Electronic and exchange coupling in a cross-conjugated D-B-A biradical: Mechanistic implications for quantum interference effects

Article abstract of DOI:10.1021/ja405354x

A combination of variable-temperature EPR spectroscopy, electronic absorption spectroscopy, and magnetic susceptibility measurements have been performed on Tp^Cum,MeZn(SQ-m-Ph-NN) (1-meta) a donor-bridge-acceptor (D-B-A) biradical that possesses a cross-conjugated meta-phenylene (m-Ph) bridge and a spin singlet ground state. The experimental results have been interpreted in the context of detailed bonding and excited-state computations in order to understand the excited-state electronic structure of 1-meta. The results reveal important excited-state contributions to the ground-state singlet-triplet splitting in this cross-conjugated D-B-A biradical that contribute to our understanding of electronic coupling in cross-conjugated molecules and specifically to quantum interference effects. In contrast to the conjugated isomer, which is a D-B-A biradical possessing a para-phenylene bridge, admixture of a single low-lying singly excited D → A type configuration into the cross-conjugated D-B-A biradical ground state makes a negligible contribution to the ground-state magnetic exchange interaction. Instead, an excited state formed by a Ph-NN (HOMO) → Ph-NN (LUMO) one-electron promotion configurationally mixes into the ground state of the m-Ph bridged D-A biradical. This results in a double (dynamic) spin polarization mechanism as the dominant contributor to ground-state antiferromagnetic exchange coupling between the SQ and NN spins. Thus, the dominant exchange mechanism is one that activates the bridge moiety via the spin polarization of a doubly occupied orbital with phenylene bridge character. This mechanism is important, as it enhances the electronic and magnetic communication in cross-conjugated D-B-A molecules where, in the case of 1-meta, the magnetic exchange in the active electron approximation is expected to be J ～ 0 cm^-1. We hypothesize that similar superexchange mechanisms are common to all cross-conjugated D-B-A triads. Our results are compared to quantum interference effects on electron transfer/transport when cross-conjugated molecules are employed as the bridge or molecular wire component and suggest a mechanism by which electronic coupling (and therefore electron transfer/transport) can be modulated.

Full text of DOI:10.1021/ja405354x

Article
pubs.acs.org/JACS
Electronic and Exchange Coupling in a Cross-Conjugated D−B−A
Biradical: Mechanistic Implications for Quantum Interference Effects
Martin L. Kirk,*,‡ David A. Shultz,*,† Daniel E. Stasiw,† Diana Habel-Rodriguez,‡ Benjamin Stein,‡
and Paul D. Boyle†,§
‡Department of Chemistry, The University of New Mexico, MSC03 2060, Albuquerque, New Mexico 87131-0001, United States
†Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, United States
S
* Supporting Information
ABSTRACT: A combination of variable-temperature EPR
spectroscopy, electronic absorption spectroscopy, and mag-
netic susceptibility measurements have been performed on
TpCum,MeZn(SQ-m-Ph-NN) (1-meta) a donor−bridge−ac-
ceptor (D−B−A) biradical that possesses a cross-conjugated
meta-phenylene (m-Ph) bridge and a spin singlet ground state.
The experimental results have been interpreted in the context
of detailed bonding and excited-state computations in order to
understand the excited-state electronic structure of 1-meta.
The results reveal important excited-state contributions to the
ground-state singlet−triplet splitting in this cross-conjugated D−B−A biradical that contribute to our understanding of electronic
coupling in cross-conjugated molecules and specifically to quantum interference effects. In contrast to the conjugated isomer,
which is a D−B−A biradical possessing a para-phenylene bridge, admixture of a single low-lying singly excited D → A type
configuration into the cross-conjugated D−B−A biradical ground state makes a negligible contribution to the ground-state
magnetic exchange interaction. Instead, an excited state formed by a Ph-NN (HOMO) → Ph-NN (LUMO) one-electron
promotion configurationally mixes into the ground state of the m-Ph bridged D−A biradical. This results in a double (dynamic)
spin polarization mechanism as the dominant contributor to ground-state antiferromagnetic exchange coupling between the SQ
and NN spins. Thus, the dominant exchange mechanism is one that activates the bridge moiety via the spin polarization of a
doubly occupied orbital with phenylene bridge character. This mechanism is important, as it enhances the electronic and
magnetic communication in cross-conjugated D−B−A molecules where, in the case of 1-meta, the magnetic exchange in the
active electron approximation is expected to be J ∼ 0 cm−1. We hypothesize that similar superexchange mechanisms are common
to all cross-conjugated D−B−A triads. Our results are compared to quantum interference effects on electron transfer/transport
when cross-conjugated molecules are employed as the bridge or molecular wire component and suggest a mechanism by which
electronic coupling (and therefore electron transfer/transport) can be modulated.
studies,15−19 and the magnitude of the magnetic exchange
INTRODUCTION
■
interaction in D+−B−A− charge-separated states.4,6,8,13 We
The relationship between donor−acceptor (D−A) interactions
have shown that stable D−B−A biradicals are effective ground-
state analogues of charge-separated states.20−22 A key finding
for D−B−A biradicals that possess conjugated bridges is the
importance of a single D → A charge transfer excited state that
configurationally mixes into the ground state to stabilize the
spin triplet.20−22
In contrast to electron-transfer systems that utilize
conjugated bridges and display a well-known reduction in
bridge-mediated electronic coupling as a function of distance,
the use of cross-conjugated bridges dramatically reduces D−A
coupling at parity of D−A distance.15 The rates of photo-
induced charge separation in D−A molecules that possess
cross-conjugated bridges are ∼30 times slower than rates of
charge separation in D−A molecules having isomeric,
and molecular electronics began when Aviram and Ratner1
suggested that a donor−bridge−acceptor (D−B−A) molecule
could function as a rectifier. The D−A paradigm has also
contributed extensively to our understanding of photoinduced
electron transfer (PET),2−8 where a spin exchange interaction
(J) exists between radical pair electrons in the D+−A− charge-
separated state. Based on the work of Anderson and others,9−12
Wasielewski and co-workers4−8,13 have shown that the rate of
photoinduced electron transfer is directly proportional to both J
and the square of the electronic coupling matrix element, Hab,
for a variety of D−B−A triads in the nonadiabatic regime. The
magnitude of the electronic coupling in D−A systems typically
displays an exponential decay as a function of increasing D−A
distance5 and is modulated by the intrinsic electronic structure
of the bridge that connects D and A. A wide array of molecular
structure-property relationships have been probed by PET rates
in D−B−A excited states,3,7,14,15 theoretical and computational
Received: June 2, 2013
© XXXX American Chemical Society
A
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1
temperature. H and 13C chemical shifts are listed in parts per million
(ppm) and are referenced to residual protons or carbons of the
deuterated solvents, respectively. Infrared spectra were recorded on a
conjugated bridges.15,23 Since the rate constant varies as Hab
,
2
this implies that Hab(cross-conjugated) ∼ Hab(conjugated)/
(30)1/2. In related electron transport systems where single
molecules bridge nanoelectrode assemblies, the use of cross-
conjugated molecules results in an effective barrier to efficient
electron transmission.16−19,24 The reduction in transmission
derives from destructive antiresonances (quantum interference
effects)17−19,24−28 that tend to cancel competing pathway
contributions to electron transfer/transport,27,29−34 and it has
recently been suggested that fast and reproducible switching16
can be actuated through the use of these quantum interference
effects. Thus, studies of cross-conjugated D−B−A systems
represent an important area of research directly related to
molecular electronics. In fact, theoretical calculations suggest
that the electron density distribution affects transmission
properties in cross-conjugated bridges such as meta-phenylene
(m-Ph) in a predictable way,15−19 effectively moving the
destructive interference feature responsible for insulator
behavior to positive and negative potentials relative to the
Fermi energy and turning on conduction.
