Complete Monitoring of Coherent and Incoherent Spin Flip Domains in the Recombination of Charge-Separated States of Donor-Iridium Complex-Acceptor Triads

Article abstract of DOI:10.1021/jacs.5b04868

The spin chemistry of photoinduced charge-separated (CS) states of three triads comprising one or two triarylamine donors, a cyclometalated iridium complex sensitizer and a naphthalene diimide (NDI) acceptor, was investigated by transient absorption spectroscopy in the ns-μs time regime. Strong magnetic-field effects (MFE) were observed for two triads with a phenylene bridge between iridium complex sensitizer and NDI acceptor. For these triads, the lifetimes of the CS states increased from 0.6 μs at zero field to 40 μs at about 2 T. Substituting the phenylene by a biphenyl bridge causes the lifetime of the CS state at zero field to increase by more than 2 orders of magnitude (τ = 79 μs) and the MFE to disappear almost completely. The kinetic MFE was analyzed in the framework of a generalized Hayashi-Nagakura scheme describing coherent (S, T₀ 虠 T_±) as well as incoherent (S, T₀ ? T_±) processes by a single rate constant k_±. The magnetic-field dependence of k_± of the triads with phenylene bridge spans 2 orders of magnitude and exhibits a biphasic behavior characterized by a superposition of two Lorentzians. This biphasic MFE is observed for the first time and is clearly attributable to the coherent (B < 10 mT) and incoherent (10 mT < B < 2 T) domains of spin motion induced by isotropic and anisotropic hyperfine coupling. The parameters of both domains are well understood in terms of the structural properties of the two triads, including the effect of electron hopping in the triad with two donor moieties. The kinetic model also accounts for the reduction of the MFE on reducing the rate constant of charge recombination in the triad with the biphenyl bridge. (Graph Presented).

Full text of DOI:10.1021/jacs.5b04868

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Article
Complete monitoring of coherent and incoherent spin
flip domains in the recombination of charge-separated
states of donor-iridium complex-acceptor triads
Johannes H. Klein, David Schmidt, Ulrich E. Steiner, and Christoph Lambert
J. Am. Chem. Soc., Just Accepted Manuscript • Publication Date (Web): 19 Jun 2015
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Complete monitoring of coherent and incoherent spin flip domains
in the recombination of charge-separated states of donor-iridium
complex-acceptor triads
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Johannes H. Klein,§ David Schmidt,§ Ulrich E. Steiner,‡* Christoph Lambert§
*
§Institut für Organische Chemie, Universität Würzburg, Wilhelm Conrad Röntgen Research Center for
Complex Material Systems, Würzburg, Center for Nanosystems Chemistry, Am Hubland, 97074
Würzburg, Germany
‡Fachbereich Chemie, Universität Konstanz
78457 Konstanz, Germany
ABSTRACT
The spin chemistry of photoinduced charge-separated (CS) states of three triads comprising one
or two triarylamine donors, a cyclometalated iridium complex sensitizer, and a naphthalene diimide
acceptor was investigated by transient absorption spectroscopy in the ns-ꢀs time regime. Strong
magnetic-field effects (MFE) were observed for two triads with a phenylene bridge between iridium
complex sensitizer and NDI acceptor. For these triads, the lifetimes of the CS states increased from
0.6 µs at zero field to 40 µs at about 2 T. Substituting the phenylene by a biphenyl bridge causes the
lifetime of the CS state at zero-field to increase by more than two orders of magnitude (τ = 79 µs)
and the MFE to disappear almost completely. The kinetic MFE was analyzed in the framework of a
generalized Hayashi-Nagakura scheme describing coherent (S,T0 ↔ T±) as well as incoherent
(S,T0 ⇌ T±) processes by a single rate constant k±. The magnetic-field dependence of k± of the triads
with phenylene bridge spans two orders of magnitude and exhibits a biphasic behavior characterized
by a superposition of two Lorentzians. This biphasic MFE is observed for the first time and is clearly
attributable to the coherent (B < 10 mT) and incoherent (10 mT < B < 2 T) domains of spin motion
induced by isotropic and anisotropic hyperfine coupling. The parameters of both domains are well
understood in terms of the structural properties of the two triads, including the effect of electron
hopping in the triad with two donor moieties. The kinetic model also accounts for the reduction of
the MFE on reducing the rate constant of charge recombination in the triad with the biphenyl bridge.
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INTRODUCTION
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Charge separation after light absorption and energy transfer is the first step in transforming
solar energy to chemical free energy in photosynthesis.1 This principle of photoinduced electron
transfer also represents the main strategy in previous and current attempts of creating molecular
systems for artificial photosynthesis by chemically linking donor and acceptor moieties. The bridge
connecting donor and acceptor may also include an active chromophore supporting charge
separation and/or exhibiting a sensitizer function.2 The interest in artificial photosynthesis has
provided the motivation for a vast number of investigations of chemically linked donor-bridge-
acceptor systems, either with metal complex bridges3 or pure organic spacers.4 These studies have
also proved most valuable in clarifying the fundamental laws governing the rate of electron transfer
such as free energy dependence,5 distance dependence,6 and the transfer mechanisms of tunneling,
superexchange, and hopping.4c,6b,6e-g In this paper, we concentrate on a specific but important detail
of charge recombination kinetics, that is the singlet-triplet equilibrium of the charge-separated states
and the magnetic-field dependence caused by the spin dynamics. In particular, we provide
experimental proof for a change of the spin-flip mechanism (coherent vs. incoherent) which has
never been observed before in such detail.
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As target molecules for these investigations, we used triads 1–3 (Chart 1) comprising one or two
triarylamine (TAA) donors, a cyclometalated iridium complex sensitizer and a naphthalene diimide
(NDI) acceptor. The TAAs were used because they have low internal reorganization energy and their
oxidized form can easily be detected by optical spectroscopy.7 The latter is also true for the NDI
acceptor.8 The dipyrrin was used as the ligand in the sensitizer because it offers several advantages
over many other iridium complexes which are i) a shift of the optical absorption down to ca. 600 nm
and ii) a ligand-centered (LC) transition in the middle of the visible spectral range much more intense
than the metal-to-ligand charge transfer (MLCT) transition of many other iridium complexes
absorbing in that spectral region.9 Triad 1 is known to exhibit sufficiently long-lived charge-separated
states (τ
≈0.6 ꢀs) upon irradiation and thus appears to be a suitable candidate10 for investigating the
spin dynamics of this state.9i
As indicated above, one of the most important aspects of charge-separated states in linked
donor/acceptor systems is related to the electron spin: these charge-separated states represent
systems with two unpaired spins, i.e. radical pairs (RPs). There are four spin configurations forming
the basis of one spin state with total spin S = 0, a singlet state, and three spin states with S = 1,
representing a triplet state. The substates of the latter can be distinguished according to their spin
orientation in space. Due to their spatial separation, there is negligible coupling between the
separate spins in triads 1–3, meaning that singlet and triplet are almost degenerate. Nevertheless,
their different total spins give rise to an important difference in their recombination rates, because
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the spin conservation rule makes recombination to a singlet ground state allowed for a singlet RP,
but forbidden for a triplet RP. Conversely, if the energy of the charge-separated state is above the
energy of a locally excited triplet state, formation of such a triplet state by charge recombination is
allowed for triplet RPs, but forbidden for singlet RPs.4c,11 Therefore, any spin dynamics
interconverting singlet and triplet RPs will affect the recombination rate of a RP. It is intriguing, that
the rates of RP spin dynamics are controlled by such weak interactions as hyperfine coupling and
Zeeman interaction. This explains why the chemical decay kinetics of a RP is affected by magnetic
isotope substitution patterns and by external magnetic fields. Spin chemistry12 has moved into focus
of recent interest because of its impact on optoelectronic processes in OLEDs13 and photovoltaic
devices.14 Radical pair spin chemistry also is an essential issue in the primary processes of
photosynthesis,15 for magnetoreception16 in animals and plants, and has found particular interest as
a potential mechanism explaining the magnetic compass of migratory birds.17
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In linked donor-bridge-acceptor systems, the spin chemistry of the charge-separated state may
be detected and characterized by the magnetic-field dependence of various observables. Transient
absorption measurements represent the predominant technique, allowing to follow e.g. the explicit
time dependence of the charge recombination,18 or the yield of triplet recombination products, if the
energy of the charge-separated state is sufficient to populate local triplets on recombination.
