Hole Transfer Processes in meta- and para-Conjugated Mixed Valence Compounds: Unforeseen Effects of Bridge Substituents and Solvent Dynamics

Article abstract of DOI:10.1021/jacs.7b01650

To address the question whether donor substituents can be utilized to accelerate the hole transfer (HT) between redox sites attached in para- or in meta-positions to a central benzene bridge, we investigated three series of mixed valence compounds based o

Full text of DOI:10.1021/jacs.7b01650

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Article
Hole Transfer Processes in meta- and para-
Conjugated Mixed Valence Compounds: Unforeseen
effects of bridge substituents and solvent dynamics
Julian Schaefer, Marco Holzapfel, Boryana Mladenova, Daniel Kattnig, Ivo
Krummenacher, Holger Braunschweig, Günter Grampp, and Christoph Lambert
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.7b01650 • Publication Date (Web): 12 Apr 2017
Downloaded from http://pubs.acs.org on April 13, 2017
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Hole Transfer Processes in meta- and para-Conjugated Mixed
Valence Compounds: Unforeseen effects of bridge substituents and
solvent dynamics
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Julian Schäfer1, Marco Holzapfel1, Boryana Mladenova2, Daniel Kattnig3, Ivo
Krummenacher4, Holger Braunschweig4, Günter Grampp2*, and Christoph Lambert1*
1Institut für Organische Chemie and Center for Nanosystems Chemistry, Universität
Würzburg, Am Hubland, D-97074 Würzburg, Germany.
2Institute of Physical and Theoretical Chemistry, Graz University of Technology,
Stremayrgasse 9, A-8010 Graz, Austria.
3Physical and Theoretical Chemistry Laboratory, University of Oxford, South Parks Road,
Oxford, OX1 3QZ, U.K.
4Institut für Anorganische Chemie, Universität Würzburg, Am Hubland, D-97074 Würzburg,
Germany.
Abstract
To address the question whether donor substituents can be utilized to accelerate the hole
transfer (HT) between redox sites attached in para- or in meta-positions to a central benzene
bridge we investigated three series of mixed valence compounds based on triarylamine
redox centers that are connected to a benzene bridge via alkyne spacers at para- and meta-
positions. The electron density at the bridge was tuned by substituents with different electron
donating or accepting character. By analyzing optical spectra and by DFT computations we
show that the HT properties are independent of bridge substituents for one of the meta-
series, while donor substituents can strongly decrease the intrinsic barrier in the case of the
para-series. In stark contrast, temperature-dependent ESR measurements demonstrate a
dramatic increase of both the apparent barrier and the rate of HT for strong donor
substituents in the para-cases. This is caused by an unprecedented substituent-dependent
change of the HT mechanism from that described by transition state theory to a regime
controlled by solvent dynamics. For solvents with slow longitudinal relaxation (PhNO2,
oDCB), this adds an additional contribution to the intrinsic barrier via the dielectric relaxation
process. Attaching the donor substituents to the bridge at positions where the molecular
orbital coefficients are large accelerates the HT rate for meta-conjugated compounds just as
for the para-series. This effect demonstrates that the para-meta paradigm no longer holds if
appropriate substituents and substitution patterns are chosen, thereby considerably
broadening the applicability of meta-topologies for optoelectronic applications.
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Introduction
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Meta- vs. para-conjugation is one of the key concepts used in organic chemistry to tune
electronic communication along extended -systems.1 Meta-conjugation is generally believed
to be weaker, because of destructive quantum interference of standing waves along the
conjugation path, while there is constructive interference in the para-case.2 The paradigm of
strong para- and weak meta-conjugation has been a useful guideline for the design of
conjugated materials for decades. In this article we address this basic theme by investigating
thermally induced superexchange hole transfer (HT) processes in organic mixed valence
(MV) radical cations by optical and ESR spectroscopy in solution. In these MV species two
redox centers are connected via a bridging benzene ring with para- or meta-topology (Fig.
1).3 We varied the electron density of the benzene bridge by substituents, hereafter referred
to as X, in order to probe electronic bridge effects for the two different substitution patterns.
In the case of a superexchange HT mechanism, one expects that electron donors lower the
energy of virtual bridge states and, thus, increase the electronic coupling between the redox
centers thereby accelerating the HT. Electron acceptors are supposed to behave oppositely.4
We also expect that the solvent will exert a distinct influence on the HT dynamics by its
polarity and also by solvent dynamic effects, which are related to the sluggish reorientation of
the solvent dipoles on the timescale of the HT. With these aims in mind, we have studied
three series of compounds as shown in Fig. 1 in several solvents. The electronic character of
the substituents was varied from strongly electron donating (X = OMe) to strongly electron
accepting (X = NO2). In two series, pX and mX, the positions of the two substituents X at the
central benzene ring are the same (positions 2 and 5; see Fig. 1, for the syntheses, see SI),
while in the mX46 series X is located at the 4- and 6-positions. This second meta-series was
included to reveal the influence of the position of X. In all compounds we used triarylamines
as redox centers because of their high radical cation stability and the important role they play
in MV chemistry and optoelectronic devices.4-5
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In order to delineate the energetic factors governing the HT in MV compounds, we use the
standard two-state model with harmonic diabatic states, which are coupled to yield the
adiabatic double-well ground state potential as shown in Fig. 1a.6 The splitting of the
adiabatic potentials at the position of the avoided crossing, i.e. at the transition state, is twice
the size of the electronic coupling V between the diabatic states. This coupling is a measure