We have used a combined spectroscopic and magnetic
approach augmented by bonding and excited-state computa-
tions to understand the electronic origin of the ground-state
magnetic exchange and electronic coupling (Hab) in D−B−A
biradicals,22 where donor = semiquinone (SQ) and acceptor =
nitronylnitroxide (NN). This has allowed us to determine Hab
in the adiabatic regime. A valence bond configuration
interaction (VBCI) model11,20,21,35,36 has been used to relate
Hab to the exchange coupling parameter, 2J, via eq 1 (where K0
is the exchange splitting of the dominantly contributing charge-
transfer (CT) excited state and U is the mean CT energy).
Bruker Vertex 80v spectrometer with Bruker Platinum ATR
̈
̈
attachment. Elemental analyses were performed by Atlantic Microlabs,
Inc. High-resolution mass spectra were obtained at the NCSU
Department of Chemistry Mass Spectrometry Facility. Compounds
4,37,38 7,39 10,40 and 1341 were prepared according to published
procedures.
Electronic Structure Calculations. Spin unrestricted gas-phase
geometry optimizations were performed at the density functional level
of theory using the Gaussian 03 software package.42 All calculations
employed the B3LYP hybrid functional. A 6-31G(d′p′) split-valence
basis set with polarization functions was used for all atoms. Input files
were prepared using the molecule builder function in the Gaussview
software package, and the t-butyl substituent on the semiquinone was
modeled as a methyl group. Frontier molecular orbitals (MOs) were
generated for the optimized ground states. Optical excitation energies
and oscillator strengths were calculated using time-dependent DFT
(TDDFT) methods. These TDDFT calculations were performed on
the optimized ground-state geometries, and the first 25 excited states
were calculated. Electron density difference maps were constructed
utilizing custom in-house software.43 Complete active space self-
consistent field (CASSCF) calculations, which are based on a
multiconfigurational approach, were carried out in the ORCA SCF-
MO program.44 The CASSCF calculations employed a def2-TZVP
triple-ζ basis set with added polarization functions and a convergence
tolerance for the orbital gradient of 1e−4. The energy was optimized
for the singlet and triplet ground states with respect to the coefficients
of the configurations that contribute to each state as well as the MO
coefficients of the spin restricted orbitals.
Electron Paramagnetic Resonance. EPR spectra were recorded
on a JEOL JES-FA100 EPR spectrometer, with low-temperature
spectra recorded by use of an ARS-LTR continuous flow cryostat. A 2
mM sample was prepared in freshly distilled 2-methyl-tetrahydrofuran
and degassed, and the spectra collected in a J. Young tube. Collected
variable-temperature (VT) data were fit using the Curie law and a
Boltzmann distribution of S = 1 to 0 ground states.
Hab2K0
J
=
U2 − K0
ab
2
(1)
Magnetic Susceptibility. Magnetic susceptibility measurements
were collected on a Quantum Design MPMS-XL7 SQUID magneto-
meter with an applied field of 0.7 T. A microcrystalline sample (∼20
mg) was loaded into a gelcap/straw sample holder and mounted to the
sample rod with Kapton tape for VT measurements. Collected raw
data were corrected with a straight line for diamagnetic response of
sample container and molecular diamagnetism using Pascal’s constants
as a first approximation, where the slope of the line represents the
residual diamagnetic correction.
Herein, we describe structural, spectroscopic, magnetic, and
computational studies of an SQ-(m-Ph)-NN biradical bridged
by the cross-conjugated m-Ph spacer. To the best of our
knowledge, this is the first detailed electronic structure study of
a D−B−A biradical system directed toward understanding the
effects of bridge connectivity on electronic coupling at parity of
D and A and the composition of the bridge. In particular, we
have determined the excited-state origin of the ground-state
exchange in a cross-conjugated D−B−A triad (1-meta), which
gives rise to quite different electronic and exchange couplings
compared to the conjugated para-isomer. Our results suggest
revealing differences in electronic coupling for D−B−A
molecules that possess cross-conjugated bridges compared to
their conjugated bridge counterparts. We show that the use of
cross-conjugated bridges in D−B−A biradicals: (1) changes the
sign of the magnetic exchange interaction from ferromagnetic
to antiferromagnetic; (2) dramatically reduces key CT
contributions to the ground-state exchange; and (3) allows
dynamic spin polarization contributions to the exchange to
dominate. Importantly, our findings have implications for
molecular design features in electron transfer/transport systems
that are subject to quantum interference effects.
Electronic Absorption Spectroscopy. Low-temperature elec-
tronic absorption spectra were obtained on a Hitachi U-3501 UV−vis-
NIR spectrometer capable of scanning a wavelength region between
185 and 3200 nm using a double-beam configuration at 2.0 nm
resolution. The instrument was calibrated to the 656.1 nm deuterium
line using the corresponding Hitachi software option. Variable-
temperature electronic absorption measurements required the removal
of the cuvette holder assembly in order to accommodate the cryostat
in the sample chamber. A custom designed Janis STVP-100
continuous flow cryostat was mounted in the sample holder allowing
for VT electronic absorption data to be conveniently collected in the
5−300 K temperature range. Sample temperature was monitored with
a Lakeshore silicon diode (PT-470) and regulated by a combination of
helium flow and dual heater assemblies. Solid-solution spectra were
collected on thin polystyrene (MW = 280 000) polymer films prepared
by evaporation of saturated polystyrene solutions cast on glass plates.
Synthesis. 3′-(tert-Butyl)-4′-hydroxy-[1,1′-biphenyl]-3-carboxal-
dehyde (6). To a 50 mL Schlenk flask, 1.00 g (4.36 mmol) 4-bromo-2-
tert-butylphenol, 4, was added with 782 mg (5.23 mmol) (3-
formylphenyl)boronic acid, 5, and 273 mg (0.24 mmol) tetrakis-
(triphenylphosphine) palladium(0), with ∼15 mL tetrahydrofuran
under nitrogen atmosphere. A 2 M solution of potassium carbonate
was degassed, and 7.6 mL was added to the reaction flask via syringe.
EXPERIMENTAL SECTION
■
General Considerations. Reagents and solvents were purchased
from commercial sources and used as received unless otherwise noted.
1H and 13C NMR spectra were recorded on a Varian Mercury 400
MHz or a Varian Mercury 300 MHz spectrometer at room
B
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Figure 1. Bond line drawings for compounds discussed in this study.
The reaction was refluxed 16 h and checked by thin layer
chromatography (TLC) (75% ethyl acetate in hexanes) to ensure
product formation. The reaction was cooled to room temperature and
quenched by addition of ∼10 mL deionized water with stirring in air
for 30 min. The reaction mixture was transferred to a separatory
funnel, washed with saturated sodium bicarbonate, and then extracted
with dichloromethane. The dichloromethane extractions were dried
over sodium sulfate, and the solvent was removed under reduced
pressure. The resulting brown oil was dissolved in diethyl ether, and
approximately an equal volume of petroleum ether was added then
filtered through medium porosity sintered glass. The solvent was
removed under reduced pressure yielding a yellow solid which was
recrystallized from warm ethyl acetate to yield 721 mg of compound 6
The product is purified by flash chromatography (20% ethyl acetate in
hexanes) to yield 401 mg of compound 9 (86% yield). 1H NMR
(DMSO-d6, δ): 10.08 (s, 1H), 9.64 (s, 1H), 8.33 (s, 1H), 8.02 (s, 1H),
7.83 (m, 2H), 7.64 (t, 3J 7.7 Hz, 1H), 7.02 (s, 1H), 6.97 (s, 1H), 1.40
(s, 9H). 13C NMR (DMSO-d6, ppm): 193.47, 145.61, 144.48, 142.00,
136.76, 136.17, 132.02, 129.71, 128.78, 127.121, 126.99, 115.71,
111.33, 34.51, 29.41. IR (cm−1): 3140 (br, νO−H), 1678 (s, νCO).
Mass spectrometry (m/z): (M + H)+ calcd for C17H18O3: 271.1334;
found: 271.1327.
