Intervalence (Charge-Resonance) Transitions in Organic Mixed-Valence Systems. Through-Space versus Through-Bond Electron Transfer between Bridged Aromatic (Redox) Centers

Article abstract of DOI:10.1021/ja037867s

Intervalence absorption bands appearing in the diagnostic near-IR region are consistently observed in the electronic spectra of mixed-valence systems containing a pair of aromatic redox centers (Ar⁺/Ar) that are connected by two basically different types of molecular bridges. The through-space pathway for intramolecular electron transfer is dictated by an o-xylylene bridge in the mixed-valence cation radical 3^.+ with Ar = 2,5-dimethoxy-p-tolyl (T), in which conformational mobility allows the proximal syn disposition of planar T^.+/T redox centers. Four independent experimental probes indicate the large through-space electronic interaction between such cofacial Ar^.+/Ar redox centers from the measurements of (a) sizable potential splitting in the cyclic voltammogram, (b) quinonoidal distortion of T^.+/T centers by X-ray crystallography, (c) "doubling" of the ESR hyperfine splittings, and (d) a pronounced intervalence charge-resonance band. The through (br)-bond pathway for intramolecular electron transfer is enforced in the mixed-valence cation radical 2a^.+ by the p-phenylene bridge which provides the structurally inflexible and linear connection between Ar^.+/Ar redox centers. The direct comparison of intramolecular rates of electron transfer (k_ET) between identical T^.+/T centers in 3^.+ and 2a^.+ indicates that through-space and through-bond mechanisms are equally effective, despite widely different separations between their redox centers. The same picture obtains for 3^.+ and 2a^.+ from theoretical computations of the first-order rate constants for intramolecular electron transfer from Marcus-Hush theory using the electronic coupling elements evaluated from the diagnostic intervalence (charge-transfer) transitions. Such a strong coherence between theory and experiment also applies to the mixed-valence cation radical 7^.+, in which the aromatic redox S center is sterically encumbered by annulation.

Full text of DOI:10.1021/ja037867s

Published on Web 11/25/2003
Intervalence (Charge-Resonance) Transitions in Organic
Mixed-Valence Systems. Through-Space versus Through-Bond
Electron Transfer between Bridged Aromatic (Redox) Centers
D.-L. Sun, S. V. Rosokha, S. V. Lindeman, and J. K. Kochi*
Contribution from the Department of Chemistry, UniVersity of Houston,
Houston, Texas 77204-5003
Received August 11, 2003; E-mail: jkochi@uh.edu
Abstract: Intervalence absorption bands appearing in the diagnostic near-IR region are consistently
observed in the electronic spectra of mixed-valence systems containing a pair of aromatic redox centers
(Ar•+/Ar) that are connected by two basically different types of molecular bridges. The through-space pathway
for intramolecular electron transfer is dictated by an o-xylylene bridge in the mixed-valence cation radical
3•+ with Ar ) 2,5-dimethoxy-p-tolyl (T), in which conformational mobility allows the proximal syn disposition
of planar T•+/T redox centers. Four independent experimental probes indicate the large through-space
electronic interaction between such cofacial Ar•+/Ar redox centers from the measurements of (a) sizable
potential splitting in the cyclic voltammogram, (b) quinonoidal distortion of T•+/T centers by X-ray
crystallography, (c) “doubling” of the ESR hyperfine splittings, and (d) a pronounced intervalence charge-
resonance band. The through (br)-bond pathway for intramolecular electron transfer is enforced in the
mixed-valence cation radical 2a•+ by the p-phenylene bridge which provides the structurally inflexible and
linear connection between Ar•+/Ar redox centers. The direct comparison of intramolecular rates of electron
transfer (kET) between identical T•+/T centers in 3•+ and 2a•+ indicates that through-space and through-
bond mechanisms are equally effective, despite widely different separations between their redox centers.
The same picture obtains for 3•+ and 2a•+ from theoretical computations of the first-order rate constants for
intramolecular electron transfer from Marcus-Hush theory using the electronic coupling elements evaluated
from the diagnostic intervalence (charge-transfer) transitions. Such a strong coherence between theory
and experiment also applies to the mixed-valence cation radical 7•+, in which the aromatic redox S center
is sterically encumbered by annulation.
Introduction
this speculative structure for the cationic naphthalene dimer 1
(Chart 1), in which the parallel pair of equivalent arene moieties
Singer, Fraenkel, and co-workers1 were among the first to
discover the interesting (intermolecular) association of aromatic
cation radicals (ArH+•) with their parent π-donors (ArH) via
the observation of “doubled” ESR spectra in naphthalene and
related hydrocarbons.2 Soon thereafter, Badger, Brocklehurst,
et al.3 observed the characteristic UV-vis absorptions of dimer
cation radicals (ArH)2•+ by γ-radiolysis of frozen naphthalene
and other arene solutions in alkane matrix; they proposed the
diagnostic (near-IR) bands to be derived via “charge-resonance”
transitions from electron delocalized ground states comprised
of cofacial ArH+•/ArH pairings.4 However, it was not until later
that single-crystal X-ray crystallographic analysis5 confirmed
is separated by the very long (noncovalent) distance of dD
)
3.20 Å6 but yet is significantly closer than the (nonbonded) van
der Waals sum of dvdW ) 3.50 Å.
Chart 1
In a much more general context, a positively charged
(paramagnetic) binary unit such as 1 is integral to a wide array
(1) (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. (c) Howarth, O.
W. Fraenkel; G. K. J. Chem. Phys. 1970, 52, 6258.
(2) (a) Gerson, F.; Kaupp, G.; Ohya-Nishiguchi, H. Angew. Chem., Int. Ed.
1977, 16, 657. (b) Wartin, A. R.; Valenzuela, J.; Staab, H. A.; Neugebauer,
F. A. Eur. J. Org. Chem. 1998, 139, 9. (c) Lau, W.; Kochi, J. K. J. Org.
Chem. 1986, 51, 1801.
(3) (a) Badger; B.; Brocklehurst, B.; Russell, R. D. Chem. Phys. Lett. 1967, 1,
122. (b) Badger, B.; Brocklehurst, B. Nature 1968, 219, 263. (c) Badger,
B.; Brocklehurst, B. Trans. Faraday Soc. 1969, 65, 2582. (d) Badger, B.;
Brocklehurst, B. Trans. Faraday Soc. 1969, 65, 2588. (e) Badger, B.;
Brocklehurst, B. Trans. Faraday Soc. 1970, 66, 2939.
(4) See also: (a) Meot-Ner, M.; Hamlet, P.; Hunter, E. P.; Field, F. H. J. Am.
Chem. Soc. 1978, 100, 5466. (b) Meot-Ner, M. J. Phys. Chem. 1980, 84,
2724. (c) Meot-Ner, M.; El-Shall, M. S. J. Am. Chem. Soc. 1986, 108,
4386. (d) Masnovi, J. M.; Kochi, J. K. J. Phys. Chem. 1987, 91, 1878. (e)
Kochi, J. K.; Rathore, R.; Le Magueres, P. J. Org. Chem. 2000, 65, 6826.
(f) Note that dimer cation radicals such as 1 belong to a larger, more diverse
group of paramagnetic (complex) associates comprised of π-radicals and
their neutral precursors such as anion radical/electron acceptor, π-radical/
π-cation, etc. for which the general term ”pimer” has been recently
proposed. (g) See: Ganesan, V.; Rosokha, S. V.; Kochi, J. K. J. Am. Chem.
Soc. 2003, 125, 2559. Lu, J.-M.; Rosokha, S. V.; Kochi, J. K, J. Am. Chem.
Soc. 2003, 125, 12161.
9
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10.1021/ja037867s CCC: $25.00 © 2003 American Chemical Society

Organic Mixed-Valence Systems
A R T I C L E S
Chart 3
of stacked arene structures in the crystalline solid state, in which
intermolecular communication relies on hole (electron) hoppings
as in molecular metals (wires), optoelectronic devices, electrical
conductors, magnets, etc. of potential development for organic
material science.7,8 To this end, we now inquire as to the more
basic evaluation of those structural factors leading to the charge-
resonance transitions inherent to dimer cation radicals such as
1. Owing to the experimental difficulty of “isolating” 1 as a
separate unit in a stacked (crystalline) lattice, it is desirable to
develop discrete molecular systems for the quantitative study
in solution of how electron (hole) transfer can occur within
ArH+•/ArH dyads.
such dimer cation-radical assemblies, we focus on Ar ) 2,5-
dimethoxy-p-tolyl (T), owing to the reversible oxidation of this
aromatic group to generate its persistent cation radical (T•+) at
an accessible potential of E°ox ) 1.10 V vs SCE.13-15
In earlier studies,9 we discussed the organic mixed-valence
system 2, as shown in Chart 2, in which various (poly)p-
phenylene structures ensure structural rigidity and can be utilized
Chart 4a
Chart 2
a Note that the junctures at which these aromatic redox centers are
connected to the bridge (br) are indicated by asterisks.
Results
I. Synthesis and Conformational Structure of Mixed-
Valence Donors. A. Synthesis. The series of mixed-valence
donors 3-5 as identified in Table 1 are governed by the
distinctive aromatic redox center T in Chart 4. The attachment
of T to the o-xylylene bridge in 3 was effected by treatment of
1,2-bis(bromomethyl)tetramethylbenzene with stoichiometric
as molecular bridges (br) in the study of intramolecular electron
transfer between the Ar•+/Ar redox centers, primarily through
(br) bond in the superexchange (hole-hopping) mechanism.9b,10-12
In this study, we examine the conformationally flexible system
3, in which the preponderance of the highly mobile equilibrium
(i.e. Chart 3) leads to the juxtaposition of a pair of Ar groups
in conformer 3b. The resulting cofacial orientation of the two
aromatic planes is reminiscent of that in the intermolecular dimer
cation radical 1; 3b thus represents the prototypical donor to
examine the direct through-space interaction of Ar+•/Ar (redox)
centers in organic mixed-valence systems. For quantitative
studies of the energetics, structures, and optical transitions in
Table 1. Structures and Oxidation Potentials of Mixed-Valence
Donors and Their Mononuclear Modelsa
(5) (a) Fritz, H. P.; Gebauer, H.; Friedrich, P.; Ecker, P.; Artes, R.; Schubert,
V. Z. Naturforsch. 1978, 33B, 498. (b) Fritz, H. P.; Gebauer, H.; Friederich,
F.; Schubert, V. Angew. Chem. 1978, 90, 305. (c) Enkelmann, V.; Morra,
B. S.; Kro¨hnke, C.; Wegner, G. Chem. Phys. 1982, 66, 303. (d) Enkelmann,
V. AdV. Chem. Ser. 1988, No. 217, 177. (e) Herwig, P. T.; Enkelmann, V.;
Schmelz, D.; Mu¨llen, K. Chem. Eur. J. 2000, 6, 1834.
(6) See also: (a) Keller, H. J.; No¨the, D.; Pritzkow, H.; Wehe, D.; Werner,
M. Mol. Cryst. 1980, 62, 181. (b) Endres, H.; Keller, H.; Mu¨ller, B.;
Schweitzer, D. Acta Crystallogr. 1985, C41, 607. (c) Stenger-Smith, J. D.;
Lenz, R. W.; Enkelmann, V.; Wegner, G. Makromol. Chem. 1992, 193,
515. (d) Note that Chart 1 is only intended to emphasize pictorially the
parallel sandwich arrangement of the two naphthalene moieties, which are
actually rotated in the plane by 90° relative to each other.
(7) (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, FL, 1987. (d) Farges, J.-P., Ed. Organic Conductors:
Fundamentals and Applications; Marcel Dekker: New York, 1994.