Measurements of the latter kind have been used to detect so-called J-resonances in the magnetic-
field dependence,11c,11e,11f,19 allowing to determine the singlet-triplet energy separation and, hence,
the extent of interaction between the unpaired electrons. Fluorescence as a very sensitive method of
detection can also be utilized, if charge recombination is combined with emission, a situation typical
for exciplex forming systems.20 Finally, the spin polarization originating from the spin dynamics in the
charge-separated state can be detected using EPR methods.4c,18g Quite recently, a model donor-
bridge-acceptor triad has been used to demonstrate that the RP spin chemistry is sensitive not only
to the strength but also to the direction of the external magnetic field,18f thus providing a paradigm
for the magnetic compass hypothesis. This particular issue has also found great interest in the field of
quantum information theory.21,22
Before we describe our experimental findings, we briefly sum up the most important principles
of RP spin chemistry. As already mentioned, the spin chemistry of RPs is characterized by the fact
that chemical rate processes, such as charge recombination, are directly coupled to the conversion
dynamics of the four spin substates S, T+, T0, T– (cf. Figure 1). The main interactions determining the
spin conversion processes are hyperfine coupling, Zeeman interaction and exchange
interaction.4a,4c,12b-d The latter causes a splitting of the center of gravity of the triplet levels and the
singlet level. It decreases exponentially with the distance between the radical centers. For distances
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on the order of 20 Å, as applies to the triad systems investigated in this work, it is small compared to
the magnitude of the hyperfine coupling, and thus can be neglected.4a,12c,12d,23
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Figure 1.
Reaction and spin conversion processes of a radical pair. The situation refers to a finite Zeeman
splitting of the triplet levels, which vanishes at zero field, and negligible exchange interaction.
The rate processes connecting the spin sublevels may be either of coherent or incoherent nature,
depending on the magnitude of the Zeeman splitting in relation to the isotropic hyperfine
couplings.
In principle, the effect of Zeeman interaction is threefold: i) it causes a splitting of the triplet
levels and thus gradually prevents the mixing of the central substates S and T0 with T+ and T– and ii) it
leads to a mixing of S and T0 if the g-factors of the two radicals are different. The latter effect is
insignificant in our present case because the g-values of organic radicals usually differ by less than
0.001 from the typical value of 2.0023 and very high magnetic fields are necessary to affect the spin
dynamics by the ꢁg mechanism.23b,23f iii) In case of anisotropic g-tensors of the radicals, the Zeeman
interaction is stochastically modulated by their rotational diffusion, which contributes to spin-
relaxation, i.e. stochastic transitions between the spin levels.12c,24 This effect, too, is not relevant to
the present work.
The by far most important interaction for organic RPs is hyperfine coupling, comprising isotropic
and anisotropic contributions. If molecular rotation is sufficiently fast, the anisotropic interactions
are averaged to zero. Nevertheless the short-time stochastic fluctuations of those anisotropic
interactions lead to spin relaxation, albeit on a much longer time scale than molecular rotation and
spin dynamics due to isotropic hyperfine interaction.25 The latter causes a coherent process, which
cannot be rigorously described by classical kinetic equations. It requires a quantum theoretical
treatment of the spin density matrix of the RP by solving an appropriate Liouville equation, which
comprises at the same time coherent spin motion and the stochastic decay into the chemical
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reaction channels.12a,12b,26 In a strict sense, quantum dynamics and chemical reaction cannot be
treated separately. As mentioned above, the coherent quantum dynamics between the central and
the outer Zeeman levels are more and more suppressed as the magnetic field increases. Finally, their
transition rate drops below those of the incoherent transitions that are due to the modulation of
anisotropic interactions and can be summarized as longitudinal (T1-) spin-relaxation processes. In
that magnetic-field regime, the description of spin transitions by rate equations is well justified.
However, it must be emphasized that the transitions between S and T0 remain coherent at any field
because their Zeeman splitting remains zero. The effective rate of these processes is field
independent if ꢁg is small, which is the case for the present systems.
In a seminal paper, Hayashi and Nagakura27 introduced the reaction scheme shown in Figure 1,
to account for the magnetic-field dependence of radical pair kinetics in the field regime where
incoherent relaxation processes dominate the S, T0 to T+, T– transitions and to explain the magnetic-
field dependence in terms of known spin relaxation mechanisms of radicals. In the present paper, we
are going to demonstrate for the investigated donor-iridium complex-acceptor triads that, formally,
the kinetic scheme in Figure 1 can be applied for a wider range of magnetic fields comprising both
the regime of dominant coherent and dominant incoherent spin processes. At all fields investigated,
the observed decay kinetics of the RPs can be perfectly fitted using that scheme in a classical kinetics
sense and treating all rate parameters as global, field independent parameters, except for k±= k±’
which depend on the magnetic field.28 The magnetic-field dependence of k±(B) shows a clear
transition between two regimes. We will show that in the first regime, k±(B) can be related to the
characteristic parameters of coherent spin dynamics due to isotropic hyperfine coupling, and in the
second regime to the characteristics of longitudinal spin relaxation in the RP.
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RESULTS
The donor-iridium complex-acceptor triads investigated in this work are shown in Chart 1. In
addition to compound
ps and ns time-regimes have been characterized in detail before,9i the modified structures
were also investigated. In 2, the phenylene group linking the iridium complex and the NDI is replaced
by a biphenyl group, and comprises only one triarylamine donor group. These modifications shall
1
, for which the photophysical and photochemical primary processes in the fs,
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and
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help to clarify structural effects on the spin chemistry of the resulting charge-separated states.
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Chart 1
X-ray crystal structure analysis. Specific information on the molecular geometry of compound 1
was obtained by X-ray crystal structure analysis (cf. Figure 2). Single crystals of 1 were grown by
liquid/liquid diffusion of hexane into a solution of 1 in dichloromethane. The structure analysis
revealed a distorted octahedral iridium complex configuration with a slightly bent dipyrrin ligand.
Furthermore, the dihedral angle between the phenylene ring and the neighboring NDI, on the one
side, and the dipyrrin fragment on the other side are 121.7° and 86.1°, respectively. There are two
different conformers of the TAAs relative to the iridium complex present in the solid state structures
which may also be the case in solution. The donor-acceptor distances between the center of the
carbon-carbon bond of the central carbon atoms of the NDI core and the two nitrogen atoms of the
TAA units are 19.1 Å and 22.9 Å for the two possible TAA conformers.
Figure 2.
X-ray crystal structure of triad 1. The ellipsoids indicate a probability level of 50 %.
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UV/Vis spectra. The steady-state spectra of the three complexes (1–3) in MeCN are shown in
Figure 3. The π−π* transition of the dipyrrin unit is observed in the visible between 15 400 and
25 000 cm–1 (with εmax.(20 800 cm–1) = 31 000 M–1cm–1).9a-c,9i Here, the main absorption is caused by
transitions to ligand-centered (LC) singlets9c while the foot at ca. 17 000 cm–1 (588 nm) may be
caused by spin-forbidden transitions to LC triplets, which gain in intensity due to the heavy-atom
effect of the Ir atom. The π−π* excitations of the NDI are located between 26 600 and 31 000 cm–1 29
and overlap little with the π−π* excitations of the TAA units, which absorb between 29 000 and
37 000 cm–1.9i,30 In case of complex 3, the latter absorption is reduced due to the absence of the
second TAA unit. In all three compounds, the three chromophore moieties are electronically well
decoupled because of the saturated bridge between TAA and the Ir-complex9i,31 and the orbital
nodes of HOMO and LUMO along the long axis of the NDI chromophore which minimizes orbital
overlap to the bridging phenylene (1 and 3) or biphenyl (2) spacer.32 In addition, both spacers show
an almost 90° dihedral angle to the meso-position of the dipyrrin ligand (see X-ray crystal structure,
Figure 2).9b,9c,9i Complexes 1 and 2 only differ by the absorption at high energy (34 000–40 000 cm–1)
due to the replacement of a phenylene by a biphenyl unit.
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λ
/ nm
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ε
ε
ε
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/ cm–1
ν
Figure 3.
Absorption spectra of 1 (black), 2 (red) and 3 (green) in MeCN. The vertical lines mark laser
energies 20 800 cm–1 (480 nm) and 24 000 cm–1 (416 nm) used in previous time-resolved laser
experiments with compound 1 (cf. text).9i
Nanosecond time-resolved laser-flash spectroscopy. Transient absorption experiments with fs-
9i
and ns-time resolution (cf. Ref. ) showed that pumping 1 in MeCN at either 20 800 cm–1 or 24 000
cm–1 (480 or 416 nm) yields a locally excited Ir-complex. After rapid (< 100 fs) intersystem crossing to
the triplet, charge separation within ca. 1 ns leads to almost quantitative formation of the charge-
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separated state TAA2-[Ir(dipy)]+-Ph-NDI– (in the following to be denoted as CS1). Further charge shift
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within less than 5 ps gives the long-lived charge-separated state TAA+ -Ir(dipy)-Ph-NDI– with a
2
lifetime of 580 ns.9i
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To study the spin effects in the long-lived charge-separated states CS2 of compounds 1–3, the
magnetic-field dependence of their recombination was studied using nanosecond laser-flash
spectroscopy. For compound 1, the transient ꢁOD spectrum of CS2 and its kinetics of formation at
zero-field were well characterized in Ref.9i For compound 3, the behavior is very similar (for details cf.
SI).