2-(3′-(tert-Butyl)-4′,5′-dihydroxy-[1,1′-biphenyl]-3-yl)-4,4,5,5-tet-
ramethylimidazolidine-1,3-diol (11). To a 10 mL pear-shaped flask,
331 mg (1.22 mmol) 9 and 279 mg (1.88 mmol) N,N′-(2,3-
dimethylbutane-2,3-diyl)bis(hydroxylamine), 10, were added with a
magnetic stir bar. A Schlenk adapter was attached and sealed with a
thick septum. The system was then attached to a Schlenk line and
pump/purged with nitrogen 5 times. In a 50 mL Schlenk flask 15 mL
methanol was degassed, and 2 mL was added to the reaction flask. The
reaction mixture was stirred for 24 h at room temperature. The
resulting opaque white solution was vacuum filtered to collect a white
solid that was collected into a sample vial and dried under reduced
1
(65% yield). H NMR (DMSO-d6, δ): 10.07 (s, 1H), 9.64 (s, 1H),
8.08 (t, 4J 1.6 Hz, 1H), 7.91 (dt, 3J 7.7 Hz, 4J 1.6 Hz, 1H), 7.79 (dt, 3J
7.7 Hz, 4J 1.6 Hz, 1H), 7.62 (t, 3J 7.7 Hz, 1H), 7.46 (d, 3J 2.2 Hz, 1H),
3
7.39 (dd, 3J 8.2 Hz, 3J 2.2 Hz, 1H), 6.91 (d, J 8.2, 1H), 1.41 (s, 9H).
13C NMR (DMSO-d6, ppm): 193.97, 156.88, 142.42, 137.40, 136.45,
132.66, 130.25, 129.95, 127.98, 127.40, 125.95, 125.61, 117.43, 35.05,
29.92. IR (cm−1): 3310 (br, νO−H), 1690 (s, νCO). Elemental
analysis: calcd (C: 80.28, H: 7.13), found: (C: 79.99, H: 7.09).
5′-(tert-Butyl)-3′,4′-dioxo-3′,4′-dihydro-[1,1′-biphenyl]-3-carbox-
aldehyde (8). To a 50 mL pear shaped flask, 593 mg (2.33 mmol) 6
and 1.33 g (4.75 mmol) 7 were added with 2 mL dimethylformamide
and stirred shielded from light for 30 h. After about 30 min, the
solution changed color from light yellow to dark green. Reaction
progress is monitored by TLC (50% ethyl acetate in hexanes) and 1H
NMR. Once all of 6 had been consumed, the reaction was poured into
100 mL water, transferred to a separatory funnel, and extracted with
ethyl acetate. The organic phase was washed three times with saturated
sodium bicarbonate solution and then twice with half-saturated sodium
chloride solution. The organic phase was then collected and dried over
sodium sulfate, and the solvent removed under reduced pressure to
1
pressure yielding 339 mg of compound 11 (80% yield). H NMR
(DMSO-d6, δ): 9.52 (br s, 1H), 8.14 (br s, 1H), 7.77 (s, 2H), 7.62 (s,
1H), 7.35 (m, 2H), 6.95 (s, 1H), 6.89 (s, 1H), 4.53 (s, 1H), 1.38 (s,
3
9H), 1.08 (d, J 4.4 Hz, 12H). 13C NMR (DMSO-d6, ppm): 145.22,
143.55, 142.22, 140.47, 135.78, 130.56, 127.77, 126.40, 126.32, 124.81,
90.32, 66.03, 34.29, 29.35, 24.25, 17.06.
3-tert-Butyl-4-(phenyl-3-nitronylnitroxide)-o-catechol (12). To a
100 mL round-bottom flask, 49 mg (0.12 mmol) 11 was added with
20 mL diethyl ether, 10 mL fresh pH 7 buffer, and magnetically stirred
at 0 °C. To a 60 mL separatory funnel, 47 mg (0.18 mmol) I2 was
added with 30 mL diethyl ether and shaken. The solution of I2 was
added dropwise with stirring to the reaction mixture. After all of the
iodine was added, the reaction stirred for 15 min, and then 100 mL pH
7 buffer was added. The reaction was transferred to a separatory funnel
and washed with 50 mL saturated thiosulfate solution twice followed
by 50 mL saturated sodium chloride solution. The organic phase was
collected and dried over magnesium sulfate, and the solvent removed
under reduced pressure to yield 53 mg of 12 (>99% yield). IR (cm−1):
3300 (br, νO−H). EPR (X-band, 298 K): pentet (1:2:3:2:1), aN = 7.6
G. Mass spectrometry (m/z): (M + H − O)+ calcd for C23H31N2O3:
383.2335; found: 383.2322.
1
yield 460.7 mg of compound 8 (70% yield). H NMR (CDCl3, δ):
8.05 (s, 1H), 7.95 (d, 3J 7.9 Hz, 1H), 7.83 (d, 3J 7.9 Hz, 1H), 7.64 (t, 3J
3
3
7.9 Hz, 1H), 7.16 (d, J 2.0 Hz, 1H), 6.49 (d, J 2.0 Hz, 1H), 1.24 (s,
9H). 13C NMR (CDCl3, ppm): 191.31, 180.14, 179.26, 151.59,
150.36, 137.98, 136.86, 134.05, 132.07, 131.95, 130.01, 127.10, 124.33,
35.71, 29.08. IR (cm−1): 1702 (s, νCO), 1653 (s, νCO).
Elemental analysis: calcd (C: 71.82, H: 5.67), found (C: 72.01, H:
5.67).
TpCum,MeZn(SQ-m-Ph-NN) (1-meta). To a 25 mL oven-dried
Schlenk flask, 42 mg (0.11 mmol) 12 and 69 mg (0.10 mmol) 13
were added with a stir bar. The reaction vessel was pump/purged with
nitrogen, and about 5 mL methanol distilled over calcium hydride was
added via purged syringe. The reaction was stirred under inert
atmosphere for 2 h. Afterward, the reaction was opened to air, stirred
overnight, and then filtered through slow filter paper. The filter paper
containing the product was placed in a beaker, and the olive green
solid was dissolved in dichloromethane. The new solution was filtered
3′-(tert-Butyl)-4′,5′-dihydroxy-[1,1′-biphenyl]-3-carboxaldehyde
(9). The quinone, 8, was dissolved in 10 mL tetrahydrofuran and
transferred to a separatory funnel. To a 25 mL Erlenmeyer flask, 328
mg (1.86 mmol) ascorbic acid was added and dissolved in 10 mL
deionized water. The ascorbic acid was added to the separatory funnel
containing 8 and shaken. The green color of 8 instantly changed to
light yellow. Saturated sodium chloride solution was added, and the
product was extracted by ethyl acetate. The organic phase was dried
over sodium sulfate, and the solvent removed under reduced pressure.
C
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Scheme 1
Figure 2. (Left) Thermal ellipsoid plot of 1-meta with H and cumenyl groups removed for clarity. (Right) Crystal packing of 1-meta along the 001
axis showing the closest oxygen−oxygen contact for the NN intermolecular interaction.
again to remove any salts and yielded 27 mg of 1-meta (25% yield).
The product was crystallized by slow evaporation of n-hexane and a
few drops of dichloromethane. Mass spectrometry (m/z): (M + H)+
calcd for C62H73BN8O4Zn: 1068.5139; found: 1068.5226.
Commercially available phenol 3 was brominated at low
temperature to yield phenol 4 in excellent yield and then
subjected to Suzuki coupling with boronic acid 5 to yield
biarylphenol 6. Oxidation of 6 to quinone 8 was achieved with
IBX (7).39 Reduction of quinone 8 to catechol 9 as a solution
in tetrahydrofuran was easily carried out in a separatory funnel
by shaking with an aqueous solution of ascorbic acid.