(8) (a) Lahti, P. M., Ed. Magnetic Properties of Organic Materials; Marcel
Dekker: New York, 1999. (b) Miller, J. S., Drillon, M., Eds. Magnetism:
Molecules to Materials; Wiley-VCH: Weinheim, Germany, 2001.
(9) (a) Lindeman, S. V.; Rosokha, S. V.; Sun, D.-L.; Kochi, J. K. J. Am. Chem.
Soc. 2002, 124, 843. (b) Rosokha, S. V.; Sun, D.-L.; Kochi, J. K. J. Phys.
Chem. A 2002, 106, 2283. (c) Sun, D.-L.; Lindeman, S. V.; Rathore, R.;
Kochi, J. K. J. Chem. Soc., Perkin Trans. 2 2001, 1585. (d) Note that the
direct observation of the (Ar-to-br) charge-transfer absorption bands in the
mixed-valence complexes 29b allowed the superexchange mechanism to
be quantitatively evaluated by the Creutz, Newton, Sutin (CNS) methodol-
ogy.10
a For structural identification of the redox center T, etc., see Charts 4
and 5. b Reversible cyclic voltammograms measured at V ) 2 V s-1. In
parentheses are given the number of electrons transferred.
(10) Creutz, C.; Newton, M. D.; Sutin, N. J. Photochem. Photobiol. A: Chem.
1994, 82, 47.
(11) For previous use of organic mixed-valence systems for intramolecular
electron-transfer studies, see: (a) Nelsen, S. F.; Adamus, J.; Wolff, J. J. J.
Am. Chem. Soc. 1994, 116, 1589. (b) Nelsen, S. F.; Trieber, D. A.; Wolff,
J. J.; Powell, D. R.; Rogers-Crowley, S. J. Am. Chem. Soc. 1997, 119,
6873. (c) Lambert, C.; Noll, G. J. Am. Chem. Soc. 1999, 121, 8434. (d)
Holzapfel, M.; Lambert, C.; Selinka, C.; Stalke, D. J. Chem. Soc., Perkin
Trans. 2 2002, 1553.
(12) See also: (a) Rak, S. F.; Miller, L. L. J. Am. Chem. Soc. 1992, 114, 1388.
(b) Lahlil, K.; Moradpour, A.; Bowlas, C.; Menou, F.; Cassoux, P.;
Bonvoisin, J.; Launay, J.-P.; Dive, G.; Dehareng, D. J. Am. Chem. Soc.
1995, 117, 9995. (c) Nelsen, S. F.; Ramm, M. T.; Wolff, J. J.; Powell, D.
R. J. Am. Chem. Soc. 1997, 119, 6863. (d) Nelsen, S. F.; Ismagilov, R. F.;
Powell, D. R. J. Am. Chem. Soc. 1997, 119, 10213. (e) Gautier, N.; Dumur,
F.; Lloveras, Vidal-Gancedo, J.; Veciana, J.; Rovira, C.; Hudhomme, P.
Angew. Chem., Int. Ed. 2003, 42, 2765.
(13) Rathore, R.; Kumar, A. S.; Lindeman, S. V.; Kochi, J. K. J. Org. Chem.
1998, 63, 5847.
(14) Eberson, L. Electron-Transfer Reactions in Organic Chemistry; Springer-
Verlag: New York, 1987.
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A R T I C L E S
Sun et al.
Figure 1. ORTEP diagrams of the o-xylylene-bridged mixed-valence donor 3 and its cation radical 3+• (as the SbCl6- salt) showing the two T centers with
anti conformation in the neutral donor (A) and syn conformation in the cation radical (B). Note that all hydrogens are omitted for clarity.
Table 2. X-ray Structural Parameters of the Redox Centers in the Mixed-Valence Donors and Their Cation Radicalsa
[σ]b
R/R′
â/â′
γ/γ′
δ/δ′
ꢀ/ꢀ′
qc
i
3
0.003 Td 1.400/1.399 [1.400] 1.397/1.396 [1.397] 1.397/1.398 [1.398] 1.376/1.377 [1.377] 1.424/1.426 [1.425]
0
-
3•+PF6
0.002 Td 1.417/1.416 [1.417] 1.402/1.399 [1.401] 1.380/1.387 [1.384] 1.347/1.349 [1.348] 1.434/1.436 [1.435] +0.5
0.004 T1 1.430/1.431 [1.431] 1.406/1.398 [1.402] 1.362/1.363 [1.363] 1.327/1.328 [1.428] 1.440/1.436 [1.438] +0.9
T2 1.396/1.400 [1.398] 1.396/1.390 [1.393] 1.371/1.380 [1.376] 1.368/1.365 [1.367] 1.433/1.425 [1.429] +0.1
3•+SbCl6
-
T•+(CH2)3T•+ e 0.004 Td 1.447/1.447 [1.447] 1.407/1.408 [1.407] 1.369/1.375 [1.372] 1.324/1.329 [1.327] 1.457/1.457 [1.457] +1.0
a Average bond lengths (Å) in brackets. b Average experimental precision. c Estimate of positive charge parameter evaluated as described in the text.
d Parameters for both donor groups are identical. e Data from ref 9a, for comparison.
amounts of TH and silver(I) perchlorate16
To modulate the steric hindrance at the planar redox center, it
was modified by bicyclic annulation as in redox center S and
by tert-butyl substitution as in redox centers U and V (Chart
4); the corresponding mixed-valence donors 7, 9, and 10 were
synthesized by essentially the same procedure (see the Experi-
mental Section).
B. Conformational Structure. Single colorless crystals of
the ortho-bridged mixed-valence donor 3, isolated by the
controlled slow removal of solvent, consisted of the stable anti
conformation 3a in eq 1, as shown by the ORTEP diagram in
Figure 1A. Otherwise, both T centers in 3 have the usual planar
centrosymmetric benzenoid geometry, as evaluated by the bond
lengths and anglessthe endocyclic R, â, and γ as well as the
exocyclic δ and ꢀ bonds being within the standard range (Table
2). For the accompanying spectral/computational examination
of the dynamic equilibrium in eq 1, see details in the
Experimental Section.
and the isomeric bridged donors 4 and 5 were prepared by an
analogous procedure from the m- and p-dibromo precursors.17
II. Electrochemical Generation of Mixed-Valence Systems.
Selective oxidations of the aromatic donors in Table 1 to the
relevant mixed-valence cation radicals were first examined by
(15) (a) Analogous studies have also been carried out with the phenothiazinyl
(P) redox center, in which the larger intrinsic barrier (λ/4) for electron
transfer of approximately 7-8 kcal mol-1 relative to the corresponding
barrier of the dimethoxytolyl redox center of ∼5 kcal mol-1 arises from
the significant configurational change of the tub-shaped donor center P to
its planar cation radical P•+ upon electron transfer. (b) Sun, D.-L.; Rosokha,
S. V.; Kochi, J. K. J. Am. Chem. Soc., in press.
(16) Za´vada, J.; Pa´nkova´, M.; Aenold, Z. Collect. Czech. Chem. Commun. 1976,
41, 1777.
(17) Za´vada, J.; Pa´nkova´, M.; Holy`, P.; Tichy`, M. Synthesis 1994, 11, 1132.
9
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Organic Mixed-Valence Systems
A R T I C L E S
the energetics of the dication comproportionation:18
3
2+ + 3 {Kcom} 3•+ + 3•+
(5)
and the position of the equilibrium was quantitatively evaluated
from the splitting: ∆E ) -∆Gcom/F, where F is the Faraday
constant and ∆Gcom is the Gibbs free-energy change. Most
importantly, the major component of the cation-radical stabiliza-
tion, i.e., -RT ln Kcom, is the electronic interaction between the
pair of T/T•+ redox centers.19 Thus, the stabilization energy of
the ortho-bridged cation radical 3•+ was evaluated as 2 kcal/
mol, whereas ∆Gcom ) 0 for the meta and para isomers. To
analyze such mixed-valence cation radicals, we now focus
primarily on the isolation and X-ray crystallographic analysis
of the bridged structures together with the spectral analysis
(UV-vis-near-IR) of their diagnostic charge-resonance absorp-
tion bands and the characteristics of the temperature-dependent
line broadenings in the ESR spectra as follows.
Figure 2. Initial positive-scan cyclic voltammogram (left) and Osteryoung
square wave voltammogram (right) of the ortho-bridged mixed-valence
donor 3 (A) and meta-bridged isomer 4 (B), including the ferrocene internal
standard at 0.5 V. (Note that the electrochemical behavior of the para-
bridged mixed-valence donor 5 coincides with that of 4).
III. Isolation and X-ray Crystallography of Mixed-Valence
Cation Radicals. Controlled-potential oxidation of the o-
xylylene-bridged donor 3 at the foot of the first anodic CV wave
(1.00 V, Figure 2a) afforded a quantitative yield of the mixed-
valence cation radical 3•+, but complete separation of the pure
salt from the supporting electrolyte proved difficult. Accord-
ingly, we employed the quantitative chemical oxidation with a
series of bona fide one-electron oxidants, including nitrosonium
(NO+) salts,20 antimony pentachloride,21 and various organic
cation radicals of octamethylnaphthalene22 and tris(dibromophe-
nyl)amine.23 Indeed, all of these reagents afforded excellent
yields of crystalline 3•+ salts, but the particularly easy removal
of the gaseous reduction product of NO+ facilitated the isolation
transient electrochemical techniques in 1 mM dichloromethane
solution containing 0.2 M tetra-n-butylammonium hexachloro-
phosphate as supporting electrolyte. Two distinctive anodic
behaviors were observed with the isomeric bridged donors 3-5
in the initial positive-scan cyclic voltammograms obtained with
a platinum electrode at a standard scan rate of V ) 2 V s-1
.
(A) With the m-xylylene- and p-xylylene-bridged isomers 4
and 5, the reversible cyclic voltammograms (Figure 2B) showed
a single two-electron anodic wave (corresponding to two
unresolved one-electron processes) at a potential of E1/2 ) 1.13
V vs SCE:
of bright yellow single crystals of 3•+SbCl6 and 3•+PF6 for
X-ray crystallographic analysis.
-
-
4 (5) - 2e {E ) 1.13 V} 42+ (52+)
(3)
1/2
The prominent feature of the ORTEP diagram of the mixed-
valence cation radical 3•+ in Figure 1B is the mutually syn
conformation of the two planar T centersswith the nearly
parallel rings offset by a dihedral angle of only 10°. Such a
cofacial arrangement occurs with the interplanar separation of
dD ) 3.2 Å, which is the same as that in dimer cation radicals
such as 1 (see Chart 1) and roughly 10% shorter than the van
der Waals contact. The latter pointed to significant electronic
interaction of the two T redox centers in 3•+, which was further
confirmed by close scrutiny of the X-ray bonding parameters
in the following way. First, the removal of a full electron from
a lone (noninteracting) T center is accompanied by a diagnostic
quinonoid distortion, which derives from the selective elongation
of the R and â bonds and concomitant contraction of the γ and
δ bonds in T•+, as compared in the first and last entries of Table
2. Second, the quantitative relationship between quinonoidal
distortion and removal of (partial) charge qi from a T center is
then given by qi ) (d0 - di)/(d0 - d1),24 where d0 and d1 are
This oxidation potential coincided with the reversible one-
electron oxidation of donor 6, which represented the mono-
nuclear model for the unambiguous oxidation of a lone T center
to the full cation radical T•+ (compare entries for 4-6 in Table
1).
