Fast photodriven electron spin coherence transfer: A quantum gate based on a spin exchange J-jump

Article abstract of DOI:10.1021/ja305650x

Photoexcitation of the electron donor (D) within a linear, covalent donor-acceptor-acceptor molecule (D-A₁-A₂) in which A ₁ = A₂ results in sub-nanosecond formation of a spin-coherent singlet radical ion pair state, ¹(D^+?- A₁^-?-A₂), for which the spin-spin exchange interaction is large: 2J = 79 ± 1 mT. Subsequent laser excitation of A₁^-? during the lifetime of ¹(D ^+?-A₁^-?-A₂) rapidly produces ¹(D^+?-A₁-A₂ ^-?), which abruptly decreases 2J 3600-fold. Subsequent coherent spin evolution mixes ¹(D^+?-A₁-A ₂^-?) with ³(D^+?-A ₁-A₂^-?), resulting in mixed states which display transient spin-polarized EPR transitions characteristic of a spin-correlated radical ion pair. These photodriven J-jump experiments show that it is possible to use fast laser pulses to transfer electron spin coherence between organic radical ion pairs and observe the results using an essentially background-free time-resolved EPR experiment.

Full text of DOI:10.1021/ja305650x

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Communication
Fast Photo-driven Electron Spin Coherence Transfer:
A Quantum Gate Based on a Spin Exchange J-Jump
Lukáš Kobr, Daniel M Gardner, Amanda L. Smeigh, Scott Michael
Dyar, Steven D Karlen, Raanan Carmieli, and Michael R. Wasielewski
J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/ja305650x • Publication Date (Web): 16 Jul 2012
Downloaded from http://pubs.acs.org on July 21, 2012
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Fast Photo-driven Electron Spin Coherence Transfer: A Quan-
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Lukáš Kobr, Daniel M. Gardner, Amanda L. Smeigh, Scott M. Dyar, Steven D. Karlen, Raanan Carmieli,
and Michael R. Wasielewski*
Department of Chemistry and Argonne-Northwestern Solar Energy Research (ANSER) Center, Northwestern University, Ev-
anston IL 60208-3113
Supporting Information Placeholder
O
N
O
O
N
O
O
N
O
O
N
O
t-Bu
ABSTRACT: Photoexcitation of the electron donor (D) within
a linear, covalent donor-acceptor-acceptor molecule (D-A1-A2) in
which A1 = A2 results in sub-nanosecond formation of a spin-
t-Bu
1
2
coherent singlet radical ion pair state, (D+•-A1-•-A2), for which
1
O
N
O
O t-Bu
the spin-spin-exchange interaction is large: 2J = 79 ± 1 mT. Sub-
N
O
sequent laser excitation of A1-• during the lifetime of (D+•-A1-•-
1
t-Bu
1
A2) rapidly produces (D+•-A1-A2-•), which abruptly decreases 2J
3600-fold. Subsequent coherent spin evolution mixes (D+•-A1-
1
3
A2-•) with (D+•-A1-A2-•) resulting in mixed states which display
tetramethylbiphenyl group (B1) to perylene (PER) in 1 and 2
shifts the 438 nm absorption maximum of PER in toluene
slightly to 446 nm (Figure 1). This is consistent with the ex-
pected molecular geometry where the durene π system should
be nearly orthogonal to that of PER due to steric effects of its
methyl groups. The absorption spectra of both naphthalene-
1,8:4,5-bis(dicarboximide) (NDI) acceptors in 1 and the single
NDI acceptor in 2 are not perturbed by their attachment to the
2,5-dimethylphenyl group (B2).6 The ground state spectra of
both 1 and 2 indicate that the electronic coupling between PER
and NDI is weak.
transient spin-polarized EPR transitions characteristic of a spin-
correlated radical ion pair. These photo-driven J-jump experi-
ments show that it is possible to use fast laser pulses to transfer
electron spin coherence between organic radical ion pairs and
observe the results using an essentially background-free time-
resolved EPR experiment.