of the electronic communication between the redox centers. The optically induced HT from
one minimum of the double well to the excited state potential surface is associated with an
intervalence charge transfer (IV-CT) absorption band in the NIR spectral region. This
optically induced HT moves a hole from the oxidized triarylamine redox center to the neutral
one. The IV-CT energy corresponds to the total reorganization energy  which comprises an
internal part i and a solvent contribution, o. An alternative HT pathway entails the thermally
induced transfer between the two minima of the ground state adiabatic potentials via the
transition state. In this process, a barrier with relative energy G* (see Fig. 1a) is to be
surmounted. This thermally induced HT is the focus of the present study.
First we will analyze the steady-state optical spectra of the radical cations of mOMe46 and
the pX and mX compounds. This will provide information about reorganization energies and
electronic couplings, which will be compared to DFT-computed properties. We will then
present the HT rate constants and HT barriers as measured by temperature dependent ESR
spectroscopy in diverse solvents with different dielectric responses. These measurements
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will inform about the HT dynamics, which for some cases will be dominated by the solvent
dynamic effect.
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Figure 1. Mixed valence compounds, potential energy diagram and optical spectra. (a) Diabatic (red,
dashed) and adiabatic (black) Gibbs energy potentials for a degenerate mixed valence radical cation.
The charge distribution and the orientation of solvent dipoles (dark blue arrows) are sketched for three
different situations: the hole located at the left triarylamine moiety, at the transition state, and at the
right triarylamine moiety. (b) Reduced Vis-NIR spectra of all pX compounds and of mOMe46 in
PhNO2. Gaussian fits to the IV-CT bands are given as dashed lines and magnified in the inset.
Results
Optical spectroscopy. Reduced7 absorption spectra of oxidized mOMe46 and the pX and
mX radical cation MV compounds were obtained after oxidation of neutral precursor
compounds in PhNO2 with SbCl5 (see Experimental and the SI for additional spectra and
their deconvolution in Figs. S1-S14).
These spectra display a Gaussian-shaped IV-CT band in the NIR with a maximum at ca.
7000-9000 cm-1 (see Fig. 1b). Depending on the nature of the bridging unit between the
triarylamines, a second band, associated with the HT from the oxidized triarylamine to the
bridge, is also visible at somewhat higher energy than the IV-CT band (ca. 10000 cm-1). This
“bridge band” strongly overlaps with the IV-CT band and the nearby * band of the
triarylamine.4,5b For the para-series the IV-CT bands are pronounced and shift slightly to
lower energies as the electron donating character of X is increased. By contrast, the IV-CT
bands for the meta-series are very weak and are hard to discern from the baseline, indicating
a much smaller electronic coupling (for spectra of mX see SI, Fig. S2). An exception is
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mOMe46, which also displays a sizable IV-CT band (Fig. 1b). For the para-series and
mOMe46, Mulliken-Hush theory was used to calculate the electronic coupling V12 from
analysis of the IV-CT band using DFT computed dipole moment differences.8
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In the framework of Marcus-Hush theory the electronic coupling V12 is given by
~
abmax
~
12
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V12 
. Here, max is the energy of the IV-CT band. The transition dipole moment ab
is the projection of the adiabatic transition dipole moment of the IV-CT band on the diabatic
12  a2b  4a2b
dipole moment difference of the fully localized (noninteracting)
diabatic states. While ab is obtained by integrating the IV-CT band, we used DFT-computed
adiabatic dipole moment difference for ab (see section below).
The so evaluated couplings are given in Table 1. We also recorded the absorption spectra of
the para-series and mOMe46 in ortho-dichlorobenzene (oDCB), which is significantly less
polar than PhNO2 and gives rise to much smaller solvent reorganization energies.
Consequently, the IV-CT band shifts to lower energies, e.g. for pOMe from 7280 cm-1 to
4670 cm-1, for pCN from 9310 cm-1 to 6680 cm-1 and for mOMe46 from 6980 cm-1 to 5700
cm-1 (for the corresponding spectra see SI, Figs. S13). In the latter case, this shift leads to a
more distinct IV-CT band, well separated from the bridge band. The IV-CT bands of the para-
series in DCM, which is a solvent of intermediate polarity, display maxima between those
found for PhNO2 and oDCB (see Fig. S14 in the SI).
TD-DFT computations. Due to the low intensity of the IV-CT band of the meta-series
cations, the Mulliken-Hush analysis could not be reliably employed to extract reorganization
and coupling parameters. Thus, we performed UDFT optimizations and TD-DFT
computations for all three series of MV compounds in PhNO2 (see Experimental).9 The
computed dipole moment differences ab between ground and IV-CT state, transition
ab
moments
and transition energies Eab are summarized in Table 2. As can be seen from
the large dipole moment differences ab, all compounds possess a strongly asymmetric and
thus localized charge distribution where one triarylamine is positively charged while the other
is neutral. Within the mX series, the dipole moment difference ab remains constant,
whereas, for the pX series it decreases as the electron donating character of the substituent
X increases. Similarly, the mX46 series shows a very moderate increase in the charge
delocalization on going from X = CN to OMe. The IV-CT transition energy Eab, and thus the
reorganization energy, decreases with increasing electron-donating strengths of X. This trend
excellently agrees with the experimental observation in the para-series, for which data are
ab
available. The transition moments
in the para-series are much larger than those in the
mX series, reflecting a more efficient electronic coupling V12 in the former. The mX46 series
of MV compounds displays intermediate behavior; the transition moments are small for X =
CN and Cl, just as for mX, but rise dramatically to values approaching those of the para-
series for mOMe46.