(B) In contrast, the reversible cyclic voltammogram of the
isomeric o-xylylene-bridged donor 3 consisted of a pair of
oxidation waves at E1/2 ) 1.07 and 1.23 V, with each wave
corresponding to a one-electron process in Figure 2A, so that
the initial production of the mixed-valence cation radical was
separately followed by its subsequent oxidation to the di-
cation:
3 {E ) 1.07 V} 3•+
{
E1/2 ) 1.23 V} 32+
(4)
1/2
The unique cyclic voltammetric behavior of the ortho-bridged
isomer 3 indicated that the initial oxidation of a T center to its
cation radical T•+ was different from that of the second aromatic
center, whereas in the meta and para isomers, the two T centers
were both oxidized at identical potentials. (It follows that the
dication in eq 4 actually consisted of a pair of equivalent, but
separate, cation-radical centers, as was later established from
its ESR spectrum (vide infra).) As such, the difference between
the first and second potentials, ∆E ) E1/2(2) - E1/2(1), reflected
(18) (a) Creutz, C. Prog. Inorg. Chem. 1983, 30, 1. (d) Demadis, K. D.;
Hartshorn, C. M.; Meyer, T. J. Chem. ReV. 2001, 101, 2655.
(19) (a) Astruc, D. Electron Transfer and Radical Processes in Transition-Metal
Chemistry; VCH: New York, 1995. (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.
(20) Lee, K. Y.; Kuchynka, D. J.; Kochi, J. K. Inorg. Chem. 1990, 29, 4196.
(21) (a) Bell, F. A.; Ledwith, A.; Sherrington, D. C. J. Chem. Soc. C 1969, 13,
2719. (b) Luken, E. A. C. J. Chem. Soc. 1969, 4963.
(22) Rosokha, S. V.; Kochi, J. K. J. Am. Chem. Soc, 2001, 123, 8985.
(23) Schmidt, W.; Steckman, E. Chem. Ber. 1980, 113, 577.
(24) Le Magueres, P.; Lindeman, S. V.; Kochi, J. K. J. Chem. Soc., Perkin
Trans. 2 2001, 1180.
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A R T I C L E S
Sun et al.
Table 3. ESR Spectral Parameters of Mixed-Valence Cation
Radicals (MVCR) and their Mononuclear Models
hyperfine splitting (G)a
MVCR
OCH
CH
n
ArH
3
3•+
1.6 (12)
3.1 (6)
3.2 (6)
3.1 (6)
3.2 (6)
3.1 (6)
3.12 (6)
3.2 (6)
3.2 (6)
1.6 (12)
1.5 (8)
2.3 (6), 3.5 (4)
4.6 (3), 6.8 (2)
4.5 (3), 6.9 (2)
4.6 (3), 6.8 (2)
4.5 (3), 6.9 (2)
4.6 (3), 6.8 (2)
4.37 (6)
2.8 (1), 7.0 (2)
4.0 (4)
3.5 (4), 2.3 (6)
3.5 (4), 2.3 (6)
0.3 (4)
0.5 (2)
0.5 (2)
0.5 (2)
0.5 (2)
0.5 (2)
0.48 (2)
0.5 (1)
0.5 (1)
0.3 (4)
0.3 (4)
32+
4•+
42+
5•+
52+
6•+ b
7•+
8•+
9•+ c
10•+ c
a In parentheses are given the number of splitting protons. b From ref
26. c See the Experimental Section.
The unchanging ESR spectra of 4•+ and 5•+ relative to 6•+
indicated that the paramagnetic redox center in the meta- and
para-bridged mixed-valence cation radicals showed no extra
temperature-dependent behavior that was not present in the
mononuclear cation radical.27 In other words, the unpaired
electron in either the m-xylylene- and p-xylylene-bridged cation
radical is frozen on a single T+• redox center
Figure 3. Comparison of the experimental (left) and computer-simulated
(right) ESR spectra of mixed-valence cation radicals of the meta-/para-
bridged 4+•/5+• (A) with that of the ortho-bridged isomer 3+• showing
doubled hyperfine splittings (B) in dichloromethane solution.
the bond lengths in the neutral T and the cation radical T•+,
respectively, and di is the bond length in the relevant T center
of the mixed-valence cation radical (3•+). For clarity, we selected
the δ bonds for calculation of qi owing to their having the largest
(bond-length) change upon oxidation; these values are listed in
the last column of Table 2. Third and most striking is the value
of qi ) +0.5 for 3•+PF6 (second entry in Table 2) reflecting
-
and any dynamic exchange with the other T center was too
slow to be observed in this temperature range. Moreover, the
ESR spectra of the dications 42+ and 52+ were essentially
identical (Table 3 and Figure S1 in the Supporting Information)
and the hyperfine splittings were the same as those in the mixed-
valence cation radicals 4•+ and 5•+. The absence of line
broadening in the same temperature range indicated each
paramagnetic redox center was isolated, and any electromagnetic
interaction between these equivalent T•+ centers was too small
to be detected in the meta- and para-bridged dications on the
ESR time scale.28
B. Temperature-Independent but “Doubled” ESR Spec-
trum. The ESR spectrum of the ortho-bridged mixed-valence
cation radical 3•+ in Figure 3B (left) showed many more
hyperfine lines than that of either the meta (4•+) or para (5•+)
isomers in Figure 3A. Most notably, the computer simulation
shown in Figure 3B (right) was derived from twice the number
of protons in each of the four sets of equivalent protons with
approximately half the coupling constants (Table 3, first entry)
relative to those found in the meta and para isomers (second
and third entries). Such increased numbers and decreased
the equal distribution of positive charge between both redox
centers. Accordingly, the structure of each T center in 3•+ is
precisely intermediate between those of T and T•+ to reflect
complete odd-electron delocalization between two equivalent
redox centers.25 Fourth, the charge distribution in 3•+ is
counterion dependent, with qi ) +0.9 on one T center (and
+0.1 on the other) in the hexachloroantimonate salt (third entry).
-
As such, the asymmetric charge distribution in 3•+SbCl6
reflects only limited (electron) delocalization extant between
these redox centers in this crystalline salt, and the charge is
essentially localized on one T center, while the other remains
(nearly) neutral.
IV. ESR Spectra and Their Line Broadening in Mixed-
Valence Cation Radicals. A. Temperature-Independent ESR
Spectra. The meta- and para-bridged mixed-valence cation
radicals 4•+ and 5•+ in dichloromethane solutions afforded the
(identical) ESR spectra shown in Figure 3A (left). The spectra
bore a strong resemblance to that of the mononuclear model
6•+, in which the hyperfine coupling constants for three sets of
equivalent protons have been established as aCH O ) 3.12 G,
3
aCH ) 4.37 G, and aH ) 0.48 G.26 Starting from these values,
3
we optimally simulated the ESR spectrum shown in Figure 3A
(right) with the hyperfine coupling constants listed in Table 3
(entries 3 and 4). Most importantly, the ESR spectra of 4•+-
6•+ were all singularly unaffected by temperature changes in
the range between 20 and -90 °C.
(27) For the accompanying ESR effects of methoxyl rotation, see: Sullivan, P.
D. J. Phys. Chem. 1970, 74, 2563.
(28) (a) Although transient electrochemistry showed that the further oxidation
of the mixed-valence cation radical 3•+ could be carried out reversibly, all
attempts to isolate crystalline salts of the 32+ dication suitable for X-ray
crystallography were unsuccessful (vide infra), owing to the competing
decomposition pathway(s). Nonetheless, 32+ was sufficiently persistent to
show that its ESR spectrum (see Figure S1) is essentially identical with
those of the meta and para isomers 42+ and 52+ and the mononuclear model
6•+. (b) The partially unstable or metastable character of 32+ suggests that
there is some electronic interaction between a pair of T+• centers in this
dication. For the resonance “stabilization” of such a pair of cofacial cation
radicals to cation-radical dimers, see Lu et al. in ref 4g.
(25) The absence of crystallographic elements of symmetry in the acentric T•+
center rules out crystal disorder, and the value of qi ) +0.5 necessarily
reflects the inherent nature of 50/50 charge distribution in 3•+PF6-. For
discussion of this point, see Lindeman et al. in ref 9a.
(26) Forbes, W. F.; Sullivan, P. D. J. Phys. Chem. 1968, 48, 1411.
9
15954 J. AM. CHEM. SOC. VOL. 125, NO. 51, 2003

Organic Mixed-Valence Systems
A R T I C L E S
splittings of hyperfine lines were characteristic of other dimer
cation radicals reported previously29 and indicated that either
the unpaired electron in the ortho-bridged 3•+ is completely
delocalized over both redox centers or electron exchange
between the redox centers
is too fast to be resolved on the ESR time scale with the half-
life τESR < 10-9 s. Moreover, the temperature-independent ESR
spectra over the 110 °C temperature range relegated the half-
life for any dynamic electron exchange to be immeasurably fast
even at -90 °C.
C. Line Broadening in ESR Spectra. Mixed-valence donors
with encumbered bulky redox-centers were prepared in two
forms (Chart 4)swith bicyclic annulation (S) and with tert-
butyl substitutions (U and V) that were found to be effective in
previous studies of sterically hindered associations.30
The ortho-bridged donor 7 with a pair of S groups afforded
its persistent mixed-valence cation radical much like the ortho-
bridged donors 9 and 10 with U and V centers. However, the
ESR spectrum of the sterically hindered 7•+ at -90 °C bore
little resemblance to the delocalized ESR spectrum of the ortho-
bridged analogue 3•+ with T•+ centers; it was instead more like
that of the localized meta- and para-bridged isomers, 4•+ and
5•+. Indeed, this ESR spectrum was strikingly similar to the
ESR spectrum of the sterically hindered cation radical 8•+ of
the mononuclear model donor SCH3, and computer simulation
with the same hyperfine coupling constants in Table 3 confirmed
the spectral assignment.
Figure 4. Temperature-dependent ESR line broadening of the mixed-
valence cation radical 7+• with sterically hindered redox centers S+•/S (left)
in comparison with the computer-simulated spectra (right) based on first-
order electron exchange.
V. Intervalence (Charge-Resonance) Transition in Mixed-
Valence Cation Radicals. The distinguishing feature in the
electronic spectra of both meta and para-bridged mixed-valence
cation-radicals 4•+ and 5•+ was the well-resolved UV-Vis
absorption with λmax ) 438 and 462 nm (Figure 5A, Table 4)
in dichloromethane solution. Since these absorption bands were
also the same as those that characterized the mononuclear model
6•+, they were assigned to the local π-π* transitions in the
T•+ redox center. By way of contrast, the ortho-bridged 3•+
showed essentially the same UV-vis bands, but the most
prominent feature of the electronic spectrum was the additional
presence of the very broad absorption band in the near-IR region
with λCR ) 1600 nm,32 the Gaussian band shape of which is
confirmed in the inset (dotted line) to Figure 5A.33 The band
intensity, which was directly proportional to the concentration
of 3•+ and quite independent of added neutral mixed-valence
donor 3, confirmed its intramolecular character. Since the further
selective oxidation of 3+• to the dication 32+ was accompanied
by the complete disappearance of only the near-IR band, it was
assigned to the intervalence transition, similar to the charge-
resonance (CR) bands observed with intermolecular dimer cation
radicals such as 1 in Chart 1.3 The electronic spectrum of the
mixed-valence cation radical 7•+ comprised the sterically
hindered (S) redox centers shown in Figure 5B is similar to
that of the analogous 3•+ containing T redox centersswith the
sole exception that the intervalence band in the near-IR region
was blue shifted to λCR ) 1100 nm, as determined by Gaussian
deconvolution (see Figure 5B, inset).
