Determining the Conformational Landscape of σ and π Coupling Using para-Phenylene and "Aviram-Ratner" Bridges

Article abstract of DOI:10.1021/jacs.5b04629

The torsional dependence of donor-bridge-acceptor (D-B-A) electronic coupling matrix elements (H_DA, determined from the magnetic exchange coupling, J) involving a spin S_D = 1/2 metal semiquinone (Zn-SQ) donor and a spin S_A

Full text of DOI:10.1021/jacs.5b04629

Communication
pubs.acs.org/JACS
Determining the Conformational Landscape of σ and π Coupling
Using para-Phenylene and “Aviram−Ratner” Bridges
Daniel E. Stasiw,† Jinyuan Zhang,† Guangbin Wang,†,∥ Ranjana Dangi,‡ Benjamin W. Stein,‡
David A. Shultz,*,† Martin L. Kirk,*,‡ Lukasz Wojtas,§ and Roger D. Sommer†
†Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204, United States
‡Department of Chemistry, The University of New Mexico, MSC03 2060, 1 University of New Mexico, Albuquerque, New Mexico
87131-0001, United States
§Department of Chemistry, University of South Florida, 4202 East Fowler Avenue, CHE 205, Tampa, Florida 33620-5250, United
States
S
* Supporting Information
Transition metal complexes with persistent SQ−B−NN (SQ
ABSTRACT: The torsional dependence of donor−
bridge−acceptor (D−B−A) electronic coupling matrix
elements (HDA, determined from the magnetic exchange
coupling, J) involving a spin SD = 1/2 metal semiquinone
(Zn-SQ) donor and a spin SA = 1/2 nitronylnitroxide
(NN) acceptor mediated by the σ/π-systems of para-
phenylene and methyl-substituted para-phenylene bridges
and by the σ-system of a bicyclo[2.2.2]octane (BCO)
bridge are presented and discussed. The positions of
methyl group(s) on the phenylene bridge allow for an
experimentally determined evaluation of conformationally
dependent (π) and conformationally independent (σ)
contributions to the electronic and magnetic exchange
couplings in these D−B−A biradicals at parity of D and A.
The trend in the experimental magnetic exchange
couplings are well described by CASSCF calculations.
The torsional dependence of the pairwise exchange
interactions are further illuminated in three-dimensional,
“Ramachandran-type” plots that relate D−B and B−A
torsions to both electronic and exchange couplings.
Analysis of the magnetic data shows large variations in
magnetic exchange (J ≈ 1−175 cm−1) and electronic
coupling (HDA ≈ 450−6000 cm−1) as a function of bridge
conformation relative to the donor and acceptor. This has
allowed for an experimental determination of both the σ-
and π-orbital contributions to the exchange and electronic
couplings.
= semiquinone; B = bridge; NN = nitronyl nitroxide) biradical
ligands offer a unique platform to experimentally evaluate the
electronic origins of bridge-mediated electronic coupling at high
resolution and at parity of D and A. Previously, we used a
combination of magnetic susceptibility, multicomponent spec-
troscopy, and electronic structure calculations to elucidate
electronic structure contributions to the magnetic exchange/
electronic coupling in a variety of SQ−B−NN systems coupled
by different bridge fragments.6−13 More specifically, we have
shown that a single D → A charge transfer excited configuration
dominantly contributes to the bridge-mediated π-superexchange
interaction (JSQ‑NN) that couples the S = 1/2 SQ and S = 1/2 NN
radicals. Herein, we present the first experimentally determined
three-dimensional (3D) plot of HDA as a function of both
donor−bridge and bridge−acceptor bond torsions in a
“Ramachandran-type”14 plot. Our analysis provides a detailed
evaluation of σ vs π contributions to the electronic and magnetic
coupling in D−B−A constructs, with σ-interactions being
effectively independent of bridge type (sp2 vs sp3) at parity of
D and A, and bridge length (i.e., D−A distance).
