Effect of Electron-Nuclear Hyperfine Interactions on Multiple Quantum

Subscriber access provided by Kaohsiung Medical University

A: Kinetics, Dynamics, Photochemistry, and Excited States

Effect of Electron-Nuclear Hyperfine Interactions on Multiple Quantum Coherences in Photogenerated Covalent Radical (Qubit) Pairs Jordan N. Nelson, Jinyuan Zhang, Jiawang Zhou, Brandon K. Rugg, Matthew D. Krzyaniak, and Michael R. Wasielewski J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.8b07556 • Publication Date (Web): 15 Nov 2018 Downloaded from http://pubs.acs.org on November 21, 2018

Just Accepted “Just Accepted” manuscripts have been peer-reviewed and accepted for publication. They are posted online prior to technical editing, formatting for publication and author proofing. The American Chemical Society provides “Just Accepted” as a service to the research community to expedite the dissemination of scientific material as soon as possible after acceptance. “Just Accepted” manuscripts appear in full in PDF format accompanied by an HTML abstract. “Just Accepted” manuscripts have been fully peer reviewed, but should not be considered the official version of record. They are citable by the Digital Object Identifier (DOI®). “Just Accepted” is an optional service offered to authors. Therefore, the “Just Accepted” Web site may not include all articles that will be published in the journal. After a manuscript is technically edited and formatted, it will be removed from the “Just Accepted” Web site and published as an ASAP article. Note that technical editing may introduce minor changes to the manuscript text and/or graphics which could affect content, and all legal disclaimers and ethical guidelines that apply to the journal pertain. ACS cannot be held responsible for errors or consequences arising from the use of information contained in these “Just Accepted” manuscripts.

is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

Page 1 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Effect of Electron-Nuclear Hyperfine Interactions on Multiple Quantum Coherences in Photogenerated Covalent Radical (Qubit) Pairs Jordan N. Nelson, Jinyuan Zhang, Jiawang Zhou, Brandon K. Rugg, Matthew D. Krzyaniak, and Michael R. Wasielewski* Department of Chemistry and Institute for Sustainability and Energy at Northwestern Northwestern University, Evanston, Illinois 60208-3113 ABSTRACT Ultrafast photo-driven electron transfer reactions starting from an excited singlet state in an organic donor-acceptor molecule can generate a spin-correlated radical pair (RP) with an initially entangled spin state that may prove useful as a two-qubit pair in quantum information protocols. Here we investigate the effects of modulating electron-nuclear hyperfine coupling by rapidly transferring an electron between two equivalent sites comprising the reduced acceptor of the RP. A covalent electron donor-acceptor molecule including a tetrathiafulvalene (TTF) donor, a 4aminonaphthalene-1,8-imide (ANI) chromophoric primary acceptor, and a m-xylene bridged cyclophane having two equivalent pyromellitimides (PI2), TTF-ANI-PI2, as a secondary acceptor was synthesized along with the analogous molecule having one pyromellitimide (PI) acceptor, TTF-ANI-PI. Photoexcitation of ANI within each molecule results in sub-nanosecond formation of TTF+•-ANI-PI-• and TTF+•-ANI-PI2-•. The effect of reducing electron-nuclear hyperfine interactions in TTF+•-ANI-PI2-• relative to TTF+•-ANI-PI-• on decoherence of multiple-quantum coherences has been measured by pulse-EPR spectroscopy. This contribution is especially relevant in the absence of modulation of exchange or dipolar interactions, as with the RP at a fixed distance in the molecules in this work. The theoretical prediction of the contribution from an ensemble of hyperfine interactions to decoherence in these RPs is shown to be less than the full width at half maximum of the quantum beat frequencies measured experimentally. Pulse bandwidth and offresonant excitation by square microwave pulses are proposed as larger contributors to decoherence in these molecules than the hyperfine interactions, and specific pulse shapes relevant to arbitrary waveform generation are introduced.

1 ACS Paragon Plus Environment

The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Introduction Photogenerated spin-correlated radical pairs (RPs) in fixed-distance, covalent electron donoracceptor (D-A) molecules are unique in research on bulk-ensemble quantum information processing due to their synthetic accessibility, well-defined structures, and initial pure, entangled singlet spin-state.1-15 Long-lived spin-correlated RPs are most often produced by photoinduced sub-nanosecond electron transfer from the electron donor to the acceptor followed in some cases by a thermal charge transfer step to a secondary donor or acceptor. Spin-correlated RPs were first observed in photosynthetic reaction center proteins,16 then in micelles,17-18 and later in covalent fixed distance donor-acceptor molecules.19-22 If the distance between the radicals comprising a RP is large enough that the differences between the local magnetic interactions of each radical, determined largely by their g-factors and hyperfine interactions (A), are on the same order of magnitude as their spin-spin exchange (J) and dipolar (D) interactions, coherent spin evolution mixes the singlet and triplet RP states due to differences in the local magnetic environment of each radical.16, 18, 23-27 This mechanism is often referred to as radical pair intersystem crossing (RPISC),28-29 and was noted in the early literature on chemically-induced dynamic electron polarization (CIDEP)28-32 as well as studies on photosynthetic reaction centers.16, 27, 33-34


Page 2 of 33

Page 3 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


A

B

Figure 1. (A) Energy level diagram (not to scale) of the four spin states of a photochemically-generated RP. The red and blue ellipses indicate the zero- and double-quantum coherences, respectively, while the green arrows depict the single-quantum coherences that exhibit allowed microwave transitions. (B) The 4 x 4 density matrix of a spin-correlated RP indicating the zero-, single- and double-quantum coherences as well as the populations (P) of the four states. The colors correspond to the transitions indicated in the energy level diagram (A).

Recently, it has been recognized that the initial spin-entangled RP produced by ultrafast electron transfer can be used to implement 2-qubit quantum information protocols,1, 3, 5, 8, 13-15, 35-36 so that implementing these protocols requires strategies for manipulating spin coherences and eliminating decoherence. Spin coherences in RPs have been measured using transient electron paramagnetic resonance (TREPR)37 and pulse-EPR38 spectroscopies with a view towards mimicking the primary events of photosynthesis,20-21 determining electron-hole pair distances,39 and measuring very small (T) magnetic interactions.40-41 For example, when a RP is photogenerated from an excited singlet state precursor in a static magnetic field that is large relative to J and D, Zeeman splitting of |T +1〉 and |T ―1〉 away from |T0〉 results in coherent |S⟩ ― |T0〉 mixing to give |ΦA〉 and |ΦB〉 , which are initially populated (Figure 1A). The laser pulse that creates the RP generates quantum coherence between |ΦA〉 and |ΦB〉, which is termed zeroquantum coherence because ∆ms = 0 for these two states, and thus microwave-induced transitions between them are forbidden.42 Using the density matrix representation (Figure 1B), it can be shown that a single microwave pulse can be used to transfer ZQC to both the single-quantum coherence (SQC, ∆ms = 1) for which microwave-induced transitions are allowed and the double-quantum 3 ACS Paragon Plus Environment


