Covalent Radical Pairs as Spin Qubits: Influence of Rapid Electron

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Covalent Radical Pairs as Spin Qubits: Influence of Rapid Electron Motion between Two Equivalent Sites on Spin Coherence Yilei Wu, Jiawang Zhou, Jordan N. Nelson, Ryan M. Young, Matthew D. Krzyaniak, and Michael R. Wasielewski J. Am. Chem. Soc., Just Accepted Manuscript • DOI: 10.1021/jacs.8b08105 • Publication Date (Web): 13 Sep 2018 Downloaded from http://pubs.acs.org on September 13, 2018

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Journal of the American Chemical Society

Covalent Radical Pairs as Spin Qubits: Influence of Rapid Electron Motion between Two Equivalent Sites on Spin Coherence Yilei Wu, Jiawang Zhou, Jordan N. Nelson, Ryan M. Young, Matthew D. Krzyaniak, and Michael R. Wasielewski* Department of Chemistry and Institute for Sustainability and Energy at Northwestern Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208-3113 Abstract: Ultrafast photo-driven electron transfer reactions starting from an excited singlet state in an organic donor-acceptor molecule generate a radical pair (RP) in which the two spins are initially entangled and, in principle, can serve as coupled spin qubits in quantum information science (QIS) applications, provided that spin coherence lifetimes in these RPs are long. Here we investigate the effects of electron transfer between two equivalent sites comprising the reduced acceptor of the RP. A covalent electron donor-acceptor molecule (D-C-A24+) including a p-methoxyaniline donor (D), a 4-aminonaphthalene-1,8-imide chromophoric primary acceptor (C), and a m-xylene bridged cyclophane having two equivalent phenyl-extended viologens (A24+) as a secondary acceptor was synthesized along with the analogous molecule having one phenyl-extended

viologen

acceptor

and

a

second,

more

difficult

to

reduce

2,5-dimethoxyphenyl-extended viologen in a very similar cyclophane structure (D-C-A4+). Photoexcitation of C within each molecule results in sub-nanosecond formation of D+•-C-A23+• and D+•-C-A3+•. The spin dynamics of these RPs were characterized by time-resolved EPR spectroscopy and magnetic field effects on the RP yield in both CH3CN and CD3CN. The data show that rapid electron hopping within A23+• promotes spin decoherence in D+•-C-A23+• relative to D+•-C-A3+• having a monomeric acceptor, while the interaction of the RP electron spins with the nuclear spins of the solvent have little or no effect on the spin dynamics. These observations provide important information for designing and understanding novel molecular assemblies of spin qubits with long coherence times for QIS applications. 1 ACS Paragon Plus Environment

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Introduction Photogenerated molecular excited states and electron transfer reactions play a major role in fields ranging from artificial photosynthesis1-3 to quantum information science (QIS).4-23 From the QIS perspective, a critical requirement for any physical qubit is preparation of a pure initial spin state.24 In addition, the preparation of two-qubit entangled states is necessary to execute fundamental quantum gate operations.25 A variety of interesting QIS experiments using molecular electron spins have been performed in the weak spin polarization regime.26,27 However, achieving high thermal electron spin polarization requires applying high magnetic fields, e.g. 3.4 T, and very low temperatures, e.g. 2.9 K, to an isolated spin system.28 In contrast, photoexcitation of a covalent organic donor-acceptor (D-A) molecule having a well-defined D-A distance and orientation can result in sub-nanosecond electron transfer to produce a spin-entangled radical ion pair (RP) 1(D+•-A-•) having an initial pure singlet spin configuration. If the spin-spin exchange (J) and dipolar (D) interactions within the RP are weaker than the electron-nuclear hyperfine interactions (a),13-21 the initially pure singlet RP will coherently mix with its corresponding triplet states 3(D+•-A-•) via the radical pair intersystem crossing (RP-ISC) mechanism to form a superposition state that can be used to implement a variety of QIS strategies.29-31 For example, we have shown recently that these RPs can maintain zero-quantum coherence for times approaching 50 ns at room temperature.22,23 In addition, it is well known that the mixed spin states having both singlet and triplet character can influence the overall charge recombination pathway either to the singlet ground state or to the lowest excited triplet state of D or A.32-36 2 ACS Paragon Plus Environment

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Figure 1. Structural formulas of the compounds used in this study.

