Intervalence near-IR spectra of delocalized dinitroaromatic radical anions

Article abstract of DOI:10.1021/ja036066m

The Class III (delocalized) intervalence radical anions of 1,4-dinitrobenzene, 2,6-dinitronaphthalene, 2,6-dinitroanthracene, 9,9-dimethyl-2,7-dinitrofluorene, 4,4′-dinitrobiphenyl, and 1,5-dinitronaphthalene show charge-transfer bands in their near-IR spectra. The dinitroaromatic radical anions have comparable but slightly larger electronic interactions (H_ab values) through the same aromatic bridges as do the corresponding dianisylamino-substituted radical cations. H_ab values range from 5410 cm^-1 (1,4-dinitrobenzene) to 3400 cm ^-1 (9,9-dimethyl-2,7-dinitrofluorene), decreasing as the number of bonds between the nitro groups increases, except for the 1,5-dinitronaphthalene radical-anion, which has a coupling similar to that of 9,9-dimethyl-2,7-dinitrofluorene. All charge-transfer bands show vibrational fine structure. The vertical excitation energies (λ_v) were estimated from the vibrational components, obtained by simulation of the entire band. The large 2H_ab/λ_v values confirm these radicals to be Class III delocalized mixed-valence species. Analysis using Cave and Newton's generalized Mulliken-Hush theory relating the transition dipole moment to the distance on the diabatic surfaces suggests that the electron-transfer distance on the diabatic surfaces, d_ab, is only 26-40% of the nitrogen-to-nitrogen distance, which implies that something may be wrong with our analysis.

Full text of DOI:10.1021/ja036066m

Published on Web 09/18/2003
Intervalence Near-IR Spectra of Delocalized Dinitroaromatic
Radical Anions
Stephen F. Nelsen,*,† Asgeir E. Konradsson,† Michael N. Weaver,† and
Joa˜o P. Telo*,‡
Contribution from the Department of Chemistry, UniVersity of Wisconsin,
1101 UniVersity AVenue, Madison Wisconsin 53706-1396, and Instituto Superior Te´cnico,
Qu´ımica Orgaˆnica, AV. RoVisco Pais, 1049-001 Lisboa, Portugal
Received May 11, 2003; E-mail: nelsen@chem.wisc.edu
Abstract: The Class III (delocalized) intervalence radical anions of 1,4-dinitrobenzene, 2,6-dinitronaph-
thalene, 2,6-dinitroanthracene, 9,9-dimethyl-2,7-dinitrofluorene, 4,4′-dinitrobiphenyl, and 1,5-dinitronaph-
thalene show charge-transfer bands in their near-IR spectra. The dinitroaromatic radical anions have
comparable but slightly larger electronic interactions (Hab values) through the same aromatic bridges as
do the corresponding dianisylamino-substituted radical cations. Hab values range from 5410 cm-1 (1,4-
dinitrobenzene) to 3400 cm-1 (9,9-dimethyl-2,7-dinitrofluorene), decreasing as the number of bonds between
the nitro groups increases, except for the 1,5-dinitronaphthalene radical-anion, which has a coupling similar
to that of 9,9-dimethyl-2,7-dinitrofluorene. All charge-transfer bands show vibrational fine structure. The
vertical excitation energies (λv) were estimated from the vibrational components, obtained by simulation of
the entire band. The large 2Hab/λv values confirm these radicals to be Class III delocalized mixed-valence
species. Analysis using Cave and Newton’s generalized Mulliken-Hush theory relating the transition dipole
moment to the distance on the diabatic surfaces suggests that the electron-transfer distance on the diabatic
surfaces, dab, is only 26-40% of the nitrogen-to-nitrogen distance, which implies that something may be
wrong with our analysis.
pairing with Bu4N+ in polar solvents causes an easily detectable
effect on the electron transfer (ET) rate constants.
Introduction
Interest in the question of charge localization versus delocal-
ization in dinitroaromatic anions began with early ESR studies
showing that 1,3-dinitrobenzene radical anion has spin localized
on one nitro group when prepared by alkali metal reduction in
an ether solvent,1 but the nitro groups appeared equivalent when
it was prepared by electrochemical reduction.2 Intense study
by many groups for a decade showed that the rate of electron
exchange between the nitro groups was very sensitive to condi-
tions and led to general agreement that interactions of the radical
anion with solvent and counterion were responsible for the
charge localization.3 More recently, the intramolecular electron-
transfer rate constants for these and many analogous systems
have been measured more accurately,4 and it was shown by
Hosoi and co-workers that reducing with excess [222]-cryptand
Surprisingly, although it is now obvious that these systems
should be considered nitro-centered intervalence (IV) com-
pounds and hence their optical spectra will be revealing about
their ET properties, we have seen no discussion of the near-IR
spectra of dinitroaromatic radical anions. We consider the
delocalized systems in this work. IV compounds have two
charge-bearing units (M), connected by a bridge (B), and ones
that have an electronic interaction through the bridge exhibit
an IV-band in their optical spectra. Symmetrical, localized IV
compounds (designated as Robin-Day Class II systems)6 that
may be symbolized as M-B-M+ or M-B-M- provide the
simplest ET systems to interpret. The Marcus-Hush two-state
model7 provides a remarkably simple way of considering their
optical spectra. As indicated at the left of Figure 1, for a
localized compound the transition energy at the band maximum
(1) (a) Ward, R. L. J. Chem. Phys. 1960, 32, 410. (b) Ward, R. L. J. Am.