Page 4 of 33

coherence (DQC, ∆ms = 2) for which they are forbidden.27 Transfer of the resulting DQC to SQC then requires a second microwave pulse.43-44 Thus, with just two microwave pulses following a laser pulse, as in the pulse-EPR experiments described herein, both ZQC and DQC can be measured indirectly by transferring these coherences to the allowed SQCs. The straightforward, but somewhat lengthy density matrix manipulations that explicitly describe the photogeneration of the ZQC in the spin-correlated RP and manipulation of SQC and DQC by two microwave pulses is given in the Supporting Information and follow the methodologies given originally by Tang and Norris.43-44 While fast pulse-EPR techniques provide the means to manipulate RP spin coherences,11, 45 knowledge of the factors that contribute to RP spin decoherence is incomplete. For example, the well-known ‘singlet-triplet dephasing’ mechanism relies on modulation of distance-dependent J and D interactions.46-49 However, in photosynthetic reaction center proteins16,

50

or in rigid,

covalent molecules,19-21 diffusion of the two radicals comprising the RP is not possible, and moreover, the RP lifetime is much longer than the spin decoherence time; so that variations in J and D are small and may not always contribute to decoherence. Nevertheless, fast decoherence times have been observed in spin-correlated RPs in photosynthetic reaction centers at 77 K that are attributed to small amplitude librational motions that are difficult to eliminate even at cryogenic temperatures.51 CS1 = 0.7 ps e-

TTF S

N S

S

O

N N

N

PI

O

TTF S S

N

eO N

S S

O

ANI eF CR = 35.6 μs

CS2 ≈ 0.2 ns

e-

eO

S

CS1  20 ps

CS2 = 0.5 ns

O

O

N N O

ANI F eCR = 9.7 μs

O

O

N O O N O

N

PI2

O O

t-Bu

N O

TTF-ANI-PI2

TTF-ANI-PI

Figure 2. Molecules TTF-ANI-PI and TTF-ANI-PI2 labeled with step-wise electron transfer events following excitation of the ANI chromophore.

4

ACS Paragon Plus Environment

Page 5 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Given that RP-ISC is most often driven by differences in effective hyperfine interactions between the two radicals comprising the RP, contributions from A to decoherence in spincorrelated RPs merit attention because the RP distances in this work are strongly constrained by their molecular structures, and thus the distant-dependent J and D interactions, are equally constrained on the EPR timescale. To examine the role of hyperfine interactions on spin decoherence in RPs, a covalent electron D-A molecule including a tetrathiafulvalene (TTF) donor, a 4-aminonaphthalene-1,8-imide (ANI) chromophoric primary acceptor, and a m-xylene bridged cyclophane having two equivalent pyromellitimides (PI2), TTF-ANI-PI2, as a secondary acceptor was synthesized along with the analogous molecule having one pyromellitimide (PI) acceptor, TTF-ANI-PI (Figure 2). Photoexcitation of ANI within each molecule results in sub-nanosecond formation of TTF+•-ANI-PI-• and TTF+•-ANI-PI2-•, whose spin dynamics and multiple quantum coherences are characterized by pulse-EPR spectroscopy. Two-dimensional (2D) pulse-EPR experiments are employed in this work to measure the allowed SQC transitions (transverse magnetization) and their modulation due to the formally-forbidden ZQC and DQC. In particular, here we investigate the effects of modulating electron-nuclear hyperfine coupling on multiple quantum coherences in a spin-correlated RP, where rapid electron hopping between two equivalent sites comprising the reduced acceptor occurs. The primary goal of this study is to investigate what causes decoherence of ZQC and DQC in spin-correlated RPs on a time scale that may limit the implementation of more lengthy microwave pulse operations relevant for quantum information processing.45,11,52 Experimental Section Synthesis. The synthesis of TTF-ANI-PI has been reported previously,8 while the synthesis of TTF-ANI-PI2 is described in the Supporting Information.



Transient Absorption Spectroscopy. The fsTA spectroscopy apparatus has been described previously,53 and here we present details specific to the present work. The 414 nm photoexcitation pulses were obtained by frequency-doubling the 828 nm fundamental in a lithium triborate (LBO,  = 90°,  = 31.7°, 1 mm) crystal. The energy of all pulses for photoexcitation was attenuated to ~1 µJ/pulse using neutral density filters and focused to a 200 m spot size at the sample. To suppress contributions from orientational dynamics, experiments were performed at a randomized pump polarization. Spectral and kinetic data were collected with separate CMOS detectors for the UV-Vis and NIR spectral regions and an 8 ns pump-probe delay track (customized Helios, Ultrafast Systems, LLC). Samples were prepared with an optical density of 0.4-0.7 at 414 nm and were irradiated in 2 mm quartz cuvettes with 0.4-0.8 μJ/pulse focused to ca. 0.2 mm diameter spot. The samples were prepared in the glovebox and degassed by multiple freeze-pump-thaw cycles prior to analysis. For TA experiments at 105 K, samples were prepared in butyronitrile at 0.4-0.7 optical density at 414 nm and sealed under nitrogen atmosphere in a 2mm-thick glass cell. This cell was secured in a Janis VNF-100 cryostat and the temperature was kept at 105 K with a CryoCon 32B temperature controller. The TA data yields a time-resolved absorption spectrum that was factored by singular value decomposition to perform species-associated fitting using the MATLAB software package.54 The singular values of the spectral data form an orthonormal set of basis spectra that describe the wavelength dependence of kinetic species. The other orthogonal eigenvector of the SVD analysis describes the time-dependent amplitude of these basis spectra.55 Except for the TA of TTF-ANIPI2 at 105K in butyronitrile, these vectors are fit using a three-step, sequential (A  B  C  ground-state), first-order kinetic model with a rate matrix that is solved numerically in MATLAB.


Page 6 of 33

Page 7 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


For the TA of TTF-ANI-PI2 at 105K in butyronitrile, the dataset was globally fit to a sum of four exponentially decaying functions. The resultant populations were used to deconvolute the dataset and reconstruct decay-associated spectra. Each function corresponds to a given population with a well-defined temporal evolution, but with a potential mixture of species. For both the decayassociated and species-associated spectra, the fitting procedure was the same: the respective solutions are convolved with a Gaussian instrument response function and least-squares fit to the kinetic data using a Levenberg-Marquardt method. EPR Spectroscopy. Compounds TTF-ANI-PI and TTF-ANI-PI2 were dissolved in toluene to achieve an optical density of 0.5 in a 2 mm cuvette at 414 nm (ca. 10-4 M according to the extinction coefficient of the chromophore). To achieve a sample height of ca. 0.5 cm, this solution was loaded into dry quartz tubes (2.8 mm o.d. x 2.6 mm id for pulse-/transient-EPR), degassed with at least three freeze-pump-thaw cycles, and flame-sealed under vacuum ( ~100 ns), the electron transfer events that generate the TTF•+ANI-PI•- and TTF•+-ANI-PI2•- are also designed to be much faster than the time scale of the twospin coherences (10s of ns). From the fsTA data (Figures S1 and S3), it is clear that both TTF•+-

50

75

100

TDAF (ns)

Beyond the requirement that a photogenerated RP lives long enough to observe and manipulate

25

Figure 8. Top: real channel of echo intensity of TTF+•-ANI-PI-• at 85K in toluene-d8 integrated from TDAF = 28-32 ns as a function of magnetic field (i.e. a field-swept echo-detected spectrum); Bottom: Traces of electron echo intensity (purple) as a delay-after-laser flash is incremented with fits (red) to exponentially damped sinusoidal functions at (a) 338.2 mT and (b) 337.5 mT (approximately marked on the field-swept spectrum on the left). The fit parameters are enumerated in the Supporting Information, but the primary parameter of interest, the lifetime of ZQC (𝑇𝑍𝑄𝐶) is included.