The spin dynamics of RPs in which the donor radical cation comprising the RP undergoes electron exchange with a second neutral donor molecule have been examined both theoretically37-39 and experimentally.40-45 Schulten and co-workers have shown that rapid spin exchange between one of the radical ions (D1+•) comprising the RP and its neutral species (D2), i.e. D1+• + D2 ↔ D1 + D2+•, results in slowing of the RP-ISC rate (kST) resulting from a decrease in the hyperfine interaction of the radical ion with its partner in the RP (A-•).37-39 It is important to note that the Schulten model assumes that the magnetic interactions between D2+• and A-• are negligible given that D1 and D2 are inequivalent sites. These predicted effects have been demonstrated for photoexcited aromatic acceptors, such as pyrene or anthracene in the presence of varying concentrations of N,N-dialkylaniline electron donors.40-43 Magnetic field effects on the fluorescence emission from a photoexcited covalent dimer of two carbazole donor molecules 3 ACS Paragon Plus Environment


covalently linked by a short alkyl chain in the presence of a 1,4-dicyanobenzene acceptor are also consistent with this model.45 Finally, molecular triads comprising a monomeric or dimeric zinc porphyrin donor with a free-base porphyrin intermediate acceptor and a pyromellitimide terminal acceptor were also examined.44

In this case, unlike the Schulten model, oxidation of

the dimeric zinc porphyrin donor results in significant magnetic interactions between the radical cation and the reduced electron acceptor irrespective of which zinc porphyrin is oxidized. The analysis of this system is complicated by the fact that the zinc porphyrin dimer is attached in an asymmetric fashion to the intermediate acceptor in the triad; however, the observed the RP decay rates in these triads are consistent with radical cation exchange between the two zinc porphyrin sites in the dimeric donor. While we have shown previously that reducing electron-nuclear hyperfine interactions increases the zero-quantum coherence lifetime of RPs,23 no experimental studies have as yet considered the influence of rapid electron hopping or delocalization on the spin dynamics of a RP with an equivalent pair of donors or acceptors. Herein, we report the effects of rapid electron hopping between two equivalent phenyl-extended viologen (ExV2+) terminal acceptor units within a m-xylene bridged cyclophane (A24+) on electron transfer and spin dynamics using a p-methoxyaniline as the donor (D) and 4-aminonaphthalene-1,8-imide as the chromophoric primary acceptor (C) (Figure 1). This molecular design shows minimal spectral overlap of its components allowing selective excitation of C and easy identification of the transient species.14 More importantly, the rigid cyclophane architecture of A24+ provides a fixed cofacial interaction

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between the two ExV2+ units devoid of significant conformational fluctuations. Charge separation and recombination rates were measured directly by femtosecond (fsTA) and nanosecond transient absorption (nsTA) spectroscopies, respectively. The spin dynamics of the RPs generated by photoinitiated two-step electron transfer were characterized by time-resolved electron paramagnetic resonance (TREPR) spectroscopy and magnetic field effects (MFEs) on the yield of the RP product. The data for the triad containing two ExV2+acceptors in a cyclophane structure (D-C-A24+) is compared to a reference compound having one ExV2+ acceptor and a second, more difficult to reduce dimethoxy-substituted, phenyl-extended viologen unit (Ex′V2+) in a very similar cyclophane structure (D-C-A4+). Unlike earlier systems, rapid electron hopping between the two equivalent ExV2+ acceptor units within D+•-C-A23+• results in comparable magnetic interactions between D+• and each of the ExV2+ acceptor units within A23+•. This makes it possible to isolate the contribution of electron-nuclear hyperfine splittings to the spin dynamics and focus on the influence of other factors contributing to spin decoherence. Results and Discussion The syntheses and characterization of the D-C-A24+ triad and its reference compounds are given the Supporting Information. While our attempts to crystallize D-C-A24+ and D-C-A4+ have thus far been unsuccessful, we have obtained a crystal structure of the asymmetric reference meta-cyclophane (Figure 2), which crystallizes into a rigid anti-conformation, where the ExV2+ unit is cofacially oriented relative to the Ex′V2+ unit with a π-stacking distance of ca. 5.1 Å. We



have recently reported the corresponding structure of the symmetrical meta-cyclophane.19


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Figure 2. (a) Top view, (b) side view and (c) end-on view of a blend of tubular and space-ﬁlling representations of the solid-state structure of A4+ showing the main structural parameters. PF6- counterions, protons, residual solvent molecules and occupancy disorder on the phenyl groups are omitted for the sake of clarity.

