Isolation of the latent precursor complex in electron-transfer dynamics. Intermolecular association and self-exchange with acceptor anion radicals

Article abstract of DOI:10.1021/ja0211611

Transient [1:1] complexes formed in the bimolecular interactions of electron acceptors (A) with their reduced anion radicals (A-are detected and characterized in solution for the first time. The recognition of such metastable intermediates as the heretofore elusive precursor complex (A₂in electron-transfer processes for self-exchange allows the principal parameters λ (Marcus reorganization energy) and H_DA (electronic coupling element) to be experimentally determined from the optical (charge-transfer) transitions inherent to these intermolecular complexes. The satisfactory correspondence of the theoretically predicted with the experimentally observed rate constants validates these ET parameters and the Marcus-Hush- Sutin methodology for strongly coupled redox systems lying in the (Robin-Day) Class II category. Most importantly, the marked intermolecular electronic interaction (H_DA) within these precursor complexes must be explicitly recognized, since it dramatically affects the electron-transfer dynamics by effectively lowering the activation barrier. As such, the numerous calculations of the reorganization energy previously obtained from various self-exchange kinetics based on λ = 4ΔG* must be reconsidered in the light of such a precursor complex, with the important result that ET rates can be substantially faster than otherwise predicted. On the basis of these studies, a new mechanistic criterion is proposed for various outer-sphere/inner-sphere ET processes based on the relative magnitudes of H_DA and λ.

Full text of DOI:10.1021/ja0211611

Published on Web 02/08/2003
Isolation of the Latent Precursor Complex in
Electron-Transfer Dynamics. Intermolecular Association and
Self-Exchange with Acceptor Anion Radicals
Vellaichamy Ganesan, Sergiy V. Rosokha, and Jay K. Kochi*
Contribution from the Department of Chemistry, UniVersity of Houston, Houston, Texas, 77204
Received September 9, 2002; E-mail: jkochi@mail.uh.edu
Abstract: Transient [1:1] complexes formed in the bimolecular interactions of electron acceptors (A) with
-•
their reduced anion radicals (A ) are detected and characterized in solution for the first time. The recognition
-
•
of such metastable intermediates as the heretofore elusive precursor complex (A
processes for self-exchange allows the principal parameters λ (Marcus reorganization energy) and HDA
electronic coupling element) to be experimentally determined from the optical (charge-transfer) transitions
2
) in electron-transfer
(
inherent to these intermolecular complexes. The satisfactory correspondence of the theoretically predicted
with the experimentally observed rate constants validates these ET parameters and the Marcus-Hush-
Sutin methodology for strongly coupled redox systems lying in the (Robin-Day) Class II category. Most
importantly, the marked intermolecular electronic interaction (HDA) within these precursor complexes must
be explicitly recognized, since it dramatically affects the electron-transfer dynamics by effectively lowering
the activation barrier. As such, the numerous calculations of the reorganization energy previously obtained
from various self-exchange kinetics based on λ ) 4∆G* must be reconsidered in the light of such a precursor
complex, with the important result that ET rates can be substantially faster than otherwise predicted. On
the basis of these studies, a new mechanistic criterion is proposed for various outer-sphere/inner-sphere
ET processes based on the relative magnitudes of HDA and λ.
Introduction
Chart 1
The preequilibrium formation of the intermolecular [1:1]
precursor or encounter complex between an electron donor (D)
and an acceptor (A) is consistently included in the most general
1
formulations of electron-transfer mechanisms, i.e.,
+
-
D + A a [D,A] a D + A
(1)
acceptors (A) illustrated in Chart 1 for three principal reasons:
a) they are all planar π-acceptors with reversible redox
(
0
However, the importance of such metastable complexes [D,A]
to the overall ET dynamics has been difficult to evaluate
quantitatively owing to the limited number of experimental
probes available for the detection of these elusive intermediates
in solution.2 As a result, most electron-transfer studies have
heretofore simply classified them generically as outer-sphere
complexes with rather small (invariant) formation constants that
by and large leave the dynamics unaffected.1
potentials in a reasonable E
radicals (A ) are stable in solution and can be rigorously
red
range, (b) the reduced anion
-
•
(
4) For the analysis of intramolecular thermal/optical electron transfer in bridged
mixed-valence systems as prototypes for the precursor complex in
intermolecular electron transfer, see: (a) Elliot, C. M.; Derr, D. L.;
Matyushov, D. V.; Newton, M. D. J. Am. Chem. Soc. 1998, 120, 11714.
-4
(b) Nelsen, S. F.; Adamus, J.; Wolff, J. J. J. Am. Chem. Soc. 1994, 116,
1589. (c) Nelsen, S. F.; Ramm, M. T.; Wolff, J. J.; Powell, D. R. J. Am.
Chem. Soc. 1997, 119, 6863. (d) Nelsen, S. F.; Trieber, D. A.; Wolff, J. J.;
Powell, D. R.; Rogers-Crowley S. J. Am. Chem. Soc. 1997, 119, 6873. (e)
Nelsen, S. F.; Ismagilov, R. F.; Powell, D. R. J. Am. Chem. Soc. 1997,
,5-7
To demonstrate quantitatively how the precursor complex
PC) plays a critical role in electron-transfer dynamics, we now
focus on the redox behavior of the prototypical (organic)
119, 10213. (f) Lindeman, S. V.; Rosokha, S. V.; Sun, D.; Kochi, J. K. J.
(
Am. Chem. Soc. 2002, 124, 843. (g) Kambhampati, P.; Son, D. H.; Kee, T.
W.; Barbara, P. F. J. Phys. Chem. A 2000, 104, 10637. (h) Son, D. H.;
Kambhampati, P.; Kee, T. W.; Barbara, P. F. J. Phys. Chem. A 2002, 106,
4591.
(
(
(
1) (a) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441. (b) Note that in
self-exchange the successor complex is equivalent to the precursor complex
denoted in generalized electron-transfer formulations.
(5) (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.
(6) (a) Astruc, D. Electron Transfer and Radical Processes in Transition-Metal
Chemistry; VCH: New York, 1995. (b) Eberson, L. Electron-Transfer
Reactions in Organic Chemistry; Springer-Verlag: New York, 1987. (c)
Cannon, R. D. Electron-Transfer Reactions; Butterworth: London, 1980.
(d) Formosinho, S. J.; Arnaut, L. G.; Fausto, R. Prog. React. Kinet. 1998,
23, 1.
2) For a trenchant evaluation of the precursor complexes in intermolecular
organic electron transfer, see: Nelsen, S.; Pladziewicz, J. Acc. Chem. Res.
2
002, 35, 247.
3) For the spectral characterization of precursor complexes in the outer-sphere
electron transfer of coordination compounds, see: (a) Khoshtariya, D. E.;
Meusinger, R.; Billing, R. J. Phys. Chem. 1995, 99 (9), 3592. (b) Curtis,
J. C.; Sullivan, B. P.; Meyer, T. J. Inorg. Chem. 1980, 19, 3833.
10.1021/ja0211611 CCC: $25.00 © 2003 American Chemical Society
J. AM. CHEM. SOC. 2003, 125, 2559-2571
9
2559