ANI-PI•- and TTF•+-ANI-PI2•- form in < 1 ns. For TTF-ANI-PI2, however, there is the added


Page 15 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


complication that the spectral feature at 730 nm, assigned to PI2·-, appears within the instrument response. Based on control experiments, there is no appreciable change in the reduction potential of PI2 relative to PI, so that the ultrafast appearance of this feature at 730 nm can only be attributed to intermolecular dimer formation between the TTF donor on one molecule and the PI2 acceptor on a second molecule. This effect is exacerbated by the slow cooling necessary to perform the fsTA experiments at low temperature. The effect of this aggregation is that a minor amount of coexcitation of TTF with 414 nm light results in formation within the instrument response of [TTF•+]A-[PI2•-]B, where the subscripts A and B refer to the two different molecules of TTF-ANIPI2. Because global analysis using a parallel kinetic model did not converge to yield the speciesassociated spectra, the fsTA data were analyzed to yield the decay-associated spectra of TTFANI-PI2 (Figure S3). These spectra have features that include a minor contribution from the ultrafast appearance and decay of [TTF•+]A-[PI2•-]B in the aggregate, and a major contribution from the somewhat slower appearance and decay of TTF•+-ANI-PI2•-. Therefore, the CS1 and CS2 rates for TTF-ANI-PI2 are given as approximate values in Figure 2, yet they are still much faster than the EPR timescale. Since the CS1 and CS2 time constants for TTF-ANI-PI and TTF-ANI-PI2 are much faster than the 7 ns laser pulse used in the EPR spectroscopy experiments. This simplifies the interpretation of quantum beats in the 2D time domain EPR spectroscopy experiments. Additionally, the nano- and microsecond TA spectra of TTF•+-ANI-PI•- (Figure S2) and TTF•+ANI-PI2•- (Figure S4) indicate that the CR lifetimes at zero magnetic field (Figure 1) are much longer than the spin coherence lifetimes for either molecule. Previous experimental work has demonstrated a greater dependence of the frequencies for short-lived, forbidden ZQC on g-factor differences rather than hyperfine differences between donor- and acceptor-localized radicals in RPs.8 The ENDOR spectra of PI•- and PI2•- show that



Page 16 of 33

the electron is hopping between the two PI molecules within PI2•- at a rate that exceeds the 1H – ENDOR time scale (>107 s-1) (Figure S5). RP-ISC is driven by the difference in electron-nuclear hyperfine interactions of each radical, ∆𝑎, eq 1:18, 24 ∆𝑎 = 0.5(∑𝑖𝑎1𝑖𝑚1𝑖 ― ∑𝑗𝑎2𝑗𝑚2𝑗)

(1)

where 𝑎1𝑖 and 𝑎2𝑗 are the individual hyperfine couplings in radicals 1 and 2 and 𝑚1𝑖 and 𝑚2𝑗 are the corresponding nuclear spin quantum numbers. If the electron hopping rate was less than the RP-ISC rate or, more accurately, the ZQC frequency, the delocalization would actually contribute to decoherence. On the other hand, if the hopping rate exceeds the RP-ISC rate, the mean of a will be essentially the same for PI•- and PI2•- because PI2•- has double the number of hyperfine interactions as PI•-, but the magnitude of each interaction is half that of PI•-. Though this simple analysis can account for similarities in coherent frequencies between TTF•+-ANI-PI•- and TTF•+-ANI-PI2•-, it does not account for the spectral width of the hyperfine interaction distribution, which can contribute to decoherence in the time domain. The laser pulse that generates these RPs in a pure initial singlet state represents a non-adiabatic change in the RP spin Hamiltonian, which has been described previously by perturbation theory.68,69 The stationary states of the new spin Hamiltonian in the high magnetic field of an EPR spectrometer have singlet |S⟩ and triplet |T0⟩ character that can be related by an angle 𝜙 that rotates these states into the mixed basis:70

|Φ𝐴⟩ = cos 𝜙|S⟩ + sin 𝜙|T0⟩

(2)

|Φ𝐵⟩ = cos 𝜙|T0⟩ ― sin 𝜙|S⟩

(3)

1

𝜙 = 2tan

(

―1

𝐵0(𝑔1 ― 𝑔2)𝜇𝐵 + ∆𝑆𝑇0𝑁 2𝐽 +

1 3𝐷

𝐻𝐹𝐼

(3𝑐𝑜𝑠2𝜁 ― 1)


)

(4)

Page 17 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


where ℏ ≡ 1 is used for brevity, indices 1 and 2 refer to each electron in the radical pair, 𝐵0 is the applied magnetic field, 𝜇𝐵 is the Bohr magneton for the electron, and 𝜁 is the angle between the electron-electron dipole and the magnetic field directions. In contrast to previous theoretical treatments,71 this formulation of eq. 4 includes ∆𝑆𝑇0𝑁𝐻𝐹𝐼, a difference in Gaussian distributions7273

of the total isotropic electron-nuclear hyperfine coupling constant 𝐴 between the two electrons,

respectively, and 𝑗 nuclei in the |S⟩-|T0⟩ basis . In practice, the Gaussian distribution ∆𝑆𝑇0𝑁𝐻𝐹𝐼 could be (a) sampled in a numerical simulation or (b) described by its scalar mean. Relevant to this work, the contribution of ∆𝑁𝐻𝐹𝐼 to linebroadening, ∆𝐸𝐻𝐹𝐼, has already been empirically confirmed for magnetic field effects on RP recombination rates and yields:74 ∆𝐸𝐻𝐹𝐼 = 2

𝜎12 + 𝜎22

(5)

𝜎1 + 𝜎2

where 𝜎1 and 𝜎2 are the root-mean squared standard deviations of the Gaussian ensemble hyperfine interactions of radicals 1 and 2, respectively, where for a sum of j nuclei: 𝜎𝑖 = [∑𝑗𝛼𝑖𝑗2𝐼𝑗(𝐼𝑗 + 1)]

1/2

(6)

where 𝜎𝑖 is the same as 𝑎𝑒𝑓𝑓 in the literature and in our recent work.9 A detailed derivation of ∆𝑁𝐻𝐹𝐼,

𝐴, and 𝜎𝑖 is presented in the Supporting Information. As ∆𝑁𝐻𝐹𝐼 or 𝑔1 ― 𝑔2 increases, the numerator of the trigonometric argument in eq. 3 does as well, and 𝜙 exponentially but asymptotically approaches π/4, at which point the basis states maximally mix to have equal singlet and triplet character. With regard to parameters in the spin Hamiltonian specifically, then, when differences in isotropic g-factor and hyperfine interactions are comparable or even slightly larger than J or D, state-mixing in the RP is efficient. Out-of-phase electron spin echo envelope modulation measurements on 141 and 2 (Figure S9) show that J  0 17 ACS Paragon Plus Environment


and D = 0.11 mT for both RPs. More interestingly, this state mixing allows for otherwise selection rule-forbidden spin coherences. This difference in width is illustrated by comparing the TREPR spectra of TTF•+-ANI-PI•- and TTF•+-ANI-PI2•- at the same time delay following the laser flash (Figure S10). These spectra are obtained at 200K, where the solvent is still a liquid, such that hyperfine splittings can be resolved. Additionally, the TREPR spectra are obtained in toluene-d8 to minimize contributions of the solvent proton spins. The spectra show that the hyperfine splittings of PI•- are resolved relative to those of PI2•-, where both radicals, respectively, are assigned to the lower g-factor components of the signal. The loss of hyperfine resolution and the line-narrowing of the PI2•- spectrum relative to that of PI•- confirms that the width of the hyperfine distribution of TTF•+-ANI-PI2•- is smaller than that of TTF•+-ANI-PI•-. This is strong evidence that the synthetic strategy utilized here was successful in providing a spin-correlated RP with one of the radicals delocalized on the EPR timescale. Because each quantum-ordered transition has a different lifetime, it is worthwhile to separate them from each other to analyze effects on decoherence unique to each quantum-ordered transition in reducing the hyperfine interaction distribution width in TTF•+-ANI-PI•- vs. TTF•+-ANI-PI2•-. In the 2D time-domain pulse-EPR experiments presented here, there are three ways to distinguish between different quantum-ordered coherences in the RPs: (i) the turning angle dependence, (ii) the phase dependence, and (iii) the time-domain behavior. With regard to (i), the elements of DQC and ZQC in the density matrix (Figure 1B) can each be modeled as a simple vector (rather than a tensor as in the SQCs).36 An eloquent qualitative explanation of this behavior describes a standard π/2(90˚) pulse ‘scrambling’ the SQCs.75 We have shown in our previous work that the ZQC of multiple spin-correlated RPs exhibits a nutation curve


