Photoinduced Dynamics of Bis-dipyrrinato-palladium(II) and Porphodimethenato-palladium(II) Complexes: Governing Near Infrared Phosphorescence by Structural Restriction

Article abstract of DOI:10.1021/acs.inorgchem.8b00974

Although superficially similar, the bis-dipyrrinato-palladium(II) complex 1 and the bridged porphodimethenato-palladium(II) complex 2 possess dramatically different structures in the ground state (proved by X-ray structure analysis) and in the singlet and

Full text of DOI:10.1021/acs.inorgchem.8b00974

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Cite This: Inorg. Chem. XXXX, XXX, XXX−XXX
Photoinduced Dynamics of Bis-dipyrrinato-palladium(II) and
Porphodimethenato-palladium(II) Complexes: Governing Near
Infrared Phosphorescence by Structural Restriction
Stefan Riese, Marco Holzapfel, Alexander Schmiedel, Ingo Gert, David Schmidt, Frank Wurthner,
̈
and Christoph Lambert*
Institute of Organic Chemistry, Center for Nanosystems Chemistry, Universitat Wurzburg Am Hubland, D-97074 Wurzburg,
̈
̈
̈
Germany
S
* Supporting Information
ABSTRACT: Although superficially similar, the bis-dipyrrinato-
palladium(II) complex 1 and the bridged porphodimethenato-
palladium(II) complex 2 possess dramatically different struc-
tures in the ground state (proved by X-ray structure analysis)
and in the singlet and triplet excited states (calculated by density
functional theory methods). While complex 2 is rather rigid,
complex 1 undergoes a major structural reorganization in the
excited state to yield a disphenoidal (seesaw) triplet state. The
dynamics of the excited states were probed by transient
absorption spectroscopy with femtosecond and nanosecond
time resolution and with fluorescence upconversion and yield
intersystem crossing rate constants of ca. (13−16 ps)−1. The
observation of significant near infrared phosphorescence in
complex 2 but the absence of any emission in complex 1 in fluid solution could be rationalized by the structural reorganization of
1 which results in a nonemissive triplet metal centered state.
INTRODUCTION
Dipyrrin is a ligand that, attached to boron difluoride, forms the
■
well-known BODIPY dyes which are widely used as strongly
fluorescent chromophores.1−4 However, dipyrrin is also known
Scheme 1. Dipyrrin Derivatives and Target Compounds 1
and 2
as a ligand to transition metals, also in form of homoleptic bis-
dipyrrinato metal complexes. Bridging the two dipyrrin ligands
leads to partially saturated porphodimethenes and, after formal
oxidation, to metalloporphyrins.5−8 While, because of the
aromatic nature of the fully conjugated porphyrin ring, the
latter show electronic properties distinctly different from the
former, the dipyrrinato metal complexes are all characterized by
a strong absorption around 20 000 cm−1 which is polarized
along the long dipyrrin axis. However, the metal atom as well as
specific groups attached to the meso-position of the dipyrrin
ligand may change the photophysical behavior considerably,
particularly concerning the lifetime of excited states.9 While
dipyrrinato metal complexes with lighter transition metals and
some main group metals have thoroughly been investigated
concerning their photophysical properties,10−16 not much is
known about homo-6,17−19 and heteroleptic6,17,20−26 complexes
of heavy transition metals with dipyrrin ligands. This is quite
unfortunate because these complexes may be of potential use as
near infrared (NIR) triplet emitters.
Received: April 13, 2018
© XXXX American Chemical Society
A
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Figure 1. X-ray crystal structure of complexes 1 and 2. Hydrogen atoms are removed for clarity. For 1, only one-half of the asymmetric cell is shown.
Thermal ellipsoids are at 50% probability level.
In particular, little is known about dipyrrinato-palladium
complexes.23 Therefore, in this study, we focus on the
photoinduced processes in bis-5-phenyldipyrrinato-palladium-
(II) 1 and 5,5′,15,15′-tetramethyl-10,20-diphenylporphodime-
thenato-palladium(II) 2 (see Scheme 1), which may be
considered as parent compounds to other more complex
structures. Although complex 2 was prepared before by Lindsey
et al.,27,28 its photophysics has not yet been investigated. While
complex 1 itself has not been reported until now, a few
comparable bis-dipyrrinato-Pd(II) complexes were synthesized
and reported to be practically nonemissive, except for a
triarylamine-substituted derivative, which has a quantum yield
of 1.5% and a fluorescence lifetime of 3.5 ns.18,19,29,30 In the
following, we first concentrate on structural aspects of the two
complexes and then on their steady-state and time-resolved
optical spectroscopic properties.