A R T I C L E S
Ganesan et al.
characterized via isolation as pure crystalline salts, and (c) their
electron-transfer rates are relatively fast and experimentally
accessible. These electron acceptors, particularly TCNQ and
of aromatic donors (ArH) complexed with their own cation
+
• 11
radicals, i.e., (ArH)2
.
Most importantly, these unusual
8
(intermolecular) complexes are spectrally characterized by
diagnostic absorption bands in the near-infrared (NIR) region11
that have been shown to arise from the charge-transfer or CT
interaction of the aromatic hydrocarbon acting as the electron
donor with its positively charged cation radical as the
TCNE, have also been recently utilized in the discovery and
development of molecule-based (semi)conductors and magnets
of importance to the burgeoning field of organic materials
9
science.
1
2
13
For the electron acceptors in Chart 1, we directly address
the simplest electron-transfer system that occurs in the absence
acceptor. The extension of the same Mulliken formulation
to the electron-poor π-acceptors in Chart l leads to negatively
charged CT complexes, with the relatively electron-rich anion
radicals acting as the π-donors. Accordingly, our primary task
lies in the unambiguous identification and spectral characteriza-
0
of any driving-force contribution (∆G ET ) 0), namely, the
detailed energy profile for the self-exchange (SE) dynamics, as
typically indicated for tetracyanoethylene in eq 2. As such, the
-
•
tion of the corresponding anion-radical π-mers (A2) for the
KSE
11l
-•
-•
electron acceptors in Chart l. We then establish how these
TCNE + TCNE
{
} TCNE + TCNE
(2)
precursor complexes lead to the mapping out of the energy
profile and to new insights into the electron-transfer mechanism
of the self-exchange process, i.e.,
presence of the precursor complex can be unambiguously
assigned to the intermolecular association of the TCNE with
its reduced anion radical to form the pertinent (preequilibrium)
intermediate, i.e.,
A + A a [A2-•] a A-• + A
-
•
KPC
-•
-•
Results
TCNE + TCNE
{
} [TCNE,TCNE ]
(3)
I. Isolation and X-ray Crystallography of Anion-Radical
Salts. The polycyano alkenes (TCNE and TCNQ) and the
quinones (DDQ and CA) were sufficiently electron deficient
to effect the one-electron oxidation of iodide for the preparation
of crystalline alkali-metal and alkylammonium salts [see
Experimental Section]. Analysis of the X-ray crystallographic
data indicated that one-electron reductions of π-acceptors
resulted in substantial (selective) changes of the bond lengths,
and the characteristic structural changes in these acceptors upon
their reduction to the corresponding anion radicals are presented
in Chart 2. [For the complete structural parameters of the
neutral donors and their anion radicals, see Table S1 in the
Supporting Information.]
X-ray crystallographic studies indicated that the characteristic
feature of π-anion radicals was their tendency for intermolecular
Although these dimeric anion-radical complexes in solution
are unreported, the possibility of such an association can be
seen in the extant solid-state data. There are also a few
examples of a somewhat related [1:1] self-association comprised
10
(
7) For kinetic studies of electron-transfer self-exchange, see: (a) Jurgen, D.;
Pedersen, S.; Pedersen, J. A.; Lund, H. Acta Chem. Scand. 1997, 51, 767.
(b) Larsen, H.; Pedersen, S. U.; Pedersen, J. A.; Lund, H. J. Electroanal.
Chem. 1992, 331, 971. (c) Fukuzumi, S.; Nakanishi, I.; Suenobu, T.; Kadish,
K. M. J. Am. Chem. Soc. 1999, 121, 3468. (d) Grampp, G.; Rauhut, G. J.
Phys. Chem. 1995, 99, 1815. (e) Grampp, G.; Jaenicke, W. J. Chem. Soc.,
Faraday Trans. 2 1985, 81,1035. (f) Nelsen, S. F.; Blackstock, S. C. J.
Am. Chem. Soc. 1985, 107, 7189. (g) Malinovski, G. L., Jr.; Bruning, W.
H.; Griffin, R. G. J. Am. Chem. Soc. 1970, 92, 2665. (h) Ward, R. L.;
Weissman, S. I. J. Am. Chem. Soc. 1957, 79, 2086. (i) Haran, N.; Luz, Z.;
Shporer, M. J. Am. Chem. Soc. 1974, 119, 6873. For theoretical (quantum-
mechanical) studies of self-exchange, see: (j) Jacobsen, S.; Mikkelsen, K.
V.; Pedersen, S. U. J. Phys. Chem. 1996, 100, 7411. (k) Mikkelsen, K. V.;
Pedersen, S. U.; Lund, H.; Swanstrøm, P. J. Phys. Chem. 1991, 95, 8892.
14
(l) Ma, S.-H.; Zhang, X.-D.; Xu, H.; Shen, L.-L.; Zhang, X.-K.; Zhang,
Q.-Y. J. Photochem. Photobiol. A: Chem. 2001, 139, 97. (m) Kelterer, A.-
M.; Landgraf, S.; Grampp, G. Spectrochim. Acta 2001, A57, 1959. (n)
Vener, M. V.; Ioffe, N. T.; Cheprakov, A. V.; Mairanovsky, V. G. J.
Electroanal. Chem. 1994, 370, 33. (o) Rauhut, G.; Clark, T. J. Am. Chem.
Soc. 1993, 115, 9127.
(11) (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. (d) Badger, B.; Brocklehurst, B.;
Dudley, R. Chem. Phys. Lett. 1967, 1, 122. (e) Badger, B.; Brocklehurst,
B. Trans. Faraday Soc. 1969, 65, 2582. (f) Badger, B.; Brocklehurst, B.
Trans. Faraday Soc. 1969, 65, 2588. (g) Badger, B.; Brocklehurst, B. Trans.
Faraday Soc. 1970, 66, 2939. (h) Meot-Ner, M.; Hamlet, P.; Hunter, E.
P.; Field, F. H. J. Am. Chem. Soc. 1978, 100, 5466. (i) Meot-Ner, M. J.
Phys. Chem. 1980, 84, 2724. (j) Meot-Ner, M.; El-Shall, M. S. J. Am. Chem.
Soc. 1986, 108, 4386. (k) All attempts to prepare the corresponding anionic
dimers in solution were unsuccessful heretofore. (l) Since the cationic and
anionic dimers are both derived from π-donor/acceptor pairs, they are
hereinafter referred to (generically) as “π-mers” or precursor complexes,
interchangeably. [The designation “dimer” is reserved for the dianionic
(
8) For kinetic measurements of electron-transfer self-exchange processes with
DDQ, TCNQ, and TCNE, see: (a) Komarynsky, M. A.; Wahl A. C. J.
Phys. Chem. 1975, 79, 695. (b) Phillips, W. D.; Rowell, J. C.; Weissman,
S. I J. Chem. Phys. 1960, 33, 626. (c) Watts, M. T.; Lu, M. L.; Chen, R.
C.; Eastman, M. P J. Phys. Chem. 1973, 77, 2959. (d) Ogasawara, M.;
Takaoka, H.; Hayashi, K. Bull. Chem. Soc. Jpn. 1973, 46, 35. (e) Grampp,
G.; Landgraf, S.; Rasmussen, K. J. Chem. Soc., Perkin Trans. 2 1999, 1897.
(
f) Grampp, G.; Jaenicke, W. Ber. Bunsen-Ges. Phys. Chem. 1991, 95,
9
04. (g) Grampp, G.; Harrer, W.; Hetz, G. Ber. Bunsen-Ges. Phys. Chem.
990, 94, 1343. (h) Grampp, G. Spectrochim. Acta 1998, A54, 2349.
1
(
9) (a) Miller, J. S. Inorg. Chem. 2000, 39, 4392. (b) Williams, J. M. Organic
Superconductors (Including Fullerenes): Synthesis, Structure, Properties
and Theory; Prentice Hall: Englewood Cliffs, NJ, 1992. (c) Ferraro, J. R.;
Williams, J. M. Introduction to Synthetic Electrical Conductors; Academic
Press: Orlando, 1987.
2
-
15,18
(A
2
)
complex.
]
(12) 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.
(13) (a) Mulliken, R. S. J. Am. Chem. Soc. 1952, 74, 811. (b) Mulliken, R. S.;
Person, W. B. Molecular Complexes; Wiley: New York, 1969.
1
0b,c,17,19
(
10) (a) There are, however, some solid-state data
of anion-radical
associates with their parent acceptors (π-mer) that are characterized by
NIR absorption bands, which are similar to the charge-resonance absorption
invariably found as a common (diagnostic) feature of cation-radical
associates.1 However, the available data did not prove the (noticeable)
(14) (a) The numbers besides the bonds in Chart 2 represent the average
1,12
-1
differences (in 10 pm) between the (corresponding) bond length in the
1
0d
association of the free anion radical with its neutral parent in solution,
anion radical and its parent acceptor (the “+” sign indicates a longer bond
in the reduced species). Note, for clarity, only changes in one of the
symmetrically equivalent bonds are shown (see Table S1, Supporting
Information, for scatter of the data). The data used are from measurements
made in this study, as well as those taken from: (b) Miller, J. S.; Krusic,
P. J.; Dixon, D. A.; Reiff, W. M.; Zhang, J. H.; Anderson, E. C.; Epstein,
A. J. J. Am. Chem. Soc. 1986, 108, 4459. (c) Miller, J. S.; Zhang, J. H.;
Reiff, W. M.; Dixon, D. A.; Preston, L. D.; Reis, A. H., Jr.; Gebert, E.;
Extine, M.; Troup, J.; Epstein, A. J.; Ward, M. D. J. Phys. Chem. 1987,
91, 4344. (d) Dixon, D. A.; Miller, J. S. J. Am. Chem. Soc. 1987, 109,
3656, and references therein.
nor allow the determination of the corresponding extinction coefficients
and formation constants. (b) The NIR charge-resonance transition in the
-•
anthracene π-mer (A
2
)
was observed after the irradiation of dianthracene
in a rigid MTHF matrix, see: Shida, T.; Iwata, S. J. Chem. Phys. 1972,
6, 2858. (c) The NIR absorption band was observed in the solid-state
5
-
2
spectrum of (TCNQ ) . See: Terashita, S.; Nacatsu, K.; Ozaki, Y.; Takagi,
S. J. Phys. Chem. 1995, 99, 3618. (d) For ESR spectroscopic indications
of the presence of (tetrafluorobenzene and octafluoronaphthalene) anion-
radical π-mers in hexane, see: Werst, D. W. Chem. Phys. Lett. 1993, 202,
1
01; Chem. Phys. Lett. 1996, 251, 315.
2
560 J. AM. CHEM. SOC. VOL. 125, NO. 9, 2003
9

Electron-Transfer Dynamics
A R T I C L E S
Chart 2
Table 1. Spectral Characteristics of the Anion-Radical Dimers,
association. One form of such an association (found for all these
acceptors) was the self-formation of diamagnetic (dianionic)
dimers, in which a pair of anion radicals were characterized
by face-to-face arrangement of planar moieties, and the inter-
planar distances were substantially less than the sum of the
corresponding van der Waals radii. The other form of association
-•
(
A2) , in Comparison with Those of Their Neutral Parent Acceptor,
-
•
A, and Anion Radicals, A , as Well as the Formation Constants,
Ka, of the Precursor Complex (A2)
-
•a
1
5
spectral characteristics, λ, nm(ꢀ, 10 M cm-1
3
-1
)
-•b
(A2)-•
KPC, M-1
acceptor
A
A
DDQ
TCNQ
TCNE
CA
280 (27) 372 (0.8)
396 (67)
270 (15)
588 (6.3)
842 (43)
428 (8.4)
449 (9.0)
1370 (1.6)
2200 (3.2)
1380 (1.0)
1355(1.3)
3
5
0.6
4
(of particular interest here) included the interaction of various
electron acceptors with their corresponding anion radicals. For
example, when the crystallization of TCNQ was carried out in
the presence of its anion radical, mixed crystals were found with
stoichiometric 1:1, 2:1, and 3:2 ratios of TCNQ relative to
287 (23) 367 (0.25)
a
In acetonitrile, at 22 °C. b The characteristics of only the most intense
band is presented. (For the other spectral bands, see Table S2 in the
Supporting Information.)
-
• 16
-•
TCNQ . The paramagnetic (TCNQ)2 dyad could be clearly
recognized in these crystals as two acceptor moieties sharing
17
one electron. The cofacial arrangement in such associations
similar to those in the dimers) occurred with an interplanar
separation (3.2-3.3 Å) that was much less than the sum of van
(
1
7
der Waals radii to indicate a substantial intermolecular
interaction between the counterparts. The structural parameters
of both components within such a dyad were indistinguishable,
with bond lengths that were intermediate between those
characteristic of the neutral acceptor and those of the anion
radical.
Crystallization from solution of a mixture of DDQ-• and DDQ
also resulted in the formation of the mixed complexes (see
Experimental Section). The molar ratio of the anion radical to
the neutral acceptor in such crystals was 2:1, but the partial
+
2-
Figure 1. Molecular structure of (Et4N )2(DDQ)3 (hydrogen atoms are
omitted for clarity). [Note that the mean interplanar separation between
DDQ/DDQ moieties is 2.90 Å compared to the sum (3.4 Å) of the van
der Waals radii.]
-
•
(crystal) disorder precluded a precise analysis of the individual
bond lengths within each moiety. Nonetheless, the cofacial
arrangement of all three moieties with an interplanar distance
substantially less than the sum of van der Waals radii can be
clearly recognized in Figure 1. In the case of TCNE and CA,
our numerous efforts to obtain crystalline associates between
the neutral acceptor and its anion radical always resulted in
mixed crystals consisting of the separate neutral acceptor and
the separate anion-radical salt. [The latter was in the form of
either the anion-radical salt itself or its dianionic dimer.]
II. Spectral Characterization and Analysis of the Precur-
sor Complexes. The electron acceptors A in Chart 1 were
characterized in solution by prominent (UV-vis) absorption
Table 1. One-electron reduction to their anion radicals A-• was
accompanied by the appearance of additional strong absorption
bands in the visible region between 420 and 850 nm (ꢀmax ≈
4
-1
-1
1
0 M cm ). The UV-vis spectra of the neutral acceptors
as well as their anion radicals showed little solvent dependence
-
1
(
∆λ < 500 cm ) in dichloromethane (apolar) and acetonitrile
(polar) solutions, and the change in the cationic counterion from
sodium to tetrabutylammonium did not materially affect the
electronic spectra (Table S2 in Supporting Information.)18 Most
important was the fact that no absorption bands were observed
in the near-IR region even at high concentrations and low
temperatures, provided solutions of the pure π-acceptor and its
anion radical were examined separately. On the other hand,
4
-1
-1
bands at 330 ( 70 nm (ꢀmax ≈ 10 M cm ), as listed in
(
15) For the crystal structures of dimers, see e.g.: (a) DDQ: Yan, Y.-K.; Mingos,
M. P.; Muller, T. E.; Williams, T. E.; Kurmoo, M. J. Chem. Soc., Dalton
Trans. 1995, 2509. (b) TCNE: Novoa, J. J.; Lafuente, P.; Del Seto, R. E.;
Miller, J. S. Angew. Chem., Int. Ed. 2001, 40, 2540. (c) TCNQ: Grossel,
M. C.; Weston, S. C. Chem. Mater. 1996, 8, 977.
-
(18) (a) It should be noted that anion radicals form dimers (A
2
)2 in the solid
1
5
state, and in solution this process is noticeable at high concentrations of
anion radicals, especially in polar solvents at low temperatures. The dimers
are characterized by absorption bands in the visible region, and these are
blue-shifted by 100-200 nm relative to the corresponding bands of
(
16) (a) Harms, R.; Keller, H. J.; Nothe, D.; Wene, D. Acta Crystallogr. 1982,
B38, 2838. (b) Bigoli, F.; Deplano, P.; Devillanova, F. A.; Girlando, A.;
Lippolis, V.; Mercuri, M.-L.; Pellinghelli, M.-A.; Trogu, E. F. J. Mater.
Chem. 1998, 8, 1145. (c) Bigoli, F.; Deplano, P.; Devillanova, F. A.;
Girlando, A.; Lippolis, V.; Mercuri, M.-L.; Pellinghelli, M.-A.; Trogu, E.
F. Inorg. Chem. 1996, 35, 5403.
2
-
monomeric anion radicals. Thus, (DDQ
2
)
is characterized by the band at
710 nm (ꢀ ) 6300) in acetonitrile, and similar bands in DMF, acetone,
1
8b
2-
THF, EtOH, and H
by bands at 370, 640, and 870 nm. The (TCNE
525 nm in ethanol and at 540 nm in MTHF. The (CA
2
O. The (TCNQ
2
)
dimer is characterized (in H
2
O)
1
8c
2-
2
)
dimer has a band at
2
-
2
)
dimer is
1
8e
(17) (a) Goldstein, P.; Seff, K.; Trueblood, K. N. Acta Crystallogr. 1968, B24,
characterized by the band at 550 nm in THF and at 380 and 670 nm in
18f
7
78. (b) Hanson, A. W. Acta Crystallogr. 1968, B24, 773. (c) Kobayashi,
EtOH. (b) Yamagishi, A. Bull. Chem. Soc. Jpn. 1975, 48, 2440. (c) Bieber,
A.; Andre, J. J. Chem. Phys. 1975, 7, 137. (d) Matsuzaki, S.; Mitsuishi,
T.; Toyoda, K. Chem. Phys Lett. 1982, 91, 296. (e) Andre, J. J.; Will, G.
Chem. Phys Lett. 1971, 9, 27. (f) Bieber, A.; Andre, J. J. Chem. Phys.
1975, 7, 137.
H. Bull. Chem. Soc. Jpn. 1974, 47, 1346. (d) Fourmigue, M.; Perrocheau,
V.; Clerac, R.; Coulon, C. J. Mater. Chem. 1997, 7, 2235. Ballester, L.;
Gutierrez, A.; Perpinan, M. F.; Rico, S.; Azcondo, M. T.; Bellito, C. Inorg.
Chem. 1999, 38, 4430.
J. AM. CHEM. SOC.
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VOL. 125, NO. 9, 2003 2561