Chem. Soc. 1961, 83, 1296. (c) Ward, R. L. J. Chem. Phys. 1962, 37, 1405.
(2) (a) Maki, A. H.; Geske, D. H. J. Chem. Phys. 1960, 33, 825. (b) Maki, A.
H.; Geske, D. H. J. Am. Chem. Soc. 1961, 83, 1852. (c) Harriman, J. E.;
Maki, A. H. J. Chem. Phys. 1963, 39, 778.
(3) Gutch, J. W.; Waters, W. A.; Symons, M. C. R. J. Chem. Soc. B 1970,
1261.
(4) (a) Grampp, G.; Shohoji, M. C. B. L.; Herold, B. J. Ber. Bunsen-Ges. Phys.
Chem. 1989, 93, 580. (b) Grampp, G.; Shohoji, M. C. B. L.; Herold, B. J.;
Steenken, S. Ber. Bunsen-Ges. Phys. Chem. 1990, 94, 1507. (c) Telo, J.
P.; Shohoji, M. C. B. L.; Herold, B. J.; Grampp, G. J. Chem. Soc., Faraday
Trans. 1992, 88, 47. (d) Telo, J. P.; Shohoji, M. C. B. L. Ber. Bunsen-Ges.
Phys. Chem. 1994, 98, 172.
and sodium in DMF5 gives about an order of magnitude higher
rate constant than electrochemical reduction,4 so that even ion
† University of Wisconsin.
‡ Instituto Superior Te´cnico.
(5) Hosoi, H.; Mori, Y.; Masuda, Y. Chem. Lett. 1998, 177.
(6) Robin, M.; Day, P. AdV. Inorg. Radiochem. 1967, 10, 247.
9
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J. AM. CHEM. SOC. 2003, 125, 12493-12501
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A R T I C L E S
Nelsen et al.
illustrated above, the conditions shown by Hosoi and co-workers
to avoid tight ion pairing.5
Localized IV compounds have their low-energy optical
transition to a steeply sloping region of the upper adiabatic
surface (Figure 1), ensuring that the absorption band will be
very broad, and precluding the resolution of vibrational fine
structure. Delocalized IV compounds have a minimum vertical
from the ground-state minimum, and can show narrow enough
lines to resolve vibrational fine structure. All of the compounds
discussed here have partially resolved vibrational fine structure,
requiring that they are delocalized (Class III) systems. Figure 2
compares the low-energy region spectra for the 1,4-PH-bridged
nitro-centered radical anion with those for the three 1,4-PH-
bridged radical cations. The 1,4-Da2PH+ spectrum was taken
in methylene chloride9,10 and the 1,4-(k33N)2PH+ and 1,4-
Hy2PH+ spectra in acetonitrile,11 but solvent effects on delo-
calized IV compound optical spectra are small.12 The NO2-
substituted radical anion spectrum shows the resolution of
vibrational structure, as does the k33N- substituted cation.
The effect of changing bridge size on three of these NO2-
centered radical anions is shown in Figure 3. As expected, Eop
decreases as bridge size increases because Hab will decrease.
All three bands show rather distinct vibrational fine structure,
with components showing maxima at ∼1450, 1550, and 1520
cm-1 higher energy than the 0,0 band as ring size increases, of
relative ꢀmax ∼0.50, 0.36, 0.36. An intermediate maximum
occurs for the smaller systems but is not noticeable for the 2,6-
AN-bridged compound. Optical data, transition dipole moments
(µ12), and related information are summarized in Table 1.
Figure 4 compares the optical spectra of the IV radical anions
of the three nine-bond bridged compounds studied, with 2,6-
AN, 2,7-M2FL, and 4,4′-BI bridges. The spectrum is noticeably
broader for the 2,7-M2FL-bridged compound and broader yet
for the 4,4′-BI-bridged one. Figure 5 compares the optical
spectra for the 1,5- and 2,6-naphthalene-bridged radical anions.
Despite a shorter distance and fewer connecting bonds, Hab is
smaller for the former compound, which certainly needs
explaining.
Figure 1. Comparison of IV charge-transfer band interpretation for
localized and delocalized IV compounds.
(Eop) on the adiabatic surfaces (solid lines) is the separation
between the ground (E1) and excited state (E2) energy surfaces,
and equals Marcus’s vertical reorganization energy λ, the vertical
gap between the minimum of one diabatic surface and the other
(the dashed parabolas marked a and b). Hush suggested how to
experimentally determine the electronic coupling between the
M units, Hab, that allows determining the electron-transfer
barrier, ∆G* (when the ET distance dab is known).7a If 2Hab
exceeds λ, the interpretation of the IV charge-transfer band is
very different (right side of Figure 1). The lower-energy surface
then has a single minimum, the compound is charge-delocalized
(Robin-Day Class III), and Eop measures 2Hab instead of λ.
We believe it was Cave and Newton who first pointed out in
their generalized Mulliken-Hush (GMH) theory that band
intensity for Class III compounds becomes a measure of dab.8
In this work we discuss the IV absorption bands of six
delocalized dinitroaromatic anions having the five-, seven-, and
nine-bond aromatic bridges shown below,
and compare their optically derived ET parameters with an IV
radical anion having 2,2-difluoro-1,3,2-(2H)-dioxaborine (Db)
units, and radical cations having dianisylamino (Da), 3-keto-
azabicycl[3.3.0]non-9-yl (k33N), and 2-tert-butyl-2,3-diazabicyclo-
[2.2.2]oct-3-yl (Hy) charge-bearing units.