Compound 9 was condensed with bishydroxylamine 10
followed by oxidation to yield catechol nitronylnitroxide 12
in excellent yield. Semiquinone complex formation yielding 1-
meta was affected using compounds 12 and 13 following
standard procedures.47,48 Crystals of 1-meta were grown by
slow evaporation of an n-hexane solution containing a few
drops of dichloromethane to dissolve 1-meta.
RESULTS AND DISCUSSION
■
Synthesis of Biradical Complex 1-meta. The com-
pounds in this study (1-meta, 1-para, and 2) are shown in
Figure 1. The synthesis and characterization of 1-para and the
parent complex, 2, have been presented in an earlier work,45,46
whereas 1-meta has been synthesized by a newly developed
route, outlined in Scheme 1, which requires no protecting
groups.
D
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Figure 3. (A) Magnetic susceptibility of 1-meta from 2 to 300 K with constant field of 7000 Oe. Inset: Fit parameters and corresponding errors. (B)
VT-EPR Curie plot. Doubly integrated ΔmS = 2 biradical signal was used to monitor triplet concentration as a function of temperature.
Figure 4. (A) Expanded view of the VT electronic absorption spectra for 1-meta. Full spectral plot is available in the Supporting Information (SI).
(B,C) Calculated Boltzmann distributions for singlet and triplet populations based on the magnetic exchange coupling determined by magnetic
susceptibility measurements. The individual data points represent normalized absorbance values at a given energy as a function of temperature.
X-ray Crystal Structure of 1-meta. The thermal ellipsoid
plot of 1-meta is shown in Figure 2 (left). Crystallographic
details and important bond lengths and torsion angles are given
in Tables S1 and S2, respectively. The o-SQ bond lengths fit
within typical values with a negligible structural deviation
parameter46 of Σ|Δi| = 0.02 Å (however, Σ|Δi| = 0.02 Å for 1-
para, but Σ|Δi| = 0.19 Å for 2) consistent with, but not proof of,
the lack of SQ(donor)−NN(acceptor) interaction dictated by
the cross-conjugated m-Ph bridge. NN bond lengths are also
within typical values with a negligible structural deviation
parameter of Σ|Δi| = 0.02 Å based on the previously reported
Catechol−NN structure.46
SQ−NN Exchange Coupling in 1-meta Measured by
Magnetic Susceptibility, Variable-Temperature Elec-
tronic Absorption and EPR Spectroscopy. The magnetic
susceptibility data for 1-meta are plotted in Figure 3A as χpara vs
T. It is clear that by the shape of the curve outlined by the data
that the complex is an antiferromagnetically coupled “spin-
dimer” with a minor paramagnetic impurity. To analyze these
magnetometry data, we use the Heisenberg−Dirac−van Vleck
Hamiltonian given in eq 2 where S1 = S2 represent the spin
operators for two different S = 1/2 spin containing groups (SQ
and NN) on the same ligand.46
̂
̂
̂
H = −2JSi·Sj
(2)
As shown in Figure 3A, the data were fit using eq 3 where
χpara is the molar magnetic susceptibility, θ is a Curie−Weiss
correction term, c is the mole fraction of pure 1-meta, and J is
the exchange coupling for 1-meta. The second term in eq 3
accounts for S = 1/2 paramagnetic impurity. Nonlinear least-
squares fitting gave JSQ−NN = −32 cm−1: net antiferromagnetic
coupling of constituent SQ and NN radicals through the m-Ph
bridge.
Ng2μB2
6e2J/k T
1 + 3e
0.375
T
⎛
⎝
⎞
⎠
B
⎛
⎜
⎞
⎟
⎜
⎜
⎟
⎟
χpara
=
c +
(1 − c)
2J/kBT
⎝
⎠
3k (T − θ)
B
(3)
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Figure 5. (A) Overlay of electronic absorption spectra for 1-meta (red), 1-para (blue), and 2 (black). (B) Pure singlet (blue) and pure triplet (red)
spectra for 1-meta. Note that transitions for triplet 1-meta are shifted ∼500−1000 cm−1 to lower energy compared to singlet 1-meta.
Figure 6. (A) Important frontier π-orbitals for 1-meta. (B) SQ-Ph-NN(LUMO) interactions in 1-para. The SQ(SOMO) → Ph-NN(e1, LUMO)
CT is responsible for the ferromagnetic exchange interaction in the VBCI model. Note that in 1-para, the SQ(SOMO) → Ph(e2, LUMO) transition
is orbitally forbidden, while in 1-meta it is allowed and contributes to band C, see text.
The closest oxygen−oxygen intermolecular distance in the 1-
meta unit cell, Figure 2 (right), is 5.1 Å which is greater than
the distance observed for dominant intermolecular contribu-
tions to exchange coupling for nitronylnitroxides.49−51 Even
though intermolecular interactions at this distance are expected
to be weak, solution phase (∼2 mM 1-meta) variable-
temperature EPR (VT-EPR) spectra were collected to confirm
the exchange coupling determined by magnetometry. The VT-
EPR Curie plot displayed in Figure 3B made use of the doubly
integrated, formally forbidden ΔmS = 2 transition to determine
triplet concentration as a function of temperature. The EPR
Curie plot was fit by a combination of the Curie Law and a
Boltzmann distribution as shown in eq 4 where C is the Curie
constant, k is a constant that corrects for poor signal-to-noise
ratio, and J is the magnetic exchange coupling (J ≈ −19 cm−1)
which is just over half the value determined by magnetometry
(J ≈ −32 cm−1). However, the fit "misses" the maximum in the
the temperature-dependent changes in the electronic absorp-
tion spectrum with the Boltzmann populations of the S = 0 and
1 ground-state spin levels derived from the magnetic
susceptibility determined J value. Variable-temperature elec-
tronic absorption spectra were collected on thin polystyrene
films of 1-meta and are displayed in Figure 4A as a stack plot.
The data in Figure 4 clearly show that as the temperature is
decreased, the thermally accessible triplet state is depopulated
and the ground-state singlet population is increased. Relative
changes in the measured absorbance at specific energies are
displayed in Figure 4B,C, and their functional form correlates
extremely well with the solid lines calculated for Boltzmann
populations of the singlet and triplet using 2J = −64 cm−1 from
the best fit of eq 4 to the magnetic susceptibility data. Thus,
magnetic susceptibility data and VT electronic absorption
spectroscopy show that the exchange coupling between the
cross-conjugated SQ(donor) and NN(acceptor) radicals is
antiferromagnetic (J ≈ −35 cm−1), while VT-EPR spectroscopy
suggests a slightly weaker antiferromagnetic coupling. The
electronic origin of the magnitude, the sign of the exchange
coupling, and the nature of electronic coupling in 1-meta are
discussed below.
doubly-integrated Δms = 2 signal which gives J ≈ 0.8 kTmax
=
−23 cm−1)
B
C
T
3e2J/k T
(1 + 3e
IEPR
=
+ k
2J/kBT
)
(4)
Electronic Absorption Spectroscopy. Electronic absorp-
tion spectroscopy reveals noteworthy differences in the spectra
of 1-meta and 1-para (Figure 5A). We previously reported a
To further relate solution phase measurement of exchange
coupling with the magnetic susceptibility results, we correlated
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Table 1. Electronic Absorption Spectral Band Assignments for 1-meta
experimental energy
(cm−1
calculated energy calculated oscillator
a
band
A
)
transition
(cm−1
)
strength
dominant MO contributions to transition
SQ-Ph (HOMO) → SQ (SOMO)
15 700
1
2
3
13 400
18 250
22 800
0.0102
0.0034
0.0397
NN(SOMO) → Ph-NN(LUMO) - Ph-NN(HOMO) → NN(SOMO)
B
23 000
Ph-NN(HOMO) →SQ(SOMO) + Ph (HOMO)→SQ(SOMO); [Ph-
NN(HOMO) → Ph-NN(LUMO)]
C
24 000−29 000
4
4′
5
23 950
26 450
28 050
28 700
0.0682
0.0554
0.0691
0.1933
SQ(SOMO) → Ph-NN(e1,LUMO)
Ph-NN(HOMO) → Ph-NN(LUMO)
NN(SOMO) → Ph-NN(LUMO) + Ph-NN(HOMO) → NN(SOMO)
SQ(SOMO) → SQ-Ph(e2,LUMO)
6
a
See Figure 6A for pertinent 1-meta frontier orbitals. One-electron promotion contributions given in brackets represent minor contributions to the
transition but are important for spin polarization contributions to the magnetic exchange interaction.