Using the above calculated data (ab,
and Eab) we estimated the electronic coupling V12
ab
by the Mulliken-Hush formalism as introduced above. With V12 values between 60 and 180
cm-1 for the mX series these couplings are much smaller than for the pX series , for which
V12 is ca. 900 cm-1 for X = NO2 to Cl, but rises for pMe (1140 cm-1) and pOMe (1320 cm-1).
As expected on the basis of the transition dipole moments, the couplings in the mX46 series
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lie between those of the mX and pX series. The magnitude of these couplings places the
thermal HT of all compounds in the so-called adiabatic regime, for which the limiting factor is
the motion over the transition state (possibly subject to solvent dynamics). As discussed in
detail below, this observation dictates the choice of the adequate rate theory for describing
the dynamic HT processes.
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The TD-DFT method was also used to estimate the electronic coupling from half of the
lowest excitation energy Eab(TS)/2 = V12,TS calculated at the geometry of the HT transition
state, which directly corresponds to half the splitting of adiabatic potentials at the avoided
crossing (see Fig. 1a). The values so obtained are summarized in Table 2; the subscript TS
is used to label the transition state-based approach. These couplings are in good agreement
with V12 for the meta-series, but exaggerate the influence of the substituents for the para-
series.
The reorganization energy (= IV-CT energy Eab) and the electronic coupling can be used to
calculate the barrier (see Fig. 1) for the thermally activated HT process via equation (1)
G* = /4-V+V2/
(1)
where  comprises a solvent (o) and an inner-sphere (i) part. For the pX series, we
observe a reduction of the Marcus-Hush barrier on going from pNO2 to pOMe. This is a
direct consequence of the increasing electronic coupling, which not only reduces the barrier
at the avoided crossing, but also increases the charge delocalization. This charge
delocalization leads to a smaller adiabatic charge transfer distance rab = ab/e and thereby
reduces the reorganization energy  = Eab by up to 20% (see Table 2) via its solvent part,
which directly depends on rab (cf. the classical Marcus expression of the outer-sphere
reorganization energy)3c. The latter aspect is usually disregarded in standard electron
transfer (ET) theories, which suggest that the reorganization energy is independent of the
electronic coupling. The mX46 series behaves similarly; in the mX systems these effects are
less pronounced. For the latter, the DFT calculations show small and weakly varying
electronic couplings V12 and Eab decreases by only ca. 900 cm-1 on going from mNO2 to
mOMe, compared to the 1900 cm-1 reduction in the para-series. The impact of this behavior
on the HT barrier becomes obvious when looking at Fig. 2a, where we have plotted the HT
barrier G*MH, the electronic coupling V12, and the hypothetical barrier in the absence of
electronic coupling (=Eab/4, cf equation 1). For the mX series Eab/4 and G*MH agree very
well and are almost independent of the substituent. However, in the para-series, G*MH
decreases strongly for pMe and pOMe, because V12 rises by almost the same amount while
Eab/4 decreases to a lesser extent. The same effects as for pX are observed for mX46 in an
even more pronounced way. For the para-series, analysis of the IV-CT bands and the DFT
computations reveal the same general trend for the electronic coupling V12 and the HT barrier
G*MH.
An alternative way to estimate the HT barrier is to use the energy difference G*TS between
the optimized ground state structure and the symmetric transition state structure which is
readily available from the optimization of the respective structures. The close agreement of
G*TS and G*MH for the para-series (see Table 2) demonstrates the correctness of the
underlying assumption of adiabatic Gibbs energy surfaces constructed from harmonic
potentials, i.e. Marcus Hush theory, and the applicability of Mulliken-Hush theory to estimate
the electronic coupling. However, a closer inspection of Fig. 2b shows that, while G*TS is
slightly higher than G*MH for X = NO2 to Me, this order is reversed for X = OMe. While this
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could be fortuitous, it might also point towards a more complex hypersurface structure at the
transition state. In previous works4,5b we found evidence that, in the case of pOMe, low lying
bridge states distort the ground state hypersurface in a way that leads to the appearance of a
third minimum on the ground state hypersurface (besides the two MV states), for which the