A R T I C L E S
Ganesan et al.
Figure 2. Spectral changes in the NIR region attendant upon incremental addition of parent acceptor molecule to the acetonitrile solution of the
+
-•
tetrabutylammonium salt of the corresponding anion radical: (A) 1.9 mM solution of Bu4N TCNQ ; concentration of neutral TCNQ (spectra from bottom
+
-•
to top): 0, 2.5, 4.4, 7.0, 8.8, 10.7, 12.5 mM; (B) 1.0 mM solution of Bu4N DDQ ; concentration of neutral DDQ (spectra from bottom to top): 0, 3.9, 7.8,
+
-•
1
(
1.6, 16.4, 20.0, 24.4 mM; (C) 1.0 mM solution of Bu4N TCNE ; concentration of neutral TCNE (spectra from bottom to top): 0, 14, 33, 53, 72, 91 mM;
+
-•
D) 2 mM solution of Bu4N CA ; concentration of neutral CA (spectra from bottom to top): 0, 6, 9, 12, 15, 18, 21 mM.
• 19
when mixtures of the neutral acceptor and its anion radical were
examined, very weak absorption bands were observed in the
NIR region. For example, the solution of pure TCNQ-• in
acetonitrile was characterized by the diagnostic absorption band
at 842 nm. The stepwise addition of the parent TCNQ
expectedly resulted in the appearance and growth of the 396
nm absorption and led to some spectral distortion of the
absorption band of TCNQ with concomitant diminution of
the absorbance (see Figure S1 in the Supporting Information).
However, careful scrutiny clearly revealed the additional ap-
pearance of a weak (broad) absorption in the NIR region at λmax
salts of (TCNQ)2-
,
were consistent with the dynamic as-
sociation of the electron acceptor with its anion radical in
solution, i.e.,
KPC
-
•
-•
TCNQ + TCNQ
{
} (TCNQ)2
(4)
Indeed, the quantitative analysis of the equilibrium in eq 4 was
successfully carried out by the Benesi-Hildebrand procedure,
-
•
20
i.e.,
-
•
[TCNQ ]/A ) 1/ꢀPC + 1/(K ꢀ [TCNQ])
PC
PC PC
)
2200 nm, which progressively grew in intensity with further
additions of TCNQ, as illustrated in Figure 2. Lowering the
temperature of the TCNQ/TCNQ-• solutions consistently led
to substantial increases in only the new NIR absorbance.
To examine whether the counterion affected the NIR spectral
changes, neutral TCNQ was incrementally added to acetonitrile
where APC was the absorbance and ꢀPC was the molar extinction
coefficient of the NIR band of the precursor complex at the
-
•
monitoring wavelength, and [TCNQ ] and [TCNQ] were the
initial concentrations of the anion radical and the parent,
respectively. The plot of [TCNQ ]/Apc versus reciprocal
concentration of added TCNQ was linear, and the least-squares
fit produced a correlation coefficient of greater than 0.99. The
values of the association constant (KPC ) 5 M ) and extinction
coefficient (ꢀPC ) 3200 M cm ) were obtained from the slope
and the intercept (see Experimental Section).
-
•
-•
solutions of TCNQ successively taken as the lithium, sodium,
and tetrabutylammonium salts. In all cases, the position of the
NIR band was unchanged (see Figure S2 in the Supporting
Information), and these measurements occurred with the same
absorbance increase observed upon the further additions of
-1
-1
-1
-•
The spectral behavior of the other electron acceptors in Chart
toward their corresponding anion radicals mirrored that of
TCNQ . Furthermore, the addition of TCNQ to its anion radical
taken as tetrabutylammonium salt) in other solvents such as
1
(
TCNQ. In each case, the appearance of a new absorption band
in the NIR region (Table 1) signaled the formation of the
intermolecular [1:1] precursor complex. Thus, the addition of
dichloromethane and acetone also resulted in the appearance
of similar NIR bands (see Table S2 in the Supporting Informa-
tion). For example, in dichloromethane the affected NIR band
at λmax ) 2400 nm corresponded to a slight shift of only 200
nm relative to that observed in the more polar acetonitrile.
These spectral observations, together with their similarity to
the solid-state (reflectance) spectrum of various anionic π-mer
(
19) Indication of the NIR band in solid-state salts containing (TCNQ
also from the data reported by: (a) Iida, Y. Bull. Chem. Soc. Jpn. 1969,
2, 637. (b) Tanaka, J.; Tanaka, M.; Kawai, T.; Takabe, T.; Maki, O. Bull.
Chem. Soc. Jpn. 1976, 49, 2358.
(20) Benesi, H. A.; Hildebrand, J. H. J. Am. Chem. Soc. 1949, 71, 2703.
)- is seen
2
4
2562 J. AM. CHEM. SOC.
9
VOL. 125, NO. 9, 2003