Steady-State Characterization. The steady-state absorption spectra of C, D-C, A24+, D-C-A24+ and D-C-A4+ are shown in Figure 3. The absorption spectra of the two triads match the sum of their components, suggesting minimal ground-state electronic coupling. The lowest energy absorption band centered around 400 nm belongs to the C chromophore, which has previously been studied in detail.46 The UV region is dominated by the intense π–π* transition of the ExV2+ unit at around 320 nm.47 The redox potentials for all the compounds used in this study are given in Table S1. Briefly, the C chromophore undergoes reversible oxidation (1.2 V vs SCE) and reduction (–1.4 vs SCE), while the electron donor unit D is substantially easier to oxidize (0.79 V vs SCE) than C because of resonance stabilization of the cation on the aniline unit by the MeO



group. The first reduction potential of A24+ occurs at –0.78 V vs SCE. Differential pulse voltammetry (DPV) on dibenzyl ExV2+ and dibenyl Ex′V2+ (Figure S1), shows that Ex′V2+ is 0.13 eV more difficult to reduce than ExV2+. These electrochemical results agree well with DFT calculations (cam-B3LYP/6-31G**, Figures S2 and S3). Specifically, a frontier molecular orbital

Absorbance

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

2.0

A4+ D-C D-C-A24+

1.5

D-C-A4+

1.0 0.5 0.0

250 300 350 400 450 500 550 Wavelength (nm)

Figure 3. Steady-state UV-Vis absorption of the indicated compounds 5 x 10-5 M in CH3CN.

analysis of D-C-A24+ and its reference reveals that both the HOMO and HOMO–1 orbitals are located on D and the LUMO and LUMO+1 orbitals are on the ExV2+ units, which are energetically degenerate in D-C-A24+ (Figure S2). On the other hand, the LUMO and LUMO+1 of D-C-A4+ are localized on the ExV2+ and the Ex′V2+ units, respectively, with a 0.11 eV difference in energy (cam-B3LYP/6-31G**, Figure S3), which agrees well with the reduction


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Scheme 1. Energy level diagram for relevant donor-acceptor electronic states of D-C-A24+at 295 K.

potentials of ExV2+ and Ex′V2+. Thus, in the case of D-C-A4+ the electron transfer should occur preferentially to the ExV2+ unit of the asymmetric cyclophane. The energies of the various RPs were determined using methods described earlier46 and given in the Table S2, while the various photophysical processes following photoexcitation of D-C-A24+ are shown in Scheme 1. Electron Sharing within the Cyclophane Acceptor. The electronic interaction between the two ExV2+ units within the cyclophane framework was investigated using Electron-Nuclear Double Resonance (ENDOR) spectroscopy on the monoreduced state of A24+, which is generated upon addition of sub-stoichiometric amount of cobaltocene as the reducing agent. The resulting ENDOR spectrum of A23+• shows a clear reduction in isotropic hyperfine coupling constants (aH) by a factor of ca. 2 compared to that of A3+• (Figure 4), meaning the unpaired electron is hopping



between the two ExV2+ units within A23+• at a rate that significantly exceeds the proton ENDOR time scale (~107 s–1).48 However, femtosecond stimulated Raman spectroscopy of A23+• shows that the unpaired electron is localized on the vibrational timescale, which implies that the electron is hopping and not delocalized between the two acceptors on time scales slower than about 10-13 s.49 With this finding in hand, we proceeded to explore how electron hopping affects the charge transfer and spin dynamics in the triads using time-resolved optical and EPR techniques.


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A3+•

A2

3+•

Figure 4. 1H-ENDOR spectra of a) A3+• and b) A23+• generated by monoreduction with cobaltocene (0.5 mM in DMF, 260 K).