detailed electronic structure study of the parent complex,
TpCum,MeZn(SQ-NN) (2), which lacks a bridge between the SQ
donor and the NN acceptor and assigned the structured band at
∼25 000 cm−1 as a D−A intraligand SQ(SOMO) → NN-
(LUMO) charge transfer (ILCT) transition.20 A subsequent
study of 1-para showed a structured band at ∼23 500 cm−1 that
was assigned as the D−A intraligand SQ(SOMO) →
NN(LUMO) charge transfer (ILCT) transition but with
considerable Ph-NN character present in the acceptor orbital
(see Figure 6A,B).21 Indeed, observation of ILCT bands in this
energy region is characteristic of TpCum,MeZn(SQ−bridge−NN)
compounds, and we have used a valence bond configuration
interaction model to show that the D−A ILCT band in both 1-
para and 2 are responsible for the extraordinarily large and
ferromagnetic biradical exchange coupling (2; J ≈ +550 cm−1,
1-para; J = +100 cm−1). Obviously, there exist fundamental
differences in the underpinning electronic structures of 1-meta
and 1-para as they relate to the cross-conjugated nature of the
bridge fragment in 1-meta, and this is reflected in their different
electronic absorption spectra. Most importantly, the ∼23 500
cm−1 SQ(SOMO) → Ph-NN(e1, LUMO) ILCT band
characteristic of both 1-para and 2 appears to be either absent
or greatly reduced in intensity in 1-meta.
The oscillator strength reduction for the SQ(SOMO) → Ph-
NN(LUMO) ILCT band is a direct result of the dramatic
reduction in orbital overlap between the SQ(SOMO) donor
and the Ph-NN(LUMO) acceptor orbitals in 1-meta compared
to 1-para (Figure 6), indicative of SQ−NN decoupling in 1-
meta due to the cross-conjugated nature of the m-Ph bridge.
This is a very important distinction since strong configurational
mixing of the SQ(SOMO) → bridge−NN(LUMO) ILCT
excited configuration (3EC(1), vide infra) into the ground-state
configuration (GC) is the dominant mechanism for ferromag-
netic biradical exchange in D−B−A biradicals that possess
conjugated bridges.21,22,52 Thus, the lack of a strong SQ-
(SOMO) → bridge−NN(LUMO) ILCT band in 1-meta is a
direct probe of the dramatic reduction in D → A coupling that
results in a radical shift in both the magnitude and the sign of
the exchange: J = +100 cm−1 in 1-para and J = −35 cm−1 in 1-
meta (vida supra).
determined from solid-state magnetic susceptibility studies
(Figure 3A), providing compelling evidence that the average
solution conformation is very similar to that observed in the X-
ray structure.45 Since the VT electronic absorption data are
1
1
3
3
comprised of both GS → ES and GS → ES contributions
(GS, ground state; ES, excited state), and the Boltzmann
populations of the 1GS and 3GS are known for a given
temperature from the magnitude of the antiferromagnetic
exchange, we can use the VT data to construct the pure singlet
and pure triplet electronic absorption spectra for 1-meta
1
1
3
3
(Figure 5B). The similarity of the GS → ES and GS → ES
component spectra indicates that there is no gross change in
the GS and ES orbital character as a function of spin and that
the observed transitions between ∼24 000 and 32 000 cm−1
occur at lower energy for the triplet configuration than for the
1
1
3
singlet configuration. For the intense GS → ES and GS →
3ES transitions in the ∼27 500 cm−1 region, the oscillator
strength of the 1GS → 1ES transition is greater than that of the
3
3
3GS → ES transition, and the ES is stabilized by ∼500 cm−1
relative to the singlet state (see Figure 5B).
Band Assignments. Electronic absorption spectral band
assignments for 1-meta have been made using a combination of
bonding and TDDFT calculations on 1-meta and Ph-NN,53
comparisons with our prior spectroscopic studies on
TpCum,MeZn(SQ), Ph-NN, 1-para, and TpCum,MeZn(SQ-NN)
(2),20,21 and complete active space multiconfiguration SCF
(MC-SCF) calculations. The MC-SCF calculations combine an
SCF and a full configuration interaction calculation using a
complete active space. The features of the spectrum labeled A−
C (Figure 5A) are discussed below, and the one-electron orbital
contributions to the transitions are listed in Table 1.
Band A. A broad, low-energy transition is observed in the 10
000−17 000 cm−1 region (ε ∼ 625 M−1 cm−1) of the electronic
absorption spectrum for TpCum,MeZn(SQ), and a vibronically
structured band has been observed at higher energy (12 000−
20 000 cm−1) for Ph-NN.20,53 Weak bands assignable as SQ-
and NN-based transitions are also observed in the 10 000−20
000 cm−1 region for 1-meta, 1-para, and TpCum,MeZn(SQ-NN)
(2).20,21 These data combined with the computationally
derived transition energies and oscillator strengths allow us to
assign the lower energy component of the broad (10 000−20
000 cm−1) structured band (in n-hexane) in 1-meta as arising
from an SQ(HOMO) → SQ(SOMO) transition and the higher
energy component as a [NN(SOMO) → Ph-NN(LUMO)−
Ph-NN(HOMO) → NN(SOMO)] transition. The SQ-
(HOMO) → SQ(SOMO) transition is y-polarized, and this
polarization direction is orthogonal to the long z-axis (C2 axis)
of the semiquinone unit and is thus predicted to possess a low
As shown in Figure 4A, the VT electronic absorption spectra
for 1-meta display a strong temperature dependence with tight
isosbestic points, indicating only two species contribute to the
VT spectra. The VT electronic absorption data display a
marked increase in absorption intensity as a function of
increasing temperature at ∼24 800 cm−1 with a corresponding
decrease in the ∼27 500 cm−1 band. In Figure 4B,C we showed
that the temperature dependence of the spectra directly
correlates with the singlet−triplet gap (2J = −64 cm−1)
G
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Figure 7. Left: The GC and EC of 1-meta. Double-headed arrows indicate dominant exchange interaction. Middle: Singlet and triplet CTCs that
result from one-electron promotions relative to the GC. Right: Closed-shell configurations that derive from one-electron promotions relative to the
EC and CTCs. These double excitations relative to the GC produce only singlet DECs. Note that DEC2 and DEC4 can also result from direct
SQ(SOMO) → NN(SOMO) and NN(SOMO) → SQ(SOMO) kinetic exchange contributions. Since the <SQ(SOMO)|NN(LUMO)> overlap
integral is essentially zero, the kinetic exchange term is also expected to be zero for 1-meta.
oscillator strength. The [NN(SOMO) → Ph-NN(LUMO)−
Ph-NN(HOMO) → NN(SOMO)] transition is also predicted
to be weak due to the opposing nature (−) of the transition
dipoles for the two one-electron promotions that contribute to
the transition. The overall structure and intensity for band A in
1-meta is virtually identical to the lowest energy band in 1-
para, indicating that transitions 1 and 2 are essentially
independent of the bridge connectivity and do not possess
appreciable CT character.
Band B. Computations indicate that a moderately intense
Ph-NN(HOMO) → SQ(SOMO) + Ph (HOMO) → SQ-
(SOMO) transition possessing Ph-NN (π) → SQ (π) CT
character should be anticipated in this energy region. As
mentioned above, an intense SQ(SOMO) → Ph-NN(e1,
LUMO) transition is observed in this energy region for 1-para
that has been assigned as the dominant contributor to the
observed GS ferromagnetic exchange coupling in this molecule.