For the D−B−A triads discussed in this work, McConnell
defines HDA as the product of the electronic coupling matrix
elements that describes the pairwise interaction within a given
D−B−A system (HDB, HBA) and the energy gap between the
localized donor and bridge states (ΔDB) as shown in eq 1.15
HDBHBA
ΔDB
HDA
=
(1)
he degree of π-orbital overlap in conjugated organic
Additionally, the HDB and HBA electronic coupling matrix
elements contained in eq 1 each possess a torsional dependence
described by eq 2, where i and j index two adjacent units of the
Tdonor−bridge−acceptor (D−B−A) triads is modulated by
torsional rotations about the D−B and B−A bonds. Although the
π-system typically dominates electronic contributions to D−A
coupling, torsional distortions effectively inhibit π-resonance
delocalization and dramatically reduce the magnitude of the
electronic coupling, HDA, between donor and acceptor. This is
important since the magnitude of HDA is central to modulating
intramolecular electron transfer rates,2 the efficiency of electron
transport in single-molecule electronic devices,3,4 and OLED
band-gaps.5
0
D−B−A system and Hij is the intrinsic electronic coupling
matrix element at cos(ϕ) = 0, where the two entities are
coplanar.16,17
Hij = Hi0j cos(ϕ)
(2)
Received: May 11, 2015
© XXXX American Chemical Society
A
DOI: 10.1021/jacs.5b04629
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Journal of the American Chemical Society
Communication
Wasielewski,16 Harriman,17 and Wenger18 have shown
independently that photoinduced electron transfer derived HDA
values follow a cos(φ) dependence for each nearest neighbor
interaction within the D−B−A system. There is an inherent
connection between intramolecular electron transfer rates and
the magnitude of the electron transport in single-molecule
devices.3,4 Since electron transfer and molecular electron
transport are each related to a bridge-dependent off-diagonal
coupling matrix element, it is important to understand the
magnitude of HDA in systems where the structural relationship
between the bridge and connecting elements is well understood.
Venkataraman19 and Mayor20 have shown a torsional (cos2 φ)
dependence on single molecule conductance using a series of
torsionally modified biphenyls. These studies solely focused on
π-system contributions to the transport behavior. However,
Newton21 has described a modified McConnell superexchange
model15 that accounts for both π- and σ-contributions to the
electronic coupling matrix element. Under quantum interference
conditions, or when π-systems of the molecule are orthogonal,
Ratner has indicated that σ-pathways may be extremely
important and effectively compete with torsionally compromised
π-pathways for molecular conductance.22 As such, direct
experimental evaluation of σ- and π-contributions to electronic
coupling as a function of molecular bond torsions will contribute
to furthering our understanding of the magnitude of the σ-
contribution when coupling via the π-system is compromised.
Using a valence bond configuration interaction (VBCI)
model,11,23 eq 3, we have determined the electronic coupling
matrix element, HSQ‑NN, for D−A in the absence of a bridge.