Photoinduced Charge Separation. Transient absorption spectroscopy was used to determine the dynamics of the photoinduced primary and secondary charge separation reactions (CS1 and CS2), as well as the charge recombination (CR1 and CR2) processes. Based on the energetics outlined in Scheme 1, D-C-A24+ is expected to undergo two-step charge separation after selective photoexcitation of C: D-1*C-A24+ → D+•-C–•-A24+ → D+•-C-A23+•. The femtosecond transient absorption (fsTA) spectra of D-C-A24+ in CH3CN (ε = 37) following 414 nm excitation in the absence of an applied magnetic field (B = 0 mT) are presented in Figure 5a. 1*C is formed within the instrument response and is characterized by positive and negative bands around 435 and 510 nm, respectively, which are assigned to

1*

C excited-state absorption (ESA) and stimulated



a)30

Delay (ps) -0.5 0.1 0.7 1.8 3.4 16

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Delay (ps) -0.5 0.2 0.7 1.8 3.4 16

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0 400 600

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800 1000 1200 1400 1600

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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

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10 0

5

0 0

4

8

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0

Delay (ps)

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8

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16

Delay (ps)

Figure 5. FsTA spectra of (a) D-C-A24+ and (b) D-C-A4+ (λex = 414 nm, 0.6 µJ/pulse, PrCN, 295 K, B = 0 mT) and their respective global kinetic fits (c) and (d).

emission (SE), respectively (Figure S4).46 Broad ESA from 700 to 1600 nm is also observed. These features rapidly evolve in ~0.5 ps to give bands at 494 nm and 425 nm, which are assigned to D+•

46

and C–•,50 respectively, within D+•-C–•-A24+. The 494 nm and 425 nm ESA bands are

replaced in ~1.2 ps by bands at 515 nm and 1125 nm. The 515 nm band results from a red shift of the 494 nm D+• band, while the 1125 nm band is assigned to formation of A23+•.48 At time delays beyond 10 ps, all transient features decay simultaneously.


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A global kinetic fit of the fsTA data using a sequential A → B → C decay model (Figure 5c) gives the rate constants kCS1 = (2.0 ± 1.2) x 1012 s-1 and kCS2 = (8.3 ± 1.2) x 1011 s-1 for D-1*C-A24+ as well as the species-associated spectra and the corresponding population decay plots (Figure S5). A similar analysis for the D-C reference compound shows that kCS1 = (2.0 ± 1.2) x 1012 s-1 and kCR1 = (5.0 ± 0.5) x 1011 s-1 (Figure S6). Thus, the quantum yield of D+•-C- A23+• formation in CH3CN is 62% because the CR1 process strongly competes with the CS2 process. As expected, the corresponding charge separation rate constants for the reference triad D-C-A4+ are very similar to those of D-C-A24+ (Figures 5, S5, and Table 1), so that the yield of final RP product is about 60%. When the same measurements are performed in CD3CN, kCS1, kCS2, and kCR1 do not change significantly (Figures S8-S9, Table 1). Table 1. Rate constants in CH3CN and CD3CN at 295 K. D-C-A24+ D-C-A4+ CH3CN (s-1) CD3CN (s-1) CH3CN (s-1) CD3CN (s-1) Process kCS1 (2.0 ± 1.2) x 1012 (2.0 ± 1.2) x 1012 (2.0 ± 1.2) x 1012 (2.0 ± 1.2) x 1012 kCS2 (8.3 ± 2.1) x 1011 (7.4 ± 1.6) x 1011 (4.8 ± 0.7) x 1011 (6.4 ± 1.2) x 1011 kCR1 (5.0 ± 0.5) x 1011 (5.0 ± 0.5) x 1011 (5.0 ± 0.5) x 1011 (5.0 ± 0.5) x 1011 Spin-Dependent Charge Recombination Dynamics. Following rapid two-step charge separation, the initial singlet RP, 1(D+•-C-A23+•) can undergo RP-ISC to generate the triplet RP, 3

(D+•-C-A23+•) (Scheme 1).32,51 The RP recombination process is spin-selective, that is, the

singlet RP recombines to the singlet ground state, whereas the triplet RP recombines to a locally excited triplet state, if its energy is lower than the triplet RP.52 For both D-C-A24+• and D-C-A4+• the lowest excited triplet state energies are those of ExV2+ in A24+ and A4+ (2.43 eV49) and C



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Figure 6. Radical ion pair energy levels as a function of magnetic field (2J > 0).