Page 18 of 33

Page 19 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


akin to that of single, stable radical, maximizing at a π/2(90˚) pulse turning angle.36 Therefore, this work utilizes a π/2(90˚) pulse for the second pulse to maximize the DQC rather than the traditional π(180˚) ‘refocusing’ pulse used in a normal Hahn echo experiment. Overall, considering decoherence is most limiting in the forbidden quantum beats, a π/2(90˚)-π/2(90˚) microwave pulse sequence is used to maximize detection of the forbidden coherences at the potential expense of the signal from SQCs. Despite this peculiarity in turning angle, the sequence of a laser pulse followed by two microwave pulses used here is comparatively simple relative to those used to observe forbidden multiple-quantum coherences in stable biradicals.76 Moving on to (ii), the phase dependence of the quantum-ordered coherences is also well established,43-44 and the strong efficacy of relevant phase cycling is demonstrated in Figure 4. The appropriate phase cycle enhances DQC by more than a factor of three for the same integrated portions of the 2D time domain EPR spectra for both TTF•+-ANI-PI•- and TTF•+-ANI-PI2•-. For this comparison, phase cycling was done in spectral post-processing, rather than on-board the spectrometer, by adding up all signals from the four-step pulse sequence ( +𝑥, +𝑥; +𝑦, +𝑥; ―𝑥, +𝑥; ―𝑦, +𝑥) with a weighting factor 𝑒 ―𝑖𝑚𝜉 where 𝑚 is the order of the quantum coherence (i.e. 𝑚 = 2 for DQC) and 𝜉 is the phase angle between the two pulses. If one is interested in using forbidden DQC transitions for RP distance determination,77 the appropriate phase cycling in postprocessing as demonstrated in this manuscript may be more straightforward and consistent then on-board phase cycling. With regard to quantum-process78 and -state tomography,79 the ease with which DQC in these photogenerated spin qubit pairs can be accessed with the correct phase cycle should not be overlooked. In Figure 5, the appropriate phase cycle is therefore used to compare the quantum-ordered coherences in the TDAF dimension of the experiment. Note that the data presented in Figures 3 and



4 are from the same 2D experiments on TTF•+-ANI-PI•- and TTF•+-ANI-PI2•-, respectively. To clarify, the 2D time-domain experiments yielding Figures 4 and 5 have a fixed 𝜏, and are not the same as the contour shown in Figure 6, where both 𝜏 and TDAF are incremented simultaneously. Regarding phase in Figure 5, an additional benefit of the correct quantum-ordered phase cycle is consistency in exhibiting the well-known out-of-phase behavior (unexpected signal in the ‘imaginary’ or ‘quadrature’ channel of a quadrature detector) of an echo generated from a spin correlated RP.42 An electron spin echo from a spin-correlated RP exhibiting contributions from multiple orders of quantum coherence is empirically difficult to measure entirely in the imaginary channel, as theory predicts. Although, comparing the data in Figure 5B to that in Figure S6, the correct single-quantum phase cycle in post processing yields an echo entirely in the imaginary channel. In comparison to the coherent beating of forbidden quantum coherences, this signal decays with the behavior of a long-lived single exponential, as is expected for the populations from which it is generated.80 Lastly, (iii), the time domain behavior of each quantum-ordered coherence, is unique depending on TDAF or 𝜏. In Figure 4, the absolute value of the echo following the laser pulse and microwave pulse sequence demonstrates a refocusing at 𝜏 (normal for a Hahn echo experiment) and at 2𝜏 (uniquely characteristic of transfer from double quantum coherence). The explanation for the secondary echo at time 2𝜏 requires one to consider that the laser pulse, creating an adiabatic change in the spin Hamiltonian, acts like a microwave pulse itself. Since 𝑛 ― 1 spin echoes are generated for any generic pulse sequence with 𝑛 microwave pulses,66 the laser-P1-P2 pulse sequence utilized here is more akin to a microwave three-pulse sequence applied to a stable radical; the secondary echo at time 2𝜏 is testament to this unique property of the photogenerated RP, i.e. a secondary echo is generated with only two microwave pulses. The difference in the time-domain


Page 20 of 33

Page 21 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


behavior of each coherence is highlighted in Figure 5. For example, as ZQC depends solely on TDAF when 𝜏 is kept constant,71 Figure 5A observes the echo at times that increase proportionally with TDAF; this yields the highest amplitude oscillations in the time-resolved spectrum. Additionally, Figure 5C affirms that the DQC is maximized at time TDAF = 𝜏,38 which is the portion of the spectrum integrated for Figure 4. Like the appearance of the secondary echo for DQC in the first place, the optimization of its refocusing at time TDAF = 𝜏 is expected from fundamental electron spin echo theory. The refocusing of an echo in an ‘echo-train’ for instance, is best achieved when the spacing between the echoes is kept uniform.81 Again, since the laser pulse actually acts somewhat akin to a microwave pulse by instantaneously perturbing the spin Hamiltonian, the DQC is maximized at time TDAF = 𝜏. This behavior was observed in the first experimental measurements of DQC in spin-correlated RPs.38 Contrary to the expectations guiding the design of TTF-ANI-PI2 in reference to TTF-ANIPI, reducing the width of the hyperfine interaction distribution in TTF-ANI-PI2 does not lengthen the lifetime of forbidden quantum beats (Figure 5A, 5C). Evidently, decoherence of the quantum beats in TTF•+-ANI-PI2•- is on the same order if not shorter than that of TTF•+-ANI-PI•- in these integrated spectral traces. Even though the difference in the mean of the Gaussian distribution of hyperfine interactions for PI2-• vs PI-• is negligible, the changes in the width of the Gaussian distribution could have a small, but discernible impact on the coherence lifetimes. The lifetimes the quantum coherences of the traces in Figure 5 as TDAF is incremented are clearly not extended for PI2-• vs. PI-•. Unexpectedly, there is no clear evidence in Figure 5 that delocalization (Figure 3B) and the resultant reduction in hyperfine reduces the decoherence of either of the forbidden coherences in these 2-spin systems.