The transition dipoles (µ12) in Table 1 were calculated as
described in the Experimental Section and converted to dab using
the generalized Mulliken-Hush formula dab ) 2µ12/e which
arises because the electron-transfer distance on the ground-state
adiabatic surface, d12, is zero for a delocalized compound.8b
Results
The optical absorption spectra of dinitroaromatic radical
anions were recorded in DMF after reduction with sodium
amalgam in the presence of a large excess of the cryptand
(8) (a) Cave, R. J.; Newton, M. D. J. Chem. Phys. 1997, 106, 9213. (b) Obtained
2
from |∆µab| ) [(∆µ12
)
+ 4(∆µ12)2]1/2 using ∆µ(D) ) 4.8032d (Å).
(9) Lambert, C.; No¨ll, G. J. Am. Chem. Soc. 1999, 121, 8434.
(10) Nelsen, S. F.; Konradsson, A. E.; Luo, Y. Kim, K. Y.; Blackstock, S. C.,
submitted for publication, reassigns the Da2Ar+ species considered here
as delocalized; Lambert and No¨ll thought it was localized.9
(11) Bailey, S.; Zink, J. I.; Nelsen, S. F. J. Am. Chem. Soc. 2003, 125, 5939.
(12) Nelsen, S. F.; Tran, H. Q. J. Phys. Chem. A 1999, 103, 8139.
(7) (a) Hush, N. S. Prog. Inorg. Chem. 1967, 8, 391. (b) Hush, N. S. Coord.
Chem. ReV. 1985, 64, 135. (c) Marcus, R. A.; Sutin, N. Biochim. Biophys.
Acta 1985, 811, 265. (d) Sutin, N. Prog. Inorg. Chem. 1983, 30, 441.
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Near-IR Spectra of Dinitroaromatic Radical Anions
A R T I C L E S
Figure 2. Comparison of ꢀ vs hν for four PH-bridged IV compounds. The Da- and NO2-bridged species are plotted versus the left ꢀ axis, and the Hy- and
k33N-bridged on the right one, which is expanded by a factor of 5 so that all four spectra may be clearly seen.
Figure 3. Comparison of the absorption spectra of the 1,4-PH, 2,6-NA, and 2,6-AN-bridged dinitroaromatic radical anions at room temperature in DMF.
Table 1. Comparison of IV Region Optical Absorption Parameters
for Delocalized Dinitroaromatic Radical Anions in DMF
III NO2-centered anions is shown in Figure 6, which compares
them with the Class III (k33N)2Ar+ and Da2Ar+ cations10 as
well as the Class II Hy2Ar+ radical cations,13 for which the
Hab values were obtained from band intensities. The ap-
proximately linear log(Hab) versus number of bonds (usually
stated as “distance”) behavior that everyone expects7 is observed,
except for the 1,5-NA bridge, as discussed below. It should be
noted that the substituents M must be attached to the bridge in
a “Kekule” substitution pattern, as they are here, for this to
occur. The bridges considered here lead to large Hab values
E
ꢀmax
(M-1 cm-1
µ12
(Debye)
dab
(Å)
dNN
(Å)a
op
(cm-1
bridge
1,4-PH
2,6-NA
2,6-AN
2,7-M2-FL 6790
4,4′-BI
)
)
dab/dNN
10820
8500
7380
20300
55200
39900
16470
9920
4.66
7.60
6.85
1.94
3.15
2.85
5.60 0.35
7.81 0.40
10.26 0.28
5.7-5.9 2.4-2.5 9.75 0.25-0.26
6900
6800
6.09
4.02
2.54
1.68
9.91 0.26
6.34 0.26
1,5-NA
6380
a From UHF/AM1 calculations.
Discussion
(13) (a) Nelsen, S. F.; Ismagilov, R. F.; Powell, D. R. J. Am. Chem. Soc. 1997,
119, 10213. (b) Nelsen, S. F.; Ismagilov, R. F.; Gentile, K. E.; Powell, D.
R. J. Am. Chem. Soc. 1999, 121, 7108. (c) Nelsen, S. F.; Trieber, D. A. II;
Ismagilov, R. F.; Teki, Y. J. Am. Chem. Soc. 2001, 123, 5684.
Hab Values. The bridge size effect on Hab ) Eop/2, displayed
versus the number of bonds between the nitrogens for the Class
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A R T I C L E S
Nelsen et al.
Figure 4. Optical spectra for the nine-bond-bridged dinitroaryl radical anions bridged by 2,6-anthracenediyl, 9,9-dimethyl-2,7-fluorenediyl, and 4,4′-biphenyldiyl
groups at room temperature in DMF.
Figure 5. Comparison of the optical spectra for the 1,5- and 2,6-dinitronaphthalene radical anions at room temperature in DMF.
because the second M substituent is attached at a carbon that
formally bears a large coefficient in the monosubstituted radical
ion, [M-Ar]•(+/-). This is called a Kekule substitution pattern
by people considering magnetic interactions between spin-
bearing centers14 because, for example, the formally “•OArO•”
compounds with these bridges are quinones, with all electrons
paired that have large energy gaps to diradical excited states.
In contrast, non-Kekule substitution pattern examples having
1,3-PH and 2,7-NA bridges, where the second O• is attached
at a carbon at a Hu¨ckel node in [O•-Ar], have to be written
with diradical Kekule structures (or small rings), have tiny
electronic interactions through the bridge, and are ground-state
triplet species. We shall discuss non-Kekule substitution pattern
(NO2)2Ar•- IV compounds in future work.