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For compound 2, we present the pertinent observations in the following. The ns-measurements
of 2 at zero magnetic field were carried out in MeCN in the same way as described for 1 in Ref.9i The
samples were excited with the frequency-tripled output of a Nd:YAG laser at 28 200 cm–1 (355 nm)
shifted to 24 000 cm–1 (416 nm) by means of a H2-Raman shifter. Pumping at this wavenumber
produces ligand-centered excited states of the iridium complex. The transient maps were obtained
by measuring the temporal decay profiles in 4 nm steps between 12 500 and 25 000 cm–1 (800–400
nm).
λ
/ nm
500
800 700
40
600
474nm
40
30
20
10
0
a
b
30
20
10
0
30
20
10
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ꢁ
ꢁ
ꢁ
0
50 100 150 200 250 300
t / ꢁs
ꢀ10
ꢀ10
14000 16000 18000 20000 22000 24000
0
100
200
300
400
500
–1
~
t / ns
ν
/ cm
Figure 4.
Transient signals observed for complex 2 under ns-laser excitation at 24 000 cm–1 (416 nm). a)
ꢁOD spectra in the time regime 0–162 ns. Blue 0–5.2 ns, cyan 5.2–26.8 ns, green 26.8–48.4 ns,
yellow 48.4–70 ns, orange 70–97.2 ns and red 97.2–162 ns. b) Decay traces at 21 100 cm–1 (474
nm) from transient absorption measurements with time windows of 0–540 ns and 0–300 µs
(inset).
Excitation of triad 2 at 24 000 cm–1 (416 nm) produces a series of ꢁOD spectra shown in Figure
4a. Starting from a strong bleaching signal, the spectra evolve to an overall positive transient
spectrum. The strong bleaching signal with a minimum at ca. 20 800 cm–1 (480 nm) proves the initial
population of ligand centered iridium complex states (see Ref.9i). A kinetic trace for the rise of the
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signal is shown in Figure 4b. The rise time of the excited state absorption is ca. 35 ns, which is much
longer than the 0.93 ns found in the case of compound 19i and also for compound 3. The relatively
long rise time is caused by the slow charge-separation process from the triplet-excited iridium
complex to the CS1 state (see Figure S3 in the SI for the state diagram of 2) because the ET has to
proceed via the biphenyl spacer. The follow-up ET to CS2 is fast again. The final ꢁOD spectrum in
Figure 4a shows the characteristic peaks of the TAA radical cation at 13 700 cm–1 (730 nm)9i,31 and of
the NDI radical anion at 21 100 cm–1 and 16 600 cm–1 (474 and 602 nm)11c,11e,29a,29b which proves
charge separation in 2. Its transient spectrum decays without further changes of spectral shape (cf.
Figure S6b). A characteristic decay curve is shown in the inset of Figure 4b. Its decay characteristics
are biexponential comprising a component of 12.3 µs (66 %) and a component of 79 µs (34 %).
For the observation of a second decay time, in principle two explanations may be offered: the
first is the possibility of a bimolecular deactivation, which can be excluded, because the two lifetimes
of the CS2 state do not change significantly with different concentrations of 8.5∙10–6–4.6∙10–5 mol L–1
and pulse energies of 0.2–1.0 mJ in the ns-time regime. The second explanation may be related to an
additional degree of freedom of triad 2 concerning conformational changes, due to the extra
phenylene ring between the NDI and the iridium complex. One can estimate that in order to observe
a biphasic decay from two different excited conformers with the given amplitudes and lifetimes, the
rate for interconversion of these conformers must not exceed 2000 s–1. However, this appears to be
much too slow for isomerization around a biphenyl axis. Thus, at the time being, we cannot offer any
reasonable explanation for this observation. We emphasize, though, that both lifetimes, 12.3 and 79
µs, are exceptionally long for the recombination of a CS state in such a small triad in fluid solution at
rt.
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Actinometry with Ru(bpy)3Cl2 in benzene was used to measure the quantum yield of the charge-
separated state (CS2) at 24 000 cm–1 (416 nm) excitation (see SI). The measurements support a very
efficient ET process with a quantum yield of 97 % which is as efficient as the quantum yield observed
for triad 1 (almost unity).
Magnetic-field effects (MFE). The recombination kinetics of the CS2 states of triads 1–3 were
investigated for their sensitivity to an external magnetic field. For these measurements, the optical
setup was changed such that the 24 000 cm–1 (416 nm) pump beam and the white light probe beam
cross each other perpendicularly in the cavity of an electromagnet (0–1.8 T) (for details of the set-up
see SI). It is crucial to deoxygenate the sample solutions carefully (see SI) because MFEs are strongly
reduced or not observable at all, if there are traces of O2 in the solution.18c,18e
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The observed magnetic field dependent decay curves are shown in Figures 5 and 6 for a
representative selection of 16 out of altogether about 50 applied magnetic fields in each case. For
triads 1 and 3, the zero-field lifetime of the CS2 state is about 0.6 µs. In both cases, the kinetic
magnetic-field effect manifests itself as a pronounced prolongation of the charge recombination
process. For compound 2, for which the zero-field lifetime of state CS2 is on the order of 79 µs, a
magnetic-field effect is hardly detectable (cf. Figure 6).
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0.02 mT
0.61 mT
1.36 mT
4.01 mT
0.27 mT
1.02 mT
2.50 mT
7.51 mT
0.00 mT
0.70 mT
1.50 mT
4.00 mT
0.30 mT
1.00 mT
2.50 mT
7.50 mT
20.0 mT
60.0 mT
180 mT
1800 mT
1.0
0.8
0.6
0.4
0.2
0.0
1.0
0.8
0.6
0.4
0.2
0.0
a
b
9.98 mT
30.4 mT
100 mT
800 mT
19.9 mT
60.0 mT
180 mT
1800 mT
10.0 mT
30.0 mT
100 mT
800 mT
0
2
4
6
8
0
2
4
6
8
t / ꢁs
t / ꢁs
Figure 5.
Selected transient absorption decay curves at 21 100 cm–1 (474 nm) at specified magnetic fields
for complex 1 (a) and 3 (b) in MeCN. The experimental data have been normalized after
correction for the finite width of the laser pulse and an offset at very long decay times (for details
cf. SI).
For triads 1 and 3, the decay curves at very low fields are monoexponential and become
biexponential above about 10 mT. The field effects saturate above 800 mT, reaching a longer lifetime
component of 2.2 µs for triad 1 and 3.9 µs for triad 3, corresponding to 3.8 fold and 6.6 fold
increases, respectively, relative to zero field. Half of the maximum lifetime effects are reached
around 50–60 mT.
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1.0
0.20
0.00 mT
1.30 mT
0.15
2.10 mT
10.0 mT
30.0 mT
60.0 mT
100 mT
600 mT
1200 mT
1800 mT
0.8
0.6
0.4
0.2
0.0
0.10
0.05
0.05
0.10
0.15
t / ms
0.20
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0.0
0.1
0.2
0.3
t / ms
Figure 6.
Experimental transient absorption decay curves for triad 2 in MeCN at various magnetic fields
observed at 21 100 cm–1 (474 nm). The experimental data are corrected for an offset at very long
decay times. Inset: Magnification of the decay curves between t = 0.05–0.24 ms.
Kinetic model of magnetic field dependent charge recombination. As a generic basis of our
kinetic simulation we will use the reaction scheme given in Figure 1. As was shown by Hayashi and
Nagakura, this scheme is an appropriate description of RP reaction dynamics if the spin processes
between the central Zeeman levels S and T0 and the outer Zeeman levels T+ and T– are due to
relaxation, i.e. incoherent processes, and the S/T0 equilibration can be considered as being fast.27 In a
more general phenomenological approach, we assume that the scheme also applies to the situation
where coherent spin processes participate in the interconversion of the four spin substates. In
setting up the kinetic equations, we take k±= k±’ which is correct if spin processes induced by electron
spin dipolar interaction can be neglected, which, like the vanishing exchange interaction, should be a
reasonable assumption for spin-spin separations on the order of 20 Å.33 Due to the symmetry of the
parameter pattern, T+ and T– will behave exactly identically. Then, the kinetic equations following
from the reaction scheme in Figure 1 are34
d[S]/dt = ꢀ k + 2k + k
[S]+ k [T ]+ k ([T ]+[T ])
± −
+
(
)
S
±
ST0
ST0
0
d[T ]/dt = k [S]− k + 2k + k
[T ]+ k ([T ]+[T ])
± −
+
(
)
0
ST0
T
±
ST0
0
(1)
d[T ]/dt = k [S]+ k [T ]− k + 2k [T ]
(
(
)
)
+
±
±
0
T
±
+
d[T ]/dt = k [S]+ k [T ]− k + 2k [T ]
−
±
±
0
T
±
−
The general solution of this system of linear differential equations is a tri-exponential function.
Although a general analytical expression could be given, it is very clumsy. Instead, solutions for
concrete parameter values were calculated by MATHEMATICA, yielding the numerical values of the
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coefficients and time constants of the exponentials. Plain tabular numerical solutions were also
obtained using MatLab. The experimentally observed decay curve represents the superposition of
the concentrations of all spin substates of the CS2 state.