RESULTS
■
Structure. Compound 2 was synthesized as previously
described by Lindsey et al.28 The synthesis of compound 1 is
based on procedures described in the literature for similar
Pd(II) complexes.18,29,30 A detailed description of the synthetic
protocols and the analytical data can be found in the
Supporting Information.
The structures of 1 and 2 in the solid state were determined
by X-ray crystal analysis and are depicted in Figure 1. Selected
dihedral angles and distances can be found in the Supporting
Information, Table S3. Compound 1 has an asymmetric unit
cell comprised of two molecules with slightly different
geometries. Because the differences between the two are
small (on the order of 0.5° for dihedral angles and 0.01 Å for
Figure 2. (a) Absorption spectra of 1 and 2 in MeCN. (b) Emission
distances) and likely due to crystal packing forces, we discuss
spectra of 1 and 2 in fluid MeCN at rt and frozen (77 K) MeTHF.
only the structural features of one molecule. Additional views of
1 and 2 depicting the complete unit cells are given in the
Supporting Information, Figure S5. In the centrosymmetric
(Ci) compound 1, the palladium possesses a square planar
coordination sphere with Pd−N distances of ca. 2.01 Å. The
two dipyrrin ligands are highly bent (145.9° dihedral angle
between planes 1 and 2) and tilted relative to the N4Pd plane
(148.4° dihedral angle between planes 3 and 4) forming a “zig-
zag” geometry as to avoid steric repulsion of the C1/C9
hydrogen atoms with those at C9′/C1′.
In 2, the palladium has a slightly distorted square planar
coordination sphere with Pd−N distances of 2.00−2.01 Å.
Furthermore, the dipyrrin chromophores in 2 are almost planar
(171.0° dihedral angle between planes 1 and 2), but the short
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Table 1. Steady-State and Time Resolved Optical Spectroscopic Data of 1 and 2 in MeCN at rt
1LC2 νmax
̃
/cm−1 (εmax/M−1 cm−1
)
1MLCT νmax
̃
/cm−1 (εmax/M−1 cm−1
)
νem
̃
/cm−1
Φem
fs-TA τ/ps
fs-FLUC t/ps (ampl.)
ns-TA τ/ns
1
20 990
26 110
17 100
0.3 (0.43)
3.0 (0.28)
13 (0.29)
(74 300)
(15 800)
2.2
14
inf.
53
2
20 160
24 860
12 800
0.008
0.1 (0.92)
1 (0.08)
(41 200)
(22 600)
16
48
inf.
129 (0.003)
81 × 103
Figure 3. Chirp corrected transient absorption spectra of 1 and 2 in MeCN at rt (a and d), EADS from a global deconvolution (b and e), and time
traces at selected wavenumbers with fit (c and f).
dimethylmethylene bridges between the two dipyrrin subunits
enforce butterfly (rooftop) geometry of the complex in which
the two dipyrrin chromophores possess a 134.4° dihedral angle
Both complexes show a strong absorption band at ca. 20 000
cm−1 which is caused by a ligand centered (LC) transition,
termed 1LC2 hereafter.18,23,32 To the lower energy side, a much
1
weaker band is visible as a shoulder, which we call LC1 in the
(plane 4 and 9) relative to each other.31
following. These two bands can be interpreted as being caused
by exciton coupling of the localized dipyrrin LC transitions,
which are polarized along the long axis of the dipyrrin ligand.
Accordingly, these two localized transition moments are face to
face, which leads to an H-aggregate-like exciton splitting where
Steady-State Optical Spectroscopy. Absorption spectra
of both complexes were measured in MeCN at rt and are
displayed in Figure 2a. Selected optical spectroscopic data are
given in Table 1.
C
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quartz cell with 2 mm optical path length under magic angle.
The instrument response was determined by fitting the
coherent artifact to be ca. 180 fs (for details, see the Supporting
Information).