(2.05 eV46); thus the 1.5 eV energies of 3(D+•-C-A23+•) and 3(D+•-C-A3+•) are about 0.9 eV below the energies of

3*

A24+ and

3*

A4+, and 0.5 eV below that of

3*

C in CH3CN at 295K, which

precludes RP recombination via the triplet channel. Given that there is no triplet RP recombination pathway open to 3(D+•-C-A23+•) and 3

(D+•-C-A3+•), all RP recombination must proceed via 1(D+•-C-A23+•) and 1(D+•-C-A3+•) to the

singlet ground state. The quantum mechanical mixing of these spin states and their spin dynamics are generally treated using a density matrix formalism based on the stochastic Liouville equation,53,54 while more recent treatments of the problem have focused on efficient semi-classical approaches.55,56 However, given the complexities of these calculations and the frequent absence of the complete set of parameters needed to carry out these computations, several groups have shown that simpler kinetic models such as that depicted in Scheme 1 can be used to fit the RP recombination kinetics in limiting cases.18,57-60 In the absence of a magnetic field, the three RP triplet states (Tx, Ty, Tz) are degenerate in fluid solution, where the spin-spin dipolar interaction is averaged to zero (D = 0), and are split from the singlet state (S) by the spin-spin exchange interaction, 2J (Figure 6). The nsTA spectra of 14 ACS Paragon Plus Environment

3

(D+•-C-A23+•) and

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(D+•-C-A3+•) in CH3CN are shown in Figures 7a and 7b, respectively.

b)

a) 9

m∆A

20

-0.001 0.0005 0.0028 0.015 0.99

6 3

600

600

800 1000 1200 1400 1600

Wavelength (nm) 9

d)

800 1000 1200 1400 1600

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c)

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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


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0

0 -0.002 0.000

0.01

0.1

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0.1

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Figure 7. NsTA spectra of (a) D-C-A24+• and (b) D-C-A4+• (λex = 414 nm, 0.6 µJ/pulse, CH3CN, 295 K, B = 0 mT) and their respective kinetic fits using eqs 1 and 2 (c) and (d). The large artifact at 1064 nm is scatter of the pump laser that generates the near-IR ns probe pulse.

The data were globally fit using the kinetic model shown in Scheme 1 and described by eqs 1 and 2: 45

= − + +

= −


(1) (2)


Table 2. Rate constants and rate constant ratios at magnetic field strength (B) and 295 K. D-C-A24+ D-C-A4+ Rate Constant CD3CN (s-1) CH3CN (s-1) CD3CN (s-1) CH3CN (s-1) at B (mT) kST (0) (5.5 ± 0.2) x 107 (1.0 ± 0.1) x 108 (7.8 ± 0.4) x 107 (1.5 ± 0.1) x 108 kTS (0) (2.6 ± 0.3) x 107 (3.7 ± 0.1) x 107 (1.7 ± 0.1) x 107 (3.2 ± 0.8) x 107 kCR2 (0) (1.5 ± 0.1) x 108 (1.8 ± 0.1) x 108 (2.6 ± 0.2) x 108 (3.0 ± 0.1) x 108 kST (25) (5.3 ± 0.3) x 107 (5.0 ± 0.3) x 107 (1.9 ± 0.1) x 107 (8.7 ± 0.5) x 107 kTS (25) (3.6 ± 0.3) x 107 (2.5 ± 0.1) x 107 (4.2 ± 0.6) x 106 (1.9 ± 0.1) x 107 kCR2 (25) (1.9 ± 0.2) x 108 (1.5 ± 0.1) x 108 (2.5 ± 0.4) x 108 (2.9 ± 0.5) x 108 kST(0)/kTS (0) 2.1 ± 0.3 2.7 ± 0.1 4.6 ± 0.3 4.7 ± 1.2 kST(25)/kTS(25) 1.5 ± 0.2 2.0 ± 0.1 4.5 ± 0.6 4.6 ± 0.4 where [T] = [Tx] +[Ty] + [Tz]. In this model RP-ISC is treated as a quasi-equilibrium between S and T with independent values of kST and kTS rather than constraining kST = kTS as has been done in some previous kinetic treatments.44,57 As will be seen below, this serves to highlight additional spin dynamics that may influence the S-T mixed states. The kinetic fits are presented in Figures 7c and 7d, while the species-associated spectra and population decay curves are given in Figure S7 and the rate constants are listed in Table 2. Importantly, the fits are constrained such that the reconstructed species-associated spectra of the singlet and triplet RPs are identical given that their energy difference is far below the spectral resolution of typical transient absorption experiments in condensed media. Additional data were obtained for both D-C-A24+• and D-C-A4+• in both