Electron-Transfer Dynamics
A R T I C L E S
Table 2. Energy of the Charge-Transfer Transition for the
the quinone acceptor DDQ to an acetonitrile solution of its anion
radical resulted in a new NIR band at λmax ) 1360 nm (Figure
Intermolecular Complexes of the Acceptors in Chart 1 with
Different Organic Donorsa
2B and Figure S1 in the Supporting Information). Similar bands
energy of the
charge-transfer transition, eV
were obtained with the tetracyanoethylene and chloranil pairs,
-•
-•
TCNE/TCNE and CA/CA in Figure 2C and D, respectively.
For each dyad, the position of the corresponding NIR band and
its intensity (at the same concentration) did not depend on
whether sodium or tetrabutylammonium was the counterion (see
E0ox
acceptor
,
Vb
DDQc
TCNEd
donor
TCNQ
CA
1
2
3
4
5
6
7
8
9
1
1
benzene
toluene
o-xylene
p-xylene
mesitylene
durene
pentamethylbenzene
hexamethylbenzene
hexaethylbenmzene
naphthalene
2.62
2.25
2.16
2.01
2.11
1.84
1.71
1.62
1.59
1.54
1.09
2.27
2.29
1.55
3.05
2.82
2.62
2.43
2.43
2.13
2.08
1.98
3.19
2.99
2.82
2.65
2.64
2.38
Figure S2 in the Supporting Information), and this accords with
previous observations21 that these anion radicals exist largely
3.03
2.87
2.61
2.53
2.39
in (polar) acetonitrile as free (separate) ions. Similar to TCNQ,
the NIR bands also appeared upon the addition of neutral
π-acceptors to their anion radicals in the other solvents. Thus
in acetone, the positions of the NIR bands were close to those
in acetonitrile, while in dichloromethane a slight (consistent)
red-shift of the NIR band was observed (see Table S2 in the
Supporting Information). Owing to the very low solubility of
alkali metal salts of anion radicals in dichloromethane, only the
π-mer formation of the tetrabutylammonium salt could be
studied, but the use of the bulky counterion limited the ion-
pairing effects. Finally, the small magnitudes of the formation
constants KPC in Table 1 indicated that the precursor complexes
were to be uniformly classified as weak.
2.32
2.10e
2.27
2.24
2.58
e
0
1
2.30e
1.62
2.01
2.58e
1.97
anthracene
12 ethylbenzene
3.01
2.97
1
1
1
1
3
4
5
6
cumene
fluorene
2,6-dimethylnaphthalene 1.36
f
f
f
1.99
2.00
1.68
2.32
2.03
biphenylene
1.30
1.16
1.7
1.55
1.7
1.81
1.70
1.94
17 pyrene
1
1
8
2,5-dimethyl-p-
dimethoxybenzene
9-methylanthracene
1.15g
f
9
0.96
1.49
0.99
1.83
1.69
1.69
1.51
0.89
20 9,10-dimethylanthracene 0.94f 1.38
2
2
1
2
perylene
octamethylbiphenylene
π-mer
0.85
1.35
III. Intermolecular Associations of Electron Acceptors
with Their Anion Radicals as Charge-Transfer Interactions.
The spontaneous association of electron acceptors with their
anion radicals as listed in Table 1 was highly reminiscent of
the behavior of other well-known electron donor/acceptor dyads,
especially when the relatively electron-rich anion radical (A )
was viewed as an electron donor. According to this analogy,
the characteristic NIR absorption bands in Figure 2 should bear
a direct relationship to the absorption bands previously associ-
ated with the charge-transfer complexes of the same acceptors
0.80d 1.43d
0.52
1.41
0.88
1.41
0.83
d
(0.56)h (0.91)h (0.89) (0.92)
h
h
a
In dichloromethane, at 22 °C, unless noted otherwise. b From ref 41,
unless noted otherwise. c From ref 22a. From Fukuzumi, S.; Kochi, J. J.
d
-
•
e
f
g
Org. Chem. 1981, 46, 4116. From ref 12b. Unpublished results. From
ref 4f. h Data in parentheses in acetonitrile.
the value at the intercept of Eox - Ered ) 0 since both reversible
-
•
electrode potentials for this anion-radical π-mer (A2 ) are
identical.
2
2
with other types of electron-rich donors. Indeed, such [1:1]
electron donor/acceptor complexes of DDQ, TCNQ, TCNE, and
CA were formed with the various types of aromatic donors listed
The striking fit of all the data to a single linear correlation
with a ≈ 1.0 in eq 3 (with correlation coefficient > 0.99)
provided compelling evidence that the precursor complex
between an electron acceptor and its anion radical in fact derived
from the charge-transfer interaction as originally defined by
23
in Table 2. In this way, the NIR absorption bands of the
precursor complexes in Figure 3 were related directly to the
charge-transfer absorption bands in Table 2, the spectroscopic
transition energies (νCT) of which followed the Mulliken
1
3
Mulliken. In accord with this conclusion, the precursor
complex will hereafter be interchangeably referred to as the
anion-radical π-mer, in which the NIR absorption corresponds
1
3
relationship, i.e.,
2
4
0
0
to the homonuclear charge-transfer band. Thus, the anion-
radical π-mer as a negatively charged homomolecular dimer is
to be also considered together with the other (uncharged)
electron donor/acceptor complexes, which then represent their
heteromolecular analogues.
hνCT ) a(E - E red) + constant
ox
0
where E red is the reversible reduction potential of the electron
0
acceptor (DDQ, TCNQ, TCNE, and CA), E ox is the oxidation
potential of the aromatic donor, and a is a constant as illustrated
in Figure 3A-D. The unique point for the precursor complex
at the origin (abscissa) of each of these plots was defined by
IV. Intermolecular Binding in Precursor Complexes
(Theoretical Basis). Electron donor-acceptor complexes in the
general context of Mulliken theory are generated by the linear
combination of the principal van der Waals (ψD,A) and dative
(
21) For example, in studies of electron-transfer self-exchange of lithium, sodium,
and potassium salts of the anion radicals of TCNQ and TCNE in acetonitrile,
the same (TCNQ) or very close (TCNE) rate constants were obtained by
Komarynsky at al.8 Similarly, the electron-transfer self-exchange of TCNE
+
-
(ψD A ) states. Such an intermolecular charge-transfer interac-
tion is conveniently described via the valence-bond approach,
a
8c
so that the ground-state and excited-state wave functions can
was considered to occur between free ions by Watts et al. Note, however,
that in the less polar dimethoxyethane, the process was considered to be
2
5
be expressed as
8
c
those of loose (solvent-separated) ion pairs. Similarly, noticeable coun-
terion effects on the kinetic parameters were found for the TCNE anion
8
d
radical in dimethoxyethane by Ogasawara, M., et al.
ΨGS ) aψD,A + bψ
+
-
(5)
(6)
D A
(22) (a) Foster, R. Organic Charge-Transfer Complexes; Academic: New York,
1
969. (b) Briegleb, G. Electronen-Donator-Acceptor Komplexe; Springer:
Berlin, 1961. See also the footnotes in Table 2.
ΨES ) bψD,A - aψD+A-
(
23) The direct relationship of the NIR bands of aromatic cation-radical π-mers
to the charge-transfer bands of the same donor with the acceptors in this
study was shown by Kochi et al. in ref 12.
The energies of the ground and excited states obtained from
J. AM. CHEM. SOC.
9
VOL. 125, NO. 9, 2003 2563

A R T I C L E S
Ganesan et al.
Figure 3. Mulliken correlations (including linear regression lines) for the charge-transfer complexes of TCNQ (A), DDQ (B), TCNE (C), and CA (D) with
-•
-•
different organic donors in dichloromethane solutions. Numbers near points identify the donors in Table 2. Corresponding π-mers [(TCNQ2) (A), (DDQ2)
-
•
-•
(
B), (TCNE2) (C), and (CA2) (D)] presented by points on the y-axes. [Note that unfilled points correspond to dichloromethane solution, and filled points
to the acetonitrile solution].
the solution of the secular equation by the variational method
ꢀD,A, and the electronic coupling matrix element is given by
2
2
+ -
(
)
constraining the mixing coefficients to the normalized a + b
1 and neglecting the overlap, i.e., ∫ψD A ψD,A ) 0) can be
25
the resonance integral ∫ψD,AHψD A ) HDA. The mixing
coefficients that determine the donor/acceptor electron density
distribution at the energy minimum are related to the electronic
coupling element as cacb ) HDA/(EES - EGS), and the energy
of the optical transition from eqs 7 and 8 is
+
-
expressed as
2
2 1/2
DA
EGS ) (ꢀD,A + ꢀ
EES ) (ꢀD,A + ꢀ
+
-
)/2 - (∆ + 4H ) /2
(7)
(8)
D A
2
2 1/2
DA
2
2 1/2
νCT ) EES - EGS ) (∆ + 4H
)
(9)
+
D A
-
)/2 + (∆ + 4H ) /2
DA
Traditional studies of charge-transfer complexes deal mainly
with static donor/acceptor systems in which oxidation potential
of the donor is substantially higher than the reduction potential
+
-
+ -
where the Coulomb integrals ∫ψD,AHψD,A and ∫ψD A HψD A
+
-
represent the energies ꢀD,A and ꢀD A of the van der Waals and
the dative states, respectively. The energy gap is ∆ ) ꢀD+A -
-
2
2
of the acceptor. Therefore, (complete) electron transfer is
energetically unfavorable, and the donor/acceptor interaction
results in the formation of more or less thermodynamically stable
complexes. Transient precursor complexes [D,A] formed via
the intermolecular donor/acceptor interaction in the course of
an electron-transfer reaction in eq 1 bear the same earmarks as
classical charge-transfer complexes. Hush and Sutin showed how
the combination of the Mulliken (charge-transfer) formalism
(
24) Since we consider anion-radical π-mers as localized systems (vide infra),
-•
the NIR bands in the (A
2
)
complex are referred to as charge-transfer
transitions. However, the analogous electronic absorptions in cation-radical
1
1,12
π-mers have been referred to as charge-resonance bands.
(
25) (a) Brunschwig, B. S.; Sutin, N. Reflections on the two-state electron-
transfer model. In Electron Transfer in Chemistry; Balzani, V., Ed.;
Wiley: New York, 2001; Vol. 2, p 583. (b) Brunschwig, B. S.; Sutin, N.
Coord. Chem. ReV. 1999, 187, 233. (c) Sutin, N. AdV. Chem. Phys. 1999,
1
06, 7. (d) Creutz, C.; Newton, M. D.; Sutin, N. J. Photochem. Photobiol.
A: Chem. 1994, 82, 47.
2564 J. AM. CHEM. SOC.
9
VOL. 125, NO. 9, 2003