Here, JDA  JSQ‑NN, HDA  HSQ‑NN, and U and K0 are the mean
SQ → NN charge transfer (CT) energy and the singlet−triplet
splitting within the CT excited state, respectively. The magnetic
exchange interaction, JDA, and spectroscopic parameters U and
K0 are all experimental observables that allow us to
experimentally evaluate HDA as a function of bridge type and
bridge length.11
(Figure 1, see Figure S1A for magnetic susceptibility plots and fit
details) as described previously.6,9,11 We also synthesized 1-
HDA2K0
JDA
=
Figure 1. Bond-line drawings, thermal ellipsoid plots (hydrogen atoms
and cumenyl groups omitted for clarity), donor and acceptor torsion
angles, magnetic exchange coupling parameters (JSQ‑NN), and donor−
acceptor distances (Å) of complexes studied in this work. Donor−
acceptor distances are listed for Cipso, SQ−Cipso, NN. The structure of 1-Ph
was reported previously.1
2
U2 − K0
(3)
For metal complexes of our D−B−A biradical ligands,
configurational mixing of the SQ → NN CT state into the
ground state also results in an exchange splitting of the ground
state to yield a singlet−triplet gap (= 2JDA), which is a fit
parameter in the analysis of variable-temperature magnetic
susceptibility data. Values of HDA for a given SQ-Bridge-NN
complex can then be determined conveniently from the ratio
BCO, which possesses the “Aviram−Ratner” diode bridge
bicyclo[2.2.2]octane, to evaluate Jσ and Hσ, explicitly in the
absence of any π-contributions to the exchange and electronic
coupling (see Supporting Information for synthetic details). The
variation in SQ-B and B-NN bond torsions are also given in
Figure 1 along with thermal ellipsoid plots for 1-Ph, 1-MePh, 1-
PhMe, 1-pXylyl, 1-PhMe4, and 1-BCO (BCO = bicyclo[2.2.2]-
octane; see Table S1 for crystallographic details). Torsion angles
for the (substituted) phenyl complexes were determined using
the mean planes of the SQ rings and bridge rings (ϕSQ‑B), and the
O−N−C−N−O atoms of NN and bridge rings (ϕB‑NN).
Utilizing the crystallographically determined ϕSQ‑B and ϕB‑NN
torsion angles (Figure 1), 3D plots have been constructed that
relate both the electronic coupling and the magnetic exchange to
donor−bridge and bridge−acceptor torsions in these SQ-
Bridge-NN complexes (Figure 2). The experimental data is
overlaid on top of a color-coded grid constructed from CASSCF
calculated J-values for various SQ-Bridge-NN ϕSQ‑B and ϕB‑NN
torsion angles. Least-squares fitting of the experimental data to
J
SQ‑B‑NN/JSQ‑NN (=HSQ−B−NN2/HSQ−NN2) where SQ-NN is the
“parent,” nonbridged biradical complex for which both JSQ‑NN
and HSQ‑NN have been experimentally determined.6,9,11
The exchange interaction in these SQ-Bridge-NN systems can
be mediated by both the σ- and π-orbitals of the bridge (JDA = Jσ +
Jπ) yielding pathway dependent contributions to the J-values.
The π-pathway is expected to display a pairwise cosϕ
conformational dependence on the electronic coupling and
cos2ϕ conformational dependence magnetic exchange couplings
as a function of the individual SQ-Ph and Ph-NN bond torsions.
In marked contrast, electronic and magnetic exchange couplings
mediated by the σ-pathway are less well understood but have
been suggested to be a function of bridge type, contact symmetry,
and D−B, B−B, and B−A bond torsions.24−26 Complexes 1-Ph
and 1-PhMe4 were synthesized in order to evaluate the torsional
dependence of the σ- and π-systems on the magnitude of JDA
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Figure 3. (A) Orbital argument for conformationally independent
coupling of radical orbitals (red/blue) through the C3-symmetric
bicyclo[2.2.2]octane bridge orbitals (black/white). (B) π-Symmetry
spin delocalization via bridgehead px and py orbitals and spin
polarization via the pz orbital (only one of the three bridge pathways
have been depicted for clarity). (C) Orbital argument for conforma-
tionally-dependent σ-coupling through the C2-symmetric phenylene
bridge.
and this will display a cos2 ϕ dependence. The second pπ
component will display a sin2 ϕ dependence on the orbital
overlap. Since cos2 ϕ + sin2 ϕ = 1 (a constant), coupling via
hyperconjugation with the bicyclo[2.2.2]octane bridge is
expected to be conformationally independent.27 Additional
support for the torsional independence of the σ-exchange
coupling derives from methyl proton hyperfine computations on
Figure 2. Electronic coupling (A) and exchange coupling (B) versus
cosine-squared of the SQ-Ph torsion angle versus cosine-squared of the
Ph-NN torsion angle for the para-phenylene bridged complexes. Data
points for J-values were determined as best fit parameters to the variable-
temperature magnetic susceptibility data (see Supporting Information).
The 3D grid of J-values represents results from CASSCF calculations.
