 1/ꢀs)
gn/(1 + [n/(n + 1)]ꢀin/ꢀs) -
∑
n
(1/ꢀin - 1/ꢀ0)
gn/(1 + [n/(n + 1)]ꢀin/ꢀ0)
∑
n
where
gn )
∆ek∆ej(rk/a0)n(rj/a0)n Pn(cos θj,k), with n ) 1 to 6
∑∑
k,j
(75) (a) Sheldrick, G. M. SADABS (ver. 2.03); 2000. (b) Sheldrick, G. M.
SHELXS 97; University of Go¨ttingen: Germany, 1997.
(76) Duling, D. PEST WinSim, version 0.96. Public EPR Software Tools,
National Institute of Environmental Health Sciences: 1996.
(77) Pople, J. A., et al. Gaussian 98, revision A.11.3 ed.; Gaussian, Inc.:
Pittsburgh, PA, 2001.
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3696 J. AM. CHEM. SOC. VOL. 129, NO. 12, 2007

Outer-/Inner-Sphere Mechanisms for Organic ET
A R T I C L E S
∆ej denotes the variation of the charge on the jth atom, N is the number
of atoms, rj locates the jth atom in space, θj,k is the angle between rj
and rk, and Pn are ordinary Legendre functions. The atomic coordinates
in the complexs were taken from their X-ray structures (if unavailable,
those the from related diamagnetic dimers (D)22+ or (A)22-], and values
of a0 were calculated from the molecular volume of such dyads (from
the single-point Gaussian 98 computation) plus 0.5 Å.77 The atomic
charges for the ion-radical π-complex in the hypothetical diabatic state
were taken via the Gaussian 98 computation of the isolated neutral
donors and acceptors and their ion radicals (ESP charges, CHELPG
option).77
separation in Figure 4, the atomic coordinates were generated by
artificially increasing the interplanar separation in the experimental
X-ray structure. For the calculation of HDA values of the complexes
with crossed monomer moieties, the atomic coordinates were generated
by rotating one of the monomeric units in the experimental X-ray
structure by 90°.
Acknowledgment. We thank J. M. Lu for the synthesis of
PrPTZ and the preparation of the single crystal, as well as the
preparation and the spectral (UV-NIR, ESR) measurements of
-
the D+SbCl6 salts; T. Y Rosokha for the preparation of the
single crystals of TPPD+•SbCl6-, DMB+•CB-, PrPTZ+•CB-,
and PTZ+•CB-, and K(15-crown-5)2+(DDQ)2-•(DDQ); A. S.
Jalilov for the synthesis of DBB, DBB+•CB- and the preparation
of the single crystals, as well as for electrochemical measure-
ments; D. Sun for the synthesis of TPPD; B. Han for ESR
The ab initio evaluation of the electronic coupling elements (HDA
)
in Table 5 between symmetry-equivalent donor/acceptor moieties was
carried out as described earlier.28,59 This was based on the single-point
Hartree-Fock and/or B3LYP Gaussian-98 computations (with 6-311G*
basis set) of the energy splitting resulting from the symmetric and
antisymmetric combinations of the localized molecular orbitals of the
monomers within the neutral closed-shell dimeric species. In particular,
for the cationic mixed-valence complexes, the coupling elements were
calculated as one-half of the difference between the HOMO and HOMO
- 1 (highest-lying alpha occupied eigenvalues) obtained using the Pop
) Regular option in the single-point Gaussian computations of the
corresponding neutral dimers. The atomic coordinates of the dyad were
taken from the X-ray structures of the appropriate cationic or dicationic
dimers (see Table S4 in the Supporting Information) but with additional
electrons to generate neutral closed-shell systems. Likewise for the
anionic mixed-valence complexes, the coupling elements were calcu-
lated as one-half of the energy difference between the LUMO + 1 and
LUMO (lowest-lying alpha virtual eigenvalues) computed for the
corresponding neutral closed-shell dyads.60 The dimeric species were
based on the geometries of the anionic or dianionic dimers but with
one or two fewer electrons. For example, to calculate HDA for the
measurements of the DDQ-• anion radical; I. S. Neretin for
+
the X-ray crystallographic analysis of K(15-crown-5)2 (DDQ)2-•
-
(DDQ), PrPTZ, and PTZ+•CB-; S. M. Dibrov for the X-ray
analysis of TPPD+•SbCl6-, PrPTZ+•CB-; and J.-J. Lu for the
X-ray analysis of DBB, DBB+•CB-, DMB+•CB- and crystal-
lographic assistance. We thank M. D. Newton for many helpful
discussions with regard to the computations of the reorganization
energies and electronic coupling elements and the R. A. Welch
Foundation and the National Science Foundation for financial
support.
Supporting Information Available: The crystallographic
+
data (Table S1), the charge analysis in K(15-crown-5)2
(DDQ)2-•(DDQ) (Table S2), computations of reorganization
energy (Table S3) and coupling element (Table S4), tempera-
ture-dependent voltammograms of the OMA (Figure S1), ESR
line broadening of DDQ-• upon addition of parent DDQ (Figure
S2), NIR spectral changes showing the formation of the
[TMPD+•, TMPD] complex (Figure S3); temperature depen-
dence of the NIR spectrum of [TCNQ-•, TCNQ] (Figure S4);
complete ref 77. This material is available free of charge via
the Internet at http://pubs.acs.org.
-•
(DDQ)2 complex, we extracted the atomic coordinates of the
centrosymmetric mixed-valence dimeric unit from the X-ray structure
of K(15-crown-5)2+(DDQ)2-•(DDQ) (vide supra). With these coordi-
nates, we carried out the single-point Gaussian computations of the
neutral (DDQ)2 dimer with the Pop ) Regular option to produce the
orbital energies. Finally, the coupling element was calculated as HDA
) 1/2[E(LUMO + 1) - E(LUMO)], where the energies of LUMO and
LUMO + 1 were taken as the lowest-lying alpha virtual eigenvalues.
For the calculations of the dependence of HDA values on the interplanar
JA069149M
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