It will be noted from Figure 6 that something in addition to
distance even for Kekule substitution pattern compounds is
clearly significantly involved in determining Hab, because the
five-bond 1,5-NA bridge not only leads to a smaller coupling
than the 2,6-NA one, it is also smaller than all three of the nine-
bond bridge examples studied. A similar pattern is calculated
to occur even for the untwisted diamino radical cations,15 and
the low coupling for the 1,5-NA bridge seems most easily
considered by considering the related quinones. The order of
the couplings in the dinitroaromatics may be noted to be that
obtained by considering the 1,5-NA-bridged compound as hav-
ing 11 bonds between the nitrogens, that is by counting around
(14) Rajca, A. Chem. ReV. 1994, 94, 871.
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Near-IR Spectra of Dinitroaromatic Radical Anions
A R T I C L E S
Figure 6. Plot of log(Hab) versus number of connecting bonds for organic
IV compounds: The five-bond bridge is 1,4-PH, the seven-bond bridge
2,6-NA, and the nine-bond bridge 4,4′-BI, except as noted for the two dinitro
compounds shown as open diamonds.
the alternating double and single bond array instead of across
the shorter distance of the single-bonded five-bond pathway.
Figure 7. Plot of log(Hab) versus the number of bonds between the
nitrogens, counted around the periphery for the 1,5-naphthalene derivative,
for delocalized intervalene dinitroaromatic anions.
Each carbonyl group in the 1,5-isomer is substituted meta (to
the other carbonyl group) on the six-membered ring to which
it is attached, which is a non-Kekule substitution pattern that
leads to small coupling. The five-bond shortest pathway is not
functional for coupling and is replaced by the 11-bond Kekule
pathway. We also show a plot of the log(Hab) values versus
this “bonds” count as Figure 7. We note that the plot is
significantly curved, so log(Hab) is not linear with the number
of bonds even for the largest Hab benzene, naphthalene, and
anthracene examples. The logarithmic dependence upon distance
was derived for bridges that consist of repeating units. Although
double and triple bonds, 1,4-benzene diyl units, and their
combinations do lead to nearly linear plots of log(Hab) versus
number of bonds or distance, even this linear fused ring aromatic
series leads to quite noticeable deviations from a linear log
relationship.
A notable aspect of Figure 6 is that (NO2)2Ar- and Da2Ar+
lead to such similar Hab values. The nitro and dianisylamine
charge-bearing units have almost nothing in common structur-
ally, but the two-state model does not consider M group
structure and should allow quantitative evaluation of the charge-
bearing unit electronic interactions of these structurally dis-
similar compounds. Da and NO2 groups do share one structural
feature: they have a single nitrogen attached to the aromatic
bridge that bears much of the spin but has substantial charge
delocalization onto the other groups attached to nitrogen.
Figure 8. Comparison of the PH-bridged NO2- and difluorodioxaborine-
centered radical anions.
This is seen to be enough similarity to give them comparable
Hab values, although the (NO2)2Ar- compounds have slightly
larger ones for all three bridge sizes studied. An even closer
congruence of Hab values for PH-bridged IV compounds occurs
for 1,4-(NO2)2Ar- and the recently reported difluorodioxaborine
radical anion Db2PH- (studied in acetonitrile);16 their optical
spectra are compared in Figure 8. Although there is even less
structural similarity in the charge-bearing units than between
Da and NO2 (which are at least both nitrogen-centered), the
compounds in Figure 8 have Hab values that only differ by 25
cm-1 (0.5%), with that for (NO2)2PH- in DMF being slightly
smaller. Figure 2 emphasizes, however, that Hab is not exclu-
sively determined by the bridge; examples are shown that differ
by over 3300 cm-1
.
It will be noted from Table 1 that Hab is about 55 cm-1
smaller for the 9,9-dimethyl-2,7-dimethylfluorenediyl-bridged
compound than for the 4,4′-biphenyldiyl-bridged one (FL/BI
(16) (a) Risko, C.; Barlow, S.; Coropceanu, V.; Halik, M.; Bredas, J.-L.; Marder,
S. R. Chem. Commun. 2003, 194. (b) We thank Professor Barlow for
providing the optical spectrum of Db2PH- for determination of µ12 and
(15) Unpublished results of semiempirical AM1 calculations.
hence dab.
9
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A R T I C L E S
Nelsen et al.
ratio 0.98). Since the fluorenediyl ring prevents twisting about
the central bond and Hab is expected to be proportional to the
cosine of the twist angle at this bond, one might have expected
Hab to be larger for the fluorenediyl compound. In fact, Hab is
signficantly larger for the fluorenediyl-bridged Hy-centered
radical cation than for the biphenyldiyl-bridged one (estimated
FL/BI ratio 1.13).13b In principle, all the charge-bearing units
(CBU) and bridge orbital interactions will contribute to Hab.17
The total Hab is the sum of all the contributions. However, these
contributions are weighted by 1/∆E, the energy difference
between each CBU and bridge orbital involved. The smallest
energy gap contribution therefore dominates Hab, and Newton
has suggested designating systems such as Hy2Ar+, that have
the CBU SOMO, bridge HOMO energy gap smallest as “hole
transfer” ones, and systems such as the (NO2)2Ar- ones
considered here, which have the CBU SOMO, bridge LUMO
energy gap the smallest, as “electron transfer” ones.