6
7
8
9
Fit strategy and evaluation of global parameters. Before fitting the CS2 decay signals, these
were standardized i) by correcting the initial part for the pulse width of the laser and the finite
response time of the detection system (for details cf. Supporting Information), ii) by subtracting a
small long-time offset showing at the end of the signals and iii) by normalizing the corrected signal
amplitude to 1.
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With regard to the kinetic parameters in Scheme 1, we note that the rate constants
, kS and
k
ST0
kT must be considered as independent of the magnetic field. The same applies to the initial spin
configuration, to be specified by the singlet probability pS. Thus, for a series of signals measured for
each of the triads under various magnetic fields, these parameters must be treated as global
constants for each triad and the only parameter varying with the field is rate constant k±. The
problem of fixing the global parameters is simplified by the fact that it seems safe to assume that
kT ≈ 0,18d because no strong spin-orbit coupling effects are to be expected for the two organic radical
moieties in the vicinity of a diamagnetic iridium core.
For the determination of a physically significant value of the rate constant
, we resort to the
k
ST0
semiclassical model of Schulten and coworkers35 for the coherent hyperfine-driven motion of the
electron spins in a radical pair. In this model, the hyperfine coupling constants aik for the individual
radicals sum up to a classical vector by ꢀꢁ = ꢃ ꢂꢁꢃ ꢀꢁꢃ and are given as follows: for NDI36 2 × αN =
∑
0.095 mT, 4 × αH = 0.190 mT; for TAA6d 4 × αH = 0.055 mT, 4 × αH = 0.203 mT, 6 × αH = 0.084 mT, 2 ×
αH = 0.160 mT, 2 × αH = 0.094 mT, 1 × αN = 0.921 mT, 1 × αH = 0.210 mT. According to Schulten and
Wolynes,35a the evolution of spin character based on these values is obtained as shown in Figure 7 for
zero field and (infinitely) high field.
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0.30
0.25
0.20
0.15
0.10
0.05
0.00
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60
0
20
40
60
80
100
t / ns
Figure 7.
Evolution of singlet probability pS in a CS2 state starting from a pure triplet spin configuration.
Solid lines (blue: zero field, red: high field) calculated according to the semiclassical model by
Schulten and Wolynes.35a Dashed lines from top to bottom represent classical kinetic behavior
according to equations (3) and (4), with
= 5∙107 s–1, 4∙107 s–1, and 3∙107 s–1 blue: zero field,
k
ST0
red: high field approximation. For details cf. text.
In order to apply the classical kinetic rate equations (1) we need to approximate the spin evolution of
the Schulten-Wolynes model by classical kinetic equations. To achieve this, we describe the approach
to spin-equilibrium using the kinetic model in Scheme 1. For convenience, we start from a pure
triplet. In this case, the general result for the evolution of singlet character is
−2(kST +k± )t
0
1
1
2



pS (t) = 1− e−4k t − e
(2)
±



4
3
3
In the limit of zero field, it can be assumed that k± ≈ kST yielding
0
pS,zf (t) = 1−e−4k
t
1
ST0
(3)
(4)
)
(
4
In the high field case, k± → 0, yielding
S,hf (t) = 1−e−2k
t
1
ST0
p
)
(
6
In Figure 7, the pertinent classical kinetics of zero- and high-field curves are shown for
= 3∙107
k
ST0
s–1, 4∙107 s–1, and 5∙107 s-–1, three representative values of kST , for which the obtained kinetics define
0
a range wherein a sensible approximation must be sought. Adopting the two extremes of these
values, the global best fit for kS was determined for a series of trial values for pS. (For details cf.
Supporting Information). It turned out that for both limiting trial values of
the global rms
k
ST0
minimum was centered around an initial singlet population of pS,0 = 0.25, i.e. full equilibrium
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between the spin substates of the RP. To proceed further, we adopted a
value of 4∙107 s–1, i.e.
kST
0
4
5
central to the two examined border cases shown in Figure 7. Values of kS = 6.7∙106 s–1 for triad 1 and
6
7
6.97∙106 s–1 for triad 3 were obtained as global minima for pS,0 = 0.25 and
= 4∙107 s–1.
k
ST0
8
9
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1.2
0.0085
0.010
0.0060
B0 = 1800 mT
B0 = 60 mT
1.0
kr = 2.8—105 s–1
kr = 5.49—105 s–1
0.0058
0.0080
0.8
0.0056
0.0075
B0 = 0 mT
0.0054
0.6
0.4
0.2
0.0
kr = 4.59—107 s–1
0.008
0.0052
0.0070
5.0—105
5.5—105
6.0—105
1—108 2—108 3—108
2.6—105
2.8—105
3.0—105
k± / s–1
k± / s–1
k± / s–1
0 mT
Fit
60 mT
Fit
1800 mT
Fit
0.02
0.00
ꢀ0.02
0
2
4
6
8
0
2
4
6
8
0
2
4
6
8
t / ꢁs
t / ꢁs
t / ꢁs
Figure 8.
Demonstration of procedure and accuracy of fitting k± as a function of magnetic field, here 0, 60
and 1800 mT. Top: observed decay curve in black and fitted curve in red, bottom: residual plot of
difference between observed and fitted decay curve. Gray: best fit, red and blue: using k± values
yielding residuals about one noise width apart. Inset: rms deviation as a function of k± with
indication of minimum and error bounds within the signal noise width. The pertinent best fit k±
values are indicated in the inset diagrams. (For more details cf. Supporting Information).
To fix the best k± values for the individual decay curves, consistent fits were performed with MatLab
and MATHEMATICA. The procedure to obtain the k± value with minimum rms deviation and the error
bounds of k± for each field is demonstrated in Figure 8. It must be emphasized that the variation of
the single parameter k± was sufficient to obtain excellent fits of the decay curves for all fields. The
resulting field dependences of k± for triad 1 and 3 are shown in Figure 9. For both compounds, the
magnetic-field dependence of the k± values could be fitted by a double Lorentzian according to
equation (5) using the parameters listed in Table 1.
khfc,0
1+(B / B
krel,0
1+(B / B
k± (B) =
+
+ krel,∞
2
(5)
2
)
)
1/2,rel
1/2,hfc
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109
k± (1)
5
6
7
8
k± (3)
108
107
106
105
Fit (1)
Fit (3)
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0.01
0.1
1
10
B / mT
100
1000
Figure 9.
Table 1.
Magnetic-field dependence of k± with error bars obtained by fitting the CS2 decay curves as
illustrated in Figure 8. Red: triad 1, green: triad 3. The solid lines represent best fits of the double
Lorentzian function of equation (5) to the data. The parameters are given in Table 1.
Fit parameters of the curves fitting k±(B) in Figure 9 according to equation (5).
krel,0 / s–1
(3.6±0.25)∙106
(1.6±0.1)∙106
B1/2, rel / mT
15±1
krel,∞ / s–1
(3.1±0.1)∙105
(1.64±0.08)∙105
khfc,0/ s–1
(4.3±0.4)∙107
(7.9±1.1)∙107
B1/2,hfc / mT
0.69±0.07
0.44±0.04
triad 1
triad 3
25±2
DISCUSSION
Initial spin population. When fitting the k± values, pS,0 = 0.25, i.e. initial spin equilibrium, had to be
assumed, because it represents the best global value for all fields. The physical reason for this
instance lies in the nature of the RP CS1, the precursor state of RP CS2. CS1 corresponds to the charge-
separated state TAA2-[Ir(dipy)]+-Ph-NDI–,9i where an unpaired electron spin is situated at the iridium
core which is in a formal Ir4+ oxidation state with a d5 electron configuration. As is well known from
Ru and Fe spin chemistry,37,38 the d5 complexes of these elements show extremely short spin
relaxation times on the order of a few ps, which are due to an efficient Orbach mechanism based on
the small energy gap between the ground and the first excited doublet state. In RPs involving such
species the spin equilibrium is also obtained within a few ps. The analogous situation can be
anticipated for Ir.
Error bars. As shown in Figure 9, for triads 1 and 3 the magnetic-field dependence of the rate
parameter k± is very well defined over 2 to 3 orders of magnitude. For triad 3, the error bars become
large only at magnetic fields below 1 mT, for triad 1, below 10 mT. The larger error bars at low fields
are due to the fact that for high values of k± the decay kinetics get less sensitive to this parameter,
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since the substate populations of the RP remain close to spin statistical equilibrium. This
circumstance is also responsible for the fact the error bars become asymmetric with a longer upper
part. However, in spite of some uncertainties of k± at low fields, the density of data points down to
0.4 mT is high enough to provide a convincing basis for defining the double Lorentzian fit, which, as
will be shown, represent the two kinetic regimes of coherent and incoherent transitions between the
central and the outer Zeeman levels of the RP.