The transient absorption (TA) spectra of 1 and 2 are
displayed in Figure 3 in the top panels. We analyzed the TA
data by a global deconvolution which uses the minimum
number of exponential functions to produce evolution
associated difference spectra (EADS) in a sequential model
with increasing lifetimes. These EADS are given in the middle
panels. In the bottom panels, time traces and the global fit for
selected wavenumbers are superimposed.
As can be seen from the global analysis, there are three EADS
for both complexes. Two of those possess lifetimes in the 2−50
ps time range, while the third one shows an infinite lifetime
within the time window (8 ns) accessible with our instrumental
setup.
In general, TA spectra may consist of ground state bleaching
(GSB), stimulated emission (SE), and excited state absorption
(ESA). Thus, we used the three EADS and subtracted the
steady-state absorption spectrum, which yields the ESA
contribution to each of the three EADS. The SE contribution
is neglected here. As can be seen from Figure 4a for EADS1 of
complex 1, this subtraction gives an ESA1 with little structure
because the EADS1 and the GSB (= negative steady state
absorption spectrum) match very well. However, for the
components ESA2 and ESA3 with longer lifetimes, there is
pronounced amplitude visible at 21 000 cm−1. Furthermore, the
absence of negative amplitudes at the low energy site of the
GSB in the ESA indicates that there is no SE contribution.
Compound 2 behaves very similarly; that is, the EADS1
matches very well with the steady-state absorption spectrum,
but the EADS associated with longer lifetimes show a strong
ESA contribution at ca. 19 500 cm−1.
Figure 4. ESA from difference spectra of EADS and steady-state
absorption spectra of 1 (a) and 2 (b) in MeCN.
The infinite lifetime of EADS3 shows for both complexes
that a distinctly long-lived component contributes to the TA
spectra. Therefore, we performed nanosecond laser flash
spectroscopy with solutions of 1 and 2 in MeCN, which
allows covering transient species down to the millisecond time
regime. Thus, excitation at the 1LC2 band shows the immediate
rise of a transient signal which matches excellently with the
longest lived EADS from the femtosecond TA analysis (see
Figure 5), that is, a strong GSB at 21 000 cm−1 for 1 and at ca.
20 000/22 000 cm−1 for 2, associated with a strong ESA at
lower wavenumbers for both complexes. Fits at selected
wavenumbers yield monoexponential decays with τ = 53 ns
for 1 and 81 μs for 2.
To complement the femtosecond transient absorption data
and gain information about intersystem crossing (ISC)
processes, we also performed fluorescence upconversion
measurements (FLUC) at 25 000 cm−1 excitation from the
frequency doubled 800 nm output of the Ti:sapphire oscillator
at 80 MHz. The fluorescence decays and their fit using several
exponential functions convoluted with the instrument response
are given in Figure 6. While complex 2 shows a decay with ca.
0.1 ps as the dominating component, complex 1 clearly displays
multiexponential decay with three almost equally contributing
components. The two longer time constants (3 and 13 ps)
agree very well with those of the EADS of the TA
measurements (2.2 and 14 ps). The time-resolved data from
the femto- and nanosecond TA as well as the femtosecond
FLUC measurements are collected in Table 1.
the upper state is strongly allowed but the lower state is
forbidden.11,18,32,33 Furthermore, at ca. 25 000−26 000 cm−1,
there is a pronounced MLCT band visible.23,34
At 77 K in frozen 2-MeTHF, both complexes show strong
and vibrationally resolved phosphorescence between ca. 14 500
and 9000 cm−1 (see Figure 2b), which is distinctly red-shifted
compared to those recently reported for two phenylpyridyl-
dipyrrin-palladium complexes.23 This situation changes dra-
matically at rt in fluid MeCN. Here, the nonbridged dipyrrin
complex 1 emits a weak and unstructured fluorescence between
13 000 and 19 000 cm−1 but no phosphorescence. In contrast,
the bridged complex 2 shows relatively strong but unresolved
phosphorescence with a quantum yield of 0.01 in MeCN (0.02
in THF) at the same spectral position as at 77 K, but no
fluorescence.
Time Resolved Optical Spectroscopy. To obtain
information about the photoinduced dynamics of complexes
1 and 2, we performed transient absorption spectroscopy with
femtosecond and nanosecond time resolution in fluid MeCN at
rt.