The ESR spectrum of sterically hindered 7•+ gradually
broadened as the temperature was progressively raised. The
uniform broadening of all the lines is shown in Figure 4 (left);
and the completely reversible line broadening was attributed to
dynamic electron exchange between the pair of redox centers
S•+ in the ortho-bridged cation radical 7+•:
Computer simulation of this intramolecular process was carried
out with the aid of the ESR-EXN program,31 and Figure 4
includes the close fits to the experimental ESR spectra (right)
with the first-order rate constants kET ) 5 × 106 s-1 at -60 °C
and 4 × 107 s-1 at -20 °C. The temperature variation of the
rate constants afforded an Arrhenius activation energy of 6.2
kcal/mol and preexponential factor of 1012.6 s-1 (Figure S5,
Supporting Information). By comparison, the sterically hindered
(tert-butyl) analogues 9•+ and 10•+ both afforded rather complex
doubled ESR spectra (see Table 3), but they were not rigorously
assigned, since the hyperfine lines showed no signs of broaden-
ing in this temperature range.
(32) (a) Compare with the near-IR bands observed in the phenylene-bridged
2a•+ by Lindeman et al. in ref 9a. (b) Furthermore, the solid-state spectra
-
(29) See Lewis, Fraenkel, et al. in ref 1 and Kochi et al. in ref 4e and references
therein.
of 3•+SbCl6-, 4•+SbCl6-, and 6•+SbCl6 are essentially the same as those
in solution (see Figure S2 in the Supporting Information).
(30) (a) Rathore, R.; Lindeman, S.; Kochi, J. K. J. Am. Chem. Soc. 1997, 119,
9393. (b) Hubig, S. M.; Rathore, R.; Kochi, J. K. J. Am. Chem. Soc. 1999,
121, 617. (c) Rathore, R.; Kochi, J. K. J. Org. Chem. 1995, 60, 4399.
(31) Heinzer, J. Quantum Chemistry Program Exchange 209, as modified by P.
A. Petillo and R. F. Ismagilov. We thank Prof. S. F. Nelsen for providing
us with a copy of this program.
(33) (a) Careful scrutiny of the UV-vis spectra of 3•+ and 7•+ in Figure 5 reveals
a minor component with λmax 900-1000 nm. Since such absorptions are
absent in the meta- and para-bridged 4•+ and 5•+, it is unlikely to derive
from the br-to-S•+ charge transfer. (b) Strong absorptions in this spectral
region are commonly observed (as an impurity?) when aromatic cation
radicals are exposed to their parent donor and thus merit further study.
9
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A R T I C L E S
Sun et al.
Figure 5. (A) Electronic spectra of mixed-valence cation radicals 3+• (solid line) and 4+• (black dashed line) and their mononuclear model 6+• (gray dashed
line) in dichloromethane solution, showing the prominent absorption in the near-IR region of 3+• only. (B) Electronic spectrum of the sterically hindered
cation radical 7+• with the prominent absorption in the near-IR region.33 Insets: Gaussian deconvolution of the low-energy absorptions of 3+• (A) and 7+•
(B).
Table 4. Electronic Spectra of Mixed-Valence Cation Radicals
Discussion
and Their Mononuclear Modelsa
The intermolecular dimer cation radicals of aromatic donors
such as 1 (Chart 1) can be characterized by the pair of equivalent
valence-bond structures shown in Chart 5, in accord with the
Badger-Brocklehurst designation of their diagnostic optical
transitions as charge resonance.3 The wide separation of dD ≈
3.2 Å between the noncovalently bonded aromatic moieties in
such cationic paramagnetic associates necessarily limits the
conceptual electron exchange or hole hopping in Chart 5 to a
through-space processsthe mechanism of which has heretofore
eluded detailed elucidation, owing to their highly transient
character when generated via diffusional encounters.
MVCR
λ (ꢀ)
3•+
4•+
5•+
6•+
7•+
8•+
9•+
438 (4.7), 464 (4.8), 600 sh, 850 sh, 1600 (1.1)
438 (5.6), 462 (5.8), 600 sh
438 (5.6), 462 (5.8), 600 sh
438 (5.7), 462 (5.9), 600 sh
440 (5.2), 471 (5.5), 600 sh, 900 sh, 1120 (0.32)
440 (5.0), 473 (5.4), 600 sh
440 (5.1), 468 (5.4), 600 sh, 732 sh, 807 (0.48),
913 (0.36)
10•+
440 (5.0), 470 (5.5), 600 sh, 728 (0.18), 797 (0.41),
933 (0.17)
a Band maxima λ in nm, with extinction coefficients, ꢀ, in 103 M-1 cm-1
.
Chart 5
Table 5. Estimation of the Electronic Coupling Elements in
Organic Mixed-Valence Cation Radicals via the Mulliken-Hush
Formalism (from the Intervalence Band) and Cyclic Voltammetry
Data
•+
•+
T
ArH /ArH ArH/ArH
a
b
MV-
CR
νIV, 103
∆νIV,a
ꢀ, 103
H ,b
∆E°ox,
V
H ,c
IV
TD
I. Through-Space Electron Delocalization in Mixed-
Valence Cation Radicals. The successful isolation of the
mixed-valence cation radical 3•+ with the bridged aromatic redox
centers (T ) 2,5-dimethoxy-p-tolyl) allows us the opportunity
now to examine the structural properties of the cofacial redox
centers responsible for the mechanism of the electron exchange
or hole hopping by the application of four independent
experimental probes, which we individually describe as follows.
A. Splitting of the Oxidation Potentials (∆E) for Mixed-
Valence Donors. The multiple electron transfer from a mixed-
valence donor such as the o-xylylene-bridged 3 defines the
comproportionation/disproportionation equilibrium. The Gibbs
free-energy change ∆Gcom for eq 6 is given by the magnitude
of the potential splitting, ∆E ) E1/2(1) - E1/2(2), as evaluated
by the transient electrochemical data in Table 1 so that ∆Gcom
) F∆E. Such a free-energy change is determined18,19,34 as the
sum of statistical, electrostatics, and inductive terms and by the
resonance stabilization ∆Gr, which is expressed as ∆Gr )
-2H2/λ where H is the critical electron coupling element
cm-1
103 cm-1
M-1 cm-1
r, Å
103 cm-1
103 cm-1
3+•
7+•
6.25
8.93
2.1
2.1
1.1
0.32
3.2d
4.0e
0.76
0.40
0.16
2.00
a Band full width at half-height. b Calculated with the Mulliken-Hush
equation.38 c Evaluated from ∆E ) -∆G/F ) 2H2/(λF). d Interplanar
distance from X-ray crystallography. e Average interplanar distance from
molecular mechanics calculations.
between the T•+/T redox centers in the mixed-valence cation
radical 3+• and λ is the Marcus reorganization energy.9 If we
assume for the moment that the resonance interaction is the
major contributor to the mixed-valence cation radical 3•+, the
electronic coupling can be directly evaluated from ∆Gcom (vide
supra), and the thermodynamics results are listed as HTD in the
last column of Table 5.35
B. Geometrical Changes and the Charge Distribution (qi)
for the Redox Centers in Mixed-Valence Cation Radicals.
X-ray crystallographic analyses of the mixed-valence donor 3
and its cation radical 3•+ identify three structural features unique
to this ortho-bridged system. First, the quantitative transforma-
tion of the overall anti conformation of the redox centers in 3
(Figure 1A) to the highly ordered syn conformation (Figure 1B)
accompanies its oxidative transformation to 3•+. Since the
(34) (a) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441. (b) 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. (c) Brunschwig, B. S.; Sutin, N. Coord. Chem. ReV. 1999, 187,
233. (d) Sutin, N. AdV. Chem. Phys, 1999, 106, 7. (e) We recognize that
the two-state model for electron transfer is based on orthogonal initial and
final diabatic states;10,34a the extent to which there is orbital overlap between
cofacial aromatic redox centers as in 3•+ (with dD ≈ 3.2 Å) could violate
this theoretical restriction.51b
(35) Note that HTD evaluated from the electrochemical data is expected to
represent an upper limit to the intrinsic electronic coupling element, owing
to the neglect of the other energy terms described above.
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Organic Mixed-Valence Systems
A R T I C L E S
-
-
Figure 6. Crystal packings in the unit cells of the mixed-valence cation-radical salts 3+•SbCl6 (A) and 3+•PF6 (B).
different conformations extant in the mixed-valence donors such
as 3 are not strongly differentiated, though the anti conformation
is slightly favored,36 the marked syn/anti conformational change
observed upon one-electron oxidation of 3 is consistent with
even a modest energy gain such as that contributed from ∆Gr.
In other words, the resonance interaction of T•+/T centers as
formalized in Chart 5 can represent a major contributor to the
formation/stabilization of the mixed-valence cation radical 3•+
that is unique to the ortho-bridged but not the meta/para isomers.
Second, the major configurational change in the redox center
attendant upon the formation of the mixed-valence cation radical,
as measured by the increase in its quinonoidal character,
quantitatively relates to the charge qi residing on the T centers-
symmetrically perturbed by PF6- so that electrostatic polariza-
tion alone can account for the complete electron/charge delo-
-
calization observed in 3•+PF6 crystals. Be that as it may, the
crystalline counterion effects clearly show that the electron/
charge distribution in the resonance stabilization of the ortho-
bridged 3•+ is highly sensitive to external electrostatics
influencessas stereoselectively imposed by the counterions in
the rigid solid-state lattice.
C. Equivalent Number and Hyperfine Splitting of Para-
magnetic Centers in Mixed-Valence Cation Radicals. The
unique sets of equivalent protons in the redox center T provides
an alternative probe for electron/charge delocalization in the
mixed-valence cation radical. Accordingly, the doubling of the
number and halving the proton splittings in the ortho-bridged
3•+ relative to those in the mononuclear model 6•+ indicate that
both of the T centers on the ESR time scale bear equally the
same odd-electron densitysconsistent with their juxtaposition
and resonance stabilization as provided by the transient elec-
trochemical and X-ray crystallographic results. Moreover, this
conclusion is unique to the ortho-bridged cation radical, since
cyclic voltammetry (Table 1), X-ray crystallography (Table 2),
and ESR spectroscopy (Table 3) for the meta and para isomers
show no such unusual behavior.
(s). The experimental value of qi ) +0.5, +0.5 in 3•+PF6
-
(Table 3) indicates that complete electron delocalization is
achieved between both redox centers, as predicted by the charge-
resonance character described in Chart 5. Third and most
important is the cation-dependent nature of qisbeing 0.9, 0.1
in 3•+SbCl6-. Such a significant difference in the charge
distribution in the pair of redox centers of 3•+ is readily
-
-
accommodated by the distinctive location of PF6 and SbCl6
in the unit cell (Figure 6). In particular, SbCl6- is asymmetrically
poised over a single redox center, whereas both centers are
D. Intervalence (Charge-Resonance) Transitions in Mixed-
Valence Cation Radicals. Electronic (UV-vis) spectroscopy
(36) For a description of the conformational syn/anti equilibrium, see the
Experimental Section.
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A R T I C L E S
Sun et al.
Table 6. Comparison of Experimental (ESR) and Calculated (MH)
Intramolecular Electron-Transfer Rate Constants in Bridged
(Mixed-Valence) Cation Radicals
provides the fastest time resolution for probing electron delo-
calization in mixed-valence cation radicals, and the observation
of the unique near-IR absorption band in the ortho-bridged cation
radical 3•+, but not in the meta and para isomers 4•+ and 5•+,
bears direct relationship to the charge-resonance bands reported
by Badger, Brocklehurst, and co-workers3 for the intermolecular
dimer cation radicals such as 1 in Chart 1. Furthermore, the
spectral observation of the charge-resonance band is even
possible in the sterically hindered mixed-valence cation radical
7+• (entry 5), despite its very short lifetime on the ESR time
scale, as indicated by the absence of the hyperfine doubling
(Table 3, entry 8). Accordingly, let us examine how the Mulliken
formalism37 of charge-transfer transition, as theoretically de-
veloped by Hush,38 can be applied to the charge-resonance bands
for the ortho-bridged cation radicals such as 3+• and 7•+.