Interestingly, the direction of the Ph-NN (π) → SQ (π) CT
character (A → D) in transition 3 is the opposite of the SQ (π)
→ Ph-NN (π) CT character (D → A) found in this energy
region for 1-para. The markedly reduced intensity of this band,
coupled with no computed SQ(SOMO) → Ph-NN(e1,
LUMO) CT contribution, nicely explains the dramatic
reduction in ferromagnetic contributions to the ground-state
magnetic exchange parameter, allowing weaker antiferromag-
netic exchange interactions to dominate.
SQ(SOMO) → Ph-NN(e1, LUMO) and Ph-NN(HOMO) →
Ph-NN(LUMO) one-electron promotions. The SQ (π) → Ph-
NN (π) CT character present in transition 4 is identical to that
observed for 1-para. However, there are numerous one electron
promotion contributions to transition 4 that result in a large
reduction in the overall SQ (π) → Ph-NN (π) CT character of
this transition, yielding reduced CT contributions to
ferromagnetic exchange in 1-meta.
The Ph-NN(HOMO) → Ph-NN(LUMO) one-electron
promotion contribution to transition 4 lacks CT character
and is computed at lower energy than the Ph-NN(SOMO) →
Ph-NN(LUMO) + Ph-NN(HOMO) → Ph-NN(SOMO)
transition. This likely reflects the large reduction in electron−
electron repulsion that derives from an EC having all of the NN
frontier orbitals being singly occupied. TDDFT calculations on
Ph-NN show the Ph-NN(HOMO) → Ph-NN(LUMO)
transition occurring at 25 959 cm−1, and this provides
additional support for these one-electron promotions con-
tributing to transition 4. The state that arises from a Ph-
NN(HOMO) → Ph-NN(LUMO) (Figure 6A) one-electron
promotion is of interest, since this state is known to strongly CI
mix into the ground-state wave function to produce negative
spin density on the NN bridgehead carbon.52,54 This
configurational mixing is important since the NN(SOMO)
wave function is nodal at the bridgehead carbon, and as such, its
one-electron occupancy does not directly contribute to the
observed spin density at this carbon. This is noteworthy,
because we will invoke the role of the Ph-NN(HOMO) → Ph-
NN(LUMO) excited state in our discussion of the electronic
origin of the observed antiferromagnetic exchange in 1-meta,
vide infra.
Band C. Band C is the most intense band in the spectrum of
1-meta, and a number of transitions are computed to
contribute to the intensity of this band. A slight shoulder is
observed on the low-energy side of band C in the room
temperature absorption spectrum at ∼25 000 cm−1 that is
clearly revealed at 25 000 cm−1 in the triplet absorption
spectrum (red line, Figure 5B) and at 26 000 cm−1 in the
singlet absorption spectrum (blue line, Figure 5B). We assign
these bands in 1-meta as arising from exchange split singlet and
triplet components of transition 4, which is comprised of
Two additional transitions contribute to the intensity of band
C. The first is calculated to possess moderate intensity and is
assigned as the [NN(SOMO) → Ph-NN(LUMO) + Ph-
NN(HOMO) → NN(SOMO)] transition with enhanced
intensity due to the additive nature of the two transition
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Figure 8. (Left and middle) Double spin polarization mechanism in the Ph-NN fragment via the EC1 excited state. (Right) In-phase Ph-NN spin
polarization and SQ spin delocalization supporting antiferromagnetic alignment of SQ and NN fragments.
dipoles for the two one-electron contributions to the transition.
Band C is markedly more intense in 1-meta than the
corresponding band in 1-para, and this is most likely due to
the presence of a very intense CT band in this spectral region
that can be assigned as the SQ(SOMO) → SQ-Ph(e2, LUMO)
transition which is primarily localized on the SQ chromophore
but possesses SQ → Ph(e2) CT character. In contrast to the
SQ → Ph-NN(e1) CT character observed in 1-para, the
phenylene (bridge) orbital of e2 symmetry possesses nodal
character at the carbon atoms that attach to the SQ and NN
fragments in 1-para and therefore is essentially nonbonding in
character with respect to the SQ and NN frontier orbitals of 1-
para (Figure 6B). Thus, differences in the CT spectra between
1-meta and 1-para reveal markedly different interactions
between SQ and NN frontier orbitals and the Ph(e1) and
Ph(e2) bridge orbitals, and this highlights the effects of
connectivity differences between para- and meta-substituted
benzene rings in these biradicals. The dominant SQ(SOMO)
→ Ph(e2) CT band in 1-meta is also fully consistent with a
marked reduction in the SQ(SOMO) → Ph-NN(e1, LUMO)
charge transfer that contributes to the efficient D → A
ferromagnetic pathway responsible for strong ferromagnetic
coupling in 1-para (Figure 6B).
Electronic Origin of the Antiferromagnetic Exchange
in 1-meta. The dominant mechanism for ferromagnetic
exchange in 1-para involves configurational mixing of an
SQ(SOMO) → Ph-NN(e1, LUMO) ILCT configuration
(3CTC2, Figure 7) into the ground configuration (3GC, Figure
7).21 In stark contrast to 1-para, the intensity of the
SQ(SOMO) → Ph-NN(e1, LUMO) CT transition for 1-
meta is dramatically reduced. The marked decrease in
SQ(SOMO) → Ph-NN(e1, LUMO) CT intensity is a function
of the cross-conjugated phenylene bridge connectivity, which
has the effect of reducing excited-state ferromagnetic exchange
contributions to the ground state and allows antiferromagnetic
contributions to dominate. Thus, the observation of ground-
state antiferromagnetic exchange coupling in 1-meta is
important and reveals the fact that other orbital pathways are
operative. In order to understand the nature of the magnetic
exchange pathways in 1-meta and correlate these pathways with
spectroscopic observables, we first construct electronic
configurations that result from one-electron promotions to
the Ph-NN(HOMO), NN(SOMO), Ph-NN(e1, LUMO), and
SQ(SOMO) frontier MOs to form the EC and CTCs of Figure
7. We stress that these orbitals represent a minimum number
(i.e., minimal complete active space (CAS)) required to
understand how singlet and triplet ECs and CTCs mix into
the GS to promote antiferromagnetic exchange coupling of the
NN and SQ spins.
Configurational mixing of the EC and CTCs depicted in
11
1
3
Figure 7 with the GC stabilizes both the GS and GS. Our
analysis of the electronic absorption spectrum for 1-meta
provides evidence for the formation of all the singly ECs
depicted in Figure 7. We expect that configurational mixing of
CTC1 and CTC2 with the GC will result in preferential
3
stabilization of the GS since the single site (NN) exchange
integral (K0) is anticipated to be large (K0 = 2275 cm−1 for
TpCum,MeZn(SQ−NN)).20 In fact, we have experimentally
determined that ∼25% of an 3CTC2-type configuration is
admixed into the 3GS of TpCum,MeZn(SQ−NN) resulting in the
observation of strong GS ferromagnetic exchange (JSQ−NN
≈
+550 cm−1). Support for at least some admixture of CTC1 and
CTC2 into the 3GS of 1-meta derives from the computed spin
density description for the 3GS (SI), which shows an increase in
spin density on the NN fragment (1.04) compared to the SQ
fragment (0.96). Spin population transfer between the SQ and
NN fragments52 derives from the fact that none of the spins in
CTC1 and CTC2 are localized on the SQ fragment since the
SQ(SOMO) is either doubly occupied or vacant in these triplet
configurations and therefore possesses no net spin density.
One way for the 1GS to be stabilized with respect to the 3GS
is by configurational mixing of ECs that lack a triplet
1
1
counterpart with the GC to stabilize the GS. Excited state
configurations that lack a triplet counterpart are closed-shell
configurations. The closed-shell double excited configurations
(DECs) shown in Figure 7 (right) can configurationally mix
11
1
with the GC in fourth order to selectively stabilize the GS.