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The regime of coherent spin flip. While Lorentzian line shapes are well founded in relaxation
theory, where they represent the energy dependence of spectral densities of stochastic
perturbations,24,39 their use to describe the magnetic-field dependence of coherent spin processes or
product yields depending on such processes has not been customary in the literature. Nevertheless,
from a formal phenomenological point of view, the Lorentzian function is quite suitable to describe
such cases, too. Examples from the literature40,18b are given in the Supporting Information. As a
qualitative rationale of such applications, one may refer to the inverse energy dependence of mixing
coefficients according to first order perturbation theory and the proportionality of reaction
probabilities to the square of mixing coefficients. Quantitative studies with freely diffusing radical
pairs have furnished the following approximate relation between the hyperfine coupling constants of
the radicals and the B1/2 field of the magnetic effect of spin-selective recombination yields:12c,19
B = 3(B2 + B22 )
(6)
1/2
1
with the individual Bi given by the following sum over the nuclei k in either radical,
B = a2 I (I +1)
(7)
∑
i
ik ik
ik
k
aik representing the isotropic hyperfine coupling constant of nucleus k in radical i. From the hyperfine
coupling constants of the CS2 radical moieties given in the Results section, a B1/2 value of 2.5 mT is
obtained for all three triads. The B1/2 values found by the Lorentzian fit of the low-field branch of the
dependence of k± on the magnetic field B, viz. 0.69 mT for triad 1 and 0.44 mT for triad 3, are
significantly smaller. However, one must note that relations as given in equation (6) result from
convolutions of spin-evolution and re-encounter probabilities, the latter usually decaying on the time
scale of a few nanoseconds. On the other hand, we are dealing here with linked radical pairs,
recombining in spin-allowed transitions on the time scale of several hundreds of nanoseconds. On
such time-scales, smaller magnetic fields are sufficient to achieve the same effect as higher fields on
the few-nanosecond time-scale. A comparison of spin-equilibration kinetics using the semiclassical
approach35 in Figure 10a and the classical kinetic approach, shown in Figure 10b, may be illuminating.
Although, in principle, the oscillatory behavior peculiar to the coherent dynamics cannot be
reproduced by the classical monoexponential kinetics, it is borne out by the two sets of curves that
the magnetic field affects the spin population on the same overall time scale. Thus it appears out of
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doubt that the first branch of the double Lorentzian in Figure 9 does indeed account for the coherent
transitions between the central and the outer Zeeman levels of the RP. A rigorous theoretical
transformation of the coherent picture of spin dynamics to the equivalent classical representation is
only possible by solving the pertinent stochastic Liouville equation of the full quantum theoretical
problem including spin dynamics and spin-selective chemical reaction simultaneously. This will be
subject to future work.
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0.3
0.2
0.1
0.0
0.3
0.2
0.1
0.0
a
b
0
20
40
t / ns
60
80
100
0
20
40
t / ns
60
80
100
Figure 10.
Establishment of spin equilibrium represented as time evolution of singlet character when
starting with a pure triplet RP. a) Results for semiclassical model,35 blue 0 mT, cyan 4.4 mT, green
7 mT, orange 10 mT, purple 15 mT, red high field limit. b) Results for classical model with k±
values according to the pertinent Lorentzian function in equation (5) and the parameters given
for triad 3 in Table 1. For comparison, the limiting zero field and high field cases in the
semiclassical mode are shown as dashed lines.
Interestingly, in spite of the identical hyperfine coupling situation, the B1/2 value of triad 1 is
significantly larger than that of triad 3. The structural property to which this difference may be
assigned is the second triarylamine donor group attached to the central complex in triad 1.
Energetically, it does not make a difference which of the two donor groups donates the electron, but
once one of them has been oxidized the possibility of degenerate hole exchange between the two
TAAs arises. Such a process limits the time period of unperturbed spin evolution due to the hyperfine
coupling at the oxidized site. It has been shown35b,41 that degenerate electron exchange leads to a
broadening of the observed magnetic-field dependence with the approximate relation
kexch
≈
γ
e ꢁB
(8)
1/2
with γe the gyromagnetic ratio of the electron. Interpreting the difference of 0.25 mT between the
B1/2,hfc values of triad 3 and 1 by equation (8), we estimate
k
exch ≈ 4.4∙107 s–1. This order of magnitude
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is in excellent agreement with recent results from EPR measurements on intramolecular hole
exchange in organic mixed-valence compounds based on symmetric bis(triarylamine)paracyclophane
redox systems with similar electron hopping distances as in the present case.42 In contrast, in a
recently published donor-iridium dipyrrin-acceptor triad where the triarylamine donors are directly
attached to the phenylpyrazole framework of the iridium complex, the coupling between the
oxidized and the neutral TAA via the iridium d-orbital is so strong that this interaction is manifested
by an intervalence charge-transfer band in the NIR spectral region.43 Thus, we see that the magnetic-
field dependence of the first Lorentzian branch carries quite specific information on the systems
investigated. Also in line with the explanation by electron exchange is the fact that in case of triad 1,
the field dependence extrapolates to lower values at zero field (khfc,0) than in case of triad 3.
Shortening the time available for coherent spin evolution by electron hopping will also decrease the
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T⇌S transition rates.
Although our present findings seem to be the first clear demonstration of the region of coherent
hyperfine induced S⇌T transitions using classical kinetics, we note that in previous work, involving
one of the present authors, on donor-acceptor systems linked through a Ru(bpy)32+ complex18c there
was an indication, albeit unnoticed in that work, of the analogous situation. The data referring to the
equivalent of the present rate constant k±, dubbed kr in ref.18c because it was meant to be entirely
due to relaxation, were sparser than in the present case and a point of inflection was not apparent.
But the field range of change of this parameter kr was too extended to be fitted by a single
Lorentzian. Thus, two Lorentzians were used, with “correlation times” of 2 ns and 0.25 ns. In our
present view, the longer correlation time corresponds to a B1/2 of 2.8 mT which exactly matches the
theoretical B1/2 calculated from the hyperfine coupling constants of that system using equation (6).
The regime of incoherent spin flip at 10 mT <B < 1 T. The second Lorentzian component in the
magnetic-field dependence of k± must be assigned to incoherent spin relaxation processes in the
individual radicals. As shown in the Supporting Information, from the longitudinal relaxation time T1
of any of the radicals, the following contribution to k± , to be denoted krel,0 in the Lorentzian domain
assigned to spin relaxation, is derived:
1
(9)
krel (T ) =
1
4T
1
Since g-tensor anisotropies are small, and the distance between the radical moieties is too large for
electron-spin dipolar interaction to become effective, the major mechanistic contribution to spin
relaxation of the radical species involved in the CS2 states should be due to the rotational modulation
of anisotropic hyperfine coupling. The dominating hyperfine interaction is due to the 14N nucleus of
the triarylamine radical moiety. For negligible g-tensor anisotropy and assumed axial anisotropy of
the hyperfine coupling the transversal relaxation time is given by44
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τc
=
I(I +1) (A − A )2
(10)
(11)
∑
ii
iso
T
1+ ω02τc2
i
1
6
7
8
9
For axial symmetry, this expression can be transformed to
1
4
τc
1+ ω02τc2
=
I(I +1)ꢁA2
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T
27
1
where the hyperfine coupling anisotropy
∆A = A|| ꢀ A⊥
is given in angular frequency units. The quantities
(12)
,
ω
0 , and τc represent total nuclear angular
I
momentum quantum number, Larmor frequency and rotational correlation time, respectively.
Combining equations (9) and (11) and substituting ꢀ = 1 for a 14N nucleus yields
2
τc
krel,0
=
ꢁA2
(13)
27
1+ω02τc2
Relating the parameters in equation (13) to the fit parameters rel,0 = 3.6∙106 s–1 and 1/2,rel = 15 mT
k
B
for triad 1 and rel,0 = 1.6∙106 s–1 and 1/2,rel = 25 mT for triad 3, yields ꢁA = 3.6 108 rad∙s–1 (2.0 mT)
k
B
and τc = 0.38 ns for triad 1 and ꢁA = 3.1∙108 rad∙s–1 (1.75 mT) and τc = 0.23 ns for triad 3. To
estimate the rotational correlation times on the basis of the Einstein-Debye equation
4π
R3
3kT
τc
=
η
(14)
we substitute 0.343 mPa∙s for the solvent viscosity of MeCN, and the values 10.6 Å and 9.54 Å (cf.
η
Supporting Information) for the hydrodynamic radii of triads 1 and 3, respectively, yielding 0.42 ns
for triad 1 and 0.30 ns for triad 3 in fairly good agreement with the correlation times from the
Lorentzian fits.
Directly applicable literature data on the anisotropy of hyperfine coupling ꢁA of the N atom in
the present triarylamine radical moieties are not available, but quantum chemical calculations for
phenoxazine radicals45 and for its sulfur and selenium heteroanalogues have shown that the
anisotropy ꢁA of hyperfine coupling of the 14N atom is about 2.7 times its isotropic value, which
indicates that it results mainly from the dipolar interaction between the nuclear spin and the
electron spin in the 2p orbital and only a small part of the isotropic hyperfine interaction is due to
spin polarization of the 2s orbital. About the same ratio is obtained for the inorganic radicals
N(SO3)22−
NH(SO )–
.