Electron-Transfer Dynamics
A R T I C L E S
Table 3. Mulliken-Hush Analysis of the Electronic Coupling
Element in Anion Radical (Precursor) Complexes with the Parent
Acceptorsa
Chart 3
precursor
complex
ν
CT
∆νCT
ꢀ
H
DA
(10 cm-1)
3
(10 cm-1)
3
(10 M cm-1
3
-1
)
(10 cm-1)
3
-
•
(
(
(
(
TCNQ)2
DDQ)2
4.6
7.3
7.2
7.4
2.2
2.7
2.8
2.7
3.2
1.6
0.8
1.3
1.15
1.10
0.79
1.00
-
•
-
•
28
TCNE)2
quinodimethane complex schematically illustrated in Chart 3,
-
•
-•
CA)2
in which the TCNQ and TCNQ moieties lie cofacially atop
one another and somewhat shifted with an interplanar separation
a
In acetonitrile at 22 °C.
1
7
of about rDA ) 3.2 Å. Both moieties in the dimeric salts of
-
•
with the Marcus (quadratic) representation of initial and final
diabatic states of the redox process allows the potential-energy
surface for electron transfer to be constructed.1,25 Most impor-
tantly, such a marriage of the static CT and the dynamic ET
theories explicitly and quantitatively takes into account the
precursor complex.1 Furthermore, such a combination focuses
on the direct relationship between the optical and thermal
electron transfer in the donor/acceptor dyads, and this methodol-
ogy allows the electron-transfer dynamics to be evaluated from
(TCNQ)2 are structurally intermediate between that of the
parent TCNQ and that of the slightly enlarged anion radical,17
as shown in Chart 2. The face-to-face arrangement of the nearly
planar moieties in the corresponding mixed complex (anion
radical/neutral acceptor) with an interplanar distance about 2.9
Å is also obtained in the DDQ systems. Although the association
in Figure 1 includes a pair of anion radicals with one neutral
acceptor, the first step of such a [2:1] complex formation must
proceed via the [1:1] complex. As such, half of the [2:1]
complex is a reasonable approximation for rDA) 3.3 Å in the
anion-radical π-mer. Additional insight into the structure of such
π-mers can be obtained from the analysis of the structural
features of other charge-transfer complexes of the corresponding
acceptors. Thus, charge-transfer complexes formed by the
π-acceptors under study with different (uncharged) planar donors
are generally characterized by face-to-face arrangements with
slightly higher interplanar donor/acceptor distances of about 3.5
,25
2
5,26
the spectral characteristics of the precursor complex.
Ac-
cording to this Marcus-Hush-Sutin (MHS) formalism, the
Marcus reorganization energy λ is equal to the energy of the
charge-transfer transition hνCT in the absence of a driving-force
contribution to electron transfer. The electronic coupling element
HDA in the precursor complex is evaluated experimentally from
the spectral data as27
1/2
2
9
HDA ) 0.0206(νCT ∆ν1/2 ꢀ ) /r
(10)
Å. Such an arrangement is similar to the experimentally
CΤ
DA
-
•
determined structure of the anion-radical π-mer of TCNQ ,
where νCT and ∆ν1/2 are the spectral maximum and full-width
and there is a reasonable basis to conclude that the structures
-
1
at half-maximum (cm ), respectively, of the charge-transfer
-•
of the precursor complex with the quinone systems (DDQ)2
-
1
-1
absorption band, ꢀCT is the extinction coefficient (M cm ) of
the precursor complex, and rDA is the separation (Å) between
the redox centers. Although the development of the MHS
approach was originally based on mixed-valence complexes in
-•
and (CA)2 , as well as that of the tetracyanoethylene system
TCNE)2 are close to that found for (TCNQ)2 . Accordingly,
-•
-•
(
we will take 3.3 Å to be a reasonable average for the interplanar
28
separations in the anion-radical π-mers generally.
4
,26
which the redox centers are fixed by a connecting bridge,
II. Electron Exchange within the Precursor Complex.
Electron (self) exchange rates between various electron acceptors
and their anion radicals have been measured by the concentra-
this limitation largely resulted from the singular absence of
intermolecular systems heretofore in which the precursor
complexes could be experimentally detected and thoroughly
characterized.
7,8
tion-dependent line-broadening of the ESR spectra. However,
such measurements in solution are incapable of distinguishing
diffusional electron transfers from those taking place within the
precursor complex. To address the latter, we note that the
Discussion
The structural and spectral characterization of the anion-
radical π-mer as the precursor complex in self-exchange electron
transfer as examined in Tables 1-3 now allows us to implement
the MHS methodology in intermolecular ET processes. Since
such an analysis requires the structural characteristics of the
complex (especially the separation parameter rDA in eq 10), let
us first turn to the structures of anion-radical π-mers.
-•
electronic interaction of A/A moieties in the intermolecular
precursor complex is related to that previously encountered in
the intramolecular mixed-valence compounds in which the
redox centers are deliberately tied together by a molecular
4,26
bridge. In such systems, the electronic interaction of A with
-•
A
is evaluated by the magnitude of the electronic coupling
element HDA (Table 3), and the rate of electron transfer between
I. Structure of the Precursor Complex in Self-Exchange.
The molecular associations of the electron acceptors A in Chart
them in governed by the Marcus reorganization energy λ.4
Figure 4 shows the plots of the free-energy change along the
reaction coordinate for the self-exchange electron transfer
-
•
1
with their anion radicals A in solution (Table 1) are
-
1
considered to be weak, typically with values of KPC < 10 M .
The structural nature of the intermolecular binding of A and
(
28) (a) Note also the possibility of (planar) slippage as in Figure 1. (b) As a
molecular parameter, rDA in eq 10 is difficult to define exactly in
intermolecular (optical and thermal) electron transfer, especially owing to
variable interplanar distances and the possibility of slippage. In addition,
the value of rDA obtained from molecular geometry of complex with
substantial coupling undoubtedly requires further correction, and it can be
substantially less than the sum of van der Waals radii, as discussed by
-•
-•
A
to form the negatively charged precursor complex (A2
)
is indicated by the X-ray crystal structure of the tetracyano-
(
26) (a) Creutz, C. Prog. Inorg. Chem. 1983, 30, 1. (b) Omberg, K. M.; Chen,
P.; Meyer, T. J. AdV. Chem. Phys. 1999, 106 (part 1), 553. (c) Demadis,
K. D.; Hartshorn, C. M.; Meyer, T. J. Chem. ReV. 2001, 101, 2655.
27) (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,
c
Newton. (c) Newton, M. D Electron Transfer: Theoretical Models and
Computational Implementation. In Electron Transfer in Chemistry; Balzani,
V., Ed.; Vol. 1, Wiley: New York, 2001; p 3.
(
(29) (a) Rathore, R.; Lindeman, S.; Kochi, J. J. Am. Chem. Soc. 1997, 119,
3
91. (d) Hush, N. S. Electrochim. Acta 1968, 13, 1005.
9393.
J. AM. CHEM. SOC.
9
VOL. 125, NO. 9, 2003 2565

A R T I C L E S
Ganesan et al.
Figure 4. Energy diagrams for electron transfer based on the diabatic reactants (left) and products (right) states (dashed lines) and showing the adiabatic
-
•
-•
ground state as the precursor complexes for (TCNQ2) (A) and for (DDQ2) (B) in black solid lines and their excited states in gray solid lines.
between A and A-• moieties with ∆G ) 0. The dashed
0
sphere mechanism in which the electronic coupling HDA is small
and does not affect the ET barrier evaluated from ∆G* ) λ/4.4
We thus conclude that the electronic effects of strong donor/
acceptor interactions must be explicitly taken into account in
any theoretical description of the self-exchange. To validate the
applicability of the electronic parameters obtained via the study
of optical transitions to the description of thermal (adiabatic)
electron transfer, we now compare the theoretical predictions
with those from the available experimental data in the following
way.
III. Electron-Transfer Kinetics for Self-Exchange Based
on the Precursor Complex. The generalized pathway for
electron-transfer self-exchange between an acceptor and its anion
radical that includes the precursor complex can be described
from Figure 4 as shown in Scheme 1, where KPC is the formation
-8
parabolic curve on the left (r) represents the reactants diabatic
noninteracting) state between A and A , and that on the right
p) is the products diabatic state between A and A [The
underline is simply a label; otherwise A and A are identical.]
The reorganization energy is given by the vertical (optical)
transition with25 λ ) νCT as listed in Table 3. The values of
HDA evaluated from the spectral data in Table 1 according to
eq 10 are listed in Table 3.
-
•
(
-
•
(
Within the framework of the Robin-Day classification of
30
mixed-valence compounds, the increasing magnitudes of the
electronic coupling reflect the progressive transition from Class
I (HDA ) 0, noninteracting redox centers), to Class II (0 < HDA
2
5
<
λ/2), and to Class III (HDA > λ/2, delocalized) systems.
Inspection of the results in Table 3 clearly reveals that the
precursor complexes relevant to the acceptors in Chart 1 are to
be classified as Class II systems since HDA < λ/2 in all cases.
This conclusion is also supported by the consistently lower CT
energies in dichloromethane relative to those in acetonitrile.
Such shifts are characteristic of Robin-Day Class II systems,
connected with the higher (outer-sphere) reorganization energy
in the more polar solvent.8
The evaluations of HDA and λ in Table 3 allow the free-energy
profile for electron exchange within the precursor complexes
to be constructed within the two-state model.25 The lower
heavy) lines in Figure 4A,B trace the energy profiles for the
prototypical acceptor systems (DDQ)2 and (TCNQ)2 , and
the activation free energy for intracomplex electron transfer is
Scheme 1
constant of the precursor complex (Table 1) and ket is electron
1
exchange rate constant within the precursor complex. The
,25
second-order rate constant for intermolecular electron transfer
is then given by
k ) K k
(12)
and the intramolecular rate constant can be evaluated from
k ) kν exp(-∆G*/RT) (13)
where k is the electronic transmission coefficient, νn is the
2
PC et
(
-
•
-•
-
1
presented as ∆G* ) 2.6 and 0.8 kcal mol , respectively. In
both systems, the transition-state energies for adiabatic electron
transfer are substantially less than the value of λ/4 (determined
at the intersection of the diabatic curves). This discrepancy is
et
n
32
-
•
nuclear vibration frequency related to electron transfer, and
especially pronounced for (TCNQ)2 , and the situation with
1
-
•
-•
-•
∆G* is the free energy of activation for electron transfer. When
(
TCNE)2 and (CA)2 is similar to that of (DDQ)2 (see
3
1
the electronic coupling is sufficiently strong (as given in Table
Figure S3 in the Supporting Information). In other words, as
a result of the electronic coupling within the acceptor/anion-
2
5
3
), the activation barriers is
-
•
radical complex, the intermolecular rates between A and A
moieties are faster than those predicted simply by an outer-
2
∆
G* ) (λ - 2HDA) /4λ
(14)
(
30) Robin, M. B.; Day, P. AdV. Inorg. Chem. Radiochem. 1967, 10, 247.
(32) The electronic transmission coefficient represents the probability that
electron transfer will occur once the system has reached the intersection
(
31) Note that quadratic dependencies of the diabatic states on the reaction
(
nuclear configuration) coordinates are used in Figure 4 in accordance with
n
region (transition state), and ν is the nuclear frequency that takes the system
5
the Marcus formulation.
through this region.
2566 J. AM. CHEM. SOC.
9
VOL. 125, NO. 9, 2003