Controlling the spin dynamics of complex multi-spin molecu-
lar systems is a major goal in spintronics and quantum infor-
mation processing.1 Fast photo-initiated electron transfer within
covalently-linked organic donor-acceptor molecules having spe-
cific donor-acceptor (D-A) distances and orientations results in
the formation of spin-entangled electron-hole pairs (i.e. radical
ion pairs, RPs) having well-defined initial spin configurations,
while time-resolved electron paramagnetic resonance (TREPR)
techniques provide an important means of manipulating and
controlling these coherent spin states.2 Organic RPs display
coherent spin motion for up to ∼100 ns,3 which makes it possi-
ble that this coherence may provide the basis for new quantum
information processing strategies based on organic molecules.
Cyclic voltammetry on 1 and 2 at a Pt electrode in butyroni-
trile containing 0.1 M Bu4NPF6 (Figures S1A,B) shows two
reversible one-electron NDI reduction waves at Ered = -0.53 and
-1.02 V vs. SCE,6 and a single reversible one-electron PER oxi-
dation wave at Eox = 1.06 V vs. SCE.7 The reduction potentials
of the two NDIs in 1 are indistinguishable; however, using dif-
ferential pulse voltammetry (Figure S1C), the second reduction
peak of 1 is somewhat asymmetric. The NDI reduction waves of
1 have about twice the current as the PER oxidation wave, so
that they result from independent reduction of each NDI with-
in 1. Using the Weller equation (see Supporting Information),
the estimated energies of PER+•-B1-NDI1-•-B2-NDI2 and PER+•-
B1-NDI1-• for 1 and 2 in toluene are both 2.46 eV, while that of
We have previously demonstrated that the RP populations
within linear and branched D-A1-A2 arrays can be controlled
using one wavelength-selective laser pulse to generate D+•-A1-•-A2
and a second, subsequent wavelength-selective laser pulse to
excite A1-• resulting in the thermodynamically uphill reaction
D+•-A1-•-A2 → D+•-A1-A2-•.4 Because of the close proximity of
D+• and A1-•, the exponentially distance-dependent Heisenberg
spin-spin exchange coupling (2J) between D+• and A1-• is neces-
sarily large,5 while that between D+• and A2-• is much smaller.
Here we show that laser excitation of the A1-• radical ion results
in coherent transfer of the initial D+•-A1-•-A2 RP spin state to
D+•-A1-A2-•.
1.2
1.0
0.8
0.6
0.4
0.2
0.0
300
350
400
450
500
The synthesis of 1 and 2 are described in the Supporting In-
Wavelength(nm)
formation. All synthetic intermediates and final products were
Figure 1. Normalized UV-vis spectra of 1 (black) and 2 (red)
in toluene.
1
characterized by H and 13C NMR, MALDI-TOF, MS-ESI, and
UV-vis spectroscopy. The attachment of the 2,3,5,6-
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+
-
D-B-*A-B-A
0.04
0.03
0.02
0.01
0.00
-0.01
-0.02
-0.03
-0.04
A
1
1
2
2
1
2
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8
A
1*D-B -A -B-A
1(D-B-A-B-A)3(D-B-A-B-A)
1
1
2
2
+
-
+
-
kCS2
1
1
2
2
1
1
2
2
480nm
kCS1
kRP
ST
k
0.015
0.010
0.005
0.000
-0.005
1 ps
CRT
+
D-B-A -B -A
-
10 ps
50 ps
150 ps
310 ps
600 ps
2.0 ns
1
1
2
2
τ
= 277 3 ps
CS
3(D-B-A-B-A )
416nm
1
1
2
2
kCRS
T
+1
0
1
2
3
4
5
6
B
B
2J
Time (ns)
9
500
600
700
800
S
T
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2J
Wavelength (nm)
D-B-A-B -A
2
0
1
1
2
0.3
0.2
B
T
ZeemanSplittingof
theTriplet Levels
-1
MagneticField
0.1
0.0
0.4
0.2
0.0
Figure 3. A) Energy levels and electron transfer pathways D =
PER, A = NDI. B) Expanded view of the RP energy levels as a
function of magnetic field (2J > 0).