CH3CN and CD3CN at applied magnetic fields of B = 0 and 25 mT (Table 2,

Figures S7, S10-S15). These data along with measurements of the TREPR spectra of the D+•-C-A23+• and D+•-C-A3+• RPs and MFEs on the RP yields are used to analyze the spin dynamics of the RPs as discussed below. As expected, the measured values of kCR2 show only minor variations with solvent, magnetic field, and whether the reduced acceptor is a monomer or 16 ACS Paragon Plus Environment

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dimer. TREPR Measurements. When the g-factors of the two radicals comprising the RP are comparable, as is the case for A23+• and A3+• (g = 2.0025) and for D+• (g = 2.002861), RP-ISC is driven by the difference in electron-nuclear hyperfine interactions of each radical, ∆, eq 3:32,62 ∆ = 0.5 ∑ − ∑ )

(3)

where and are the individual hyperfine couplings in radicals 1 and 2 and and are the corresponding nuclear spin quantum numbers. Using the measured hyperfine couplings of A23+• and A3+• (this work) and that of D+• 61 (Table S3), ∆a = 0.85 mT and 0.94 mT for D+•-C-A23+• and D+•-C-A3+•, respectively. If 2 < ∆, RP-ISC mixes all three triplet states with the corresponding singlet state.14,16,63,64 TREPR spectroscopy was used to certify that 2 < ∆ for D+•-C-A23+• and D+•-C-A3+•. Application of a static magnetic field results in Zeeman splitting of the |" 〉 and |$ 〉 states away from |% 〉 resulting only in S-T0 mixing. When S-T0 mixing occurs, the two mixed states are preferentially populated due to the initial population of the |& state, so that four microwave-induced transitions can occur between these mixed states and the initially unpopulated |" 〉 and |$〉 states producing a spin-polarized TREPR spectrum.32,51 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 determined by J and D. 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:16,65 Γ = µ·sign(J) = (-) gives e/a or = (+) gives a/e, where µ is -1 or +1 for a



singlet or triplet excited state precursor, respectively. Thus, if J > 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 doublets overlap strongly, and appear as a distorted (e,a) signal. TREPR spectra of both D+•-C-A23+• and D+•-C-A3+• using continuous microwave irradiation at X-band (9.5 GHz) following a 7 ns laser pulse at 414 nm show overlapping signals from the radicals comprising the RP resulting in (e,a) polarization (Figure 8). The spin-correlated radical pair model was employed to simulate these spectra using the g-factors and the hyperfine coupling constants of the radicals comprising the RP.32,34,51,62,66 Details of the simulations are

Figure 8. TREPR spectra of a) D+•-C-A23+• and b) and D+•-C-A3+• at 105K in PrCN after 414 nm, 7 ns, 2 mJ excitation pulse. Spectral simulations are overlaid in red.

provided in the SI. The simulations require that J ≤ 0.05 mT, so that in both cases 2 ≪ ∆. Magnetic Field Effects. The effect of a static magnetic field on the RP recombination reaction rates and yields provides additional information about the spin dynamics of this process. The MFE can be described briefly by first assuming that the singlet and triplet RP recombination 18 ACS Paragon Plus Environment

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pathways are both viable and that D = 0 in solution. Referring to Figure 6, when B = 0 and 2 ≪ ∆, RP-ISC mixes the RP singlet and the three RP triplet states resulting in a total RP population with 75% triplet character. As B increases, Zeeman splitting of the |" 〉 and |$ 〉 states reduces their mixing with the RP singlet state, which in the limit where B >> 2J results only in S-T0 mixing to produce a RP population with only 50% triplet character. Thus, the yield of triplet recombination product decreases as B increases.19,52 However, in the case of 3

(D+•-C-A23+•) and 3(D+•-C-A3+•), there is no low-lying neutral triplet state accessible for triplet

RP recombination. In both RPs, RP-ISC results in a biexponential decay of the RP to ground state via the singlet RP. When B = 0, 75% of the RP population is “trapped” temporarily in triplet RP state, while increasing B lowers that amount to 50%. This produces an overall reduction in total RP population because having a higher singlet RP population results in more RP recombination to ground state because kCR2 is fast.