II. Intramolecular Electron Transfer in Mixed-Valence
Cation Radicals. A. Application of Mulliken-Hush Theory.
For mixed-valence complexes (particularly with transition-metal
redox centers), Hush identified the intervalence (charge-transfer)
transition to reflect the electronic coupling element according
to the relationship34,38 HIV ) 0.0206(νmax∆ν1/2ꢀ)1/2/r, where νmax
and ∆ν1/2 are the maximum and full width at half-heights of
the near-IR absorption band (in cm-1), ꢀ is the molar extinction
coefficient at the absorption maximum (in M-1 cm-1), and r is
the effective separation of redox centers in the mixed-valence
complex (in Å). The direct application of the intervalence
spectral parameters in Table 4 and the separation parameter from
the X-ray crystallographic analysis for the ortho-bridged mixed-
valence cation radicals 3+• and 7+• to the Hush equation yields
the values of the electronic coupling element HIV in Table 5,
column 6.
a From ∆G*) (λ - 2HMH)2/(4λ). b Calculated from kET ) 1012 exp(-
∆G*/RT). c Evaluated from ESR line broadening. d At -60 °C. e At -20
°C.
intramolecular first-order rate constant for electron transfer
within the mixed-valence complex can be evaluated as kET
)
kνn exp(-∆G*/RT), where k is the electronic transmission
coefficient, νn is the nuclear vibration frequency related to
electron transfer, and ∆G* is the free energy of activation for
electron transfer.34 When the electronic coupling is sufficiently
strong (as given in Table 5), electron transfer is adiabatic with
k ≈ 1, and the activation barrier is given by34
∆G* ) (λ - 2H)2/4λ
(8)
The combination of the reorganization energy λ, the electron
coupling element HIV obtained from the intervalence transition
in Table 5, and νn ) 1012 s-1 41 leads to the first-order rate
constants in Table 6 (columns 3 and 5). The experimental first-
order rate constants for the mixed-valence cation radicals 3•+,
with a pair of T centers, and 7•+, with a pair of sterically
hindered S centers, are also included in Table 6, columns 4
and 6.
It is noteworthy that the experimental first-order rate constants
in Table 6 (columns 4 and 6) for the intramolecular electron
transfer obtained from the ESR line-broadening studies agree
satisfactorily with the predictions of Marcus-Hush theory
(columns 3 and 5). First, the fast electron-transfer rate constant
of kET > 109 s-1 for 3•+ at all accessible temperatures derives
from the very low barrier of ∆G* ) 2.6 kcal mol-1 predicted
by Marcus-Hush theory; this is in accord with the absence of
the experimental line broadening at the upper limit of the ESR
time scale. The latter thus limits the half-life for electron transfer
between T•+/T centers in the ortho-bridged cation radical to
τET < 10-9 s-1sin complete accord with the conclusion derived
from the experimental probes (vide supra) explored in this study.
Second, the significantly slower rate of intramolecular electron
exchange in 7•+ (with the sterically hindered S•+/S centers)
allows the quantitative application of the ESR line-broadening
methodology. Indeed, the results for 7•+ in Table 6 (column 6)
obtained from the line-broadening study at high temperature
(30 °C) agree easily within an order of magnitude of the
predictions of Marcus-Hush theory (column 5). Third, at the
other extreme of low temperature (-80 °C), the first-order rate
constant near 106 s-1 for 7+• borders the lower limit too closely
to be reliably measured by their ESR line-broadening. Nonethe-
less, the estimates listed in Table 6 (column 4) generally are in
accord with the predicted rate constant based on ∆G* ) 5.4
kcal mol-1 calculated from eq 9 and the value of HIV in Table
5.
We note that the values of the electronic coupling element
HIV in Table 5 (column 6) determined from the intervalence
charge-resonance transition with the aid of the Mulliken-Hush
formalism37,38 are significantly smaller than HTD evaluated from
the thermodynamic data in Table 1 (column 8). Part of this
discrepancy is doubtless due to the neglect of other (energy)
terms in the thermodynamic treatment, as described above;
however, the question does arise as to whether Mulliken-Hush
theory is applicable to through-space electron transfer (ET) of
the type extant in the o-xylylene-bridged cation radical, as
presented in the previous section. The principal test of the
validity of such a theoretical formulation to identify the optical
charge-resonance transitions in mixed-valence cation radicals
is the direct comparison of the predicted rates of intramolecular
electron transfer with the experimental rates obtained indepen-
dently,39 as follows.
B. Theoretical and Experimental Comparison of (Electron-
Transfer) Rates. According to Marcus-Hush theory,40 the
(37) (a) Mulliken, R. S. J. Am. Chem. Soc. 1952, 74, 811. (b) Mulliken, R. S.;
Person, W. B. Molecular Complexes: Wiley: New York, 1969.
(38) (a) Hush, N. S. Z. Electrochem. 1957, 61, 734. (b) Hush, N. S. Trans.
Faraday Soc. 1961, 57, 557. (c) Hush, N. S. Prog. Inorg. Chem. 1967, 8,
391. (d) Hush, N. S. Electrochim. Acta 1968, 13, 1005. (e) We have
evaluated the separation parameter r in the Hush equation for HIV from
the molecular geometry on the basis of either the X-ray crystallographic
parameter or molecular mechanics computations.38g Such assignments are
at best only estimates of the molecular redox centers as complex as T, S,
and P;38f however, even substantial deviations are not sufficient to
qualitatively change the conclusions. (f) See also: Nelsen, S. F.; Newton,
M. D. J. Phys. Chem. 2000, 104, 10023. (g) HyperChem Release 5.11 Pro
for Windows Molecular Modeling System; Hypercube, Inc., 1999.
(39) For previous examples of the application of such a test, see: Elliot, C. M.;
Derr, D. L.; Matyushov, D. V.; Newton, M. D. J. Am. Chem. Soc. 1998,
120, 11714. See also Nelsen and co-workers in ref 11.
(40) (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.
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Organic Mixed-Valence Systems
A R T I C L E S
C. Electron-Density Distribution between Redox Centers
in Mixed-Valence Cation Radicals. Substantial changes in the
ground-state distribution of the electron density of the redox
centers in mixed-valence cation radicals and thus their molecular
structures are predicted when the magnitude of the electronic
coupling element between redox centers is substantial relative
to the reorganization energy.34 In terms of the ET reaction
coordinate, such increasing values of H/λ result in the gradual
shift of the reactant minimum from (a) Xmin ) 0 with H ) 0, at
which the charge distribution is +1.0/0 and the molecular
structure corresponds to a pair of noninteracting T•+/T centers,
to (b) Xmin ) 0.5 with H g λ/2, at which electron delocalization
is complete so that both redox centers bear a +0.5 charge. As
such, the changing values of Xmin reflect partial transfer of
electron density and translate into structural changes in the redox
centersswhich in the case of the highly variable T center is
represented by partial quinonoid distortion (see Table 2).
For the ortho-bridged mixed-valence cation radical 3•+, the
theoretical estimates of Xmin evaluated from the relationship34
Xmin ) 1/2[1 - (1 - 4H2/λ2)1/2] are Xmin ) 0.02 based on HIV
and Xmin ) 0.12 based on HTD in Table 5, columns 6 and 8,
favorable in the analogous mixed-valence cation radical 7•+, in
which steric encumbrance by annulation precludes the same
close approach of the S•+/S redox centers, resulting in almost
halving of the HIV values. Although we were unable to isolate
crystalline salts of 7•+ for X-ray crystallographic analysis,
preliminary molecular mechanics computations suggest a van
der Waals distance of approximately 4.0 Å.38g If so, the
significant difference between the HIV values for 3•+ and 7•+
suggest that the effectiveness of the through-space mechanism
for electron exchange between redox centers in eq 8 drops off
sharply with separation.44
For a more comprehensive consideration of the distance
dependence of intramolecular electron transfer in mixed-valence
cation radicals, we now compare the through-space mechanism
allowed by the o-xylylene-bridged cation radical 3•+ in Chart 3
with the through-bridge mechanism enforced by the rigid
p-phenylene bridge in the mixed-valence cation radical 2a•+ in
Chart 2.
III. Through-Space versus Through-Bond Electron Trans-
fer in Mixed-Valence Cation Radicals. For the intramolecular
electron exchange via the through-space mechanism,45,46 the
redox centers T•+/T in the conformationally mobile cation
radical 3•+ are disposed cofacially, as depicted in Figure 1B
for conformer 3b described in Chart 5 at an interplanar
separation of dD ) 3.2 Å. For the contrasting through-bond
mechanism applicable to the structurally rigid cation radical
2a•+, the same T•+/T centers lie coplanar and are linearly
connected end to end by the rigid p-phenylene bridge, which
separates the redox centers by ∼8 Å. For the comparison of
the through-space/through-bond electronic interactions of the
redox centers in mixed-valence cation radicals, we focus on three
different facets as follows.
A. Our initial study9 of intramolecular electron exchange in
the mixed-valence cation radical 2a•+ followed from earlier
studies that employed the same p-phenylene bridge in various
mixed-valence cation radicals with redox centers derived from
alkylhydrazines, phenylenediamines, triarylamines, and related
N-centered donors.11,12c,d In those cases, the quantitative analysis
of the intervalence charge-transfer bands by application of the
Marcus-Hush two-state model to the p-phenylene-bridged
cation radicals47 afforded intramolecular first-order rate constants
that agreed with experimental values obtained independently
by dynamic ESR measurements. If such impressive agreements
serve as a valid test of the two-state model to predict intramo-
lecular electron exchanges generally for mixed-valence cation
radicals with p-phenylene bridges, then the spectral analysis of
the intervalence charge-resonance transition in our cation radical
2a+• by the same Marcus-Hush methodology, as presented in
Table 7, entry 2,48 should serve to validate the predicted rate
constant in column 7 for the through (br)-bond electron transfer
between T•+/T centers. Indeed, the calculated value of HIV in
column 5 for the para-bridged 2a•+ from the intervalence band
35
respectively. Such small values of Xmin correspond to only
minor changes in both T•+ and T centers relative to those in
noninteracting redox sites;42 this charge distribution is experi-
mentally observed in the crystalline hexachloroantimonate salt
of 3•+ (see Table 2, third entry). Thus, 3•+SbCl6- clearly resides
in the class II (localized) category according to the Robin-
Day classification of mixed-valence systems.43
On the other hand, the experimental X-ray structural analysis
of the crystalline hexafluorophosphate salt of 3•+ establishes
an equal charge distribution between both redox centers.
Generally speaking, such an unusual charge distribution in
crystalline 3•+PF6 can be attributed to (a) crystallographic
-
statistical disorder, (b) dynamic disorder arising from fast
electron transfer, or (c) complete static charge delocalization
between redox sites. The absence of crystallographic symmetry25
allows alternative a to be excluded, and the observation of
Robin-Day class II behavior in the structurally equivalent
3•+SbCl6- salt strongly disfavors alternative c. Accordingly, we
conclude that the fast intramolecular process observed for 3•+
with τ < 10-9 s-1 must derive from the very low activation
barrier of ∆G* ) 2.6 kcal mol-1 for electron exchange (see eq
7), as predicted by the large electronic coupling element HIV in
Table 5. The latter is structurally consistent with the close
cofacial separation between T•+/T centers of dD ) 3.2 Å
-
evaluated by X-ray crystallographic analysis of both 3•+SbCl6
and 3•+PF6 salts. This spatial situation is considerably less
-
(41) For this study, we have simply taken νn to be uniformly 1012 s-1, the same
value as previously used for the description of electron transfer in
phenylene-bridged organic mixed-valence cation radicals9 with similar redox
centers, and this value of νn agrees reasonably well with that employed in
the kinetics evaluation of the intermolecular anion-radical self-exchange.41b
(b) See Ganesan et al. in ref 4g.