hole is localized at the bridge moiety. This leads to an additional decrease of the TS energy.
One could easily conceive a situation in which this TS becomes one of higher order, a
suggestion that might be indicated by the two imaginary frequencies of the “transition state”
of pOMe (see Table 2).
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The influence of the solvent dielectric properties on the reorganization energy is one of the
decisive aspects in Marcus ET theory, We thus set out to test the performance of the DFT
computations in this regard. We chose pCN as an exemplary MV compound and re-
computed all pertinent quantities from Table 2 in oDCB and in the intermediately polar
dichloromethane (DCM), see Table 3. While the general red-shift of the IV-CT band energy
on going from PhNO2 to oDCB is well reflected in these computations, its magnitude is
underestimated. The (transition) dipole moments and the electronic coupling appear to be
solvent dependent to a much lesser extent. Accordingly, the HT barrier drops from PhNO2 to
oDCB because of the smaller IV-CT band energy, i.e. reorganization energy.
Figure 2. Energy parameters depending on substituents for PhNO2 solvent. (a) DFT computed
potential energy parameters Eab/4 (black symbols), G*MH (blue symbols) and V12 (red symbols) of pX
(dashed lines), mX (solid lines), and mX46 (dash-dotted lines) compounds. The data points for Eab/4
of pX and mX46 are almost superimposed. (b) Hole transfer barriers of pX in PhNO2 determined by
analysis of the IV-CT band, ESR spectra or DFT calculations using the Marcus-Hush (MH) formalism
or explicit calculations at the transition state (TS). (c) The same parameters as in b), in DCM, where
available. (d) The same parameters as in b), in oDCB, where available.
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Table 1. Experimental data evaluated from the IV-CT band analysis and from
temperature dependent ESR spectra in PhNO2 and in oDCB at 295 K
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IV-CT band
ESR
T range /
K
IVCT
~
V12
kESR
(295
K) /
107 s-1
40
4.8
1.1
2.5
1.3
1.5
1.0
57
G*IV-CT
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
max
/
ab /D
G*ESR
/cm-1
/ cm-1
d
e
cm-1
a
/ cm-1
b,e
mOMe46
mMe46
mOMe
mMe
mCl
mCN
mNO2
pOMe
pMe
pCl
pCN
pNO2
mOMe46
mMe46
pOMe
pMe
6980
8410
3.0
1.1
320
140
1430
1970
290-315
280-300
280-345
280-360
280-335
285-350
280-320
280-320
295-345
280-325
280-320
280-310
260-300
255-275f
260-305g
1970  150
1360  110
1640  30
1740  20
1600  70
1630  20
1790  140
1700  90
1380  60
1420  50
1430  50
1410  80
970  50
1080  30
1250  40
-
900  40
840  60
970  20
1008  40
1210  20j
660  50
970  20
1020  20h
1050  20i
-
mX46
mX
7280
8310
8980
9310
9100
5700
7020
4670
5860
6480
6680
6760
6110
7970
6010
7110
7710
8030
8010
5.0
4.7
4.1
3.5
3.7
3.6
1.8
7.4
5.9
4.4
4.3
3.9
3.4
1.7
7.4
6.2
4.6
4.1
3.9
550
540
480
420
450
330c
180
510 c
470 c
370 c
370
340 c
330
200
650
600
470
420
410
1310
1570
1790
1930
1850
1120
1580
710
1030
1270
1320
1370
1220
1800
920
35
11
9.9
11
pX
87
mX46
pX
14a
201
-
pCl
pCN
260-280f
260-285f
260-275f
235-260
240-280f
200-230g
250-310
220-250f
220-260f
-
16a
14a
16a
160a
11a
322a
114
29a
21a
-
pNO2
mOMe46
mMe46
pOMe
pMe
pCl
pCN
pNO2
mX46
1230
1490
1610
1620
pX
aExtrapolated to 295 K. bCalculated by Mulliken-Hush theory using experimental data and the
c
DFT computed dipole moment difference ab, see Table 2. Using DFT computed dipole
d
moment differences in DCM, which hardly differ from those in oDCM, see Table 3. ±5%.
e±20%. Rate constants at higher temperatures than the indicated range deviate from the
f
g
linear trend in the ln(kESR/T1/2) vs. 1/T plot towards lower rates. Rate constants at higher
temperatures than the indicated range deviate from linearity in the ln(kESR/T1/2) vs. 1/T plot
towards higher rates.
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Table 2. TD-DFT computed data in PhNO2
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Eab
/cm-1
mOMe46 7256
V12 /cm-1
Eab(TS)/2 =
V12,TS /cm-1
1137
183
166
ab /Da ab
G*MH
/cm-1
1063
1784
2069
2196
2061
1946
2127
2153
2185
769
G*TS
/cm-1
1005b
1837
2089b
2151
/D
7.57
2.39
1.09
1.29
0.55
1.55
0.84
1.33
1.30
12.48
10.47
8.29
7.57
7.85
62.83 850
70.23 279
72.55 133
72.70 167
72.83 64
73.76 178
74.61 100
73.83 167
74.55 163
65.57 1319
71.51 1139
76.38 937
77.24 888
75.01 950
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mMe46
mCl46
mCN46
mOMe
mMe
8216
8800
9442
8496
8480
8904
9271
9382
7414
8106
8829
9237
9267
mX46
mX
221
209
156
192
2273c
2142
2165b
mCl
mCN
mNO2
pOMe
pMe
pCl
pCN
1825
1094
581
415
426
628c
1119
1482
1622
1579
1048
1370
1506
1464
pX
pNO2