τ
= 603
±
12 ns
50 ns
CR
-0.1
-0.2
-0.3
250 ns
500 ns
1000 ns
4000 ns
ground state and the triplet RP recombines to yield the neutral
local triplet (Figure 3A). Application of a static magnetic field
causes Zeeman splitting of the RP triplet sublevels, and varying
the field strength modulates the efficiency of RP-ISC by adjust-
ing the energies of triplet sublevels relative to that of the singlet
level (Figure 3B). When the Zeeman splitting of the triplet RP
sublevels equals the intrinsic singlet-triplet splitting, 2J, of the
RP, there is an increase in the RP-ISC rate. This increase trans-
lates into a maximum in triplet RP production and therefore a
maximum in neutral local triplet yield upon CR. By monitor-
ing the yield of local triplet production as a function of applied
magnetic field, the magnitude of 2J can be measured directly.12
The value of 2J within PER+•-B1-NDI1-•-B2-NDI2 was measured
using the effect of a magnetic field on the 3*PER yield moni-
tored at 480 nm and 4 ꢀs following the laser pulse. The 3*PER
yield for 1 exhibits a resonance at 2J = 79 ± 1 mT (Figure 4),
while a similar resonance is observed for 2 at 2J = 82 ± 1 mT
(Figure S3). The similarity of the 2J values for 1 and 2 provides
additional evidence that PER+•-B1-NDI1-•-B2-NDI2 is primarily
populated within 1. Since 2J depends exponentially on distance,
moving the electron to NDI2 should result in a large decrease in
2J.
0
1
2
3
4
Time
(
ꢀ
s)
400
500
600
700
800
Wavelength (nm)
Figure 2. Transient absorption spectra of 1 in toluene at
295K. A) following a 416 nm, 120 fs laser pulse. Inset: transi-
ent kinetics monitored at 520 nm. B) following a 416 nm, 7
ns laser pulse. Inset: transient kinetics monitored at 480 nm.
PER+•-B1-NDI1-B2-NDI2-• for 1 is 2.62 eV. Since the 1*PER en-
ergy is 2.76 eV, the free energies for photogenerating all RPs are
favorable. However, the significantly longer RP distance of
PER+•-B1-NDI1-B2-NDI2-• (29.0 Å) relative to that of PER+•-B1-
NDI1-•-B2-NDI2 (16.6 Å) results in an additional 0.16 eV Cou-
lombic energy change making electron transfer to NDI2 energet-
ically less favorable than that to NDI1.
The transient absorption spectra of 1 in toluene at 295K fol-
lowing selective photoexcitation of PER with a 416 nm, 120 fs
laser pulse (Figure 2A) show the initial formation of a strong
1*PER absorption band at 720 nm,8 which decays with the sim-
ultaneous appearance of a broad PER+• absorption centered
around 550 nm9 and two NDI-• absorption bands at 480 nm
and 610 nm.6 The charge separation (CS) kinetics are fit at 520
nm to a time constant of τCS = 277 ± 3 ps. Given that the
1*PER lifetime is 4.6 ns,10 the resultant quantum yield of charge
separation is 94%. At later times, the corresponding nanosec-
ond transient absorption spectra (Figure 2B) show that the
PER+• and NDI-• absorptions decay with a charge recombina-
tion (CR) time constant of τCR = 603 ± 12 ns. The residual
long-lived absorption near 500 nm results from 3*PER produced
by CR in a 45% yield.11 Corresponding data acquired for con-
trol dyad 2 (Figures S2A and S2B) give τCS = 300 ± 3 ps and τCR
= 680 ± 3 ns. The similarity between the time constants for
both charge separation and recombination in 1 and 2 indicates
that 416 nm excitation produces only PER+•-B1-NDI1-•-B2-NDI2
in 1, which is consistent with the fact that moving the electron
from NDI1 to NDI2 requires a Coulomb energy penalty of 0.16
eV.