Figure 9. Comparison of the relationship between dab and Hab for 1,4-
PH-bridged IV compounds.
for Da2PH+ and (NO2)2PH-, the dab value obtained for the
latter is significantly smaller. For the other anion considered
here, Db2PH-, the dab value obtained is 1.6 Å (it would rise
to 1.8 Å if ꢀmax for this rather unstable species had been
underestimated by 20%) and even smaller than that for
(NO2)2PH-. The lower values for the nitro and difluoro-di-
oxaborine-centered compounds are consistent with anions
showing smaller dab values than cations, although why this might
happen is not clear. From the data of Table 1, not only is dab
a
rather small fraction of dNN, but also the values obtained are
smaller for all three nine-bond-bridged dinitro compounds (4,4′-
BI and 2,6-AN) than for the 7-bond 2,6-NA-bridged one. Such
an inversion of dab as the bridge size increases does not occur
for the Da-centered cations.10 Although the anions studied here
are less stable than the previously studied cations and could
not be purified by crystallization, the ꢀmax values obtained for
different experiments are reproducible to about 10%, thus, we
do not believe that either the large deviation for the nitro
compound point in Figure 9 or the anomalously small values
for the nine-bond-bridged compounds are caused by experi-
mental error in calculating dab (which would be caused by errors
in the concentration). One might question whether the concept
of the two-state model dab value for these delocalized com-
pounds is especially useful, but the quite remarkable success
of the two-state model for quantitatively interpreting electron-
transfer rate constants for Class II systems13 indicates that it
works rather well, and these are the results it gives for
delocalized systems.
Apparently the change in the dominant ring orbital for these
systems is more than enough to offset the effect of twisting at
the central bond.
Electron-Transfer Distance on the Diabatic Surfaces (dab).
According to the generalized Mulliken-Hush theory of Cave
and Newton,8 when a compound is delocalized, the electron-
transfer distance on the adiabatic surfaces (d12) drops to zero;
therefore, the electron-transfer distance on the diabatic surfaces
(dab) may be directly obtained from the transition dipole moment
µ12 using dab (Å) ) 2µ12(Debye)/4.8032. Values of dab
determined by this method are included in Table 1. Also listed
is the distance between the nitrogen atoms that are bonded to
the bridge (dNN), which is the “edge-to-edge” distance between
the charge-bearing units, that has very often been used as dab
in calculating Hab values for localized IV compounds.9 The dab
values for 1,4-PH-bridged compounds with the charge-bearing
units under discussion are compared visually in Figure 9. We
note that dab for the same bridge is obviously dependent upon
the Hab that the charge-bearing unit causes, decreasing signifi-
cantly as Hab increases. Even for the charge-localized Class II
Hy-centered compound, where the Hab value is significantly
smaller, dab is significantly smaller than dNN,
18 and the dab values
for delocalized compounds obtained from µ12 very clearly drop
as Hab increases.
As emphasized in our discussion of the delocalized Da-
centered compounds,10 dab depends on the structure of the
charge-bearing units, and the use of dNN as a measure of dab
leads to large errors when used for organic compounds. It seems
obvious from this plot that dNN would only be an appropriate
ET distance in the limit of small Hab, which is rarely the case
for IV compounds. Note also that despite the similarity of Hab
Intervalence Band Vibrational Structure and λv. The line
widths of the four 1,4-PH-bridged IV compounds shown in
Figure 2 are very different. The localized Hy2PH+ has by far
the largest line width and the nearly Gaussian shape (high-energy
side only slightly broader than the low-energy side) of most
other Class II IV compounds. Da2PH+ has a narrower band
that is considerably broader on the high-energy side than the
low-energy side9 but has no vibrational structure resolved. As
discussed in detail elsewhere, although Da2PH+ is delocalized,
it has a 2Hab/λ ratio not very far from the Class III/II borderline
value of 1. For example, the nine-bond Da2-4,4′-BI-bridged
species appears to be delocalized in methylene chloride but
localized in acetonitrile.10 The more strongly delocalized k33N-
and NO2-centered species show partially resolved vibrational
structure, although the latter clearly has narrower lines. The band
resolution is slightly better for Db2PH- than for (NO2)2PH-
(17) Newton, M. B. Chem. ReV. 1991, 91, 767.
(18) Nelsen, S. F.; Newton, M. D. J. Phys. Chem. A 2000, 104, 10023.
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Near-IR Spectra of Dinitroaromatic Radical Anions
A R T I C L E S
Table 2. Comparison of the (NO2)2-PH- IV Band Simulation Parameters with a Density Functional Theory Vibrational Frequency
Calculation
-1
simulation (Γ)556 cm
)
B3LYP/6-31+G* calculation
-1
-1
hνq (cm-1
)
∆
q
λv(q) (cm
)
vibration number
frequency (cm
)
rel. Raman intensity
description of vibration
310
590
990
0.58
0.79
0.86
52.1
184.1
366.1
7
12
13
16
21
25
32
38
42
306
557
623
695
847
1119
1394
1639
3246
0.04
0.001
0.003
0.03
0.07
0.59
0.23
1.00
0.05
CNO2,CNO2 stretch
NO2 in plane rock
chair deformation of ring
O’s out + C2C6 in
O’s out + C2C6 out
C-H bend + C1,4 stretch
C1,4-N stretch
C2-C3 stretch
CH stretch + C6 breathe
1460
1640
(3200)
0.53
0.47
0.21
205.1
181.1
(64.0)
(see Figure 8) with separation of the maximum from the features
of largest separation of 1460 and 1420 cm-1, respectively.