Electron-Transfer Dynamics
A R T I C L E S
Table 4. Comparison of the Experimental (ESR) and Theoretical (Optical) Electron-Transfer Rate Constant for the Acceptor/Anion-Radical
Self-Exchangea
λb
HDAc
∆G*d
(kcal/mol)
e
f
g
theor h
obs
k
SE
k
et
K
a
k
2
k
SE
(109 s-1
)
(M )
-1
(10 M s-1
9
-1
)
(10 M s-1
9
-1
)
(10 M s-1)
9
-1
acceptor
(kcal/mol)
(kcal/mol)
DDQ
TCNQ
TCNE
CA
21.4
13.5
21.1
21.7
3.2
3.4
2.3
2.9
2.6
0.8
3.2
2.9
12
240
4.3
7.5
3
5
0.5
4
36
1200
2.2
30
12
18
1.9
11
2.5i
3.8j
2.2j
a
In acetonitrile, at 22 °C, tetrabutylammonium counterion. b Reorganization energy, based on data from Table 3 (λ ) νCT). Data from Table 3. d From
c
e
12 -1 34 f
From Table 1. g From eq 12 based on ket
eq 14, based on λ and HDA from columns 2 and 3. From eq 13 with ∆G* from column 3 and kν ) 10
s
.
and Ka from columns 5 and 6. h From eq 15. Reference 8e. Reference 8h.
i
j
3
3
owing to adiabatic electron transfer with k ≈ 1. The calculated
values of the bimolecular electron transfer obtained from the
measured value of KPC in Table 1, together with the reorganiza-
tion energy, the electron coupling element (obtained from the
theoretical evaluation of the precursor complex in Table 3), and
intermolecular processes such as those based on ESR line-
3
5a
broadening measurements. The agreement obtained in Table
4 indicates that the MHS methodology provides reasonable
evaluations of the electronic coupling interaction (HDA) and the
reorganization energy (λ) for the intermolecular electron-transfer
process between an electron acceptor and its anion radical
(despite the possibility of some overlap in anion-radical
1
2
-1 34
νn ) 10
in the range 10 -10
s
lead to the second-order rate constants that lie
9
10
-1 -1
M
s
(Table 4). For such fast reactions,
35b
6-8
the effects of diffusion (kdiff) must be explicitly taken into
account.7 Thus, for comparison with the experimental values
of the self-exchange rate constant (kSE), the theoretical rate
constant is corrected as
complexes ). Indeed, the earlier (substantial) underestimation
,8
of the predicted rate constants in anion-radical self-exchange
processes can be directly attributed to the neglect of the strong
electronic interaction in the precursor complex in the theoretical
calculation of the activation barrier.
theor
B. Evaluation of the Reorganization Energy for Self-
Exchange. The optical data in Table 3 allow us to verify the
previous estimates of the reorganization energy in such systems.
According to Marcus theory, the overall reorganization energy
λ is expressed as the sum of the inner-sphere reorganization
energy λi and the outer-sphere term λo (which represent the
energy of solvent reorganization). Inner-sphere reorganization
energies can be evaluated from the bond length/angle differences
between the oxidized and reduced species that participate in
the redox process (see Chart 2), together with the corresponding
1
/kSE
) 1/k + 1/k
(15)
2
diff
where k2 is the second-order rate constant without the diffusional
10
-1 -1
correction, and kdiff is taken as 1.9 × 10
M
s
in acetonitrile
at 22 C.8 The theoretically predicted rate constants (kSE
f
theor
)
evaluated in this manner are compared with the experimental
values (k ) in the last two columns of Table 4. We consider
the agreement between these to be satisfactory, especially if
we take into account the uncertainty in the evaluation of the
preexponential factor in eq 13.34 Although a more rigorous
comparison of the experimental and theoretical rate constants
is desirable (particularly in the preexponential factor), the
analysis of the extant data allows several important conclusions
to drawn.
A. Validation of the Marcus-Hush-Sutin Methodology.
Although there were several previous attempts at the estimation
of electron-transfer rate constants based on HDA and λ derived
from optical data, only the results of this study allow the direct
comparison of the theoretically predicted and the experimentally
determined rate constant for electron-transfer self-exchange in
obs
36
force constants. Outer-sphere reorganization is usually calcu-
lated from the effective radii of the reactants considered as either
spheres or ellipsoids, the reaction distance, and the Born model
36
of the solvent as a continuous dielectric medium. On the other
hand, the reorganization energy λ is usually evaluated experi-
mentally from the kinetics of the self-exchange processes, based
on the simple relationship
3,4
k2 ) Z exp(- ∆G*/RT)
(16)
with ∆G* ) λ/4 and collision frequency Z ) 1011 M-1 s .
-1 7,8
(
33) When the electronic interaction between the reactants is weak, kel , 1,
and the electron transfer occurs in the nonadiabatic regime. In such a case
(35) (a) For a similar application of the MHS (two-state) model to intermolecular
electron transfer of arene donors with NO+ via of the [1:1] precursor
complex (Class III), see: Rosokha, S. V.; Kochi, J. K. New J. Chem. 2002,
26, 851. (b) Since the MHS (two-state) model requires the diabatic states
2
3
∆
o n
G* ) λ/4 (where λ ) λin + λ ) and kelν ) νel ) (2HDA /h)(π /λRT).
Thus, when the electronic coupling is weak (nonadiabatic limit), HDA
explicitly determines the preexponential factor (or probability of electron
transfer in the transition state). When the electronic interaction is strong
25d
to be orthogonal, the small orbital overlap that may exist in anion-radical
complexes may necessitate some correction of the parameters obtained via
(
strongly adiabatic limit), HDA affects the exponential factor (i.e., transition-
2
5d
state energy). Therefore, eq 16, which is frequently used for the estimation
eqs 8-14. However, Creutz et al. successfully applied the MHS model
to ruthenium complexes (with a similar overlap problem), and we depend
on the same approach. In particular, we judge the validity of the two-state
model by recognizing the reasonable correspondence between the experi-
mental and theoretically predicted rate constants presented in Table 4.
Clearly, a more quantitative analysis will ultimately be needed, the impetus
for this being hopefully provided from studies such as that described herein.
(36) (a) If donor/acceptor separation in electron transfer is larger than the sum
6
-8
of the intermolecular electron-transfer rate constant,
is valid only in a
very limited range of HDA values (usually from about 30-50 to 150-200
-1
cm ).
(34) Since the electron-transfer self-exchanges of anion radicals involve numer-
-
1
-1
ous molecular (∼500-3000 cm ) and solvent (∼10-100 cm ) vibrational
2
1/2
1
modes, the preexponential factor ν
n
) (∑ν
i
λ /Σλ
i
i
)
[as described by Sutin ]
is difficult to rigorously calculate from the available data. Thus for this
1
2 -1
study, we have simply taken ν
n
to be uniformly 10
s
, a value similar to
of their radii, the relationship is λ
0 o A 0 o
) (e N /4πꢀ )g(r,d′)γ, where γ ) 1/ꢀ
those previously used for the description of electron transfers in coordination
- 1/ꢀ (ꢀ and ꢀ are the optical and static dielectric constants), and g(r,d′)
s
o
s
1
,26
compounds (approximated by few modes) or taken a priori as kT/h.
is a function of the effective molecular radius as described by Grampp et
al. in ref 8f. (b) However, note that for the cofacial arrangement of planar
reactants in the precursor complex the previous estimates based on a point-
dipole-in-a-sphere model (with the sphere corresponding to the precursor
According to Sutin, such a choice derives from the effective frequency
that is dominated by solvent modes, especially when the solvent barrier is
relatively large (although the frequency of the intramolecular vibrations is
substantially higher). Most importantly, this choice leads to calculated rate
constants that agree with the experimental kinetics (Table 4), and a
substantial increase in the preexponential factor will shift the rate constants
to the (unrealistic) diffusion-controlled limit.
complex having the overall radius of the reactant pair) lead to values of λ
o
that can be off by a factor of 2 (or more) relative to one that considers the
8a
reactants as touching spheres or ellipsoids. (c) For the quantum-mechanical
calculation of the inner-sphere reorganization energy, see refs 7j-o.
J. AM. CHEM. SOC.
9
VOL. 125, NO. 9, 2003 2567

A R T I C L E S
Ganesan et al.
Table 5. Comparison of the Experimental and Theoretical
Reorganization Energies for A /A Self-Exchange
cross-exchange can actually be higher than those estimated from
self-exchange kinetics, as reported earlier by Nelsen et al. ]
-
•
a
2
theor
theor
λtheor e
f
λg
λ
i
λ
o
λ
SE
C. Mechanism for Self-Exchange and the Evaluation of
HDA. The kinetics formulation in Scheme 1 can be used to verify
estimates of the electronic coupling element, particularly for
the organic redox processes under discussion. Thus the values
of HDA established for the self-exchange electron transfers of
acceptor
(kcal/mol)
(kcal/mol)
(kcal/mol)
(kcal/mol)
(kcal/mol)
b
b
DDQ
TCNQ
TCNE
10.0
19.5
22.4
26.0
29.5
28.8
29.2
8.4
7.2
8.8
21.4
13.5
21.1
c
d
6.4
c
d
3.3
a
In acetonitrile, at 22 °C. Reference 8e. c Reference 8f. d Reference
b
-•
-•
TCNQ and DDQ in Table 3 agree with the theoretical
molecular orbital calculations, while the experimental value for
6
d. e Obtained as λi
theor
+ λo
theor
from columns 2 and 3. Experimental
f
reorganization energy estimated as 4∆G* from the self-exchange kinetics
1
1
-1 -1
-•
8
[
∆G* is calculated via eq 16 using Z ) 10
M
s
(collision frequency)
TCNE is substantially larger than the predicted one. Although
other theoretical data are not yet available, the values of HDA
in Table 3 generally correspond to the estimates based on the
indirect analysis of anion-radical (redox) kinetics by Eberson
obs
-1
obs
-1 -1
and k2 ) (1/kSE - 1/kdiff) , where kSE is taken from the last column
1
0
s
]. g Experimental reorganization
in Table 4 and kdiff ) 1.9 × 10
M
energy evaluated from the charge-transfer (NIR) absorption band of the
corresponding complex.
3
7
and Shaik from a different perspective. Most importantly, the
sizable values of HDA relative to the reorganization barrier
cannot be neglected in any prediction of the activation barrier
for electron transfer, and significant rate increases do result from
the decrease of the TCNQ barrier by roughly 75%, of the DDQ
and CA barrier by 50%, and of the TCNE barrier by 40%
according to the significant presence of the precursor complex
as formulated in Scheme 1.
In the case of outer-sphere redox processes of coordination
compounds, the theoretically estimated reorganization energy
generally allows satisfactory predictions of the rate constants
1
for the self-exchange processes. In other words, the theoretically
predicted reorganization energy in outer-sphere electron transfer
is close to that experimentally determined from the kinetic data
based on λ ) 4∆G*. However, in the case of self-exchange
processes for electron transfer of organic molecules, the
theoretically predicted reorganization energy is in many cases
substantially larger than that evaluated from the kinetic data.
IV. Comments on the Role of the Precursor Complex in
Outer-Sphere and Inner-Sphere (Electron-Transfer) Mech-
anisms. The precursor complex in outer-sphere electron transfer
between a donor and acceptor according to Taube38 involves
no bond breaking or bond forming (ligand exchange) prior to
[For example, see the analysis presented by Eberson in ref 5
for large numbers of organic systems.] In particular, for the
π-acceptors in Chart 1, the theoretical estimates of λtheïr (column
1,5
the activated complex. Likewise in Marcus theory, the outer-
4
in Table 5) are roughly 400% larger than λSE evaluated simply
sphere precursor complex is limited to only weak (unperturbed)
donor/acceptor interactions, in which the probability of electron
transfer is close to unity (adiabatic) or substantially less than
unity (nonadiabatic). As a result, most quantitative studies of
basic electron transfer (experiment and theory) have focused
as 4∆G* obtained from the kinetic data, and the results obtained
in this study clarify such discrepancies of the reorganization
energies in the following way. First, the strong electronic
interaction between the donor/acceptor moieties within the
precursor complex leads to substantial lowering (40-75%) of
the activation barrier for electron transfer relative to that simply
based on λ/4. Therefore, the relationship ∆G* ) λ/4, which is
valid for weakly interacting systems, is not generally a reliable
method for the evaluation of the reorganization energy, par-
ticularly of π-systems. [This is seen from a comparison of data
in columns 5 and 6 in Table 5 with λSE estimated from self-
exchange kinetics which are substantially lower than λ obtained
from optical data.] Second, the reorganization energies in Table
1
,3,6,39
primarily on outer-sphere processes.
However, when the
redox centers are intimately shared (as in ligand exchange), the
inner-sphere process must involve stronger intermolecular
electronic interactions and substantial increases in electron-
transfer rates. Heretofore, the effects of the strong donor/acceptor
coupling in the inner-sphere precursor complexes have been
considered only qualitatively, the sole exception being the
intramolecular mixed-valence complexes in which the donor/
acceptor centers are directly bridged, as in the original Creutz-
4
,27,40
Taube ion and other organic analogues.
Since the present
3
that are experimentally derived from the optical data are
theïr
study clearly demonstrates how the electronic coupling in the
precursor complex can dramatically affect the dynamics of
intermolecular electron transfer, let us briefly consider how our
conclusions impinge on various redox systems more generally.
substantially lower than the theoretical estimates of λ
cited
6
-8
in the literature (compare columns 4 and 6 in Table 5). This
discrepancy is at least partially ascribable to the neglect of the
precursor complex in which the planar donor/acceptor dyads
lie intimately (i.e., face-to-face) and largely preclude any
intervening solvent from the activated complex.8 Such transi-
tion-state structures must clearly be recognized in redox
processes of organic π-donors, especially those of the aromatic
analogues with nonspherical shapes. Thus, a theoretical calcula-
tion can overestimate the reorganization energy due to enhance-
ment of the outer-sphere component, and the calculations of
the reorganization energy based on self-exchange kinetics can
substantially underestimate its real value owing to the effective
lowering of the barrier due to the strong electronic interaction,
such that ∆G* < λ/4. [It is interesting to note that since the
electronic coupling in the precursor complexes in the cross-
exchange is expected to be less effective (due to symmetry
reasons), the values of reorganization energy estimated from
The quantitative analyses of synthetically significant organic
processes involving a critical electron-transfer step reveal strong
donor/acceptor interactions indicative of the inner-sphere path-
a
4
1
way. We believe the inner-sphere precursor complex is
important whenever the reactant structure allows substantial
overlap of the donor/acceptor orbitals. Thus, organic systems
such as planar aromatic donors and acceptors (unencumbered
(
37) Eberson, L.; Shaik, S. S. J. Am. Chem. Soc. 1990, 112, 4484.
38) Taube, H. Electron-Transfer Reactions of Complex Ions in Solution;
Academic Press: New York, 1970.
39) Moreover, as recently noted by Bixon and Jortner, “... the majority of
thermal outer-sphere ET in solution and photoinduced ET via bridges in
organic and inorganic supermolecules proceed via non-adiabatic ET...”.
See: Bixon, M.; Jortner, J. AdV. Chem. Phys. 1999, 106 (part 1), 35.
40) Haim, A. Prog. Inorg. Chem. 1983, 30, 273.
(
(
(
(41) Rathore, R.; Kochi, J. K. AdV. Phys. Org. Chem. 2000, 35, 193.
2568 J. AM. CHEM. SOC.
9
VOL. 125, NO. 9, 2003