TREPR spectra were acquired using continuous microwave
irradiation in a ∼350 mT magnetic field (see Supporting Infor-
mation), so that the Zeeman split triplet RP sublevels are best
described by the T+1, T0, and T-1 eigenstates that are quantized
along the applied magnetic field, while the singlet RP energy
1.4
1.3
1.2
1.1
1.0
0.9
Rapid charge separation from the 1*PER precursor state re-
sults in formation of the singlet RP: 1(PER+•-B1-NDI1-•-B2-NDI2),
which may undergo electron-nuclear hyperfine coupling-
induced radical pair intersystem crossing (RP-ISC) to produce
0
30
60
90
120
150
Magnetic Field (mT)
Figure 4. Relative triplet yield monitored at 480 nm as a
function of magnetic field strength for 1 in toluene at 295 K
following a 416 nm, 7 ns laser pulse.
the triplet RP, (PER+•-B1-NDI1-•-B2-NDI2). The subsequent CR
3
is spin selective; i.e. the singlet RP recombines to the singlet
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with the very large 2J value measured directly by the magnetic
2000ns
field effect on the 3*PER yield. The large 2J value inhibits S-T0
mixing resulting in a greatly decreased transition probability
between these states and T±1.2g,14,17b The weak signal observed
for 1 most likely results from generation of a small population
of NDI2-• that is strongly spin-polarized.
1
2
3
4
1500ns
1000ns
5
Our previous results have shown that photoexcitation of
NDI-• at 480 nm produces its excited doublet state (2*NDI-•)
that has a 260 ps lifetime.6 This lifetime is sufficiently long to
allow electron transfer from 2*NDI-• to nearby electron accep-
tors.4 The presence of the short-distance B2 bridging molecule
between the two NDI molecules in 1 makes electron transfer
from 2*NDI1-• to NDI2 kinetically favorable. In principle, fast
electron transfer from NDI1-• to NDI2 should not perturb the
coherence of the two spins within the initial RP, but transfer it
intact to the second RP. Selective 416-nm photoexcitation of
PER within 1 at t = 0 followed by selective 480-nm photoexcita-
tion of NDI1-• at t = 15 ns results in the appearance of a strong
spin-polarized RP signal (Figure 5). Irradiation of 1 and 2 with a
single laser pulse at 480 nm, which is not absorbed by their
ground states does not result in any EPR signals (Figure S4).
Simulation of the experimental spin-polarized RP spectra using
the model of Till and Hore17b yields 2J = 0.022 mT (Figure S5).
Thus, rapid photo-driven electron transfer from the initial RP
to the secondary RP results in a nearly 3600-fold decrease in 2J.
6
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350ns
300ns
250ns
200ns
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100ns
50ns
340 341 342 343 344 345
MagneticField(mT)
The spin-polarized RP signal that appears following photoex-
citation of 1 with an initial 416 nm laser pulse at t416 = 0 and a
second, subsequent 480 nm laser pulse at t480 shows an interest-
ing dependence on t480 - t416 , the time delay between the 416 nm
and 480 nm laser pulses (Figure 6). The times of the laser pulses
are measured at the maximum intensity of each pulse. The data
is fit to the convolution of a Gaussian function with a width of
10 ± 1 ns and a single exponential decay of 11 ± 1 ns. Since the
416 nm and 480 nm laser pulse widths (FWHM) are both 7 ns,
the slow rise of the spin-polarized RP EPR signal results from
the build-up of the initial PER+•-B1-NDI1-•-B2-NDI2 population
during the 416 nm pulse convolved with the electron transfer
Figure 5. TREPR spectra of 1 in toluene at 295 K at the indi-
cated times following a single 416 nm, 7 ns laser pulse at t416 = 0
(red traces), and following the two-pulse sequence: 416 nm, 7 ns
laser pulse at t416 = 0; 480 nm, 7 ns laser pulse at t480 = 15 ns
(black traces).
level (S) is unaffected (Figure 3B).2b,2d,13 RP-ISC depends on
both the spin-spin exchange interaction (2J) and the dipolar
interaction (D) between the two radicals that comprise the RP.