Bre´das and co-workers have recently estimated vibrational
reorganizational energies (λv) for electron transfers by analysis
of spectra that show partial resolution of vibrational fine
structure, including the photoelectron spectra of anthracene,
tetracene, and pentacene,19 and the absorption spectrum of
Db2PH-.16 A problem with doing this is that such spectra can
be fit with few modes (Bre´das and co-workers used three for
the compounds mentioned), but many more are probably
involved, quite possibly leading to underestimation of the
reorganization energy. Bre´das and workers’ λv estimates from
vibrational analysis of the photoelectron spectra of acenes are
51-59% as large as the calculated values.19 Our resonance
Raman study of (k33N)2PH+ identified nine symmetrical
vibrational modes (each having significant calculated nonreso-
nance Raman intensity) contributing to its IV band and gave
the experimental ∆ values for each which allow accurate
calculation of the λv value.11 Resonance Raman data are not
available for the much less stable dinitroaromatic radical anions
studied here. Nevertheless, obtaining a fit to an absorption
spectrum that shows vibrational structure places limits on the
size of λv that is probable, and we analyze the spectrum of the
dinitro compounds studied here to estimate λv, allowing estima-
tion of 2Hab/λv.
In the absence of resonance Raman data, only a simplified
fitting treatment is appropriate, because both the frequencies
and their dimensionless displacements (∆q) must be assumed.
We used Zink’s simulation program abs/emis/Raman (see
Experimental Section) that assumes pure harmonic oscillators,
no change in force constant between the ground and excited
states, and neither vibrational nor electronic state coupling,
assumptions that do not have to be made when resonance Raman
excitation profiles are available.11,20 Using these assumptions,
the dimensionless displacement for a mode is related to the
Huang-Rhys factor (S), which is the intensity ratio of the first
vibrational component to the second component,21 by the
vibrations present in the compound; instead, observed features
occur between values of normal modes.20 Although the region
of the spectrum of (NO2)2-PH- showing the three maxima could
be fit modestly well using only three modes (1590, 960, and
580 cm-1, producing λv ) 1050 cm-1, see Supporting Informa-
tion for details), more modes are doubtless involved. A density
functional theory calculation of (NO2)2-PH- at the B3LYP/
6-31+G* level gave a very slightly asymmetrical structure with
nine modes having the significant nonresonance Raman intensity
expected for modes that would contribute to the IV transition
(see Table 2, and Supporting Information for more detail). As
documented in the Supporting Information, rather similar fits
to the region of the three maxima can be obtained with three,
four, five, and six modes, chosen to be reasonably close to the
calculated modes or averages of them, with ∆q values chosen
to still fit the spectrum. The fits obtained are certainly not
unique, and a good fit could be obtained with other hνq,∆q
combinations. Furthermore, smaller frequencies can to some
extent be incorporated into the damping parameter, Γ, which is
the full width at half-height employed for the components of
the spectrum. We found best fit to the low-frequency region by
using two modes with frequencies below 900 cm-1 and using
a relatively small Γ value (556 cm-1). The five-mode fit for
which parameters are shown in Table 2 is compared with the
observed spectrum in Figure 10. The only Raman-active C-H
stretching mode is also included in Table 2 because it involves
a small but noticeable breathing motion of the benzene ring
and hence could be involved in the optical transition. Fit to the
experimental spectrum is improved by including a small ∆q
mode near this frequency (see Supporting Information), although
the high-energy end of most optical transitions begins to overlap
with other bands, so it is not really clear whether a better fit to
this region is a good criterion for including high-frequency
modes. Inclusion of this CH mode raises the λv estimate from
989 to 1059 cm-1 (see the summary in Table 3). The estimated
λv is relatively insensitive to the number of modes used to fit
the spectrum, and we include only two fits for each in Table 3,
one with high-frequency modes and one without. The optical
spectrum of (NO2)2PH- is therefore consistent with a vibrational
reorganization energy for the IV transition of this Class III IV
compound of 990-1060 cm-1, comparable to those calculated
for formation of acene radical cations (about 1100 cm-1 for
anthracene, 910 for tetracene, and 800 for pentacene).19 The
value of 2Hab/λ for (NO2)2PH- is therefore estimated at over
10, making it only slightly smaller than the value of 11.6
obtained from the resonance Raman study of the p-phenylene-
diamine derivative (k33N)2PH+.11 Despite slightly stronger
2
2
relation S ) 1/2∆q , so that λV(q) ) 1/2∆q hν(q). Another factor
that must be considered in analyzing spectra to extract λv is the
“missing mode effect” (MIME) that ensures that the vibrational
features observed in the optical spectrum do not correspond to
(19) Coropceanu, V.; Malagoli, M.; da Silva Filho, D. A.; Gruhn, N. E.; Bill,
T. G.; Bre´das, J.-L. Phys. ReV. Lett. 2002, 275503.
(20) Zink, J. I.; Shin, K.-S. K. Molecular Distortion in Excited Electronic States
Determined from Electronic and Resonance Raman Spectroscopy. AdV.
Photochem. 1991, 16, 119.
(21) Brunold, T. C.; Gu¨del, H. U. Luminescence Spectroscopy. In Inorganic
Electronic Structure and Spectroscopy; Solomin, E. I., Lever, A. B., P.,
Eds; Wiley: New York, 1991; Vol. 1, p 259.
9
J. AM. CHEM. SOC. VOL. 125, NO. 41, 2003 12499

A R T I C L E S
Nelsen et al.
Figure 10. Comparison of the spectrum of 1,4-(NO2)2-PH- (black) with a simulation (red) using the five-mode calculation summarized in Table 2.