Electron-Transfer Dynamics
A R T I C L E S
by bulky substituents), as well as sterically accessible inorganic
complexes such as the linear Ag(I) and Hg(II), trigonal Al(III),
and square-planar nickel(II) and copper(II), etc., are prone to
the new definition allows a variety of donor/acceptor dyads to
be included (in addition to coordination compounds), and it thus
readily accommodates hybrid redox systems involving organic
and inorganic donor/acceptor dyads of particular importance to
organometallic and biochemical oxidation-reductions. We
envisage a wide (structural) array of redox systems to be
included in the inner-sphere pathway. Therefore, to provide an
operational basis for further studies of inner-sphere electron
transfer, we distinguish three subclasses.
+
-
interact with relatively small reagents such as Br2, NO , Cl2 ,
S2O82 , and H2O2 to form transient inner-sphere complexes.
Despite their seminal importance in the development of
electron-transfer theory, the weakly interacting donor/acceptor
dyads in outer-sphere electron transfer actually represent a
minority and are largely limited to coordinatively saturated
-
(
octahedral) complexes and involve rather long-range electron
(i) Inner-Sphere Systems with 0.025 < HDA/λ < 0.1. The
effects of increasing HDA in this range can lead to the lowering
of the activation barrier by 10-40% with concomitant increase
in the rate constant predictions by 1-2 orders of magnitude.
As a result, the precursor complex must be considered explicitly
despite the experimental difficulties that may be encountered
in the detection/characterization of such weakly interacting
transfer. In this regard, let us reconsider Taube’s traditional
classification (centered as it is on only inorganic coordination
compounds) in a broader quantitative context for the following
reasons: (1) A viable electron-transfer classification should
include the wide spectrum of organic, inorganic, and biochemi-
cal donor/acceptor dyads, independent of the presence of ligands;
4
4
(2) the span of donor/acceptor interactions should be considered
associations.
incrementally from nonadiabatic electron transfer of weakly
bound dyads at one extreme to those involving chemical bonds
at the other extreme; (3) strongly interacting donor/acceptor
dyads merit more careful and quantitative consideration since
they will include chemically important redox systems for
electrical conductors, magnets, sensors, etc., of potential rel-
evance to material science.
Mechanistic Proposal. Owing to the importance of the
electronic coupling element HDA to the redox characteristics of
the precursor complex, we follow Sutin’s development of the
(ii) Inner-Sphere Systems with 0.1 < HDA/λ < 0.5. In this
intermediate region, the effects of HDA on the energy barrier
can be dramatic, with decreases in the activation barrier of as
much as 40%-99% and discrepancies in the rate predictions
of more than 3 orders of magnitude. [The self-exchange in the
acceptor/anion-radical dyads studied here fall into this category.]
Although the association constants are not high, by careful
(spectral) analysis it should be possible to experimentally detect
and characterize the precursor complex.
(iii) Inner-Sphere Systems with HDA/λ > 0.5. This extreme
region corresponds to Class III in the Robin-Day classification.
As such, electron donors form stable complexes with acceptors,
which can be characterized spectroscopically and isolated as
single crystals for X-ray crystallographic analysis. [Examples
of such systems are octamethylbiphenylene cation-radical
two-state model,1 the Robin-Day classification, together with
,25
30
42
Nelsen’s suggestion, and employ the normalized ratio HDA/λ
as the single parameter43 to classify electron-transfer mecha-
nisms, especially as a basis for further study and comment.
Outer-Sphere Mechanism with HDA/λ < 0.025. In this
limited region, the effects of HDA on the activation barrier will
be less than 10% (relative to the those calculated as λ/4). Thus,
for redox systems with reorganization energies in the range λ
-
1
π-mers with Ka ) 350 M and intermolecular complexes of
+
arenes with nitrosonium (NO ) which have association constants
6
-1 12,35a
of up to 10 M .
] The electron is extensively delocalized
)
25 ( 15 kcal/mol, the rate constant will be within an order
within such precursor complexes. As such, there is essentially
no barrier for electron transfer from the donor to the acceptor,
and the electronic interaction within such precursor complexes
can be basically considered as strongly bonding.
of magnitude of that without the correction. Since such an
uncertainty is insufficient for any mechanistic distinction, this
redox process is defined as outer-sphere. The outer-sphere
precursor complex is likely to be experimentally detected only
with additional ion-pairing effects and/or at extremely high
Summary and Conclusion
3
concentrations.
The precursor (or encounter) complex, despite its integral role
in intermolecular electron-transfer processes, has been largely
neglected (or completely overlooked) as a metastable intermedi-
ate owing to the paucity of structural data heretofore. To
quantitatively establish how the precursor complex is critical
to electron-transfer dynamics, we thus focused on the self-
exchange kinetics of a series of π-acceptors A with their reduced
Inner-Sphere Mechanism with HDA/λ > 0.025. For these
redox systems, the energy barriers and electron-transfer rates
will be substantially affected by the electronic coupling (binding)
within the precursor complex, and we correspondingly define
such processes as inner-sphere. We note that Sutin considers
redox systems with HDA > 200 cm to be strongly adiabatic
26
-
1
-1
(
Class II), and this coupled with λ ≈ 25 kcal mol corresponds
-•
anion radicals A in which the precursor complex is the
to HDA/λ ) 0.025. Accordingly, this proposed definition of
inner-sphere electron transfer corresponds to a strongly adiabatic
process.
-•
intermolecular π-mer A2 and can be subjected to thorough
structural characterization. Since this basic (redox) system occurs
in the absence of a driving-force contribution, the electron-
transfer dynamics can be quantitatively evaluated with the aid
of only the Marcus reorganization energy (λ) and the inter-
molecular electronic coupling element (HDA) based on the two-
In essence, such a global definition of outer-sphere and inner-
sphere electron-transfer mechanisms encompasses the Taube
classification, but it is not dependent on structural types. Thus,
(
42) Nelsen, S. In Electron Transfer in Chemistry; Balzani, V., Ed.; Wiley-
VCH: New York, 2001; Vol. 1, p 342.
(44) (a) Since the energy gain due to electronic coupling is proportional to
2
-1
H
DA /λ, the association constant here is expected to be less than 1 M , as
(43) The use of this normalized ratio is based on the fact that HDA and λ
determine the barrier for electron transfer (eq 14), the stabilization of
observed in systems with higher values of HDA/λ. (b) When the optical
(charge-transfer) transition is experimentally unobservable, alternative
theoretical (quantum mechanical) treatments are favored for the evaluation
2
precursor complex (as HDA /λ), and the charge transferred from the donor
to acceptor.2
5,35a
of HDA.
J. AM. CHEM. SOC.
9
VOL. 125, NO. 9, 2003 2569