Considering that the overall yield TTF•+-ANI-PI2•- results in lower signal/noise in the spectra, the evaluation of the hyperfine interaction distribution width on the forbidden coherences was investigated in more detail for TTF•+-ANI-PI•- alone. The potential to evaluate the decoherence of all RP density matrix elements in a single pulse-EPR spectroscopic experiment is proven in Figure 6. In stark contrast to previous experiments, the DQC continues to be detected for hundreds of nanoseconds, even without application of a DQC-selective phase cycle (Figure 6). The spectral broadening of the most limiting, shorter-lived ZQC frequencies (Figure 7), then, is explicitly analyzed via LPSVD as a source of decoherence in relation to ∆𝐸𝐻𝐹𝐼. The analysis leading to Figure 7 may seem complicated for those not familiar with LPSVD, but as LPSVD utilizes a Fourier basis, it is essentially interchangeable with Fourier analysis. The benefit of LPSVD is in immediately separating the phase information (which often has arbitrary offsets in Fourier analysis depending on pre-processing) from the frequency profile. Most assuredly, the maximum in the frequency profile of Figure 7 for TTF-ANI-PI, centered around 25-26 MHz in a histogram with finer bins (Figure S8), is rather close to that determined by Fourier analysis (22 MHz).8. The disagreement is likely due to known biases in the statistics of frequency estimation with LPSVD.82 An unfortunate conclusion from this statistical interpretation with LPSVD is that the SQC and DQC are not properly sampled in the 2D-time domain experiment of Figure 6 to yield clustering in the histogram and the same meaningful analysis by LPSVD (Figure S8). This is where LPSVD can provide a strength to future work as well: unlike Fourier analysis, LPSVD does not require linearly sampled points, and can be utilized in large 2D time-domain experiments that should use nonlinear sampling to save time in sufficiently measuring the longerlived SQC, DQC and the shorter-lived ZQC in the same experiment.


Page 22 of 33

Page 23 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Numerically, the ensemble average difference in hyperfine values ∆𝐸𝐻𝐹𝐼 for TTF•+-ANI-PI•is calculated to be ca. 10 MHz. Accounting for the reduced hyperfine of the PI2 moiety, ∆𝐸𝐻𝐹𝐼 of TTF•+-ANI-PI2•- is just under 20% less than that for TTF•+-ANI-PI•- (Figure 3A). Yet the FWHM is ca. 50 MHz (Figure 7) for the kernel density estimate of a histogram of ZQC frequencies across the relevant portion of 2D time experiment in Figure 6. The breadth of the frequency distribution determined by LPSVD of the short-lived ZQC of TTF•+-ANI-PI•- quantitatively explains the inefficacy of reducing hyperfine interactions towards eliminating decoherence in these pulse-EPR spectra. That is, ∆𝐸𝐻𝐹𝐼 for either TTF•+-ANI-PI•- is a minority contribution to decoherence from frequency-broadening, and the specific decrease in ∆𝐸𝐻𝐹𝐼 from TTF•+-ANI-PI•- to TTF•+-ANIPI2•-is even smaller still (ca. 1.5 MHz). Considering that hyperfine interactions are not significantly limiting the coherence times in TTF•+-ANI-PI•- and TTF•+-ANI-PI2•-, the question remains: when J and D interactions are very small41 and not modulated, what is the limiting factor for decoherence in these quantum beat experiments? Experiments at 5K (not presented here) have not been shown to reduce ZQC dephasing, which is the shortest-lived forbidden coherence (Figure 6). The most significant source of decoherence is therefore tentatively attributed to spectral diffusion from limits in pulse bandwidth of the square microwave pulses used in this work. In practice, the forbidden coherences depend strongly on the fixed field point at which the spectrum is irradiated: a shift of 0.7 mT away from the center of the 4 mT-wide field-swept echo spectrum of the RP of TTF•+-ANI-PI•- (to a maximum representing PI•-) results in a greater than 30% decrease in the ZQC lifetime (Figure 8). From this brief test, the excitation bandwidth of the microwave pulses used in these experiments is deemed unlikely to be negligible compared to the width of the spectrum. Considering this and the sine-cardinal (sinc) frequency profile of the square 23 ACS Paragon Plus Environment


pulse, it is unlikely that all of the spins in the RP are uniformly excited such that spectral diffusion is negligible—even at the central magnetic field point where the spectrum of Figure 6 was taken. In light of this conclusion, the relatively long-lived ZQC measured previously8 in a RP without the TTF moiety and with a narrow spectrum (ca. 1.2 mT-wide field-swept echo spectrum) may be explained in the lower bound where the pulse bandwidth is sufficient for those experiments. Considering recent advances in arbitrary waveform generation (AWG), current efforts are being pursued to measure these same molecules and others previously studied with pulses of arbitrary bandwidth formed with an AWG module at X-band. Considering the desire to remain in the adiabatic pulse regime, non-linearly frequency-swept pulse shapes seem particularly wellsuited towards the goal of eliminating contributions from incomplete excitation and spectral diffusion. Compared to the well-known sech/tanh pulse, WURST pulses are known to show better bandwidth for a given pulse length and microwave power83 and are the most likely candidates for future experiments with AWG. Ultimately, although the TTF•+ moiety in TTF•+-ANI-PI•- and TTF•+-ANI-PI2•- greatly enhances quantum beating in these RPs by increasing the difference in gfactors, it may also harm the ability to fully excite the EPR spectrum with 16 ns square microwave pulses like those used in this work; by the same token, spectral diffusion in the pulse-EPR experiments presented for TTF•+-ANI-PI•- and TTF•+-ANI-PI2•- potentially overshadows attempts to reduce hyperfine splitting with the goal of eliminating decoherence of quantum beats. Conclusions We have shown that electron-nuclear hyperfine interactions in covalently-attached RPs can be easily modified with appropriate molecular designs. The theoretical broadening due to hyperfine interactions in TTF•+-ANI-PI•- vs TTF•+-ANI-PI2•-, however, has been determined to be less than the empirical broadening of forbidden coherences with the shortest lifetime (ZQC), which


Page 24 of 33

Page 25 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


indicates there are additional, more significant sources of decoherence in RPs that also need to be addressed. Considering microwave pulse bandwidth as perhaps the most significant of these sources, we propose that TTF•+-ANI-PI•- and TTF•+-ANI-PI2•- are excellent targets for future experiments with arbitrary waveform generation, whereby the entire spectrum can be excited with appropriately short microwave pulses. If spectral diffusion can be eliminated as a source of decoherence in RPs, the effect of reducing hyperfine interactions in TTF•+-ANI-PI2•- vs TTF•+ANI-PI•- may become noticeable. Once decoherence is further reduced, applications of RPs as a source of pure, entangled spin qubits can be further explored. ASSOCIATED CONTENT Supporting Information Detailed synthetic procedures and spectroscopic (NMR, fsTA, nsTA, and EPR) data are included within SI. This material is available free of charge via the Internet at http://pubs.acs.org. ■ AUTHOR INFORMATION Corresponding Authors [email protected] Notes The authors declare no competing ﬁnancial interest. ■ ACKNOWLEDGEMENTS This research was supported by the National Science Foundation under grant no. CHE-1565925. The authors would like to thank Dr. Yilei Wu for previous synthetic efforts. ■ REFERENCES 25 ACS Paragon Plus Environment