Values for the electronic coupling and 3D grid (A) were calculated via eq
3.
•
the ethyl radical (CH3CH2 ), which reveals average isotropic
hyperfine coupling constants for the three methyl protons of 19.7
MHz (staggered geometry, ∼cos2 φ in Figure 3A) and 19.6 MHz
(eclipsed geometry, ∼sin2 φ in Figure 3A).29
A second pathway for spin polarization, which is also
independent of conformation, involves the σ-system and utilizes
the a1 orbital of the bridgehead carbon. This is depicted in Figure
3B. Thus, regardless of the exchange mechanism (spin
delocalization or spin polarization), coupling through the BCO
bridge is expected to be conformationally independent.
As can be seen from Figures 1 and 2B, the values of J and HDA
for 1-PhMe4 are quite close to those of 1-BCO. The small
differences in these measured σ-mediated couplings most
certainly originate from the differences in the sp3 and sp2 carbon
centers of the respective bridges and the fact that there are two
pathways for the sp2 σ-bridge and three pathways for the sp3 σ-
bridge. Nevertheless, the magnitudes of the couplings suggest
weak, conformationally independent σ-superexchange is oper-
ative in the phenylene series as well (favoring a spin polarization
mechanism analogous to Figure 3B). Thus, σ-type magnetic
exchange and electronic coupling appears to be bridge-carbon
hybridization independent, suggesting a spin polarization
mechanism for the σ-magnetic exchange in phenylene bridged
systems that are orthogonal to D and A.
the CASSCF surface function reveals an excellent correlation
described by R2 = 0.899 for both the electronic- and exchange-
coupling plots.
The 1-PhMe4 complex does not display perfectly perpendic-
ular donor−bridge and bridge−acceptor fragments to allow for
an exact evaluation of σ-only D−B−A communication. Thus, the
σ-pathway has been explicitly evaluated using 1-BCO, which
possesses a saturated σ-only bridge entirely comprising sp3-
hybridized carbons, Figure 1. The exchange coupling parameter
for 1-BCO determined from a fit to the variable-temperature
magnetic susceptibility data (see Figure S1B) is only JSQ‑NN = +1
cm−1, consistent with the value calculated from our CASSCF
calculations. Thus, the predicted σ-superexchange through a
para-phenylene ring perpendicular to both SQ and NN is
equivalent (∼1.7 cm−1), within the limitations of our
susceptibility measurements, to the σ-superexchange mediated
by a saturated BCO bridge.27 Moreover, since all the carbon
atoms of the phenylene ring are sp2 and those of the BCO bridge
are sp3, there is no measurable hybridization-dependent
difference in the magnitude of the σ-contribution to the
superexchange,28 nor is there a measurable difference due to
the fact that BCO comprises three −CH2CH2− σ-pathways,
while para-phenylene has just two pathways.
The conformational independence of Jσ for 1-BCO can be
understood with the aid of Figure 3. If we consider the view along
the axis that contains both bridgehead carbons, the three
Cbridgehead−Cethano σ-bonds transform as a1 and e in the local
idealized C3v symmetry of the bridgehead carbon. As per a
hyperconjugative interaction, the degenerate e-symmetry set has
the proper symmetry to mix with the pπ orbitals of the donor and
acceptor. Orbital overlap of either the D or A spin containing pπ-
orbitals with the first component of the e-set is shown in Figure 3,
We have shown that D−B−A triads with nearest-neighbor
torsional dependence of the exchange-/electronic coupling for
para-phenylene-bridged D−B−A biradical complexes can be
described by a 3D surface with torsionally independent HDB and
H
BA couplings. The data indicate that when the phenylene bridge
is perpendicular to either D or A (cos(ϕSQ‑B) = cos(ϕB‑NN) = 0)
the π-contribution to electronic and magnetic couplings is zero,
and a weak σ-only pathway dominates. The magnitude of the
predicted electronic coupling at conformations with orthogonal
D/A−B dihedral angles is determined by the magnitude of the
exchange parameter measured for 1-BCO (JSQ‑NN = +1 cm−1).