3
39
and
If we assume the same relationship to hold for the present triarylamine
radical, ꢁA would be on the order of 2.7×0.92 mT ≈ 2.5 mT. The observed values are not far off,
indeed.
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The regime of incoherent spin flip at
B
> 1 T. The magnetic field independent contributions
4
5
∞ to the rate constants k± were found to be 3.1∙105 s–1 for triad 1 and 1.64∙105 s–1 for triad 3. These
krel,
6
7
8
9
values are on the same order of magnitude as the value of 5∙105 s–1 reported for a radical pair
constituted by the diquat monoradical cation and the oxazin radical cation.45 Spin-rotational coupling
as a magnetic field independent mechanism of spin relaxation may be discarded for that as well as
the present cases because in the systems under consideration the spin-orbit coupling effects are
small as indicated by g-tensor values close to that of a free electron. Apparently, only a “local mode”
mechanism that modulates spin-orbit coupling can be held responsible here as was also postulated in
case of trityl radicals.46 Systematic studies of structural variations affecting this mechanism, however,
seem not to be available in the literature.
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1.0
0.8
0.6
0.4
0.2
0.0
0
50
100
150
200
250
t / ꢁs
Figure 11.
Prediction of magnetic-field effect for triad 2. Black solid line: simulation of observed decay curve
at zero field by a superposition of two exponentials shown separately as red and blue solid
curves. Dashed curves: estimated magnetic-field effects for high fields, assuming rel,∞ = 105 s–1.
k
For details cf. text.
The MFE in triad 2. Our discussion of the behavior of triads 1 and 3 has shown that their
magnetic field dependent kinetics represent a rich source of information on the internal spin
dynamics of the charge-separated states. However, for triad 2, magnetic-field effects are hardly
observable. This goes along with the fact that in this case the recombination of the CS2 state is about
a factor of 100 slower than for triads 1 and 3. It takes place on the time scale of about 100 µs while in
the former cases, it is completed in less than 10 µs at zero field. This lifetime effect is clearly a
consequence of the longer separation of the acceptor part by a biphenyl bridge. Furthermore, also
distinct from triads 1 and 3, for triad 2 the decay is biexponential even at zero field. Such a behavior
is not explicable in terms of spin dynamics, which is expected to occur at the same rate as in the
other two cases, such that on the 10–200 µs time scale spin equilibrium should be always established
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and the four spin states should decay as one kinetic quasi species. Thus, the biexponential decay at
zero field can be only assigned to the decay of two distinct species CS2 and CS2’ that are not in rapid
equilibrium. In Figure 11, the biexponential decomposition is shown, which is characterized by the
amplitudes 0.66 and 0.34, and the decay constants 8.12∙104 s–1 and 1.26∙104 s–1, respectively.
9
kST
Assuming that in each species, CS2 and CS2’, the rate constant
and k± correspond to those of
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0
triads 1 and 3, and that we start with spin equilibrium (
p
S = 0.25) at t = 0, fitting each of the
exponentials in Figure 11, yields
k
S values of 3.2∙105 s–1 and 5.0∙104 s–1 for the CS2 species with the
faster and the slower decaying exponential, respectively. With all these parameters fixed, we can
estimate the maximum expectable magnetic-field effect at high fields, by setting rel,∞ = 105 s–1, i.e.
k
the same order of magnitude as observed for triads 1 and 3. The resulting decay curves are shown as
dashed lines in Figure 11. They are in good agreement with the experimental observations (see
Figure 7). This shows that, just by reducing the recombination rate S , the magnetic-field sensitivity
k
is greatly reduced. What is still not clear at present is the structural nature of the two modifications
of CS2 in case of triad 2. Several conceivable possibilities have been already rejected in the Results
section. Another obvious explanation might be the inequivalence of the two donor groups (cf.
structure in Figure 2). However, if the electron hopping rate of about 5∙107 s–1, deduced from the
B
1/2,hfc shift of the low-field Lorentzian between triads 1 and 3, is realistic, the two donor sites cannot
exhibit different kinetics on the time-scale of 100 µs, because the exchange is too rapid.
CONCLUSIONS
The present work investigates the spin chemistry of three structurally related rigid donor-iridium
complex-acceptor triads by means of a MFE on the recombination kinetics and reveals a number of
remarkable novel features. Over the full magnetic field range from 0–2 T, the observed kinetic MFE
could experimentally be resolved in unprecedented detail and consistently be reproduced by an
extended version of the Hayashi-Nagakura scheme. We have shown that this scheme is not only
suitable to simulate the incoherent T1-type spin relaxation processes at higher fields, but that a
single, magnetic field dependent rate constant k±(B) can also be used to account for coherent S, T0
↔ T± mixing at low fields. Phenomenologically, the full field dependence of k± can be decomposed
into two clearly separated Lorentzian branches. The parameters of the low field branch (khfc,0 and
B1/2,hfc) can be related to the coherent spin motion driven by isotropic hyperfine coupling, and reveals
quantitative information even on such fine details as the presence of degenerate electron exchange
between the two donor moieties in triad 1, which becomes evident from the comparison with triad
3, comprising only one donor. In contrast, the high-field Lorentzian branch is due to T1 spin
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relaxation, driven by rotational modulation of anisotropic hyperfine coupling, whereby the B1/2,rel
values clearly indicate the molecular radius effect on the rotational correlation time. In addition, the
very weak kinetic MFE of triad 2, containing a biphenyl linker between complex and acceptor part, is
consistently accounted for by the spin chemical kinetic scheme. Since the longer biphenyl linker
slows down the back electron transfer by more than two orders of magnitude, this process becomes
too slow to be an efficient monitor of the magnetic-field dependence of the much faster spin
processes. Thus, our interpretation of the first clearly observed biphasic, double Lorentzian spin-flip
characteristics is well supported and opens up important new insight into the details of molecular
motion, spin interconversions and chemical rate processes of the charge-separated states of metal-
complex sensitized triads.
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The small B1/2,hfc values for triad 1 (0.69 mT) and for triad 3 (0.44 mT) characterizing the coherent
spin-flip process are about one order of magnitude larger than the earth magnetic field (0.048 mT).
Modifying one or two spin bearing units in order to decrease the effective magnetic moment (see eq.
7) thus seems to be a viable way to construct artificial systems that are sensitive to the earth
magnetic field and to mimic magnetoreceptors as they might be involved e.g. in the avian magnetic
compass of birds, specifically studied in references.18f,18g,26,47
ASSOCIATED CONTENT
Supporting Information.
Synthesis, single-crystal structure analysis, cyclic voltammetry, transient absorption spectra and
global analysis data, spin chemical equations, and global fitting procedure. This material is available
free of charge via the Internet at http://pubs.acs.org.
AUTHOR INFORMATION
Corresponding Authors
*christoph.lambert@uni-wuerzburg.de
*ulrich.steiner@uni-konstanz.de
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGEMENTS
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The group at Würzburg acknowledges generous support within the collaborative research project
“Solar Technologies Go Hybrid” by the Bavarian State Ministry for Science, Research and the Arts,
and support from the EU COST-Action “Perspect H2O”. Furthermore, we would like to thank
Alexander Schmiedel and Dr. Marco Holzapfel for the measurement and analysis of the fs-pump-
probe measurements of triad 2 (see SI).
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REFERENCES
(1)
(2)
Hall, D. O.; Rao, K. K. Photosynthesis; Cambridge University Press: Boca Raton, FL,
(a) Kodis, G.; Lidell, P. A.; Moore, A. L.; Moore, T. A.; Gust, D. J. Phys. Org. Chem.
1994.
2004, 17, 724. (b) Tachibana, Y.; Vayssieres, L.; Durrant, J. R. Nat. Photonics 2012, 6, 511. (c)
McConnell, I.; Li, G.; Brudvig, G. W. Chem. Biol. 2014, 17, 434.
(3)
(a) Wenger, O. S. Coord. Chem. Rev. 2009, 253, 1439. (b) Flamigni, L.; Collin, J. P.;
Sauvage, J. P. Acc. Chem. Res. 2008, 41, 857. (c) Magnuson, A.; Anderlund, M.; Johansson, O.;
Lindblad, P.; Lomoth, R.; Polivka, T.; Ott, S.; Stensjo, K.; Styring, S.; Sundstrom, V.; Hammarstrom, L.
Acc. Chem. Res. 2009, 42, 1899. (d) Baranoff, E.; Collin, J. P.; Flamigni, L.; Sauvage, J. P. Chem. Soc.
Rev. 2004, 33, 147. (e) Balzani, V.; Credi, A.; Venturi, M. ChemSusChem 2008, 1, 26.
(4)
Chem. Rev. 1992, 92, 435. (c) Wasielewski, M. R. J. Org. Chem. 2006, 71, 5051.
(5) (a) Marcus, R. A. J. Chem. Phys. 1955, 24, 966. (b) Miller, J. R.; Calcaterra, L. T.; Closs,
G. L. J. Am. Chem. Soc. 1984, 106, 3047.
(a) Verhoeven, J. W. J. Photochem. Photobiol. C 2006, 7, 40. (b) Wasielewski, M. R.