1. Kobr, L.; Gardner, D. M.; Smeigh, A. L.; Dyar, S. M.; Karlen, S. D.; Carmieli, R.; Wasielewski, M. R., Fast Photodriven Electron Spin Coherence Transfer: A Quantum Gate Based on a Spin Exchange J-Jump. J. Am. Chem. Soc. 2012, 134, 12430-12433. 2. Carmieli, R.; Smeigh, A. L.; Mickley Conron, S. M.; Thazhathveetil, A. K.; Fuki, M.; Kobori, Y.; Lewis, F. D.; Wasielewski, M. R., Structure and Dynamics of Photogenerated Triplet Radical Ion Pairs in DNA Hairpin Conjugates with Anthraquinone End Caps. J. Am. Chem. Soc. 2012, 134, 11251-11260. 3. Carmieli, R.; Thazhathveetil, A. K.; Lewis, F. D.; Wasielewski, M. R., Photoselective DNA Hairpin Spin Switches. J. Am. Chem. Soc. 2013, 135, 10970-10973. 4. Gardner, D. M.; Chen, H.-F.; Krzyaniak, M. D.; Ratner, M. A.; Wasielewski, M. R., Large Dipolar Spin-Spin Interaction in a Photogenerated U-Shaped Triradical. J. Phys. Chem. A 2015, 119, 8040-8048. 5. Krzyaniak, M. D.; Kobr, L.; Rugg, B. K.; Phelan, B. T.; Margulies, E. A.; Nelson, J. N.; Young, R. M.; Wasielewski, M. R., Fast Photo-Driven Electron Spin Coherence Transfer: The Effect of Electron-Nuclear Hyperfine Coupling on Coherence Dephasing. J. Mater. Chem. C 2015, 3, 79627967. 6. Horwitz, N. E.; Phelan, B. T.; Nelson, J. N.; Krzyaniak, M. D.; Wasielewski, M. R., Picosecond Control of Photogenerated Radical Pair Lifetimes Using a Stable Third Radical. J. Phys. Chem. A 2016, 120, 2841-2853. 7. Horwitz, N. E.; Phelan, B. T.; Nelson, J. N.; Mauck, C. M.; Krzyaniak, M. D.; Wasielewski, M. R., Spin Polarization Transfer from a Photogenerated Radical Ion Pair to a Stable Radical Controlled by Charge Recombination. J. Phys. Chem. A 2017, 121, 4455-4463. 8. Nelson, J. N.; Krzyaniak, M. D.; Horwitz, N. E.; Rugg, B. K.; Phelan, B. T.; Wasielewski, M. R., Zero Quantum Coherence in a Series of Covalent Spin-Correlated Radical Pairs. J. Phys. Chem. A 2017, 121, 2241-2252. 9. Wu, Y.; Zhou, J.; Nelson, J. N.; Young, R. M.; Krzyaniak, M. D.; Wasielewski, M. R., Covalent Radical Pairs as Spin Qubits: Influence of Rapid Electron Motion between Two Equivalent Sites on Spin Coherence. J. Am. Chem. Soc. 2018, 140, 13011-13021. 10. Sato, K.; Nakazawa, S.; Nishida, S.; Rahimi, R. D.; Yoshino, T.; Morita, Y.; Toyota, K.; Shiomi, D.; Kitagawa, M.; Takui, T., Novel Applications of ESR/EPR Quantum Computing/Quantum Information Processing. Prog. Theor. Chem. Phys. 2013, 25, 163-204. 26 ACS Paragon Plus Environment

Page 26 of 33

Page 27 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


11. Sato, K., et al., Molecular Electron-Spin Quantum Computers and Quantum Information Processing: Pulse-Based Electron Magnetic Resonance Spin Technology Applied to Matter SpinQubits. J. Mater. Chem. 2009, 19, 3739-3754. 12. Sato, K., et al., Quantum Computing Using Pulse-Based Electron-Nuclear Double Resonance (Endor): Molecular Spin-Qubits. In Molecular Realizations of Quantum Computing 2007, Nakahara, M.; Ota, Y.; Rahimi, R.; Kondo, Y.; TadaUmezaki, M., Eds. 2009; Vol. 2, pp 58-162. 13. Salikhov, K. M.; Golbeck, J. H.; Stehlik, D., Quantum Teleportation across a Biological Membrane by Means of Correlated Spin Pair Dynamics in Photosynthetic Reaction Centers. Appl. Magn. Res. 2007, 31, 237-252. 14. Kandrashkin, Y. E.; Salikhov, K. M., Numerical Simulation of Quantum Teleportation across Biological Membrane in Photosynthetic Reaction Centers. Appl. Magn. Res. 2010, 37, 549-566. 15. Volkov, M. Y.; Salikhov, K. M., Pulse Protocols for Quantum Computing with Electron Spins as Qubits. Applied Magetic Resonance 2011, 41, 145-154. 16. Thurnauer, M. C.; Norris, J. R., An Electron Spin Echo Phase Shift Observed in Photosynthetic Algae : Possible Evidence for Dynamic Radical Pair Interactions. Chem. Phys. Lett. 1980, 76, 557561. 17. Sakaguchi, Y.; Hayashi, H.; Murai, H.; I'Haya, Y. J., Cidep Study of the Photochemical Reactions of Carbonyl Compounds Showing the External Magnetic Field Effect in a Micelle. Chem. Phys. Lett. 1984, 110, 275-9. 18. Closs, G. L.; Forbes, M. D. E.; Norris, J. R., Spin-Polarized Electron-Paramagnetic ResonanceSpectra of Radical Pairs in Micelles - Observation of Electron Spin-Spin Interactions. J. Phys. Chem. 1987, 91, 3592-3599. 19. Hasharoni, K.; Levanon, H.; Greenfield, S. R.; Gosztola, D. J.; Svec, W. A.; Wasielewski, M. R., Mimicry of the Radical Pair and Triplet-States in Photosynthetic Reaction Centers with a Synthetic Model. J. Am. Chem. Soc. 1995, 117, 8055-8056. 20. Hasharoni, K.; Levanon, H.; Greenfield, S. R.; Gosztola, D. J.; Svec, W. A.; Wasielewski, M. R., Radical Pair and Triplet State Dynamics of a Photosynthetic Reaction-Center Model Embedded in Isotropic Media and Liquid Crystals. J. Am. Chem. Soc. 1996, 118, 10228-10235. 21. Carbonera, D.; Di Valentin, M.; Corvaja, C.; Agostini, G.; Giacometti, G.; Liddell, P. A.; Kuciauskas, D.; Moore, A. L.; Moore, T. A.; Gust, D., EPR Investigation of Photoinduced Radical