In the femtosecond experiments, solutions of 1 or 2 in
MeCN were excited with laser pulses (<150 fs, 1 kHz,
generated using an OPA pumped with the amplified output of a
1
Ti:sapphire laser at 800 nm) at the maximum of their LC2
band. The excited states were probed by a white light
continuum, which was delayed by a controlled stage equipped
with a retroreflector. The pump and probe beam met in a
D
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Figure 5. Nanosecond transient absorption spectra of 1 and 2 in MeCN at rt (a and c) and selected time traces with monoexponential fit (b and d).
Density Functional Theory (DFT) Computations. To
gain insight into structural and electronic aspects of the excited
states of complexes 1 and 2, we performed DFT and time-
dependent TD-DFT computations. Optimization of the ground
states of 1 and 2 using the PBE1PBE functional and SDD-6-
31G* basis set combination shows excellent agreement with the
X-ray crystal structure data; for a comparison of structural data,
see Supporting Information, Table S3. For 1, we also found a
ground state structure with D2 symmetry in which the
palladium possesses a distorted tetrahedral coordination sphere.
However, this structure is about 1600 cm−1 higher in energy
than the Ci symmetric structure, which corresponds to the
experimental crystal structure. On the other hand, for 2, only
one ground state structure with CS symmetry was found. Based
on these DFT optimized ground state structures with minimal
energy (Ci for 1 and Cs for 2), we computed the vertical
excitations into the LC states by the TD-DFT method. As
1
anticipated above, the lowest excited LC1 state is forbidden in
1
both complexes, but LC2 is allowed (see Table 2). This is the
consequence of a symmetric (Ag for 1 and A′′ for 2) and
antisymmetric (Au for 1 and A′ for 2) combination of dipyrrin
transition moments. The absolute energies of these computed
Figure 6. Fluorescence decay from fluorescence upconversion
measurements of (a) 1 and (b) 2 in MeCN at rt at 25 000 cm−1
excitation. The fluorescence was gated at 17 200 cm−1 (IRF 0.24 ps)
for 1 and at 18 700 cm−1 (IRF 0.17 ps) for 2.
transitions into LC2 are by ca. 1500 cm−1 too high compared
1
to the experimental energies (see Table 1). However, the
Table 2. DFT Calculated Energies (cm−1), Oscillator Strength (f), and Symmetry of Franck−Condon (FC) and Optimized
Excited States (TD-DFT for Singlet and UDFT for Triplet States)
1LC1(FC) (f)
1LC2(FC) (f)
1LC1
1LC1
1LC1
3LC
3LC
3MC
12 567
(disph, ∼C2)
a
a
1
2
21 737 (0.0000)
(Ci)
22 918 (0.0176)
(Ci)
24 037
20 767
19 272
(C1)
19 268
16 692
(Ci)
(D2)
(Ci)
(D2)
20 008 (0.0006)
(Cs)
21 640 (0.0270)
(Cs)
18 405
(∼Cs)
14 616
(∼Cs)
a
Transition state.
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the computed D2 ground state structure) also turned out to be
transition states by frequency analysis.
For the corresponding triplet states, we used the UDFT
method. Engels et al.35 recently showed that using this strategy
yields reasonable singlet−triplet energy differences. Here, we
found three different minimum structures: one with Ci
symmetry which corresponds to the crystal structure with
square planar coordinated palladium and bent dipyrrin ligands
(see Figure 7a), a second one in which the palladium has a
strongly distorted tetrahedral coordination sphere (D2) with
planar dipyrrin ligands (see Figure 7b), and a third, where the
palladium possesses a disphenoidal (seesaw) coordination
sphere (∼C2) and planar ligands (Figure 7c). For the D2 and
the ∼C2 triplet structures, we did not find any corresponding
minimum singlet excited state structures, but transition states.
Clearly, the disphenoidal structure is the lowest energy triplet
structure (see Table 2). In this structure, the spin density is
localized at the palladium atom (see Figure 7c), which also
leads to an elongation of the Pd−N bonds which are 2.102 and
2.114 Å. Thus, the disphenoidal triplet state can be viewed as a
metal centered 3MC state. While usually a square planar
coordination sphere predominates for Pd(II) complexes in the
ground state, some exceptions are known, which include
tetrahedral,36 trigonal pyramidal,37 and disphenoidal38 struc-
tures. For the tetrahedral structure, a triplet state was
rationalized based on magnetic measurements which show
that deviations from square planar geometry can indeed be
preferred for open-shell Pd(II) species as is the triplet MC state
here.36
The other two triplet states of 1 have distinctly higher
energy, and the spin density is delocalized over the dipyrrin
ligands with little, if at all, participation of the metal atom.