The magnitude of 2J depends exponentially on the distance (r)
between the two radicals, and is assumed to be isotropic, while
D depends on 1/r3 and is anisotropic. In fluid solution, howev-
er, D is rotationally averaged to zero for small molecules such as
1 and 2.
-•
from ND11 to NDI2 induced by the second 480 nm pulse.
Rapid photogeneration of PER+•-B1-NDI1-•-B2-NDI2 using 416
nm excitation results in zero quantum coherence (ZQC) be-
tween the S and T0 energy levels.3c,17a,18 Rapid dephasing of the
ZQC results from the interaction of the electron spins with
their environment, and only a very small amount of S-T0 mixing
occurs because 2J is large.14 If the 480 nm pulse is applied prior
to dephasing, then the ZQC is transferred from PER+•-B1-
NDI1-•-B2-NDI2 to PER+•-B1-NDI1-B2-NDI2-•, wherein the abrupt
When 2J is large, such as the ∼80 mT values observed for
PER+•-B1-NDI1-•-B2-NDI2 and PER+•-B1-NDI1-•, S-T0 mixing is
generally weak.14 However, when 2J is generally <10 mT, coher-
ent S-T0 mixing occurs,2b,2d,13 and the two resulting mixed states
are preferentially populated due to the initial population of S,
so that the four EPR transitions that occur between these mixed
states and the initially unpopulated T+1 and T-1 states are spin
polarized.14a,15 The TREPR spectrum consists of two anti-phase
doublets, centered at the g-factors of the individual radicals that
comprise the pair, in which the splitting of each doublet is de-
termined by 2J. The electron spin polarization pattern from
low field to high field of the EPR signal, i.e. which transitions
are in enhanced absorption (a) or emission (e), is determined by
the sign rule:2d,16 Γ = µ·sign(2J) = (-) gives e/a or = (+) gives a/e,
where µ is -1 or +1 for a singlet or triplet excited state precursor,
respectively. Thus, if 2J > 0, singlet excited state precursors
yield an (e,a,e,a) line pattern. If the g-factors of the two radicals
are similar and are split by hyperfine couplings, the two dou-
blets overlap strongly, and appear as a distorted (e,a) signal. The
spectra are simulated by applying the spin-correlated radical pair
model using 2J along with the g-factors and the hyperfine cou-
pling constants of D+• and A-•.14-15,17
12
10
8
6
4
2
0
0
10
20
30
40
50
t480- t416 (ns)
Figure 6. Intensity of the spin-polarized EPR signal of 1 in
toluene at 295 K and 100 ns as a function of the time delay,
t480 - t416, between the 416 nm, 7 ns laser pulse at t416 = 0 and
The TREPR spectra of 1 and 2 in toluene at 295 K following
selective 416-nm photoexcitation of PER show only a very weak
signal for 1 (Figure 5) and no signal for 2. This is consistent
the second 480 nm, 7 ns laser pulse at t480
.
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Ardavan, A.; Lyon, S. A.; Briggs, G. A. D.; Morton, J. J. L. Phys. Rev.
Lett. 2011, 106, 110504/1.
reduction in 2J greatly increases S-T0 mixing and the transition
1
2
3
4
5
6
7
8
probability from the mixed states to T±1 resulting in the appear-
ance of the spin-polarized EPR signal.14 In contrast, when the
480 nm pulse is applied after dephasing in PER+•-B1-NDI1-•-B2-
NDI2 is complete, 2J is still dramatically reduced, but coherent
S-T0 mixing does not occur. The small amount of S-T0 mixing
generated in PER+•-B1-NDI1-•-B2-NDI2 is insufficient to produce
an observable spin-polarized EPR signal in PER+•-B1-NDI1-B2-
NDI2-•. In fact, no spin-polarized EPR signal is observed when
t480 - t416 > 50 ns. Thus, the observed 11 ± 1 ns decay time of the
EPR signal most likely reflects the ZQC dephasing time of
PER+•-B1-NDI1-•-B2-NDI2.