Pair Formation and Decay to a Triplet State in a Carotene−Porphyrin−Fullerene Triad. J. Am. Chem. Soc. 1998, 120, 4398-4405. 22. Kobori, Y.; Yamauchi, S.; Akiyama, K.; Tero-Kubota, S.; Imahori, H.; Fukuzumi, S.; Norris, J. R., Jr., Primary Charge-Recombination in an Artificial Photosynthetic Reaction Center. Proc. Natl. Acad. Sci. U.S.A. 2005, 102, 10017-10022. 23. Tang, J.; Norris, J. R., Theoretical Calculations of Microwave Effects on the Triplet Yield in Photosynthetic Reaction Centers. Chem. Phys. Lett. 1983, 94, 77-80. 24. Buckley, C. D.; Hunter, D. A.; Hore, P. J.; McLauchlan, K. A., Electron Spin Resonance of Spin-Correlated Radical Pairs. Chem. Phys. Lett. 1987, 135, 307-312. 25. Hore, P. J., Analysis of Polarized Electron Paramagnetic Resonance Spectra. In Advanced EPR in Biology and Biochemistry, Hoff, A. J., Ed. Elsevier: Amsterdam, 1989; pp 405-440. 26. Gierer, M.; Van der Est, A.; Stehlik, D., Transient EPR of Weakly Coupled Spin-Correlated Radical Pairs in Photosynthetic Reaction Centers: Increased Spectral Resolution from Nutation Analysis. Chem. Phys. Lett. 1991, 186, 238-47. 27. Hoff, A. J.; Gast, P.; Dzuba, S. A.; Timmel, C. R.; Fursman, C. E.; Hore, P. J., The Nuts and Bolts of Distance Determination and Zero- and Double-Quantum Coherence in Photoinduced Radical Pairs. Spectrochim. Acta, Part A 1998, 54A, 2283-2293. 28. Adrian, F. J., Theory of Anomalous Electron Spin Resonance Spectra of Free Radicals in Solution. Role of Diffusion-Controlled Separation and Reencounter of Radical Pairs. J. Chem. Phys. 1971, 54, 3918-23. 29. Adrian, F. J., Singlet-Triplet Splitting in Diffusing Radical Pairs and the Magnitude of Chemically Induced Electron Spin Polarization. J. Chem. Phys. 1972, 57, 5107-5113. 30. Hore, P. J.; Joslin, C. G.; McLauchlan, K. A., The Role of Chemically-Induced Dynamic Electron Polarization (Cidep) in Chemistry. Chem. Soc. Rev. 1979, 8, 29–61. 31. Pedersen, J. B.; Freed, J. H., Theory of Chemically Induced Dynamic Electron Polarization. I. J. Chem. Phys. 1973, 58, 2746-2762. 32. Pedersen, J. B.; Freed, J. H., Theory of Chemically Induced Dynamic Electron Polarization. II. J. Chem. Phys. 1973, 59, 2869-2885. 33. Borovykh, I. V.; Kulik, L. V.; Dzuba, S. A.; Hoff, A. J., Selective Excitation in Pulsed EPR of Spin-Correlated Radical Pairs: Electron-Electron Interactions, Zero-, Single-, and DoubleQuantum Relaxation and Spectral Diffusion. Chem. Phys. Lett. 2001, 338, 173-179. 28 ACS Paragon Plus Environment

Page 28 of 33

Page 29 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


34. Kobori, Y.; Ponomarenko, N.; Norris, J. R., Time-Resolved Electron Paramagnetic Resonance Study on Cofactor Geometries and Electronic Couplings after Primary Charge Separations in the Photosynthetic Reaction Center. J. Phys. Chem. C 2015, 119, 8078-8088. 35. Miura, T.; Wasielewski, M. R., Manipulating Photogenerated Radical Ion Pair Lifetimes in Wire-Like Molecules Using Microwave Pulses: Molecular Spintronic Gates. J. Am. Chem. Soc. 2011, 133, 2844-2847. 36. Kelber, J. B.; Panjwani, N. A.; Wu, D.; Gomez-Bombarelli, R.; Lovett, B. W.; Morton, J. J. L.; Anderson, H. L., Synthesis and Investigation of Donor-Porphyrin-Acceptor Triads with LongLived Photo-Induced Charge-Separate States. Chem. Sci. 2015, 6, 6468-6481. 37. Kothe, G.; Weber, S.; Bittl, R.; Ohmes, E.; Thurnauer, M. C.; Norris, J. R., Transient EPR of Light-Induced Radical Pairs in Plant Photosystem I: Observation of Quantum Beats. Chem. Phys. Lett. 1991, 186, 474-80. 38. Dzuba, S. A.; Bosch, M. K.; Hoff, A. J., Electron Spin Echo Detection of Quantum Beats and Double-Quantum Coherence in Spin-Correlated Radical Pairs of Protonated Photosynthetic Reaction Centers. Chem. Phys. Lett. 1996, 248, 427-433. 39. Borbat, P. P.; Freed, J. H., Multiple-Quantum ESR and Distance Measurements. Chem. Phys. Lett. 1999, 313, 145-154. 40. Santabarbara, S.; Kuprov, I.; Hore, P. J.; Casal, A.; Heathcote, P.; Evans, M. C. W., Analysis of the Spin-Polarized Electron Spin Echo of the [P700+A1-] Radical Pair of Photosystem I indicates that both Reaction Center Subunits are Competent in Electron Transfer in Cyanobacteria, Green Algae, and Higher Plants. Biochemistry 2006, 45, 7389-7403. 41. Carmieli, R.; Mi, Q. X.; Ricks, A. B.; Giacobbe, E. M.; Mickley, S. M.; Wasielewski, M. R., Direct Measurement of Photoinduced Charge Separation Distances in Donor-Acceptor Systems for Artificial Photosynthesis Using Oop-Eseem. J. Am. Chem. Soc. 2009, 131, 8372-8373. 42. Norris, J. R.; Morris, A. L.; Thurnauer, M. C.; Tang, J., A General Model of Electron Spin Polarization Arising from the Interactions within Radical Pairs. J. Chem. Phys. 1990, 92, 42394249. 43. Tang, J.; Thurnauer, M. C.; Norris, J. R., Abnormal Electron Spin Echo and Multiple-Quantum Coherence in a Spin-Correlated Radical Pair System. Appl. Magn. Res. 1995, 9, 23-31. 44. Tang, J.; Norris, J. R., Multiple-Quantum EPR Coherence in a Spin-Correlated Radical Pair System. Chem. Phys. Lett. 1995, 233, 192-200. 29 ACS Paragon Plus Environment


45. Mehring, M.; Mende, J., Spin-Bus Concept of Spin Quantum Computing. Phys. Rev. A 2006, 73, 052303. 46. Shushin, A. I., The Effect of the Spin Exchange Interaction on Snp and Rydmr Spectra of Geminate Radical Pairs. Chem. Phys. Lett. 1991, 181, 274-278. 47. Shushin, A. I.; Pedersen, J. B.; Lolle, L. I., Theory of Magnetic Field Effects on Radical Pair Recombination in Micelles. Chem. Phys. 1994, 188, 1-17. 48. Fukuju, T.; Yashiro, H.; Maeda, K.; Murai, H.; Azumi, T., Singlet-Born SCRP Observed in the Photolysis of Tetraphenylhydrazine in an SDS Micelle: Time Dependence of the Population of the Spin States. J. Phys. Chem. A 1997, 101, 7783-7786. 49. Miura, T.; Murai, H., Effect of Molecular Diffusion on the Spin Dynamics of a Micellized Radical Pair in Low Magnetic Fields Studied by Monte Carlo Simulation. J. Phys. Chem. A 2015, 119, 5534-5544. 50. Wasielewski, M. R.; Bock, C. H.; Bowman, M. K.; Norris, J. R., Controlling the Duration of Photosynthetic Charge Separation with Microwave Radiation. Nature 1983, 303, 520-522. 51. Hasegawa, M.; Nagashima, H.; Minobe, R.; Tachikawa, T.; Mino, H.; Kobori, Y., Regulated Electron Tunneling of Photoinduced Primary Charge-Separated State in the Photosystem II Reaction Center. J. Phys. Chem. Lett. 2017, 8, 1179-1184. 52. Mehring, M.; Mende, J.; Scherer, W., Entanglement between an Electron and a Nuclear Spin 1/2. Phys. Rev. Lett. 2003, 90, 153001/1-153001/4. 53. Young, R. M.; Dyar, S. M.; Barnes, J. C.; Juricek, M.; Stoddart, J. F.; Co, D. T.; Wasielewski, M. R., Ultrafast Conformational Dynamics of Electron Transfer in Exbox4+perylene. J. Phys. Chem. A 2013, 117, 12438-12448. 54. MATLAB, Matlab. 2018, The Mathworks, Inc., Natick, Massachusetts, United States. 55. Berberan-Santos, M. N.; Martinho, J. M. G., The Integration of Kinetic Rate Equations by Matrix Methods. J. Chem. Educ. 1990, 67, 375-9. 56. Koehl, P., Linear Prediction Spectral Analysis of Nmr Data. Prog. Nucl. Magn. Reson. Spectrosc. 1999, 34, 257-299. 57. Wax, M.; Kailath, T., Detection of Signals by Information Theoretic Criteria. IEEE Transactions on Acoustics Speech and Signal Processing 1985, 33, 387-392.