b
Projection of transition moment onto the dipole moment difference vector ab. Minimum according
to frequency calculation. cTwo imaginary frequencies.
Table 3. TD-DFT computed data for pCN in PhNO2, DCM and oDCB
Eab
V12 /cm-1 Eab(TS)/2
G*MH
ab /Da
ab
/D
G*TS
/cm-1
=
/cm-1
V12,TS
/cm-1
/cm-1
415
PhNO2
DCM
oDCB
9237
8026
8033
7.57
8.12
8.10
77.24 888
77.78 820
77.94 817
1506
1270
1274
1622
pCN
760
1321b
1366b
429

b
Projection of transition moment on the dipole moment difference vector ab. Minimum according to
frequency calculation.
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Figure 3. ESR spectra and rate constant analysis. (a) Linear fit of experimental ln(kESR/T1/2) vs 1/T for
four exemplarily chosen MV species in PhNO2. The dashed line is at 295 K. (b) ESR spectra of pOMe
and mOMe at selected temperatures in PhNO2 and their calculated best fitting lineshapes.
Temperature-dependent ESR measurements of the MV radical cations were used to
determine the HT rate constants kESR in PhNO2 by digital line shape analysis and the HT
barriers from the slope of ln(kESR/T1/2) vs 1/T plots (see Experimental and Fig. 3 for selected
examples and Table 1).10 From the experimental ESR data in Table 1 some preliminary
conclusions can be drawn. 1) At 295 K, the HT rate constants of all mX compounds are an
order of magnitude smaller than those of the pX compounds. This qualitatively agrees with
general observations made before for other MV compounds in a similar context.11 2) The rate
constants are almost independent of the substituents within the mX series. 3) Within the pX
series the rate constants are constant for acceptor substituents (X = NO2, CN, Cl) but
increase on going from pCl to compounds with donor substituents (X = Me, OMe). This
demonstrates that strong donor substituents, which increase the electron density at the
bridge, can be used to accelerate the HT rates. 4) Within the mX series the ET barriers are
almost independent of the substituents (average G*: 1680 ± 80 cm-1). 5) Within the pX
series the barriers are constant for the substituents NO2, CN and Cl and significantly lower
than those of the mX series. However, for X = OMe, the barrier is much larger and
approaches those of the mX series. The latter effect is surprising, as, at first sight, it appears
to contradict the concomitant increase in HT rate. The same holds true for mOMe46.
In order to elucidate the solvent dependence of this unforeseen effect we also measured the
rate constants and barriers for the pX series and selected mX46 species in the significantly
less polar solvents oDCB and DCM. These results are included in Table 1 and show the
analogous effect concerning the HT rate constants, that is, kESR is almost independent of
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substituent for X = NO2 to Cl and similar in all three solvents but rises dramatically for X =
OMe in oDCB and particularly in DCM. Compared to the results in PhNO2, the barriers are
significantly lower in oDCB, because the less polar solvent exerts smaller solvent
reorganization energy in line with the observations made above for the IV-CT band.
However, for X = OMe, the barrier is significantly higher than that for all other bridge
substituents in PhNO2 and in oDCB, while in DCM it is lower. At this point we note that most
compounds in oDCB and in DCM display either positive or negative deviations of the
ln(kESR/T1/2) vs 1/T plot in the higher temperature regime which we assign to decomposition
processes. In these cases only the data at low temperatures were used for the analysis of
the barriers and the rate constants were extrapolated to room temperature.
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Discussion
HT dynamics. In order to explain the observations above concerning the HT dynamics we
tried to calculate the HT barrier and rate constants using established electron transfer
theories.12 In general, rate constants of electron transfer processes are given by equation (2)


G *
kBT



,
(2)
k  A exp 



where G* is the HT barrier, given by equation (1). In principle four different scenarios could
apply to the HT process in the present setting, which, depending on the coupling matrix
element and the dielectric relaxation properties of the solvent, give rise to different pre-
exponential factors in equation (2):13 I) strongly diabatic limit, II) strongly adiabatic solvent
dynamic controlled situation with cusped barrier, III) the same as II) but with parabolic barrier
and, IV) adiabatic transition state theory. Only cases III) and IV) apply to the present work,
for reasons given in the SI.
In case III) solvent friction controls the dynamics by the longitudinal solvent relaxation time L.
For larger couplings a parabolic free energy surface (PAR) at the TS results and A is given
by:
o
82V12
1
.
1
(3)
APAR

L
In case IV), with uniform motion to the transition state, the pre-exponential factor, which can
be interpreted as a well frequency, is:13-14
2s  
3sg
2kBT
1
ATST


with  
,
(4)
2
I
where s and ∞ are respectively the static and optical dielectric constants of the solvent, g is
the Kirkwood correlation factor and I is the average moment of inertia of the solvent
molecule, as given in the SI.15
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Rips and Jortner16 have suggested inequalities based on the adiabaticity parameter
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4V 2L
to decide upon the electron transfer regime and, thus, which prefactor
A 
o
applies. If A lies in the interval given by
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kBT
1
4
2rotL




,
(5)
2rotL  A 
 V12



where
is the rotation frequency of the solvent molecules, transition state theory
rot