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Our data illustrate how laser manipulation of coherent spin
states can control the magnetic interactions between the spins
offering new opportunities to design molecular systems for
studying quantum information processing.
(3)(a)Kothe, G.; Weber, S.; Ohmes, E.; Thurnauer, M. C.; Norris, J.
R. J. Phys. Chem. 1994, 98, 2706; (b)Laukenmann, K.; Weber, S.;
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Dzuba, S. A.; Timmel, C. R.; Fursman, C. E.; Hore, P. J. Spectrochim.
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ASSOCIATED CONTENT
Supporting Information Available: Experimental details including
synthesis, electrochemistry, and additional transient optical and
EPR data. This material is available free of charge via the Internet
at http://pubs.acs.org.
(4)(a)Debreczeny, M. P.; Svec, W. A.; Marsh, E. M.; Wasielewski, M.
R. J. Am. Chem. Soc. 1996, 118, 8174; (b)Lukas, A. S.; Miller, S. E.;
Wasielewski, M. R. J. Phys. Chem. B 2000, 104, 931; (c)Lukas, A. S.;
Bushard, P. J.; Wasielewski, M. R. J. Am. Chem. Soc. 2001, 123, 2440.
AUTHOR INFORMATION
(5)Heisenberg, W. Z. Phys. 1926, 38, 411.
Corresponding Author
(6)Gosztola, D.; Niemczyk, M. P.; Svec, W.; Lukas, A. S.;
Wasielewski, M. R. J. Phys. Chem. A 2000, 104, 6545.
m-wasielewski@northwestern.edu
(7)Kubota, T.; Miyazaki, H.; Ezumi, K.; Yamakawa, M. Bull. Chem.
Soc. Jap. 1974, 47, 491.
Notes
The authors declare no competing financial interest.
(8)Pagès, S.; Lang, B.; Vauthey, E. J. Phys. Chem. A 2003, 108, 549.
(9)Shida, T. Electronic Absorption Spectra of Radical Ions; Elsevier: New
York, 1988.
ACKNOWLEDGMENTS
The authors thank Dr. Oleg Poluektov (Argonne National Labora-
tory) for stimulating discussions. This work was supported by the
National Science Foundation under Grant No. CHE-1012378.
DMG thanks the NDSEG for a graduate fellowship. ALS and RC
were supported as part of the ANSER Center, an Energy Frontier
Research Center funded by the U.S. Department of Energy (DOE),
Office of Science, Office of Basic Energy Sciences, under award
number DE-SC0001059.
(10)Katoh, R.; Sinha, S.; Murata, S.; Tachiya, M. J. Photochem
Photobiol. A 2001, 145, 23.
(11)(a)Bensasson, R.; Land, E. J. Trans. Faraday Soc. 1971, 67, 1904;
(b)Rachford, A. A.; Goeb, S.; Ziessel, R.; Castellano, F. N. Inorg. Chem.
2008, 47, 4348.
(12)(a)Anderson, P. W. Phys. Rev. 1959, 115, 2; (b)Shultz, D. A.;
Fico, R. M., Jr.; Bodnar, S. H.; Kumar, R. K.; Vostrikova, K. E.; Kampf,
J. W.; Boyle, P. D. J. Am. Chem. Soc. 2003, 125, 11761; (c)Scott, A. M.;
Miura, T.; Ricks, A. B.; Dance, Z. E. X.; Giacobbe, E. M.; Colvin, M.
T.; Wasielewski, M. R. J. Am. Chem. Soc. 2009, 131, 17655.
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