(42) Note that the value of Xmin ) 0.02 is beyond X-ray structural analysis to
readily distinguish from Xmin ) 0, even with the best accuracy provided
by this method.
(43) (a) Robin, M. B.; Day, P. AdV. Inorg. Chem. Radiochem. 1967, 10, 247.
(b) For the application of the Robin-Day classification to organic mixed-
valence systems, see Lambert et al. in ref 12c and Lindeman et al. in ref
9a. (c) To the extent to which the mixed-valence cation radical falls from
the class III (delocalized) to the class II (localized) category, the charge-
resonance designation should be replaced by charge transfer. (d) Although
a reviewer has suggested that electrostatic polarization could induce an
asymmetric structure of a class III mixed-valence cation radical, the
evaluation of H and λ in Table 5 indicates that 3•+SbCl6 belongs in class
II.
(44) In addition, the cofacial S•+/S centers in 7•+ are offset.
(45) Note that the absence of electronic interaction between T•+/T centers in
the meta- and para-bridged cation radicals 4•+ and 5•+ shows that the
through (br)-bond mechanism also does not play a role in the ortho isomer
3•+
.
(46) For previous studies on this type of through-space electronic interactions,
see: Rathore, R.; Kochi, J. K. Can. J. Chem. 1999, 77, 913.
(47) As applied to mixed-valence cation radicals, the resonance “structures” a
and b in Chart 5 relate directly to the initial and final diabatic states in the
two-state model for electron transfer.
(48) Data taken from Lindeman et al. in ref 9a.
9
J. AM. CHEM. SOC. VOL. 125, NO. 51, 2003 15959

A R T I C L E S
Sun et al.
Table 7. Comparison of the Electron-Transfer Parameters in
Mixed-Valence Cation Radicals via Through-Bond and
Through-Space Interactions
comparable and both are experimentally confirmed by (a) the
splitting of the CV waves and (b) the intramolecular first-order
rate constant evaluated by dynamic ESR measurements.15b
Summary and Conclusions
The through-space versus through-bond pathways for in-
tramolecular electron transfer between a pair of bridged aromatic
redox centers are provided by the syntheses of the mixed-valence
donors 3 and 2a depicted in Charts 3 and 2, respectively.49
Selective oxidation generates the mixed-valence systems with
the pair of aromatic redox centers Ar•+/Ar separated by a
conformationally flexible o-xylylene bridge in 3+• and the rigid
p-phenylene bridge in 2a•+ to serve in this study as through-
space and through-bond prototypes, respectively.
a Broadened two-electron oxidation wave with ∆E ≈ 0.02 V. b At -40
°C. c At -100 °C, from ref 9.
correctly accounts for the very low activation energy ∆G* for
through (br)-bond electron transfer and the observed splitting
of ∆E observed for the CV waves established experimentally.
When the same two-state model methodology is applied to the
intervalence charge-resonance band of ortho-bridged 3•+ ex-
amined in this study, the calculated value of the electronic
coupling element (Table 7, column 5) predicts the same kinetics
behavior (compare entries 1 and 2) for through-space electron
transfer from almost the same splitting of the CV wave; most
importantly, it leads to the same values of λT for the reorganiza-
tion energy (column 4), despite the widely divergent symmetry
pattern of orbital overlap extant in 3•+ vis a´ vis 2a•+. Accord-
ingly, we conclude that both 3•+ and 2a•+ represent ground states
with high degrees of electron delocalization between T•+/T
centers on the ESR time scale; this is in accord with X-ray
structural analysis of the quinonoidal distortions and their
particularly high degree of electrostatic polarizability by the
accompanying negatively charged counterionssall independent
of whether through-space or through-bond electron transfer
pertains.
B. The further pursuit of the distance comparison is presented
in Table 7, in which the through-space separation of the cofacial
redox centers by steric encumbrance, as in cation radical 7•+
containing the annulated S•+/S pair, is considered in the context
of the through-bond extension via the incorporation of another
(br) link, as in the p-biphenylene-bridged 2b•+ identified in Chart
2. In each case, the increased distance between the cofacial redox
centers in 7•+ by an incremental amount of only ∼0.5 Å (relative
to that in 3•+) and the larger linear separation of ∼5 Å in 2b•+
(relative to that in 2a•+) inflict more or less comparable
diminutions in the values of the electronic coupling element
(compare the third/fourth entries in Table 7). Most notably, the
accompanying increases in the calculated reorganization energies
(column 5) and activation energies (column 6) in both 7•+ and
2b•+ correctly predict the intramolecular first-order rate constants
for the electron exchange kET, which have been independently
confirmed by ESR line-broadening measurements.
Through-space electron transfer is established in 3•+ by the
mutually syn conformations of T•+/T centers that are cofacially
separated by dD ) 3.2 Å, as determined by X-ray crystal-
lographic analysis in Figure 2. Strong electronic interaction
between such nonbonded aromatic centers is reminiscent of that
extant in a dimer cation radical such as 1 in Chart 1 and
previously evaluated by their pronounced “charge-resonance”
absorption bands in the near-IR region.3,4 Independent measure-
ments of the potential splitting in the cyclic voltammograms
(Table 1), quinonoidal distortion of both T•+/T centers by X-ray
crystallographic analysis (Table 2), and the “doubling” of the
ESR spectra (Table 3) all lead to the same conclusion of the
effectiveness of the cofacial disposition of Ar•+/Ar redox centers
in intramolecular electron transfer. Strong electronic interaction
between T•+/T centers in 3•+ lead to the first-order rate constant
kET > 109 s-1, as qualitatively deduced from ESR spectroscopy.
Such fast electron-transfer rates with kET ) 4 × 109 s-1 also
derive from Marcus-Hush theory as a result of the sizable
electronic coupling element evaluated from the charge-resonance
absorption band according to the Mulliken-Hush formalism.
More to the point, the same treatment of the mixed-valence
donor with the sterically hindered redox center S leads to cation
radical 7•+, exhibiting substantially slower rates with kET ) 1.5
× 107 s-1 that are readily measured by quantitative ESR line-
broadening studies; the same theoretical value of kET ) 1.3 ×
107 s-1 derives from the application of the Marcus-Hush theory
and the use of the electronic coupling element evaluated from
the intervalence charge-resonance transition. Even more im-
portant is the magnitude of the Arrhenius activation energy of
Ea ) 6.2 kcal mol-1 from the ESR line broadening, which is
close to the Gibbs activation free-energy change of ∆G* ) 5.4
kcal mol-1 calculated from the Marcus-Hush equation (8) and
the value of HIV ) 400 cm-1 evaluated from the intervalent
(charge-resonance) band in Table 5.50
Through (br)-bond electron transfer is enforced by the
structurally rigid p-phenylene bond in the mixed-valence cation
C. We also evaluate the through-space/through-bond di-
chotomy49 via the use of a different redox center, P (phenothi-
azinyl), in which the reorganization energy of λP ) 1 × 104
cm-1 is substantially larger than that of the redox center T or
S.15 Despite this distinction, the analysis of the intervalence
charge-resonance transitions with the aid of the two-state model
provides a calculated value of the electron coupling element
for the P•+/P centers in the o-xylylene-bridged cation which is
the same as that in the p-phenylene-bridged cation radical. As
a result, the predicted activation energy and reorganization
energy for through-space/through-bond electron transfer are
(49) For some previous studies of the through-space/through-bond dichotomy,
see: (a) Clayton, A. H. A.; Scholes, G. D.; Ghiggino, K. P.; Paddon-Row,
M. N. J. Phys. Chem. 1996, 100, 10912. (b) Bell, T. D. M.; Jolliffe, K. A.;
Ghiggino, K. P.; Oliver, A. M.; Shephard, M. J.; Langford, S. J.; Paddon-
Row, M. N. J. Am. Chem. Soc. 2000, 122, 10661. (c) Koeberg, M.; de
Groot, M.; Verhoeven, J. W.; Lokan, N. R.; Shephard, M. J.; Paddon-
Row, M. N. J. Phys. Chem. A 2001, 105, 3417. (d) Pullen, S. H.; Studer-
Martinez, S. L.; Edington, M. D.; Harris, A. L.; Long, A.; Baldwin, S. W.;
Staab, H. A.; Simon, J. D. J. Phys. Chem. A 1999, 103, 10220. (e) Arimura,
T.; Ide, S.; Suga, Y.; Nishioka, T.; Murata, S.; Tachiya, M.; Nagamura,
T.; Inoue, H. J. Am. Chem. Soc. 2001, 123, 10744.
(50) Note that this direct comparison of experimental with theoretical barriers
of electron transfer is independent of any ambiguity in our evaluation of
the preexponential factor.41
9
15960 J. AM. CHEM. SOC. VOL. 125, NO. 51, 2003

Organic Mixed-Valence Systems
A R T I C L E S
bis(bromomethyl)tetramethylbenzene.16 Then 2,5-dimethoxytoluene was
arylmethylated17 with 1,2-bis(bromomethyl)tetramethylbenzene in an-
hydrous benzene in the presence of silver perchlorate as a promoter
and calcium carbonate as the acid scavenger to afford 3 in 47% yield.
1,2-Bis(2,5-dimethoxy-4-methyltolyl)tetramethylbenzene (3): mp
radical 2a•+ reported earlier.9a Indeed, the four experimental
probes for electronic interaction of T•+/T centers including (a)
splitting of the CV wave, (b) quinonoidal distortion of T in the
X-ray structure, (c) doubling of the ESR spectrum, and (d)
pronounced intervalence absorption bands were characteristics
that are all shared in common with the through-space interactions
observed with mixed-valence cation radicals 3•+ and 7•+ (vide
supra)sand the quantitative comparisons in entries 1 and 2 in
Table 7 reinforce this direct correspondence. The same picture
emerges from the experimental (first-order) rate constants kET
measured by ESR line broadening in comparison with the
computed results from Marcus-Hush theory using the electronic
coupling element derived from the intervalence transition with
the aid of the Mulliken-Hush formalism. Such a quantitative
coherence of experimental results with theoretical calculations
indicates that the two-state model may be reliably applied more
generally to through-space electron transfer in other organic
mixed-valence cation radicals;51 such a conclusion is strongly
supported by our results with the phenothiazinyl (P) redox center
in the direct comparison of through-space/through-bond mech-
anisms in intermolecular and intramolecular ET pathways.15b
1
183-185 °C; H NMR (CDCl3) δ 6.64 (s, 2H), 6.17 (s, 2H), 3.86 (s,
4H), 3.78 (s, 6H), 3.53 (s, 6H), 2.28 (s, 6H), 2.19 (s, 6H), 2.12 (s, 6H);
13C NMR (CDCl3) δ 152.1, 151.3, 134.7, 133.1, 127.8, 124.4, 120.0,
113.4, 112.9, 56.5, 56.1, 29.7, 16.8, 16.7, 15.8; MS (m/e) 463 (M+
+
1, 22), 462 (M+, 75), 297 (37), 279 (100). Anal. Calcd for C30H38O4:
C, 77.92; H, 8.23. Found: C, 77.84; H, 8.28.