Much in contrast to 1, for 2, besides a nearly symmetric 1LC1
state (∼Cs) whose butterfly geometry is even stronger folded
than in the ground state (θ4/9 = 120.3° (1LC1) vs 133.9° (S0)),
we found only one excited triplet state which has a similar
1
geometry as the LC1 state (∼Cs, dPd−N = 1.995 and 2.006 Å ;
θ4/9 = 123.3°). Here, the spin density is delocalized over the
two dipyrrin ligands (see Figure 7d). The relative energies of all
these states are collected in Table 2.
Figure 7. UDFT calculated geometries and spin densities of excited
triplet states of 1 and 2.
DISCUSSION AND CONCLUSION
■
splitting ΔE = 1180 cm−1 (1) and 1632 cm−1 (2) of the two
transitions which corresponds to twice the exciton coupling
energy appears to be reasonable when compared to the
With the spectroscopic and computational information at hand,
we can construct a state diagram for the photophysical
processes in complexes 1 and 2 which are sketched in Figure
8. In these diagrams, the corresponding 00-energies of states
were estimated from the intersection of the energy axis with
tangents drawn at the low energy side of absorption or high
energy side of emission spectra.
1
1
difference of the experimental 00-energies of LC1 and LC2
from Figure 8 (1500 cm−1 (1) and 1600 cm−1 (2)).
We also optimized the lowest lying excited states of 1 and 2
1
using two different strategies. The singlet LC1 state of 1 was
optimized by TD-DFT, which gave a structure very similar to
the ground state structure. Optimized in Ci symmetry, this
structure turned out to be a transition state by frequency
analysis but a distorted structure (C1) is a minimum on the
excited state hypersurface. While the four Pd−N distances in
this symmetry-broken singlet structure vary slightly (1.991 and
1.974 Å to one dipyrrin ligand and 2.071 and 2070 Å to the
other), the strongest differences to the ground state structure
refer to the dihedral angles between planes 3/4 (= θ3/4). This
angle is 157.2° in the singlet excited state which deviates
Fluorescence decays as measured by FLUC at a single
wavenumber give a first hint about the early photoinduced
1
1
dynamics involving both LC2 and LC1 states because the
fluorescence from these states is expected to be broad and
strongly overlapping. For complex 1, excitation into the intense
1LC2 band populates a very short-lived singlet state whose
existence cannot be proved by TA spectroscopy but is evident
by the 300 fs time constant of the fluorescence decay in the
FLUC measurement. This time constant refers to the internal
1
conversion to the LC1 state which is visible in the TA spectra
somewhat from that of the DFT optimized ground state (θ3/4
=
as an EADS which consists of almost pure GSB. The fact that
1
149.0°) and the experimental crystal structure (θ3/4 = 148.4°).
Another singlet 1LC1 state with exact D2 symmetry and
distorted tetrahedral coordination sphere of Pd (which refers to
the LC2 state is not visible in the TA spectra is probably
caused by the fact that it is very short-lived and consists almost
purely of GSB and therefore cannot be distinguished from the
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Figure 8. State diagram of 1 and 2. The energies (cm−1) of states were estimated by the intersection of a tangent at the low (high) energy flank of
the corresponding absorption (emission) band with the energy axis. The corresponding excited state structures are calculated at the DFT level. The
given lifetimes refer to states but approximate inverted rates if one assumes that the assigned process dominates. If two lifetimes are given, the first
refers to the TA measurement, the second to the FLUC measurement. Energies in round brackets are emission energies upconverted in the FLUC
measurements. The dotted wavy arrow indicates a process at rt which was not observed but also cannot be excluded from our experiments (see main
text for details).
ISC process to the 3LC state. However, from TA spectroscopy,
the EADS with τ = 16 ps shows a similar spectral change to the
following EADS as in the case of complex 1. Thus, it is likely
that this process refers to ISC with 1/τ = (16 ps)−1. This
change of electronic structure goes along with the rise of a
strong ESA in the TA spectra as is also visible in the following
EADS with τ = 48 ps (see Figure 4b). We assign this time
1LC1 state. A component with τ = 3 ps in the FLUC decay
indicates vibrational relaxation within the LC1 state. This is
1
supported by two very similar EADS in the deconvolution of
the TA spectra (see Figure 3b). Finally, ISC to the lowest lying
triplet state occurs with τ = 13 ps. This change of electronic
structure is also visible in the TA spectra by the EADS with τ =
14 ps which, in contrast to the 1LC states, also shows a
pronounced ESA, see Figure 4a. The fact that we observe
3
constant to a slow vibrational relaxation within the LC state.