(6)
(a) Closs, G. L.; Calcaterra, L. T.; Green, N. J.; Penfield, K. W.; Miller, J. R. J. Phys.
Chem. 1986, 90, 3673 . (b) Paddon-Row, M. N. Aust. J. Chem. 2003, 56, 729. (c) Edwards, P. P.; Gray,
H. B.; Lodge, M. T. J.; Williams, R. J. P. Angew. Chem., Int. Ed. 2008, 47, 6758. (d) Kattnig, D. R.;
Mladenova, B.; Grampp, G.; Kaiser, C.; Heckmann, A.; Lambert, C. J. Phys. Chem. C 2009, 113, 2983.
(e) Wenger, O. S. Acc. Chem. Res. 2011, 44, 25. (f) Arrigo, A.; Santoro, A.; Indelli, M. T.; Natali, M.;
Scandola, F.; Campagna, S. Phys. Chem. Chem. Phys. 2014, 16, 818. (g) Natali, M.; Campagna, S.;
Scandola, F. Chem. Soc. Rev. 2014, 43, 4005.
(7)
(a) Cias, P.; Slugovc, C.; Gescheidt, G. J. Phys. Chem. A 2011, 115, 14519. (b) Lambert,
C.; Schelter, J.; Fiebig, T.; Mank, D.; Trifonov, A. J. Am. Chem. Soc. 2005, 127, 10600. (c) Lin, B. C.;
Cheng, C. P.; Lao, Z. P. M. J. Phys. Chem. A 2003, 107, 5241. (d) Malagoli, M.; Bredas, J. L. Chem. Phys.
Lett. 2000, 327, 13.
(8)
H. B.; Tang, X. D.; Wu, Y.; Su, Z. M.; Liao, Y. J. Mater. Chem. 2011, 21, 15558.
(9) (a) Yadav, M.; Singh, A. K.; Pandey, D. S. Organometallics 2009, 28, 4713. (b)
(a) Adiga, S. P.; Shukla, D. J. Phys. Chem. C 2010, 114, 2751. (b) Geng, Y.; Wu, S. X.; Li,
Bronner, C.; Veiga, M.; Guenet, A.; De Cola, L.; Hosseini, M. W.; Strassert, C. A.; Baudron, S. A. Chem.-
Eur. J. 2012, 18, 4041. (c) Hanson, K.; Tamayo, A.; Diev, V. V.; Whited, M. T.; Djurovich, P. I.;
Thompson, M. E. Inorg. Chem. 2010, 49, 6077. (d) Gupta, R. K.; Pandey, R.; Sharma, G.; Prasad, R.;
Koch, B.; Srikrishna, S.; Li, P. Z.; Xu, Q.; Pandey, D. S. Inorg. Chem. 2013, 52, 3687. (e) Gupta, R. K.;
Sharma, G.; Pandey, R.; Kumar, A.; Koch, B.; Li, P.-Z.; Xu, Q.; Pandey, D. S. Inorg. Chem. 2013, 52,
13984. (f) Paitandi, R. P.; Gupta, R. K.; Singh, R. S.; Sharma, G.; Koch, B.; Pandey, D. S. Eur. J. Med.
Chem. 2014, 84, 17. (g) Yadav, M.; Singh, A. K.; Pandey, D. S. J. Organomet. Chem. 2011, 696, 758. (h)
Bronner, C.; Baudron, S. A.; Hosseini, M. W. Inorg. Chem. 2010, 49, 8659. (i) Klein, J. H.; Sunderland,
T. L.; Kaufmann, C.; Holzapfel, M.; Schmiedel, A.; Lambert, C. Phys. Chem. Chem. Phys. 2013, 15,
16024.
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2
3
(10)
It should be noted, however, that a too strong reduction in the rate of charge
recombination can be counter-productive (cf. the behavior of triad 2). The optimum charge
4
5
recombination rate for detecting spin effects should match the rate of spin dynamics.
6
(11)
(a) Colvin, M. T.; Ricks, A. B.; Scott, A. M.; Smeigh, A. L.; Carmieli, R.; Miura, T.;
7
8
9
Wasielewski, M. R. J. Am. Chem. Soc. 2011, 133, 1240. (b) Dance, Z. E. X.; Mi, Q. X.; McCamant, D. W.;
Ahrens, M. J.; Ratner, M. A.; Wasielewski, M. R. J. Phys. Chem. B 2006, 110, 25163. (c) Lukas, A. S.;
Bushard, P. J.; Weiss, E. A.; Wasielewski, M. R. J. Am. Chem. Soc. 2003, 125, 3921. (d) Weiss, E. A.;
Chernick, E. T.; Wasielewski, M. R. J. Am. Chem. Soc. 2004, 126, 2326. (e) Weiss, E. A.; Ratner, M. A.;
Wasielewski, M. R. J. Phys. Chem. A 2003, 107, 3639. (f) Weiss, E. A.; Tauber, M. J.; Ratner, M. A.;
Wasielewski, M. R. J. Am. Chem. Soc. 2005, 127, 6052. (g) Weiss, E. A.; Ahrens, M. J.; Sinks, L. E.;
Gusev, A. V.; Ratner, M. A.; Wasielewski, M. R. J. Am. Chem. Soc. 2004, 126, 5577.
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
(12)
(a) Salikhov, K. M.; Molin, Y. N.; Sagdeev, R. Z.; Buchachenko, A. L. Spin polarization
and magnetic effects in radical reactions; Elsevier: Amsterdam, 1984. (b) Steiner, U. E.; Ulrich, T.
Chem. Rev. 1989, 89, 51. (c) Steiner, U. E.; Wolff, H. J. Magnetic Field Effects in Photochemistry In
Photochemistry and Photophysics; Rabek, J. J., Scott, G. W., Eds.; CRC Press: Boca Raton, FL, 1991;
Vol. IV, p 1. (d) Hayashi, H. Introduction to Dynamic Spin Chemistry; World Scientific Publishing:
Singapore, 2004; Vol. 8.
(13)
(a) Desai, P.; Shakya, P.; Kreouzis, T.; Gillin, W. P. J. Appl. Phys. 2007, 102, 073710. (b)
Goto, Y.; Noguchi, T.; Takeuchi, U.; Hatabayashi, K.; Hirose, Y.; Uchida, T.; Sasaki, T.; Hasegawa, T.;
Shimada, T. Org. Electron. 2010, 11, 1212. (c) Ehrenfreund, E.; Vardeny, Z. V. Isr. J. Chem. 2012, 52,
552. (d) Wang, J. P.; Chepelianskii, A.; Gao, F.; Greenham, N. C. Nat. Commun. 2012, 3, 1191.
(14)
(a) Hanna, M. C.; Nozik, A. J. J. Appl. Phys. 2006, 100, 074510. (b) Smith, M. B.; Michl,
J. Chem. Rev. 2010, 110, 6891. (c) Jadhav, P. J.; Mohanty, A.; Sussman, J.; Lee, J.; Baldo, M. A. Nano
Lett. 2011, 11, 1495. (d) Ehrler, B.; Walker, B. J.; Bohm, M. L.; Wilson, M. W. B.; Vaynzof, Y.; Friend, R.
H.; Greenham, N. C. Nat. Commun. 2012, 3, 1019. (e) Smith, M. B.; Michl, J. Annu. Rev. Phys. Chem.
2013, 64, 361. (f) Wilson, M. W. B.; Rao, A.; Ehrler, B.; Friends, R. H. Acc. Chem. Res. 2013, 46, 1330.
(15)
Biophysics of Photosynthesis; Golbeck, J. H., Van der Est, A., Eds.; Springer: New York, 2014, p 141.
(16) (a) Grissom, C. B. Chem. Rev. 1995, 95, 3. (b) Hore, P. J. Proc. Natl. Acad. Sci. U. S. A.
Céspedes-Camacho, I. F.; Matysik, J. Spin in photosynthetic electron transport In The
2012, 109, 1357. (c) Lambert, N.; Chen, Y. N.; Cheng, Y. C.; Li, C. M.; Chen, G. Y.; Nori, F. Nat. Phys.
2013, 9, 10.
(17)
(a) Ritz, T.; Adem, S.; Schulten, K. Biophys. J. 2000, 78, 707. (b) Rodgers, C. T.; Hore,
P. J. Proc. Natl. Acad. Sci. U. S. A. 2009, 106, 353. (c) Dodson, C. A.; Hore, P. J.; Wallace, M. I. Trends
Biochem. Sci. 2013, 38, 435.
(18)
(a) Werner, U.; Sakaguchi, Y.; Hayashi, H.; Nohya, G.; Yoneshima, R.; Nakajima, S.;
Osuka, A. J. Phys. Chem. 1995, 99, 13930. (b) Kuciauskas, D.; Liddell, P. A.; Moore, A. L.; Moore, T. A.;
Gust, D. J. Am. Chem. Soc. 1998, 120, 10880. (c) Klumpp, T.; Linsenmann, M.; Larson, S. L.; Limoges, B.