1,4-Bis(2,5-dimethoxy-4-methyltolyl)tetramethylbenzene (5): mp
1
191-192 °C; yield 43%; H NMR (CDCl3) δ 6.78 (s, 2H), 6.21 (s,
2H), 4.09 (s, 4H), 3.95 (s, 6H), 3.56 (s, 6H), 2.27 (s, 6H), 2.21 (s,
12H); 13C NMR (CDCl3) δ 150.1, 150.5, 133.3, 132.2, 125.7, 123.2,
111.9, 110.8, 55.1, 54.9, 28.8, 15.6, 15.0. MS (m/e) 463 (M+ + 1, 34),
462 (M+, 100), 297 (49), 279 (31). Anal. Calcd for C30H38O4: C, 77.92;
H, 8.23. Found: C, 78.17; H, 8.21.
1,3-Bis(2,5-dimethoxy-4-methyltolyl)tetramethylbenzene (4): mp
1
180-181 °C; yield 45%; H NMR (CDCl3) δ 6.69 (s, 2H), 6.13 (s,
2H), 3.99 (s, 4H), 3.87 (s, 6H), 3.46 (s, 6H), 2.26 (s, 3H), 2.19 (s, 6H),
2.18 (s, 6H), 2.04 (s, 3H); 13C NMR (CDCl3) δ 150.6, 150.1, 133.0,
132.9, 132.8, 131.6, 125.7, 123.3, 111.9, 111.1, 55.4, 54.9, 28.7, 15.8,
15.7, 15.3, 14.9; MS (m/e) 463 (M+ + 1, 34), 462 (M+, 100), 297
(49), 279 (31). Anal. Calcd for C30H38O4: C, 77.92; H, 8.23. Found:
C, 78.10; H, 8.17.
Experimental Section
Materials and Synthesis. 1,2,3,4-Tetramethylbenzene, 1,2,3,5-
tetramethylbenzene, 1,2,4,5-tetramethylbenzene, pentamethylbenzene,
benzyl bromide, iodobenzene, 1,4-diiodobenzene, silver perchlorate,
calcium carbonate, paraformaldehyde, 37% hydrobromic acid, meth-
ylhydroquinone, and tert-butylhydroquinone (from Aldrich, Acros, and
Alfa) were used without further purification. Dichloromethane, toluene,
hexane, and tetrahydrofuran were purified according to published
procedures.52 1,2-Bis(bromomethyl)tetramethylbenzene, 1,3-bis(bro-
momethyl)tetramethylbenzene, and 1,4-bis(bromomethyl)tetramethyl-
benzene were prepared by bromomethylation of benzenes according
to the literature.16 4,5-Dimethyl-1,2-diiodobenzene was synthesized by
iodination of o-xylene with I2.53a The mononuclear model donor 1,4-
dimethyl-2,5-dimethoxybenzene (6) was synthesized as described.9 2,5-
Dimethoxymethylbenzene, 2,5-dimethoxy-tert-butylbenzene, and 2,5-
diethoxybutylbenzeneweresynthesizedbythealkylationofhydroquinones
with dialkyl sulfates.53b 1,4-Dimethoxy-5,8-methanotetrahydronaph-
thalene and 1,4-dimethoxy-2-methyl-5,8-methanotetrahydronaphthalene
(8) were obtained in four steps as described earlier.30c The neutral
precursors of tris(2,4-dibromobenzene)amine, tris(4-bromobenzene)-
amine, and their radical cations (MG•+) as hexachloroantimonate and
hexafluorophosphate salts were prepared according to the literature
procedure.54 All of the compounds prepared were characterized by 1H
NMR, 13C NMR, MS, melting points, and elemental analysis. The
methylene-bridged alkyhydroquinones were readily prepared in two
steps. For example, 1,2,3,4-tetramethylbenzene was bromomethylated
with hydrogen bromide and formaldehyde in acetic acid to give 1,2-
1,2-Bis(1,4-dimethoxy-5,8-methano-5,6,7,8-tetrahydronaphthalene-
2-methylenyl)tetramethylbenzene (7): mp 135-136 °C; yield 21%;
1H NMR (CDCl3) δ 5.92 (s, 2H), 3.90 (s, 4H), 3.71 (s, 6H), 3.53 (s,
6H), 2.25 (s, 6H), 2.12 (s, 6H), 1.87 (m, 4H), 1.67 (d, J ) 8.4 Hz,
2H), 1.44 (d, J ) 8.4 Hz, 2H), 1.12 (m, 4H); 13C NMR (CDCl3) δ
148.8, 145.6, 139.8, 134.5, 133.9, 133.0, 132.9, 131.1, 109.1, 60.7,
56.2, 56.1, 48.8, 40.9, 39.6, 30.0, 27.0, 26.6, 16.8.
1,2-Bis(2,5-dimethoxy-4-tert-butyltolyl)tetramethylbenzene (9):
mp 179-181 °C; yield 19%; 1H NMR (CDCl3) δ 6.75 (s, 2H), 6.17 (s,
2H), 3.87 (s, 4H), 3.78 (s, 6H), 3.48 (s, 6H), 2.25 (s, 6H), 2.10 (s, 6H),
1.33 (s, 18H); 13C NMR (CDCl3) δ 152.4, 150.4, 135.8, 134.1, 132.9,
127.2, 113.6, 109.2, 55.9, 55.8, 34.6, 28.7, 28.4, 16.8.
1,2-Bis(2,5-dimethoxy-4-tert-butyl-p-tolyl)tetramethylbenzene (10):
mp 194-195 °C; yield 17%; 1H NMR (CDCl3) δ 6.76 (s, 2H), 6.17 (s,
2H), 3.94 (q, J ) 7.2, 4H), 3.86 (s, 4H), 3.66 (q, J ) 7.2, 4H), 2.25 (s,
6H), 2.19 (s, 6H), 2.11 (s, 6H), 1.34 (s, 18H), 1.29 (t, J ) 9.6, 12H);
13C NMR (CDCl3) δ 151.6, 149.8, 135.7, 134.5, 132.9, 132.8, 127.6,
113.6, 111.2, 64.6, 63.8, 34.5, 29.8, 29.4, 16.8, 16.8, 15.0, 14.8.
Conformational Equilibrium of Mixed-Valence Donor 3. Theo-
retical computations with Spartan software55 indicated that the energies
of the syn and anti conformers of 3 were rather close, although the
energy of the syn conformer was about 2 kcal/mol higher than that of
the anti conformer. The thermodynamics of the syn/anti equilibrium
were experimentally studied by NMR spectroscopy, and Table S1 in
the Supporting Information presents the chemical shifts of different
sets of protons of 3 measured in the temperature range from +20 to
-80 °C. The data indicated the upfield shift of the positions of all the
chemical groups with increasing temperature, and the most prominent
changes were related to the methylene bridge protons. On the basis of
literature data,56 such spectral changes were assigned to the shift of
conformational equilibrium of 3 in eq 1sthe temperature decrease being
accompanied by a shift of the equilibrium to the energetically preferred
anti conformation. On the basis of values of the chemical shifts of
methylene (bridge) protons (most sensitive to conformational changes),
the anti/syn equilibrium constant K ) [anti-3]/[syn-3] was calculated
(51) (a) Provided due cognizance is presently taken of the rigorous definitions
of the separation parameter38e and the preexponential factor41 for reliable
computations of the Mulliken-Hush (MH) electronic coupling element,
as described herein. Nonetheless, the ability of the two-state model to utilize
the intervalence absorption bands to correctly predict the electron-transfer
rates of mixed-valence cation radicals 3•+ and 7•+ underscores its utilitarian
value for further use. (b) We hope that ongoing collaborative interactions
with M. D. Newton will provide theoretical guidelines for critically assessing
the quantitative application of the two-state model to mixed-valence cation
radicals such as 3+• involving orbital overlap of juxtaposed (cofacial) redox
centers.
(52) Perrin, D. D.; Armarego, W. L. F.; Perrin, D. R. Purification of Laboratory
Chemicals, 2nd ed.; Pergamon: New York, 1980.
(53) (a) Hart, H.; Harada, K.; Du, C.-J. F. J. Org. Chem. 1985, 50, 3104. (b)
Hiers, G. S.; Hager, F. D. Organic Syntheses; Wiley: New York, 1932;
Collect. Vol. 1, p 58.
(54) Bell, F. A.; Ledwith, A.; Sherrington, D. C. J. Chem. Soc. C 1969, 2719.
Also see: Connelly, N. G.; Geiger, W. E. Chem. ReV. 1996, 96, 877 and
references therein.
(55) PC Spartan MM3 Plus V; 2.0 Wavefunction, Inc., Irvine, CA, 1999.
(56) Compare: (a) Dix, D. T.; Fraenkel, G.; Karnes, H. A.; Newman, M. S.
Tetrahedron Lett. 1966, 5, 517. (b) Jensen, F. R.; Bushweller, C. H. In
AdVances in Alicyclic Chemistry; Hart, H., Karabatsos, G. J., Eds; 1971;
Academic Press: New York, Vol. 3, p 139.
9
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A R T I C L E S
Sun et al.
as56 K ) (δsyn - δobs)/(δobs - δanti), where δobs was the observed
chemical shift at different temperatures and δanti and δsyn were the proton
chemical shifts in the anti and syn conformations of 3, respectively.
Note that δanti ) 3.4 ( 0.1 and δsyn ) 4.2 ( 0.2 ppm, as estimated by
the linear plot of 1/T vs ln K. From the plot of 1/T vs ln K with R2 >
0.998 (as shown in Figure S4 in the Supporting Information), the
enthalpy change of the anti/syn transformation was estimated to be
1.5 ( 0.5 kcal/mol, which was consistent with the theoretical
calculations. In addition, the fact that the averaged values of methylene
(proton) shifts were observed at all temperatures indicated the fast anti/
syn transformation on the NMR time scale of 10-3 s, even at -80 °C,
in agreement with the electrochemical results of 3 (vide infra).
dications 42+ and 52+ were similarly produced using a 2:1 molar ratio
of nitrosonium to the bridged donor. The purities of all salts were
determined by iodometric titration and were found to be greater than
98%.13 The dication 32+ and cation radicals and dications of donors
7-10 were not isolated in the solid state, owing to partial decomposition
in the process of oxidation/isolation; they were therefore prepared and
examined in situ, as described below.
UV-Vis-Near-IR Spectroscopic Characterization of the Mixed-
Valence Cation Radicals and Dications. The pure isolated salts of
the mixed-valence cation radicals and dications were dissolved in
dichloromethane, and the UV-vis-near-IR absorption spectra were
recorded with a Cary 500 spectrometer. Alternatively, cation radicals
and dications were prepared in situ by oxidation with MG•+SbCl6- with
E°red ) 1.55 V vs SCE. For example, a 1 cm quartz cuvette equipped
with a Schlenk adaptor was charged with a freshly prepared stock
Electrochemistry. Cyclic voltammetry (CV) and Osteryoung square
wave voltammetry (OSWV) were performed on a BAS 100A electro-
chemical analyzer, as described previously.9 The electrochemical study
of the ortho-bridged donor 3 included a variation of the scan rate from
10 to 2500 mV/s and of the temperature from -30 to +60 °C. This
revealed that the characteristics of the first oxidation wave (Eox ) 1.07
V) did not depend on the temperature and scan rate. The second
oxidation wave was temperature and scan-rate dependent. Thus, at room
temperature and high scan rate (1-2 V s-1) only a single one-electron
wave at 1.23 V was observed. However, the decrease of the scan rate
resulted in the current decrease of this wave and the appearance and
intensity increase of an additional wave at 1.35 V. The ratio of the
intensity (or current) of the wave at 1.23 V to that at 1.37 V diminished
with decrease of the scan rate and with increasing temperature: i.e.,
the anodic current at 1.37 V was maximum at low scan rates of 20-
50 mV/s and at high temperatures of 50-60 °C, and (vice versa) it
was almost absent at high scan rates and/or very low temperatures
approaching -30 °C. The first oxidation wave corresponded to the
oxidation of the neutral donor to its cation radical, and its potential
was determined by the free-energy difference between these two states.