The double excited states DEC2 and DEC4 are identical to the
states that result from a direct Anderson-type kinetic exchange
contribution involving the SQ and NN SOMOs and resemble
the metal-to-metal charge transfer (MMCT) states of
transition-metal dimers.11 However, due to the lack of direct
orbital overlap between the SQ(SOMO) and the NN(SOMO)
the kinetic exchange term is anticipated to be negligible in 1-
I
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meta. DEC1 and DEC3 are double excitations from the Ph-NN
(HOMO) to the two SOMOs and to the Ph-NN (LUMO),
respectively. The role of DECs in the stabilization of the 1GS is
well documented11,55 and was recently suggested to be
promotion of both Ph-NN(HOMO) electrons to the Ph-
NN(e1, LUMO). Interestingly, no closed-shell singlet DECs
were observed to contribute to the 1GS in the MC-SCF
calculations within a cutoff of 1%. The large contribution of the
EC (Figure 7) to the ground-state exchange is precisely what
we derived from the MO spin polarization analysis detailed
above and provides a key state description of the spin density
derived from the spin-unrestricted DFT calculations.
Comparison of Electronic Coupling Through para-
Phenylene to Electronic Coupling Through meta-
Phenylene. One of the fundamental comparisons of electronic
coupling between a donor and acceptor is between structures in
which the donor and acceptor are connected to a bridge giving
rise to a conjugated pathway between donor and acceptor, and
structures in which the donor and acceptor are bonded to the
bridge such that the π-pathway from donor to acceptor is cross-
conjugated. Indeed, Wasielewski and co-workers15 as well as
Bardeen et al.23 have shown a factor of ∼30 decrease in charge
separation rate when a donor and acceptor are bridged by
conjugated and cross-conjugated bridges, which in turn
suggests an attenuation of (30)1/2 ≈ 5.4 in Hab. However,
there has been no report of a direct comparison of Hab values
for the fundamental bridge units, meta- and para-phenylene.
The CI approach to exchange coupling in 1-meta presented in
the previous section allows for such a comparison. One can
approximate the relationship between electronic and exchange
coupling using eq 5.10
1
important for the stabilization of the GC in meta-poly acene
(n > 3) bridged Cr(III) dimers.56
In spite of the well-known role of DECs contributing to
ground-state antiferromagnetic exchange, there is no direct
1
experimental evidence that they contribute to GS stabilization
in 1-meta. This derives from the fact that band A in singlet 1-
meta and triplet 1-para are identical, and the VT electronic
absorption spectra in the region of band C show that the triplet
excited states occur at lower energy than the singlets. The
fundamental difference in the electronic absorption spectra of
1-meta and 1-para occurs in the region of band B. Here, the
SQ(SOMO) → Ph-NN(LUMO) transition that results in
ground-state ferromagnetic exchange in 1-para is dramatically
reduced in intensity for 1-meta. Thus, it would appear that
excited-state antiferromagnetism, which contributes to GS
antiferromagnetic exchange through CI mixing of DECs with
11
1
1
the GC via ECs, likely only contributes to a reduction in
excited-state ferromagnetic contributions to the GS exchange.
Spin unrestricted broken-symmetry DFT calculations on 1-
meta indicate a large (∼0.75 eV) exchange splitting between
the spin-up and spin-down orbitals of the Ph-NN(HOMO)
orbital resulting from strong exchange interactions between the
spin-up and spin-down electrons in the Ph-NN(HOMO) and
the unpaired electron spins in the NN(SOMO) and the
SQ(SOMO). A spin polarization mechanism57 can therefore be
He2ff
ΔE
1
2J =
invoked in order to explain how the GS is stabilized with
(5)
respect to the 3GS, and we start with a simple spin polarization
analysis of occupied Ph-NN(HOMO) orbitals using the four
orbital model depicted in Figure 8. Here, configurational mixing
of the 1,3ECs (Figure 7) into the ground state results in a spin
polarization of the doubly occupied Ph-NN(HOMO) orbital
shown in the center of Figure 8.52,58,59 The electron−electron
repulsion between these spin polarized core electrons and the
NN(SOMO) and SQ(SOMO) spins result in a stabilization of
the singlet ground configuration (1GC) over the triplet with an
antiparallel orientation of the NN(SOMO) and SQ(SOMO)
spins. This spin polarization argument also allows one to
predict the signs of the atomic spin populations in 1-meta, and
these are in excellent agreement with those computed from a
If one uses 25 750 cm−1 for ΔE (NN-Ph (HOMO) → NN-Ph
(LUMO) energy; Table 1) with |2J| = 64 cm−1 in eq 5, one can
obtain an effective Hab (Heff) of 1284 cm−1. This value may be
compared with an Heff ∼ 664 cm−1 obtained by dividing Hab
=
3632 cm−1 for 1-para21 by (30)1/2. Thus, eq 5 provides
estimation of Heff for m-Ph which may be compared to the
previously determined value of Hab for 1-para and is nearly
twice the value predicted by the square root of the ratio of
charge separation rates in the nonadiabatic regime reported by
Wasielewski et al. and Bardeen et al.23 We note however that
distinctly different CI mechanisms contribute to the electronic/
exchange coupling in 1-meta compared to 1-para such that
orbital contributions to Heff are quite different from those
described by the Hab value determined for 1-para. The different
CI mechanisms are illustrated schematically in Figure 9: in 1-
meta the electronic/exchange coupling is turned on by the
generation of an electron/hole pair involving the Ph-NN
1
spin-unrestricted DFT calculation of the GS (Figure 8 right).
1
This analysis underscores the importance of the EC to the
observed magnetic exchange, which arises from a Ph-NN-
(HOMO) → Ph-NN(LUMO) one-electron promotion with
appreciable contributions from the m-Ph bridge.
This analysis can be more quantitatively evaluated in the
context of MC-SCF calculations. We initially performed MC-
SCF calculations on 1-meta using an active space spanning just
the NN(SOMO) and SQ(SOMO) orbitals. The results of this
calculations yield a triplet ground state comprised solely of the
3GC depicted in Figure 7 and a small ferromagnetic S-T
splitting of 2J = +0.4 cm−1. Increasing the active space to
include the Ph-NN(HOMO), SQ(HOMO), NN(SOMO),
SQ(SOMO), Ph-NN(e1, LUMO), and Ph(e2, LUMO) orbitals
yields a 1GS stabilized by 2J = −35 cm−1 (∼50% the
experimental value) with respect to the 3GS, in good agreement
Figure 9. Cartoon descriptions of the dominant CI mechanisms for
antiferromagnetic exchange coupling of SQ and NN spins in cross-
conjugated 1-meta (left) and ferromagnetic exchange coupling in
conjugated 1-para (right). Note that the exchange interaction in both
1-meta and 1-para is zero in the active electron approximation where
only the SQ and NN SOMOs are considered.
1
with the experimental results (2J = −64 cm−1). The GS wave
1
function is found to be dominantly comprised of the GC
1
(88%) listed in Figure 7 with CI mixing of the EC (Figure 7;
7%) and a small degree (3%) of an EC resulting from
J
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HOMO and LUMO, while in 1-para, the electronic/exchange
coupling is a consequence of D → A/SQ → Ph-NN(e1,
LUMO) charge transfer.