Table 3. Summary of λv Values Obtained from Fitting Optical Spectra of Dinitroaromatic Radical Anions
-1
-1
bridge
modes
frequencies (cm
)
λv (cm-1
)
G (cm
)
E
00 (cm-1
)
2H /λv
ab
1,4-PH
5
6
6
8
6
8
6
1640, 1460, 990, 590, 310
3200,1640,1460,990,590,310
1630,1470,1060,850,610,310
3240,2250,1630,1470,1060,850,610,310
1600,1470,1060,850,610,310
3000,2160,1600,1470,1060,830,610,310
1660,1150,940,670,550,300
3000,2200,1650,1160,940,570,550,300
1640,1490,1110,850,610,310
3240,2310,1640,1490,1110,850,610,310
1610, 1430, 980, 610,310
3250,2200,1620,1430,980,610,310
989
1059
788
888
738
872
992
1286
1216
1919
912
556
556
506
506
559
559
639
666
849
849
994
1016
10800
10800
8470
8470
7340
7340
6760
6760
6770
6770
6690
6700
10.9
10.2
10.7
9.5
9.9
8.5
6.8
5.3
5.6
3.5
2,6-NA
2,6-AN
2,7-M2-
-FL
4,4′-BI
6
8
5
7
1,5-NA
7.3
5.6
1163
delocalization, the optical spectrum of (k33N)2PH+ shows less
resolution, presumably because of more modes contributing in
the presence of the 21-atom dialkylamino M unit than for the
three-atom nitro one. The combination of larger line width
caused by smaller 2Hab/λ and more active modes caused by
the 31-atom dianisylamino M group causes the broad envelope
observed for 1,4-Da2PH+ absorption (Figure 2).
the other compounds. Miller, Closs, and co-workers have
discussed the importance of such torsional motion, to which
they attribute a λv increment of about 1050 cm-1 when biphenyl
is a charge-bearing unit in their σ-bond-bridged quinone,
biphenyl systems.22
Summary
The vibrational structures observed for 2,6-(NO2)2 NA- and
2,6-(NO2)2 AN- are rather similar to that of their PH analogue,
although the maximum observed near 950 cm-1 decreases in
importance, and the λv estimated from the fitting parameters
drops, but not as much as Hab, so that 2Hab/λv decreases as aryl
bridge size increases. The spectra of 2,7-(NO2)2-M2FL and 4,4′-
(NO2)2-BI- are noticeably broader than those of the other cases
and require a larger Γ for their fit. Their 2Hab/λv values are
also significantly smaller. It appears that Γ increases significantly
as Hab/λv approaches the Class II, Class III borderline value of
1, although other factors may be involved in determining the Γ
required for fitting.
The value of λv obtained from the fit is larger for 1,5-(NO2)2-
NA- than for its 2,6-isomer, which might be caused by twisting
the CAr-NO2 bonds in this more hindered compound; AM1
calculations optimize the 1,5-isomer with the NO2 group twisted
10.6° out of the ring plane. 4,4′-(NO2)2-BI- has an even larger
λv, which we suggest is probably a result of the twisting mode
about the central CC bond, a structural feature not present in
Dinitroaromatic radical anions of the Kekule substitution
pattern are delocalized (Class III) IV compounds, as demon-
strated by the vibrational fine structure observed in their near-
IR absorption bands. Their electronic couplings (Hab) decrease
as expected as the number of bonds between the nitrogen atoms
increase for the bridges 1,4-PH (five bonds), 2,6-NA (seven
bonds), 2,6-AN (nine bonds), but the five-bond 1,5-NA system
has a smaller electronic coupling than all of these systems. It is
about the size expected when counting the 11 bonds around
the CdC-C periphery instead of across the formally single-
bonded five-bond pathway. The ET distances on the hypothetical
diabatic surfaces (dab) obtained from the transition dipole
moments using generalized Mulliken-Hush theory are 26-40%
of the N,N distances. The physical significance of these numbers
is not obvious, but the nitro-substituted radical anions show
much smaller dab at comparable Hab than do IV radical cations.
(22) Miller, J. R.; Paulson, B. P.; Bal, R.; Closs, G. L. J. Phys. Chem. 1995,
99, 6923.
9
12500 J. AM. CHEM. SOC. VOL. 125, NO. 41, 2003

Near-IR Spectra of Dinitroaromatic Radical Anions
A R T I C L E S
Table 4. Summary of Band Maxima for Delocalized (NO2)2Ar-
1/2
1000 ln(10)3hc
8π3NA
ꢀ(νj)
νj
|µ12| ) N
dνj
)
∫
-1
hνmax (cm-1
)
ꢀmax (M-1 cm-1
)
∆hν (cm
)
ꢀ ratio
(
)
band
bridge
1/2
1,4-PH
10820
11750
12270
8500
9470
10050
7380
8900
6790
8365
6900
8440
6800
8120
20300
11910
10250
55200
19460
19860
39870
14320
16470
9257
-
930
1450
-
-
ꢀ(νj)
νj
N0.09584
dνj
(1)
0.59
0.50
-
∫
band
(
)
2,6-NA
2,6-AN
It allows evaluation of bands showing fine structure, which cannot
be done properly using the more common formulation that puts the
wavenumber (νj) divisor outside the integral or Hush’s simple formula
for Gaussian-shaped bands.7a The constant given is that required for
evaluation of µ12 in Debye using νj in cm-1. We also include in eq 1
the solvent refractive index (n) correction, N (eq 2), to ꢀ that was first
incorporated into interpreting ET using optical analysis by the Kodak
group.27
970
1550
-
0.35
0.36
-
1520
-
0.36
-
9,9-Me2
FL
4,4′-BI
1575
-
0.56
-
9920
8480
6380
4030
1540
0.85
1,5-NA
1320
0.63
x
3
n
N )
(2)
(n2 + 2)
The DFT calculation used the Gaussian program,28 the band
integrations using eq 1 were done with software written by A.E.K.,
and the spectral simulations including vibrational fine structure (Table
3, Figure 10, and Supporting Information) were done with program
abs/emis/Raman, obtained from J. I. Zink, which is based on a time-
dependent Hamiltonian spectral analysis.20
The dinitroaryl radical anion IV bands show good enough
vibrational resolution to extract estimated λv values, which are
about 1000 cm-1 for the PH-bridged system and decrease as
bridge size is increased for 1,4-PH, 2,6-NA, and 2,6-AN bridges.