In particular, the negative shift of the oxidation potential relative to
the mononuclear model and meta and para derivatives 4 and 5 was
related to the resonance stabilization in the syn conformation of 3•+
(see text). Thus, the scan rate and temperature constancy of the first
wave indicated that (a) practically all of the cation radical existed in
solution in the syn conformation and (b) there was the possibility of
fast interconversion from anti to syn conformations. Indeed, only the
syn conformation of 3•+ was resonance stabilized. Therefore, if there
were a substantial fraction of the anti conformation of 3•+ in solution,
the syn/anti equilibrium would have been temperature dependent, thus
leading to the temperature dependence of the oxidation potential. In
addition, the neutral donor 3 existed mainly in the anti conformation
and most of cation radical 3•+ in the syn conformation. However, the
potential of the first oxidation wave was scan-rate independent, which
indicated that the anti/syn transformation was fast on the CV time scale;
otherwise, a shift of the first oxidation wave to higher potential or even
its splitting with an increase in the scan rate would have been observed.
The second wave in the cyclic voltammogram of 3 corresponded to
the oxidation of the cation radical 3•+ to the dication 32+. The splitting
of this wave into two components at slow scan rate and high temperature
indicated the existence of an additional transformation affecting this
process. Note that the relative (current) intensity of the second positive-
shifted component increased with increasing temperature and decreasing
scan rate. However, the precise conformational nature of this process
is unclear at this juncture.
-
solution of MG•+SbCl6 in anhydrous dichloromethane, and a neutral
donor such as 3 was added incrementally under an argon atmosphere
at -60 °C. The solution immediately took on a yellow coloration, and
the UV-vis-near-IR absorption spectrum was recorded. In case of
mixed-valence donors 4, 5, and 7, the measurements were taken in the
presence of a large excess of neutral donor to ensure the maximum
shift of the comproportionation equilibria to the cation radical.57
Diffuse-Reflectance Spectroscopy. The single crystals of cation-
radical salts with hexachloroantimonate were mixed with potassium
hexafluorophosphate (KPF6), ground to a fine powder to form a 20 wt
% dispersion, and stored in a 1 mm quartz cuvette. The diffuse-
reflectance spectra were collected on a Cary 500 spectrometer. The
spectra were presented as percentage absorption (% ABS) as defined
by % ABS ) 100(1 - R/R0) with R and R0 representing the intensities
of the diffuse-reflected probe light and of the reference light, respec-
tively.
ESR measurements were performed on either a Bruker ESR-300
X-band or Varian E-line Century 100 ESR spectrometer from +20 to
-90 °C. The samples were prepared under argon by dissolving the
isolated salt in anhydrous dichloromethane or by oxidation with
MG•+SbCl6 or NOSbCl6 in situ at -60 °C in a Schlenk tube. These
-
solutions were then transferred under an argon atmosphere into a quartz
2 mm diameter ESR tube connected to a 5 mL Pyrex tube equipped
with a Teflon valve. The tube was placed in a quartz Dewar placed in
the center of a the rectangular cavity, and the temperature was regulated
by an IBM temperature controller to within (0.5 K. Compressed
nitrogen was guided through the cavity to remove any adventitious
moisture condensed onto the Dewar surface at low temperatures. ESR
simulations were carried out with the PEST WinSim program, version
0.96 (Public EPR Software Tools, National Institute of Environmental
Health Sciences), by variation of the splitting parameters and line widths
to obtain the best correspondence of simulated and experimental spectra.
The ESR hyperfine splittings of the mononuclear model 6+• were used
as the starting set of parameters.26 Dynamic ESR spectra simulations
were carried out with the aid of the ESR-EXN program.31 In these
cases, the parameters obtained in the ESR simulation for the mono-
nuclear model cation radical were used as the starting point, and the
rate constants were varied to obtain the best correspondence between
the calculated and experimental spectra. The electron-transfer rate
constants kET evaluated from the line-broadening experiments were most
reliable in a rather narrow (temporal) range: 5 × 106 < kET < 108 s-1
.
At slower rates, the line broadening was insufficient to be observed; at
faster rates the line broadening was too severe. When the ET rate
constant was very high on the ESR time scale of τ < 10-9 s, the values
of the hyperfine splittings became nearly half and the number of nuclei
doubled as compared with those at the slow-rate limit. We were unable
to carry out precise dynamic ESR spectral simulations in the fast-
Isolation of Mixed-Valence Cation-Radical and Dication Salts.
The addition of 1 equiv of NOSbCl6 to the mixed-valence donor 3 (4
mM) in dichloromethane at -40 °C produced yellow solutions of the
cation radical. After removal of NO (gas) and approximately 50% of
the dichloromethane (in vacuo), toluene was added and the dark yellow
precipitate of the cation radical was filtered and washed with cold
toluene. A similar procedure but with a 1:2 molar ratio of oxidant to
donor in order to prevent the disproportionation of the cation radical
led to the mixed-valence cation radicals 4•+ and 5•+. Mixed-valence
(57) The electronic and ESR spectra were essentially unaffected when the molar
ratio of the neutral donor to cation radical was deliberately varied from
2:1 to 10:1, indicating that the effects of comproportionation can be
neglected.
9
15962 J. AM. CHEM. SOC. VOL. 125, NO. 51, 2003

Organic Mixed-Valence Systems
A R T I C L E S
Table 8. Crystallographic Data for Aromatic Donors and Their
exchange limit. To exclude effects of methoxyl group rotation, the
temperature dependence of the ESR spectrum of 7+• was measured at
relatively low temperatures (-80 to -30 °C).57,58 Likewise, to exclude
any contribution of the comproportionation equilibria on the line
broadening of 7•+, the ESR spectra were measured in the presence of
added donor 7sand found to be invariant with various amounts in
excess. Owing to the limited (insufficiently resolved) experimental data,
computer simulations of the ESR spectra of cation radicals 9•+ and
10•+ can also be derived from alternative sets of splitting parameters
Cation Radicals
3‚0.75CH Cl2
3
•+SbCl6‚CH Cl2
3
•+PF ‚CH Cl2
6 2
2
2
empirical formula
C
30.75H39.5
Cl1.5O4
-
C31H40Cl8-
O4Sb
C31H40Cl2-
F6O4P
formula wt
cryst syst
space group
a, Å
b, Å
c, Å
526.30
triclinic
P1h
8.445(1)
12.666(2)
13.717(2)
94.64(1)
91.18(1)
99.10(1)
881.98
triclinic
P1h
692.50
monoclinic
P21/c
11.348(1)
10.152(1)
27.762(2)
90
93.23(1)
90
10.126.1(1)
13.043(1)
14.533(1)
77.25(1)
84.41(1)
81.52(1)
1847.4(2)/2
1.586
(e.g. aOCH ) 3.2 G, aCH ) 6.9 and 1.7 G, and aArH ) 0.5 G). As such,
3
the data presented for these entries in Table 3 are considered tentative
and subject to further verification.
R, deg
â, deg
γ, deg
X-ray Crystallography of the Cation Radicals. The intensity data
were collected with aid of a Siemens SMART Apex diffractometer
equipped with a CCD detector using Mo KR radiation (λ ) 0.710 73
Å), at -150 °C unless otherwise specified. The structures were solved
by direct methods and refined by full-matrix least-squares procedures
with IBM Pentium and SGI O2 computers.59 Note that the X-ray
structure details of various compounds mentioned here are on deposit
and can be obtained from the Cambridge Crystallographic Data Center,
12 Union Road, Cambridge CB2 1EZ, U.K. A yellow solution of (2
mM) nitrosonium hexachloroantimonate (NO•+SbCl6-) and 3 (2 mM)
in dichloromethane (20 mL) was prepared under an argon atmosphere
at -60 °C. The solution was carefully layered with toluene and placed
in the cold bath (-60 °C). After 7 days, dark green single crystals
were formed as the cation-radical salt (3•+SbCl6-) suitable for X-ray
crystallographic analysis. Single crystals of the cation-radical salt
3•+PF6- were similarly obtained using tris(4-bromophenyl)amine cation
radical hexafluorophosphate as the oxidant. Single crystals of the neutral
V, Å3/Z
1443.1(3)/2
1.211
3193.3(5)/4
1.440
F
calcd, g/cm3
total/unique
20 598/12 410 18 985/10 746 26 315/10 459
no. of rflns
no. of data (I > 2σ(I)) 7795
R1a/wR2b
0.059/0.163
7815
0.042/0.089
7806
0.057/0.154
2 2
a R1 ) ∑||Fo| - |Fc||/∑|Fo|. b wR2 ) {∑[w(Fo2 - Fc2)2]/∑[w(Fo ) ]}1/2
.
mixed-valence donor 3 were obtained by slow evaporation of the
solvent. Crystallographic data for the pertinent aromatic donors and
their cation radicals are presented in Table 8.
Acknowledgment. We thank Professor S. F. Nelsen for kindly
providing us with a copy of the ESR-EXN line-broadening
program, J. M. Lu for help with the ESR spectral measurements,
and the R. A. Welch Foundation and National Science Founda-
tion for financial support.
(58) Temperature dependence of the hyperfine splitting constants due to the
rotation of the methoxyl group was described by Sullivan in ref 27. Since
such an effect was most pronounced in cation radicals containing a methoxyl
and (additionally) two ortho-substituted groups,27 it did not substantially
affect the temperature dependence of the ESR spectra of cation radicals
2•+-6•+. However, methoxyl rotation in 7•+ can account for noticeable
changes in the hyperfine splitting constants and the appearance of additional
components in ESR spectra at room temperature similar to those observed
in the ESR spectrum of the cation radical of the mononuclear sterically
hindered donor 9,10-dimethoxy-1,4:5,8-dimethano-1,2,3,4,5,6,7,8-octahy-
droanthracene (CRET•+).30c However, for CRET•+, the ESR spectra were
invariant in the temperature range from -90 to -20 °C, and the line widths
were practically constant at all temperatures. The same temperature-
independent ESR spectra were observed in the -90 to -20 °C range for
the mononuclear model 8+•. We thus conclude that line broadening observed
in the ortho-bridged cation radical 7•+ in the temperature range -90 to
-30 °C can be reliably assigned to intramolecular electron transfer.
(59) Sheldrick, G. M. SHELXS-86, Program for Structure Solution; University
of Gottingen, Gottingen, Germany, 1986.
Supporting Information Available: Temperature dependence
of the chemical shifts in the H NMR spectrum of 3 (Table
1
S1), ESR spectra of dications 32+, 42+, and 52+ (Figure S1),
solid-state (UV-vis-near-IR) spectra of cation radicals 3•+, 4•+,
and 6•+ as the SbCl6- salts (Figure S2), temperature dependence
of the syn/anti equilibrium constant in the mixed-valence donor
3 (Figure S3), and Arrhenius activation energy for intramolecular
electron exchange (kET) in the sterically hindered mixed-valence
cation radical 7•+ (Figure S4). This material is available free of
charge via the Internet at http://pubs.acs.org.
JA037867S
9
J. AM. CHEM. SOC. VOL. 125, NO. 51, 2003 15963