A R T I C L E S
Ganesan et al.
°C. The structures were solved by direct methods47 and refined by full
matrix least-squares procedure with IBM Pentium and SGI O comput-
2
state Hush-Sutin treatment. Most importantly, we underscore
the caveat that the “true” reorganization energy obtained from
the optical (charge-transfer) transition inherent to these precursor
complexes is substantially higher than that obtained from the
self-exchange data by the indiscriminate application of Marcus
ers. [Note that the X-ray structure details of compounds mentioned
here are on deposit and can be obtained from Cambridge Crystal-
+ 2-
4 2 3
N ) (DDQ ) : A 100 mL flask
lographic Data Center, U.K.] (Et
equipped with a Schlenk adapter was charged with 17 mg (about 0.05
(outer-sphere) theory.
+
-•
4
mmol) of (Et) N DDQ and 20 mg (about 9 mmol) of DDQ, and 10
mL of dichloromethane was added under argon atmosphere. After
dissolution, the solution was covered with hexane and put into a cold
Experimental Section
(
Pr
-65 °C) bath. Brown rhombic crystals were formed in 5-7 days.
Materials. Acetonitrile, dichloromethane, acetone, and hexane
+
-•
Merck) were purified according to standard laboratory procedures45
4
N CA : A 100 mL flask equipped with a Schlenk adapter was
(
+
-•
4
charged with 21 mg (about 0.05 mmol) of Pr N CA , and 10 mL of
and were stored in Schlenk flasks under an argon atmosphere. Neutral
acceptors TCNQ, DDQ, TCNE, and CA (Aldrich) were purified by
repeated recrystallization and/or sublimation in vacuo. Sodium iodide,
lithium iodide, tetrabutylammonium iodide, and tetraethylammonium
iodide (Acros) were used as received. Anion-radical salts were prepared
by the interaction of the neutral acceptors with 1.5-3 molar excess of
dichloromethane was added under argon atmosphere. After dissolution,
the solution was covered with hexane and put into a cold (-65 °C)
bath. Orange crystals were formed during 3-5 days. The X-ray
crystallographic analyses for DDQ and Et
in the literature) were remeasured at -150 °C to obtain better precision.
+
-•
4
N DDQ (data available
+ 2-
4 2 3 6 8 6
N ) (DDQ ) . Formula: C40H40Cl N O , M 941.50, monoclinic
+
+•
(Et
/n, a ) 13.084(1) Å, b ) 12.693(1) Å, c ) 13.656(1) Å, â )
the corresponding alkali-metal or alkylammonium iodide. Bu
4
N TCNQ
+
+•
P2
112.61(1)°, V ) 2093.9(2) Å , D ) 1.493 gcm , Z ) 2. The total
number of reflections measured were 22997, of which 6779 reflections
were symmetrically nonequivalent. Final residuals were R1 ) 0.1061
and wR2 ) 0.1995 for 5882 reflections with I > 2σ(I).
1
and Bu
ing alkali-metal salts.
4
N CA were isolated after ion-exchange with the correspond-
3
-3
1
4,46
+
-•
c
Thus, Li TCNQ was prepared by the
addition of a hot solution of 4 g (0.03 mol) of LiI in 10 mL of
acetonitrile to a boiling solution of 2.04 g (0.01 mol) of TCNQ in 200
mL of acetonitrile. After cooling and standing for 4 h at room
temperature, the solid was collected and successively washed with
+
-•
Pr
4
N CA ‚CH
2 2 6 2
Cl . Formula: C19H30Cl NO , M 517.14, monoclinic
-
•
C , a ) 19.885(1) Å, b ) 7.8652(4) Å, c ) 18.427(1) Å, â )
121.04(1)°, V ) 2469.3 (2) Å
number of reflections measured were 13363, of which 6949 reflections
were symmetrically nonequivalent. Final residuals were R1 ) 0.030
and wR2 ) 0.0769 for 6689 reflections with I > 2σ(I).
acetonitrile and ether. Sodium salts of TCNQ were prepared in a
c
-
•
3
, D ) 1.391 g cm-3, Z ) 4. The total
similar way. To prepare the tetrabutylammonium salt of TCNQ , the
corresponding lithium salt (570 mg) was dissolved in water, and 1.01
g of tetrabutylammonium iodide was added. The blue precipitate was
c
+
-•
filtered, washed, and air-dried. To prepare Na DDQ , 219 mg (0.96
mmol) of DDQ in 10 mL of acetonitrile was added to 144 mg of NaI
in 10 mL of acetonitrile. The volume of the solution was reduced to 8
mL, and the mixture was stored at -30 °C for 3 days. The precipitate
was filtered and washed with small amounts of cold acetonitrile. The
+
-•
Et
4 2 3 2 1
N DDQ . Formula: C16H20Cl N O , M 357.25, monoclinic P2 /
n, a ) 6.879(1) Å, b ) 20.031(2) Å, c ) 12.409(1) Å, â ) 99.84(1)°,
V ) 1684.6 (3) Å , D ) 1.409 g cm , Z ) 4. The total number of
reflections measured were 16604, of which 5118 reflections were
symmetrically nonequivalent. Final residuals were R1 ) 0.0304 and
wR2 ) 0.0815 for 4745 reflections with I > 2σ(I).
3
-3
c
-•
tetrabutylammonium salt of DDQ was prepared similarly. To prepare
-
•
the sodium salt of TCNE , 1.1 g of NaI (7.4 mmol) was added to 315
mg (2.5 mmol) of TCNE in 5 mL of acetonitrile. The precipitate formed
in the course of 30 min stirring was filtered, washed with dichloro-
methane, and dried in vaccuo. The tetrabutylammonium salt of TCNE
anion radical was prepared similarly. However, a 1.5 mol excess of
iodide was used and the solution kept in the refrigerator for 3 days to
DDQ. Formula: C Cl N O , M 227.00, orthorhombic Pbca, a )
8
2
2
2
3
16.464(1) Å, b ) 5.8609(2) Å, c ) 17.715(1) Å, V ) 1709.4 (1) Å ,
D ) 1.764 g cm , Z ) 8. The total number of reflections measured
were 24307, of which 3849 reflections were symmetrically nonequiva-
lent. Final residuals were R1 ) 0.0358 and wR2 ) 0.0956 for 3081
reflections with I > 2σ(I).
-
3
c
+
-•
obtain yellow crystals of Bu
4
N TCNE . TCNE anion-radical salts were
alternatively prepared by the interaction of the parent acceptor with
Spectral Measurements. The absorption spectra were recorded on
a HP 8453 diode-array spectrometer (UV-vis) and Varian Cary 500
spectrometer (UV-vis-NIR). Low-temperature studies were carried
out with the aid of a low-temperature Dewar equipped with quartz
windows for UV-vis measurements. All operations were performed
with freshly prepared solution of anion-radical salts in an inert (argon)
atmosphere with Teflon-capped cuvettes (0.1-1.0 cm) equipped with
sidearms. Typically, 2-4 mL aliquots of the 2-4 mM solutions of
anion-radical salts in acetonitrile were placed in a 1 cm cuvette, and
the solid parent acceptor was added in increments. Alternatively, the
anion-radical solution was added with the aid of a hypodermic syringe
to the cuvette charged with the solid (parent) acceptor. The absorbance
of new the NIR band at its maximum was measured at different
concentrations of the neutral acceptor, and the data were evaluated with
the aid of the Benesi-Hildebrand correlation. [The upper limit of the
concentration of the neutral acceptor was limited by its solubility and
varied from ∼15 mM for TCNQ to ∼0.7 M for TCNE. It should be
also noted that although small amounts of the anion-radical dimers were
present in the acetonitrile solutions, their concentrations (estimated
+
-
+
- 46b
4
Na CN and Bu N CN , but the results did not depend on the
reducing agent. The sodium salt of chloranil anion radical was prepared
by the slow addition of 780 mg (3.2 mmol) of CA to a solution of
.44 g (9.6 mmol) of NaI in 100 mL of acetone stirred in a cold bath
1
at 0 °C. Stirring was continued for 2 h, and the precipitate was filtered
and washed with small amounts of cold acetone and dichloromethane.
The potassium salt of chloranil anion radical was prepared similarly.
-•
To prepare the tetrabutylammonium salt of CA , tetrabutylammonium
+
-•
chloride (233 mg) was added at 0 °C to a solution of K CA (239
mg) in acetone. The precipitate was filtered, and the filtrate was
concentrated in vaccuo to dryness. The residue was recrystalized from
2 2
a CH Cl /pentane mixture. The purity of all compounds was checked
spectrophotometrically (using the spectral characteristics of anion
radicals in Table 1) and by titration with ammonium cerium(IV) nitrate
(
Acros).
X-ray Crystallography. The intensity data for all the compounds
were collected with a Siemens SMART diffractometer equipped with
a 1K CCD detector using Mo KR radiation (λ ) 0.71073 Å) at -150
18
spectrophotometrically based on the literature data ) were less than
% relative to the concentration of anion radical, and therefore did not
1
(
45) Perrin, D. D.; Armarego, W. L.; Perrin, D. R. Purification of Laboratory
Chemicals, 2nd ed.; Pergamon: New York, 1980.
46) (a) Melby, L. R.; Harder, R. J.; Hertler, W. R.; Mahler, W.; Benson, R. E.;
Mochel, W. E. J. Am. Chem. Soc. 1962, 84, 3374. (b) Webster, O. W.;
Mahler, W.; Benson, R. E. J. Am. Chem. Soc. 1962, 84, 3678. (c) Torrey,
H. A.; Hunter, W. H. J. Am. Chem. Soc. 1912, 34, 702.
materially affect the calculations.] The Benesi-Hildebrand procedure
(
(47) Sheldrick, G. M. SHELXS-86, Program for Structure Solution; University
of Gottingen: Germany, 1986.
2570 J. AM. CHEM. SOC.
9
VOL. 125, NO. 9, 2003

Electron-Transfer Dynamics
A R T I C L E S
and the spectroscopic study of CA/CA-• systems, S. V.
Lindeman for crystallographic assistance, and the R. A. Welch
Foundation and the National Science Foundation for financial
support.
provided reliable results only if one reactant was present in great excess,
and the complexation of the reactant (in deficit) was in the 20-80%
range. (Such conditions were difficult to achieve for all the systems
due to the relatively small formation constants and limited solubility.)
Therefore, the formation constants and extinction coefficients were
checked by treatment of the absorption data with the aid of the Drago
Supporting Information Available: Structural data (bond
lengths) of the acceptors and their anion radicals (Table S1) as
well as the spectral characteristics of anion radicals and their
π-mers measured with alkali-metal and tetrabutylammonium
counterions in different solvents (Table S2). Spectral changes
in the UV-vis and NIR region upon the addition of neutral
acceptors to their anion radicals (Figure S1), comparison of the
π-mer spectra in systems with different counterions (Figure S2),
-
1
48
procedure involving the construction of plots of K with ꢀ.
Additionally, the extinction coefficients and the formation constants
were checked by the temperature dependencies of the NIR absorptions.
The bandwidths ∆νCT in Table 3 were obtained by Gaussian decon-
volution of the NIR bands using Microcal Origin 6.0. To follow
simultaneously the spectral changes observed in the UV-vis (anion
radical) and NIR (π-mer), a 1 mm cuvette was used [owing to the high
extinction coefficients of anion radicals in Table 1].
-•
and the energy diagrams for electron transfer in TCNE /TCNE
Acknowledgment. We thank D. Sun for synthesis of the
chloranil anion-radical salts, the preparation of their crystals,
-•
and CA /CA systems (Figure S3). This material is available
free of charge via the Internet at http://pubs.acs.org.
JA0211611
(
48) Drago, R. S. Physical Methods in Chemistry; W. B. Saunders Company:
Philadelphia, 1977.
J. AM. CHEM. SOC.
9
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