I
(TST) applies. If A is smaller than the left-hand term the HT is diabatic, if it is significantly
larger than the right-hand term, the reaction is adiabatic and controlled by solvent dynamics.
For the majority of scenarios relevant here (e.g. with V12 = 200 cm-1, o = 6000 cm-1, L = 4.3
× 10-12 s-1, I = 742 × 10-47 kg m2, s = 35.90, ∞ = 3.48, g = 1), the adiabaticity parameter A is
much larger than unity (e.g. A = 67.8) and larger than the left-hand term in equation (5) (e.g.
0.029) but smaller than the right-hand term (e.g. 147), indicating uniform adiabatic behavior
as described by TST. However, for larger couplings, e.g. V12 = 1000 cm-1, the adiabaticity
parameter A = 1697 is much larger than the right-hand limit, indicating that solvent
controlled dynamics dominate, which is covered by case III (and II).
In case III) the temperature dependence of L
1
1
(6)

exp( HL /kBT )
L L0
induces an effective increase of the HT barrier.17 The barrier HL amounts to 1439 cm-1 (L0 =
3.55 × 10-15 s) for nitrobenzene in the investigated temperature range18 and, thus, cannot be
disregarded. However, this value contradicts the experimental activation barriers as,
following this model, HL would constitute the major part of the barrier, while the intrinsic
Marcus barrier Eab/4 (and hence the reorganization energy) would be predicted as
unreasonably small.
On the other hand, IV) appears to be reasonable for electronic couplings on the order of 100-
600 cm-1 and given the high moment of inertia of nitrobenzene. Therefore, we used equation
(2) with the ATST prefactor to estimate the electronic coupling and the reorganization energy
from the experimental barriers and rate constants at 295 K. The applicability of the TST also
1/ 2
ln

k
ESR /T

vs. 1/T (see Fig. 3). For the
justifies the estimation of the HT barrier by plotting
mX series with V12 = 200 cm-1
constants (kTST = 1.5 × 107 s-1) and barriers (G* = 1805 cm-1) were obtained in comparison
with the experimental data (see Table 1). For the para-series with X = NO2 to Me plausible
rate constants (kTST = 8.6 × 107 s-1) and barriers (G* = 1445 cm-1) could be estimated by
increasing V12 to 600 cm-1. However, the markedly high rate and barrier of both pOMe and
mOMe46 could not be modelled by equations (3) and (4).20
19
and o = 6000 cm-1 (v = 2000 cm-1) reasonable rate
Using large coupling coefficients (in agreement with the results from the optical data)
increases A beyond the upper limit in equation (5). This again hints at a regime controlled by
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solvent dynamics. In agreement with this finding, we used an interpolation between the TST
and the PAR regime, which is given by equation (7):
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kPAR kTST
kPAR  kTST
.
(7)
k 
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With this interpolation, a larger coupling V12 = 1200 cm-1 together with a somewhat smaller
solvent reorganization energy (o = 5000 cm-1) gives k = 74 × 107 s-1 and G* = 1700 cm-1.
These values are in much better agreement with the experimental values for pOMe (kESR
=
57 × 107 s-1 and G*ESR = 1700 cm-1) and mOMe46 (kESR = 40 × 107 s-1 and G*ESR = 1970
cm-1). Thus, it appears that the higher electronic coupling in pOMe and mOMe46 shifts the
system towards the solvent dynamically controlled regime with the consequence that both
the barrier (via the additional activation energy HL in the pre-exponential term) and the rate
constant increase compared with the respective values for pMe.
In order to support this interpretation we also analyzed the results for the pX series in two
other solvents that differ significantly from PhNO2 with respect to their dielectric properties,
that is, in oDCB, a distinctly less polar solvent compared to PhNO2 that nonetheless shows a
very similar longitudinal solvent relaxation time L (6.0 ps for oDCB and 4.3 ps for PhNO2 at
295 K, see SI), and in DCM, which is somewhat more polar than oDCB but exhibits a much
shorter relaxation time (0.49 ps, see SI).
Although not as satisfactory as in PhNO2, transition state theory again gives the best
agreement with the experimental data in oDCB for pNO2, pCN, and pCl. e.g. with V12 = 300
cm-1, o = 3500 cm-1, i = 2000 cm-1, I = 736 × 10-47 kg m2, s = 9.93, ∞ = 2.03, and g = 1 we
obtain k = 50 × 107 s-1 and G* = 1091 cm-1. Within TS theory no reasonable combination of
parameters could be found which for pOMe reproduced the observed increase of both the
rate constant and the HT barrier. However, as above, using eq. 7 as the interpolation to the
solvent dynamic regime together with eqs. 3, 4 and 6 with o = 3000 cm-1, V12 = 1000 cm-1
and assuming a temperature dependence of the longitudinal solvent relaxation with a
somewhat lower barrier (HL = 1080 cm-1) for oDCB as PhNO2 (see SI) we obtain k = 176 ×
107 s-1 and G* = 1278 cm-1 in good agreement with the experimental data.
Assuming similar HT parameters for the para-series in DCM (V12 = 200 cm-1, o = 4000 cm-1,
v = 2000 cm-1, I = 48 × 10-47 kg m2, s = 8.83, ∞ = 1.98, g = 1) TS theory yields k = 68 × 107
s-1 and G* = 1307 cm-1. Both values are slightly larger than those observed for X = CN and
Cl. Increasing the electronic coupling to V12 = 1200 cm-1 and applying eq. 7 gives a barrier of
721 cm-1 with kTST = 1133 × 107 s-1. Both values are in good agreement with experiment.
Thus, in contrast to PhNO2 and oDCB, in DCM the barrier in the pX compounds becomes
smaller with rising rate constant. This is due to the fact that the DCM relaxation constant
causes only a small barrier HL = 401 cm-1 [see SI]. This finding proves that the rise of the HT
barrier for pOMe in PhNO2 and in oDCB is indeed caused by the additional barrier exerted by
the solvent dynamics.
It is important to note that what we measured by ESR spectroscopy is an “apparent” barrier,
1/ 2
ln