Page 30 of 33

Page 31 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


58. Kung, S. Y.; Arun, K. S.; Rao, D. V. B., State-Space and Singular-Value Decomposition-Based Approximation Methods for the Harmonic Retrieval Problem. J. Opt. Soc. Amer. 1983, 73, 17991811. 59. Barkhuijsen, H.; Debeer, R.; Vanormondt, D., Improved Algorithm for Noniterative TimeDomain Model-Fitting to Exponentially Damped Magnetic-Resonance Signals. J. Magn. Reson. 1987, 73, 553-557. 60. Papy, J.-M.; De Lathauwer, L.; Van Huffel, S., Exponential Data Fitting Using Multilinear Algebra: The Decimative Case. J. Chemom. 2009, 23, 341-351. 61. Alexiou, M. S.; Tychopoulos, V.; Ghorbanian, S.; Tyman, J. H. P.; Brown, R. G.; Brittain, P. I., The Uv-Visible Absorption and Fluorescence of Some Substituted 1,8-Naphthalimides and Naphthalic Anhydrides. J. Chem. Soc. Perkin Trans. 2 1990, 2, 837-842. 62. McConnell, H. M., Indirect Hyperfine Interactions in the Paramagnetic Resonance Spectra of Aromatic Free Radicals. J. Chem. Phys. 1956, 24, 764-766. 63. Hibbert, D. B.; Hamedelniel, A. E.; Sutcliffe, L. H., Electron-Spin-Resonance and TheoreticalStudy of Tetrathiofulvalene and Dibenzotetrathiofulvalene and Their Radical Cations. Magn. Reson. Chem. 1987, 25, 648-652. 64. Wu, Y.; Han, J.-M.; Hong, M.; Krzyaniak, M. D.; Blackburn, A. K.; Fernando, I. R.; Cao, D. D.; Wasielewski, M. R.; Stoddart, J. F., X-Shaped Oligomeric Pyromellitimide Polyradicals. J. Am. Chem. Soc. 2018, 140, 515-523. 65. Hore, P. J.; Hunter, D. A.; Mckie, C. D.; Hoff, A. J., Electron-Paramagnetic Resonance of Spin-Correlated Radical Pairs in Photosynthetic Reactions. Chem. Phys. Lett. 1987, 137, 495-500. 66. Schweiger, A., Principles of Pulse Electron Paramagnetic Resonance Spectroscopy; Oxford University Press, 2001, p 672. 67. Hornak, J. P.; Freed, J. H., Spectral Rotation in Pulsed ESR Spectroscopy. J. Magn. Reson. 1986, 67, 501-18. 68. Tang, J.; Norris, J. R., Theoretical Calculations of Kinetics of the Radical Pair Pf State in Bacterial Photosynthesis. Chem. Phys. Lett. 1982, 92, 136-40. 69. Zwanenburg, G.; Hore, P. J., EPR of Spin-Correlated Radical Pairs. Analytical Treatment of Selective Excitation Including Zero-Quantum Coherence. Chem. Phys. Lett. 1993, 203, 65-74.



70. Schaeublin, S.; Hoehener, A.; Ernst, R. R., Fourier Spectroscopy of Nonequilibrium States, Application to CIDNP (Chemical Induced Dynamic Nuclear Polarization), Overhauser Experiments, and Relaxation Time Measurements. J. Magn. Reson. 1974, 13, 196-216. 71. Tang, J.; Thurnauer, M. C.; Norris, J. R., Electron Spin Echo Envelope Modulation Due to Exchange and Dipolar Interactions in a Spin-Correlated Radical Pair. Chem. Phys. Lett. 1994, 219, 283-290. 72. Schulten, K.; Wolynes, P. G., Semi-Classical Description of Electron-Spin Motion in Radicals Including Effect of Electron Hopping. J. Chem. Phys. 1978, 68, 3292–3297. 73. Merkulov, I. A.; Efros, A. L.; Rosen, M., Electron Spin Relaxation by Nuclei in Semiconductor Quantum Dots. Phys. Rev. B Condens. Matter Mater. Phys. 2002, 65, 205309/1-205309/8. 74. Weller, A.; Nolting, F.; Staerk, H., A Quantitative Interpretation of the Magnetic Field Effect on Hyperfine-Coupling-Induced Triplet Formation from Radical Ion Pairs. Chem. Phys. Lett. 1983, 96, 24-7. 75. Hasharoni, K.; Levanon, H.; Tang, J.; Bowman, M. K.; Norris, J. R.; Gust, D.; Moore, T. A.; Moore, A. L., Singlet Photochemistry in Model Photosynthesis: Identification of Charge Separated Intermediates by Fourier Transform and CW-EPR Spectroscopies. J. Am. Chem. Soc. 1990, 112, 6477-81. 76. Saxena, S.; Freed, J. H., Theory of Double Quantum Two-Dimensional Electron Spin Resonance with Application to Distance Measurements. J. Chem. Phys. 1997, 107, 1317-1340. 77. Saxena, S.; Freed, J. H., Double Quantum Two-Dimensional Fourier Transform Electron Spin Resonance: Distance Measurements. Chem. Phys. Lett. 1996, 251, 102-10. 78. Poyatos, J. F.; Cirac, J. I.; Zoller, P., Complete Characterization of a Quantum Process: The Two-Bit Quantum Gate. Phys. Rev. Lett. 1997, 78, 390-393. 79. Altepeter, J. B.; Jeffrey, E. R.; Kwiat, P. G., Photonic State Tomography. In Adv. At., Mol., Opt. Phys., Berman, P. R.; Lin, C. C., Eds. Academic Press: 2005; Vol. 52, pp 105-159. 80. Ernst, R. R.; Bodenhausen, G.; Wokaun, A., Principles of Nuclear Magnetic Resonance in One and Two Dimensions; Clarendon Press, Oxford, 1987. 81. Levitt, M. H.; Freeman, R., NMR Population Inversion Using a Composite Pulse. J. Magn. Reson. 1979, 33, 473-476. 82. Lin, Y.-Y.; Hodgkinson, P.; Ernst, M.; Pines, A., A Novel Detection–Estimation Scheme for Noisy Nmr Signals: Applications to Delayed Acquisition Data. J. Magn. Reson. 1997, 128, 30-41. 32 ACS Paragon Plus Environment

Page 32 of 33

Page 33 of 33 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


83. Spindler, P. E.; Schöps, P.; Kallies, W.; Glaser, S. J.; Prisner, T. F., Perspectives of Shaped Pulses for EPR Spectroscopy. J. Magn. Reson. 2017, 280, 30-45. TOC Graphic:

O

S S

N S

N

S

O

vs. O

S S

N S

S

O

T2

O

N

N N O

N

N

O

O

O

O

N

O

O

O

N O

time

N

O

N O

t-Bu

ΔEHFI

T2 ?


Effect of Electron-Nuclear Hyperfine Interactions on Multiple Quantum

Recommend Documents