R.; Burssner, D.; Krissinel, E. B.; Elliott, C. M.; Steiner, U. E. J. Am. Chem. Soc. 1999, 121, 1076. (d)
Mori, Y.; Sakaguchi, Y.; Hayashi, H. J. Phys. Chem. A 2002, 106, 4453. (e) Rawls, M. T.;
Kollmannsberger, G.; Elliott, C. M.; Steiner, U. E. J. Phys. Chem. A 2007, 111, 3485. (f) Maeda, K.;
Henbest, K. B.; Cintolesi, F.; Kuprov, I.; Rodgers, C. T.; Liddell, P. A.; Gust, D.; Timmel, C. R.; Hore, P. J.
Nature 2008, 453, 387. (g) Maeda, K.; Wedge, C. J.; Storey, J. G.; Henbest, K. B.; Liddell, P. A.; Kodis,
G.; Gust, D.; Hore, P. J.; Timmel, C. R. Chem. Commun. 2011, 47, 6563.
(19)
(20)
(21)
Weller, A.; Staerk, H.; Treichel, R. Faraday Discuss. 1984, 78, 271.
Staerk, H.; Kühnle, W.; Treichel, R.; Weller, A. Chem. Phys. Lett. 1985, 118, 19.
(a) Cai, J.; Guerreschi, G.; Briegel, H. J. Phys. Rev. Lett. 2010, 104, 220502. (b) Gauger,
E. M.; Rieper, E.; Morton, J. J. L.; Benjamin, S. C.; Vedral, V. Phys. Rev. Lett. 2011, 106, 040503.
(22)
(23)
Jones, J. A.; Hore, P. J. Chem. Phys. Lett. 2010, 488, 90.
(a) Closs, G. L.; Doubleday, C. E. J. Am. Chem. Soc. 1973, 95, 2735. (b) Haberkorn, R.;
Michel-Beyerle, M. E. Biophys. J. 1979, 26, 489. (c) Schulten, K.; Weller, A. Biophys. J. 1978, 24, 295.
(d) Weller, A. Z. Phys. Chem. Neue Fol. 1982, 130, 129. (e) Hoff, A. J. Q. Rev. Biophys. 1981, 14, 599. (f)
Brocklehurst, B. Chem. Soc. Rev. 2002, 31, 301.
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2
3
(24)
Banci, L.; Bertini, L.; Luchinat, C. Nuclear and Electron Relaxation; VCH: Weinheim,
New York, Basel, Cambridge, 1991.
4
5
6
7
8
(25)
(26)
(27)
(28)
Lüders, K.; Salikhov, K. M. Chem. Phys. 1987, 117, 113.
Lewis, A. M.; Manolopoulos, D. E.; Hore, P. J. J. Chem. Phys. 2014, 141, 044111.
Hayashi, H.; Nagakura, S. Bull. Chem. Soc. Jpn. 1984, 57, 322.
If intermolecular spin-dipolar interactions between the radicals can be neglected, i.e.
9
if the interactions mixing the spin levels are purely local interactions in the two radicals, the
couplings between S and T± and between T0 and T± are of the same magnitude, differing only in sign.
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14
15
16
17
18
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20
21
22
23
24
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29
30
31
32
33
34
35
36
37
38
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40
41
42
43
44
45
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47
48
49
50
51
52
53
54
55
56
57
58
59
60
(29)
(a) Bhosale, S. V.; Jani, C. H.; Langford, S. J. Chem. Soc. Rev. 2008, 37, 331. (b) Andric,
G.; Boas, J. F.; Bond, A. M.; Fallon, G. D.; Ghiggino, K. P.; Hogan, C. F.; Hutchison, J. A.; Lee, M. A. P.;
Langford, S. J.; Pilbrow, J. R.; Troup, G. J.; Woodward, C. P. Aust. J. Chem. 2004, 57, 1011. (c) Barros,
T. C.; Brochsztain, S.; Toscano, V. G.; Berci, P.; Politi, M. J. J. Photochem. Photobiol. A-Chem. 1997,
111, 97.
(30)
(31)
(32)
Amthor, S.; Noller, B.; Lambert, C. Chem. Phys. 2005, 316, 141.
Geiss, B.; Lambert, C. Chem. Commun. 2009, 1670.
(a) Bullock, J. E.; Vagnini, M. T.; Ramanan, C.; Co, D. T.; Wilson, T. M.; Dicke, J. W.;
Marks, T. J.; Wasielewski, M. R. J. Phys. Chem. B 2010, 114, 1794. (b) Gawrys, P.; Djurado, D.;
Rimarcik, J. R.; Kornet, A.; Boudinet, D.; Verilhac, J. M.; Lukes, V.; Wielgus, I.; Zagorska, M.; Pron, A. J.
Phys. Chem. B 2010, 114, 1803.
(33)
The order of magnitude of electron dipolar interaction is given by g2β2/r3 At a
distance of 20 Å, this corresponds to an equivalent hyperfine field of 0.23 mT. However, the dipolar
interaction is fully anisotropic and averaged to zero by molecular rotation.
(34)
A similar set of equations has been set up by Werner et al.18a According to their
definition, [T±]=[T+]=[T–]. It should be noted that a factor of 2 before k3 in the bracket factor before
[S] is missing in the first line of eq. (3).
(35)
(a) Schulten, K.; Wolynes, P. G. J. Chem. Phys. 1978, 68, 3292. (b) Knapp, E. W.;
Schulten, K. J. Chem. Phys. 1979, 71, 1878.
(36)
2005, 81, 573.
(37)
Reszka, K. J.; Takayama, M.; Sik, R. H.; Chignell, C. F.; Saito, I. Photochem. Photobiol.
Hötzer, K. A.; Klingert, A.; Klumpp, T.; Krissinel, E.; Bürßner, D.; Steiner, U. E. J. Phys.
Chem. A 2002, 106, 2207
(38)
Gilch, P.; Pollinger-Dammer, F.; Musewald, C.; Michel-Beyerle, M. E.; Steiner, U. E.
Science 1998, 281, 982.
(39)
Hall, 1967.
Carrington, A. A.; McLachlan, A. D. Introduction to magnetic resonance; Chapman and
(40)
(41)
Weller, A.; Nolting, F.; Staerk, H. Chem. Phys. Lett. 1983, 96, 24.
(a) Justinek, M.; Grampp, G.; Landgraf, S.; Hore, P. J.; Lukzen, N. N. J. Am. Chem. Soc.
2004, 126, 5635. (b) Grampp, G.; Hore, P. J.; Justinek, M.; Landgraf, S.; Lukzen, N. N. Res. Chem.
Intermed. 2005, 31, 567.
(42)
Mladenova, B.; Kattnig, D. R.; Kaiser, C.; Schäfer, J.; Lambert, C.; Grampp, G. J. Phys.
Chem. C 2015, 119, 8547.
(43)
Lambert, C.; Wagener, R.; Klein, J. H.; Grelaud, G.; Moos, M.; Schmiedel, A.; Holzapfel,
M.; Bruhn, T. Chem. Commun. 2014, 50, 11350.
(44)
(45)
Mailer, C.; Nielsen, R. D.; Robinson, B. H. J. Phys. Chem. A 2005, 109, 4049.
Rawls, M. T.; Kuprov, I.; Elliott, C. M.; Steiner, U. E. Spin Relaxation in Ru-
Chromophore-Linked Azine/Diquat Radical Pairs In Carbon-Centered Free Radicals and Radical
Cations; Forbes, M. D. E., Ed.; John Wiley & Sons: Hoboken, New Jersey, 2010.
(46)
(a) Meyer, V.; Eaton, S. S.; Eaton, G. R. Appl. Magn. Reson. 2014, 45, 993. (b) Yong,
L.; Harbridge, J.; Quine, R. W.; Rinard, G. A.; Eaton, S. S.; Eaton, G. R.; Mailer, C.; Barth, E.; Halpern, H.
J. J. Magn. Reson. 2001, 152, 156.
(47)
(a) Solovo'yov, I. A.; Ritz, T.; Schulten, K.; Hore, P. J. A chemical compass for bird
navigation In Quantum effects in biology; Mohseni, M., Omar, Y., Engel, G., Plenio, M. B., Eds.;
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Cambridge University Press: Cambridge, UK, 2014. (b) Ritz, T.; Wiltschko, R.; Hore, P. J.; Rodgers, C.
T.; Stapput, K.; Thalau, P.; Timmel, C. R.; Wiltschko, W. Biophys. J. 2009, 96, 3451. (c) Hogben, H. J.;
Efimova, O.; Wagner-Rundell, N.; Timmel, C. R.; Hore, P. J. Chem. Phys. Lett. 2009, 480, 118. (d)
Efimova, O.; Hore, P. J. Biophys. J. 2008, 94, 1565. (e) Cintolesi, F.; Ritz, T.; Kay, C. W. M.; Timmel, C.
R.; Hore, P. J. Chem. Phys. 2003, 294, 385.
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