k
ESR /T

calculated as the derivative of
vs. 1/T. The intrinsic Marcus barrier as defined
by eq. 1 decreases for both pOMe and mOMe46 as a result of the deformation of the
hypersurface in the TS region. This can be seen from both the analysis of the IV-CT band
and the DFT computations. This relationship is most obvious when looking at Fig. 2b where
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the barriers of the pX compounds obtained by the three different methods are plotted. Here,
the most interesting aspect is the deviating behavior of the ESR-determined apparent
barriers. While there is a very good agreement with the DFT computed values for X = NO2 to
Cl, the transition of the HT mechanism towards the solvent dynamic regime leads to an
increase of the apparent barrier for pMe and, in particular, pOMe. The same holds true for
the barriers in oDCB (Fig. 2d) but not for DCM (Fig. 2c), for which solvent dynamics do not
add much to the apparent HT barrier.
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Electronic coupling. The manifold influences of bridge substituents on the electronic coupling
in the para- and the meta-series of MV compounds is the central point of this work.
Comparing the rate constants of mOMe46 and mMe46 with all the other compounds in the
studied solvents shows that the HT rate of mOMe46 is similar to pOMe or pMe while the rate
of mMe46 is similar to pX with X = CN to NO2. This demonstrates that placing strong donor
substituents in 4- and 6-position at the central benzene bridge in the meta-series can
accelerate the HT to enter the regime observed for the para-series. This is most likely
caused by a surprisingly large electronic coupling in the mOMe46 as can be seen from the
data in Table 1 and 2. As we have shown above, the IV-CT energy at the TS corresponds to
twice the electronic coupling V12. This excitation is caused by the promotion of an electron
from the -HOMO to the -LUMO orbital (see Fig. 4 for selected examples with X = Me)21 in
an unrestricted UDFT computation where the -orbitals contain n and the orbitals n-1
electrons in different spin orbitals. In general, electron donating substituents (Me and in
particular OMe) exert a destabilizing effect on the MOs when attached to positions where
there is a significant orbital coefficient at the benzene bridge. Consequently the -LUMOs of
mMe46 and of pMe are destabilized. This also applies to mMe, but to a much lesser extent,
because only one of the methyl substituents is attached to a benzene position with significant
orbital coefficient. In this way, the symmetry of the involved MOs and the position of the
substituents play a decisive role in determining the electronic coupling.
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mMe46 -HOMO
mMe46 -LUMO
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mMe -
mMe -
HOMO
LUMO
pMe -
HOMO
pMe -LUMO
Figure 4. Selected -HOMO and -LUMO plots of transition states. The UDFT computed MOs of
mMe46, mMe and pMe that are responsible for the lowest energy excitation at the geometry of the
transition state.
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Figure 5. ESR determined (= apparent) HT barriers G*ESR and HT rate constants kESR for the mX46
(dashed dotted line), pX (solid line) and mX (dashed line) series of MV compounds in PhNO2.
6
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Conclusions
8
9
The main conclusions of this work are summarized in Fig. 5: The schizophrenic observation
that the HT rate constants and the apparent (ESR measured) HT barriers increase
simultaneously for pMe and pOMe in PhNO2 and oDCB can be explained by an increasingly
important solvent dynamic effect and an additional, effective barrier that is associated with
the longitudinal solvent relaxation time. To our knowledge, this is the first time that such a
transition of mechanism from the regime where TST applies to the regime where for a
parabolically (PAR) shaped transition state solvent dynamics control the charge transfer has
been clearly observed. While this aspect pertains to solution reactions only, the influence of
bridge substituents has to be considered for any bridge moiety and, thus, is of crucial
importance for, for example, organic electronic devices, be it on the molecular level or in the
bulk. Here we have shown that both rate constants and HT barriers are almost independent
of substituents for the mX series, while in the pX series there are dramatic changes for
donor-substituted derivatives. Thus, HT rate constants can easily be tuned in para-
conjugated systems by attaching substituents to the bridge units. This is a result of orbital
symmetry in the transition state. Due to vanishing orbital coefficients at the bridge, these
influences are much weaker in the mX conjugated systems. The mX46 series bridges the
gap between the mX and pX compounds. That is, for electron-withdrawing substituents
these compounds behave like the mX compounds, but for electron-donating substituents
they are rather similar to the pX compounds. Our findings complement a recent study by
Grozema et al.1j, which discusses the differences of constructive and destructive quantum
interference in cross-conjugated vs. linearly conjugated pathways in donor-bridge-acceptor
and analogous metal-bridge-metal junctions. In this study it became clear that hole-,
electron- and mixed electron/hole-transfer pathways may experience different quantum
interference effects depending on the involved bridge orbitals and their symmetry. However,
in our study we could show that the mere topology of the conjugation pathway is no longer
the decisive factor but can be overruled by substituent effects. Thereby, the long-standing
para-meta paradigm can be overcome, which broadens the use of conjugative topologies for
new applications such as organic field effect transistors or photovoltaic devices where e.g.
charge transport in ring- or helix-like structures based on meta-connected tolan units could
provide interesting novel applications.
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Experimental
MH Analysis. For all MV compounds we measured the Vis/NIR optical spectra of the
monoradical cations by oxidative titration of solutions in nitrobenzene (PhNO2) ortho-
dichlorobenze (oDCB) and dichloromethane (DCM) with solutions of SbCl5 in the respective
solvent. Although comproportionation during the oxidation step inevitably leads to a mixture
of neutral, monocation and dication species,5a only the monocation is mixed valent and
displays a IV-CT band. This band was evaluated by fitting the reduced spectra with Gaussian
functions (see SI). IV-CT band integration then yields the adiabatic transition moment ab.
DFT Computations. Structure optimizations of the ground states and TD-DFT computations
of the excited states were performed for all three series of MV compounds using a specially
adjusted hybrid functional with 35% exact-exchange admixture, a SVP basis set and the
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COSMO polarizable continuum model accounting for solvent effects9a,9b using Gaussian09.22
The time-dependent (TD-DFT) calculations were done at the same level of theory. G*MH in
Table 2 was evaluated from equation (1) and the computed data. The transition state was
optimized at constrained geometries, imposing either Ci or Cs symmetry where possible. The
nature of the stationary states was characterized by frequency calculations, which gave one
imaginary frequency in most cases. In some cases we obtained zero or two imaginary
frequencies. The hypersurface is so shallow in this region that we nonetheless assume that
these structures correspond closely to the true transition state.
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ESR Spectroscopy. We measured temperature-dependent ESR spectra of the radical
cations in fluid PhNO2 and oDCB between 280 and 360 K and in DCM between 220 and 300
K in order to determine the HT barriers. For some compounds in oDCB and in DCM we
experienced instability approaching rt and above. Therefore, only measurements at lower
temperature were used for the analysis and the reported rate constant at 295 K (see Table 1)
was estimated by extrapolation. The radical cations were generated at a concentration of ca.
1×10-4 M by oxidation with tris(bromophenyl)ammonium hexachloroantimonate (Aldrich).
ESR measurements were performed on a Bruker ELEXSYS E-500 X-band ESR
spectrometer or on a Bruker ELEXSYS E-580 CW/FT spectrometer equipped with a digital
Bruker-temperature control unit. Variable temperatures were kept constant at ± 0.5 K.
Experimental details concerning the sample preparation and handling, the ESR-
spectroscopic measurements, and the evaluation of the rate constants from line-broadening
effects are all explained in detail in our previous paper.10b HT rate constants kESR were
determined from lineshape analysis using hyperfine coupling constants determined from
model compounds with only one triarylamine as given in references.10 In particular, we used
aH,1
the hfc of two triarylamine ortho-protons of the two anisyl groups (4 x
= 0.188 mT) and
aH,2
the two ortho-protons of the phenylene ring, which is joined to the bridge (2 x
= 0.159
mT). The nitrogen hfc (ca. 0.9 mT) was freely fitted for each spectrum at each temperature
as it is slightly temperature dependent. All other hfcs are very small and were neglected.
Activation barriers were then obtained by linear fits of
vs. 1/T.
ln k