CONCLUSIONS
■
We have developed a new synthetic approach to the
preparation of catechol−B−NN ligands, which obviates
protecting groups used previously.45 This new approach will
allow us to synthesize a diverse array of D−B−A biradical
complexes. In addition, we have performed VT-EPR, VT-
magnetic susceptibility, and VT-electronic absorption experi-
ments on a new D−B−A biradical (1-meta) that possesses a m-
Ph bridge, and the results show moderate antiferromagnetic
exchange coupling between the NN and SQ spin centers. The
electronic origin of the magnitude of 2J is of extreme interest
since 1-meta is cross-conjugated and, within the active electron
approximation, is not anticipated to possess an appreciable
exchange interaction due to zero overlap and zero overlap
density between the SQ(SOMO) and NN(SOMO). Therefore,
in order to understand the mechanism for the observed
electronic and magnetic coupling in cross-conjugated 1-meta,
we must move beyond the active electron approximation. Thus,
we have evaluated the results of the magnetic and spectroscopic
data in the context of detailed bonding, configuration
interaction, and spectroscopic computations. Specifically, the
spectroscopic results strongly suggest that only one singly
excited configuration (1EC) provides a mechanism for
antiferromagnetic exchange in 1-meta. MC-SCF calculations
reveal no appreciable configurational mixing of CTCs with the
GS, and this is important because a CTC2 configuration
resulting from a SQ(SOMO) → Ph-NN(e1, LUMO) one-
electron promotion has been shown to be responsible for the
observed ferromagnetic exchange in isomeric 1-para (Figure 7).
The minor role of singly excited CTCs to the ground-state
exchange coupling in 1-meta is also supported by the
deconvoluted pure singlet and triplet absorption spectra for
1-meta (Figure 5B). Here, 3GS → 3ES transitions that
contribute to band C in 1-meta lie ∼500−1000 cm−1 lower
Relationship to Quantum Interference Effects on the
Conductance of Cross-Conjugated Molecules. The results
of this work suggest that configurational mixing of specific ECs
into the ground state may be important for modulating
electronic communication and electron transport mediated by
cross-conjugated bridges. The conductance (g) of a molecular
junction is related to the transmission probability (T(EF))
evaluated at the Fermi energy according to eq 6.
2e2
h
g =
T(EF)
(6)
The magnitude of the transmission coefficient is proportional
to the magnitude of the retarded (R) and advanced (A) Green’s
function of the molecule, G(0)R/A, which in turn may be related
to frontier MO theory through the Green’s function matrix
element by eq 7.60,61
*
CrkClk
G(0)(E ) =
∑
F
rl
EF − εk iη
(7)
k
Here, r and l are the right and left side orbitals of the bridge
that are connected to the electrode, Cij are the atomic orbital
coefficients of the kth MO located on the left and right atoms of
the bridge that spans the electrode, εk is the energy of the kth
MO, and iη is related to the imaginary part of the Green’s
function and the local density of states. For cross-conjugated
bridge molecules, eq 6 predicts strong antiresonan-
ces16−19,24,25,27,28,62 near the Fermi energy that result in a
dramatic reduction in the transmission probability. If we
consider the NN and SQ moieties as molecular analogs of
biased electrodes and use only the Cr and Cl coefficients for the
quaternary carbons of the SQ(SOMO) and NN(SOMO)
frontier MOs that connect to the m-Ph bridge in 1-meta, one
would expect the transmission at EF to be zero due to three of
the Cij values being equal to zero (Figure 8, left). However, it is
important to note that the conductance described by eqs 6 and
7 is a sum over all filled and empty orbitals and not simply the
frontier orbitals. The anticipated value of zero for the
transmission mediated by the frontier MOs is related to the
magnitude of the magnetic exchange interaction (J ∼ 0) that we
calculate for 1-meta in the active electron approximation,57
where the active space in the MC-SCF calculations is restricted
to the NN(SOMO) and the SQ(SOMO) orbitals. Only
through CI mixing of higher energy configurations do we
obtain a spin density description of 1-meta that spans the entire
molecule with nonzero spin populations on the carbons that
connect to the m-Ph bridge and obtain a magnetic exchange
interaction that is nonzero. To the extent that CI similarly
affects electron transport in cross-conjugated molecule-bridged
systems, a state description of electron transport may provide
greater insight into important molecular design concepts for
control of electron transport in the quantum interference
regime.63−65 In line with our description of the magnetic
exchange in 1-meta, the inclusion of ECs in transport
calculations may have the effect of modulating the magnitude
of antiresonance contributions to the electron transport by
increasing π-type electronic communication. This idea may also
transfer to modulating photoinduced electron-transfer rates in
cross-conjugated D−B−A systems as well.15
1
1
in energy than the corresponding GS → ES transitions. To
the extent that these triplet CT excited states configurationally
mix with the GS, the energy denominator terms indicate that
admixture of excited triplet CTCs with the GC will result in
3
preferential stabilization of the GS; a result that is opposite of
what is observed experimentally (i.e., a singlet GS). Thus,
second-order CT contributions to electronic/exchange cou-
pling in cross-conjugated 1-meta are inherently weak (or
negligible) and provide for a unique electronic structure that
allows spin polarization contributions to play a dominant role
in defining the nature of the ground-state magnetic exchange
interaction. From a CI perspective, it appears that smaller Hab
values for cross-conjugated bridges are a natural consequence of
inherently weaker CT contributions to the CI expansion of the
GS wave function, compared to the stronger CT contributions
present in D−B−A systems with conjugated bridges. This
concept is in agreement with the results of photoinduced
electron-transfer experiments that compare conjugated and
cross-conjugated bridges in D−B−A systems.15
Our understanding of D−A electronic coupling in 1-meta
may provide new insight into how quantum interference
effects15,16,19,62 on electron transfer/transport can be modu-
lated by excited-state contributions. Thus, by understanding the
excited-state origin of the electronic and magnetic exchange
coupling in cross-conjugated systems, we have a mechanism by
which we can modulate the coupling.
Our conclusions regarding bridge parity effects on D−A
electronic coupling directly apply to electron transport in
K
dx.doi.org/10.1021/ja405354x | J. Am. Chem. Soc. XXXX, XXX, XXX−XXX

Journal of the American Chemical Society
Article
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single-molecule devices since the transmission varies linearly
with the square of the electronic coupling matrix element. One
important distinction is that in contrast to the growing number
of computational and experimental papers describing trans-
mission through conjugated vs cross-conjugated bridges, the
“biased electrodes” in D−B−A biradicals are the SQ donor and
the NN acceptor, which have π-contacts to the bridge, whereas
the most common single-molecule devices use metal−thiol−
bridge−thiol−metal constructs where the σ-contacts to the
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manifest themselves in the transmission local density of states
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single molecule devices with π-contacts to the electrodes should
be dominated by the bridge/contact π-system.67,68 If this is
true, it would prove valuable to further explore how bridge
substituents might modulate electronic coupling, particularly in
the case of cross-conjugated bridges with strong π-connectivity
to donors, acceptors, and nanoelectrode assemblies. Our
understanding of the superexchange pathway responsible for
electronic coupling in 1-meta indicates that the addition of
electron-withdrawing groups (EWGs) and electron-donating
groups (EDGs) oriented meta to the D and A, and para to A
and ortho to D will allow for exquisite control of D−A coupling
in cross-conjugated systems and provide valuable new insight
into quantum interference effects and gated electron trans-
port69 mediated by cross-conjugated molecules placed between
biased electrodes. Efforts along these lines are underway that
will determine the effect of EWGs and EDGs on CI
contributions to D−A coupling in D−B−A biradicals.
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ASSOCIATED CONTENT
* Supporting Information
X-ray crystallographic details, EPR spectra and DFT-computed
spin densities for 1-meta. This information is available free of
charge via the Internet at http://pubs.acs.org.
■
S
AUTHOR INFORMATION
Corresponding Authors
mkirk@unm.edu
■
shultz@ncsu.edu
Present Address
§Department of Chemistry, University of Western Ontario,
London, Ontario, Canada
Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS
■
D.A.S. thanks the National Science Foundation (NSF CHE-
1213269) and M.L.K. acknowledges the National Science
Foundation (NSF-CHE-1012928) for financial assistance.
Funding for the NCSU Department of Chemistry Mass
Spectrometry Facility was obtained from the North Carolina
Biotechnology Center and the NCSU Department of
Chemistry.
(35) Kirk, M. L.; Shultz, D. A.; Depperman, E. C. Polyhedron 2005,
24, 2880.
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