The λv is larger for both the 1,5-NA-bridged compound (twisted
at the CAr-NO2 bonds) and the 4,4′-BI-bridged one (twisted at
the central bond), and their intrinsic line widths (as represented
by the Γ fitting parameter) are also larger.
Acknowledgment. We thank the National Science Foundation
for financial support through Grants CHE-9988727 and CHE-
0240197 (S.F.N.) and the Portuguese F.C.T through I.S.T-Centro
de Processos Qu´ımicos and PRAXIS/2/2.1/QUI/306/94 Project
(J.P.T.). We thank Gu¨nter Grampp (Techn. Univ. Graz) for
supplying the 2,6-dinitronaphthalene sample employed. We
thank Jeffrey Zink (UCLA) for supplying his program abs/emis/
Raman and his graduate students Susan Baily and Jenny
Lockhard for benchmarks and preliminary calculations.
Experimental Section
Commercial 1,4-dinitrobenzene was purified by elution with toluene
from a short column packed with alumina, followed by recrystallization
from ethanol. 2,6-Dinitronaphthalene was kindly supplied by G.
Grampp. The 2,6-dinitronaphthalene was prepared from commercially
available 2,6-dihydroxynaphthalene (EGA-Chemie, Germany) by treat-
ing it with aqueous ammonia in an autoclave forming the 2,6-
diaminonaphthalene, which was then oxidized to the final dinitronaph-
thalene23 (mp 278 °C, lit.23b 279 °C). 2,6-Dinitroanthracene was prepared
by pyrolysis of a mixture of 2,6- and 2,7-dinitro-9,10-ethano-9,10-
dihydroanthracene24 and separated from the 2,7-dinitro isomer by a
combination of column chromatography and fractional recrystallization
Supporting Information Available: 1,4-(NO2)2-PH- B3LYP/
6-31+G* vibrations and displacement vector pictures for the
Raman-active bands, six calculated fits for the 1,4-(NO2)2-PH-
spectrum, and the fits corresponding to the other entries in Table
3 (PDF). This material is available free of charge via the Internet
at http://pubs.acs.org.
1
from chlorobenzene, mp >300°; m/z 268 (M+); H NMR (300 MHz;
DMSO-d6) δ 9.28 (s, 2H1,4), 9.20 (s, 2H9,10), 8.42 (d, 2H3,6 J ) 9.3
Hz), 8.42 (d, 2H4,8 J ) 9.3 Hz). 4,4′-Dinitrobiphenyl was prepared
by deamination of commercial 4,4′-dinitro-2-biphenylamine, mp )
239-240 °C (lit.25 239 °C).
JA036066M
(23) (a) Chatt, L.; Wayne, W. P. J. Chem. Soc., Perkin Trans. 1 1946, 33. (b)
Vesely, V.; Jakes, M. Bull. Soc. Chim. France 1923, 33, 942.
(24) Tanida, H.; Ishitobi, H. Tetrahedron Lett. 1964, 15, 807.
The radical anions were prepared in vacuum-sealed glass cells
equipped with an ESR tube and a quartz optical cell. Reduction was
achieved by contact with 0.2% Na-Hg amalgam. The nitro compound,
a 100-fold excess of commercial cryptand, and the Na-Hg amalgam
were introduced in different chambers of the cell under nitrogen. The
cryptand was degassed by melting under high vacuum before addition
of DMF. The concentration of the samples was determined spectro-
photometrically before reduction. UV/vis/NIR spectra were recorded
at room temperature with a Shimadzu 3101 PC spectrometer at several
stages of reduction, so that the radical anion oxidation level spectrum
could be selected.
(25) Gull, H. C.; Turner, E. E J. Chem. Soc. 1929, 491.
(26) Liptay, W. Angew. Chem., Int. Ed. Engl. 1969, 8, 177.
(27) (a) Gould, I. R.; Noukakis, D.; Gomez-Jahn, L.; Young, R. H.; Goodman,
J. L.; Farid, S. Chem. Phys. 1993, 176, 439. (b) Gould, I. R.; Young, R.
H.; Albrecht, A. C.; Mueller, J. L.; Farid, S. J. Am. Chem. Soc. 1994, 116,
8188. (c) Although the Kodak group first used a larger factora they very
soon argued that the smaller factor shown in (3) is a better one to use,b but
also cautioned that the true solvent effect is proably more complex.
(28) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M.
A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A. J.; Stratmann,
R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin,
K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi,
R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.;
Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.;
Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz,
J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.;
Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham,
M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.;
Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.;
Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian
98, Revision A.7; Gaussian, Inc.: Pittsburgh, PA, 1998.
The observed optical band positions and maxima are summarized
in Table 4.
We evaluated µ12 using Liptay’s formulation of the integral over
the absorption band (eq 1).26
9
J. AM. CHEM. SOC. VOL. 125, NO. 41, 2003 12501