C
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Journal of the American Chemical Society
Communication
(7) Kirk, M. L.; Shultz, D. A.; Stasiw, D. E.; Habel-Rodriguez, D.; Stein,
B.; Boyle, P. D. J. Am. Chem. Soc. 2013, 135, 14713.
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Accordingly, the π-contribution to electronic coupling is ∼13
times greater than the σ-contribution for a planar SQ-Ph-NN
system (HDAπ/HDAσ ∝ √(Jπ/Jσ) = √(180/1). Our results
include experimentally determined values of σ- and π-
contributions to electronic coupling and a minimal dependence
of σ-mediated electronic coupling on the carbon hybridization of
the bridge.
This work also has implications for furthering our under-
standing of conductance in π-conjugated molecular transport
junctions when individual components of the π-system become
decoupled. Here, we anticipate that conductance (G) mediated
by a molecular π-junction will be ∼180 times greater ((Gπ/Gσ) ≈
(Jπ/Jσ) = (180/1) = 180) than that mediated by the
corresponding σ-system, in general accordance with theory.22,30
Full details of the spectroscopy and computational studies for the
biradicals presented here will be reported in a future manuscript.
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Kampf, J. W.; Kirk, M. L.; Kumar, R. K.; Lappi, S.; Peariso, K.; Preuss, K.
E.; Shultz, D. A. Inorg. Chem. 2006, 45, 4461.
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ASSOCIATED CONTENT
■
S
* Supporting Information
Experimental and computational details. Synthetic- and X-ray
crystallographic details, magnetic susceptibility data and fits, as
well as absolute energies (in Hartrees) and the coordinates of the
atoms in all the molecules whose geometries were optimized.
The Supporting Information is available free of charge on the
ACS Publications website at DOI: 10.1021/jacs.5b04629.
(23) Tuczek, F.; Solomon, E. I. Coord. Chem. Rev. 2001, 219, 1075.
(24) Hadt, R. G.; Gorelsky, S. I.; Solomon, E. I. J. Am. Chem. Soc. 2014,
136, 15034.
(25) Ricks, A. B.; Solomon, G. C.; Colvin, M. T.; Scott, A. M.; Chen,
K.; Ratner, M. A.; Wasielewski, M. R. J. Am. Chem. Soc. 2010, 132, 15427.
(26) Su, T. A.; Li, H.; Steigerwald, M. L.; Venkataraman, L.; Nuckolls,
C. Nat. Chem. 2015, 7, 215.
(27) Beratan, D. N. J. Am. Chem. Soc. 1986, 108, 4321.
(28) Goldsmith, R. H.; Vura-Weis, J.; Scott, A. M.; Borkar, S.; Sen, A.;
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(29) Chipman, D. M. J. Chem. Phys. 1991, 94, 6632.
(30) Solomon, G. C.; Bergfield, J. P.; Stafford, C. A.; Ratner, M. A.
Beilstein J. Nanotechnol. 2011, 2, 862.
AUTHOR INFORMATION
■
Corresponding Authors
*shultz@ncsu.edu
*mkirk@unm.edu
Author Contributions
∥CombiBlocks, San Diego, California 92126, United States.
Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
D.A.S. thanks the National Science Foundation (CHE-1213269)
for financial support. D.E.S. thanks the Department of Education,
Graduate Assistance in Areas of National Need (GAANN)
Program for a Fellowship (Nanoscale Electronic and Energy
Materials; P200A090041 and P200A120021). M.L.K. acknowl-
edges the National Science Foundation (NSF CHE-1301142)
for financial assistance. B.W.S. acknowledges NSF Grant No. IIA-
1301346. The single crystal diffraction data for 1-PhMe and 1-
pXylyl were collected at the USF X-ray Facility, Department of
Chemistry, University of South Florida, Tampa.
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■
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DOI: 10.1021/jacs.5b04629
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