1
As shown by nanosecond TA spectroscopy, this state has a
lifetime of 82 μs (see Figure 5d) and is also emissive both at rt
in fluid MeCN and in frozen MeTHF (see Figure 2b) because
it cannot rearrange to a disphenoidal structure as in case of 1.
Nanosecond TA measurements in fluid THF and toluene gave
almost identical results with somewhat longer lifetimes (see
Figures S3 and S4 in the Supporting Information), ruling out
the participation of any interligand CT states in the relaxation
pathway.10
In conclusion, the photophysics of complexes 1 and 2 is
governed by a fast ISC process from LC states to triplet states
(1/τ ≈ (13 ps)−1 − (16 ps)−1). This ISC rate constant is
comparable to those of other Pd(II) complexes.40 While the
bis-dipyrrin complex 1 can undergo structural reorganization
toward a nonemissive 3MC state, this is impeded by the
structurally more rigid bridged ligand in complex 2 which
therefore shows significant NIR phosphorescence even in fluid
solution at rt.41,42
fluorescence from the LC1 state which, according to exciton
coupling theory, should be a dark state, is probably caused by
structural flexibility of 1 which disturbs the Ci symmetry by an
1
asymmetric vibration and makes fluorescence from the LC1
state partially allowed.
In fluid solution, we expect that the lowest energy triplet
state of 1 adopts disphenoidal geometry as supported by the
DFT calculations. This state has a rather short lifetime (53 ns),
as was proved by nanosecond TA spectroscopy (see Figure 5c),
3
which is typical of states with pronounced MC character. In
3
agreement with our observations, such a MC state should be
nonemissive.39 However, complex 1 in frozen MeTHF matrix
shows a strong, structured emission, in agreement with
phosphorescence from a 3LC state which cannot undergo
structural reorganization into the 3MC state because of the rigid
matrix (see Figure 2b). At this point, we stress that we cannot
3
exclude that even at rt a LC is slowly populated by ISC from
1
3
the LC1 state and then relaxes quickly to the MC state
because, if this scenario applies, the intermediate concentration
ASSOCIATED CONTENT
* Supporting Information
■
3
of LC would be too low to be detectable.
S
Complex 2 cannot undergo such structural reorganization as
1 because the relative orientation of dipyrrin subunits and
thereby the coordination sphere of the Pd atom is fixed by the
two dimethylmethylene bridges. On the other hand, the ground
state structure is different from that of 1, as was discussed
above. Excitation of the strongly allowed 1LC2 state is followed
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/acs.inorg-
chem.8b00974.
Synthesis, analytical methods, steady state electronic
spectra, transient absorption spectra, X-ray crystallo-
graphic data, and computational results (PDF)
1
by IC to the dark LC1 state with 1/τ = (0.1 ps)−1 as seen in
the FLUC experiment (see Figure 6b). A weak component with
τ = 1 ps may indicate vibrational relaxation within the LC1
state. This state is so weakly fluorescent that we were unable to
get reasonable data by FLUC spectroscopy to characterize the
Accession Codes
1
CCDC 1835934−1835935 contain the supplementary crystal-
lographic data for this paper. These data can be obtained free of
charge via www.ccdc.cam.ac.uk/data_request/cif, by emailing
G
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data_request@ccdc.cam.ac.uk, or by contacting The Cambridge
Crystallographic Data Centre, 12 Union Road, Cambridge CB2
1EZ, UK; fax: +44 1223 336033.
AUTHOR INFORMATION
Corresponding Author
*E-mail: christoph.lambert@uni-wuerzburg.de.
■
ORCID
Frank Wurthner: 0000-0001-7245-0471
̈
Christoph Lambert: 0000-0002-9652-9165
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
We thank the Deutsche Forschungsgemeinschaft for support of
this work in the GRK 2112 and the Bavarian Ministry of
Education, Culture, Research, and the Fine Arts for Support
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