ESR / T

Associated Content
Supplementary information
Experimental and computational details. This material is available free of charge via internet
at http://pubs.acs.org.
Author Information
Corresponding Author
christoph.lambert@uni-wuerzburg.de
Notes
The authors declare no competing financial interests.
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Acknowledgement
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We thank the Deutsche Forschungsgemeinschaft and the FWF for support of this work (La
991/15-1 and DACH-DFG-FWF I733-N19) as well as the SolTech Initiative of the Bavarian
State Ministry of Education, Culture, Science, and the Arts.
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(19) Comparing the electronic coupling as derived from optical methods, DFT
computations and ESR measurements it appears that – although the same trends within the
series of compounds studied are observed - the magnitude differ in detail. At this point it is
worth mentioning that the electronic coupling itself is not a measureable quantity but refers to
a diabatic basis and thereby inherently depends on model assumptions which – without
mentioning them explicitly – differ for the methods employed.
(20) For example, further increasing the coupling to V12 = 1000 cm-1 gave kTST = 41 × 107
s-1 but a much too low barrier (G* = 1125 cm-1). On the other hand, increasing the
reorganization energy by 3000 cm-1 (o =9000 cm-1) yielded a reasonable barrier (G* = 1841
cm-1) but a much too small rate constant (kTST = 1.2 × 107 s-1)
(21) Although the destabilizing effect of OMe is much stronger we present here the orbitals
for X = Me because of the higher symmetry of the involved MOs.
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