D-C-A24+ / CH3CN

1.00

D-C-A4+ / CH3CN

0.95

RP/RP0

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

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D-C-A24+ / CD3CN D-C-A4+ / CD3CN

0.90 0.85 0.80 0.75 0

5

10

15

20

25

Magnetic Field (mT) Figure 9. Relative radical ion pair population as a function of magnetic field for D+•-C-A23+• and D+•-C-A3+• in CH3CN and CD3CN at averaged over 5-40 ns and 480-520 nm following a 100 fs, 414 nm laser pulse.

Figure 9 shows a plot of the total RP population at a given magnetic field B relative to that for B = 0 mT monitored at the D+• absorption for D+•-C-A23+• and D+•-C-A3+• in both CH3CN and CD3CN. The magnetic field at which half of the population change has occurred, B1/2, is 3.0 ± 0.2 mT and 3.3 ± 0.2 mT for D+•-C-A23+• and D+•-C-A3+•, respectively, in CH3CN, and 3.1 ± 0.2 mT and 3.4 ± 0.2 mT for D+•-C-A23+• and D+•-C-A3+•, respectively, in CD3CN. It is well known that the value of B1/2 obtained from the MFE plot is a function of the total effective hyperfine interaction of all the nuclei within radicals 1 and 2, ()) and ()) , respectively, that drive RP-ISC as determined by eqs 4 and 5:67 ()) = *∑ + + + 1

-/ =

3 3 /0112 "/0113

/0112"/0113

(4) (5)

where i = 1 or 2, I is the nuclear spin quantum number and j is summed over all nuclear spins 20 ACS Paragon Plus Environment

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within radical i. Using eqs 4 and 5, and the hyperfine couplings of A23+•, A3+•, and D+• 61 (Table S3), the estimated hyperfine contribution to B1/2 is 3.7 mT for both D+•-C-A23+• and D+•-C-A3+•. This results from the fact that even though the hyperfine splittings of A23+• are about half those of A3+•, the dimeric acceptor has twice as many nuclear spins. Thus, the width of the MFE curve results almost exclusively from the hyperfine splittings of the radicals comprising the RP. Moreover, the measured B1/2 values of the MFE plots for D+•-C-A23+• and D+•-C-A3+• in CH3CN and CD3CN are the same within experimental error, implying that the influence of the 1H nuclear spins on the RP spin dynamics is negligible. Spin Dynamics and Decoherence. The values of kST for both D+•-C-A23+• and D+•-C-A3+• are about 108 s-1, which is typical of S-T mixing by the RP-ISC mechanism. On the other hand, the values of kTS are somewhat smaller than kST and result in the observed biexponential decays of the total RP population. When B = 0, in the absence of competing processes, one expects kST/kTS = 3 as a result of the statistical factor of having one singlet and three degenerate triplet states involved in this quasi-equilibrium process; however, when B is large, in this case 25 mT, only S-T0 mixing occurs and one expects kST/kTS = 1.57 In contrast, when spin relaxation processes, such as S-T decoherence intervene, these ratios can change.18,58,68,69 For example, if spin decoherence is more rapid than the intrinsic spin relaxation rate between the triplet sublevels, kST/kTS should decrease. The measured rate constant ratios at B = 0 mT are kST(0)/kTS (0) = 2.1 ± 0.3 for D+•-C-A23+• and kST(0)/kTS (0) = 4.6 ± 0.3 for D+•-C-A3+• in CH3CN (Table 2), so that the quasi-equilibrium



favors the triplet RP for the monomeric acceptor more so than for the dimeric acceptor. Rapid S-T spin decoherence18,58,68,69 may result from J modulation18,57-60,70 and/or electron hopping37-45 from either radical comprising the RP to a third site. These decoherence rates are typically ~109 s-1 and are thus much faster than the typical ~106 s-1 spin lattice relaxation rates of organic radicals.71 Contributions from J modulation are usually attributed to bond rotations in the covalent structures linking the radicals comprising the RP. However, the number and type of connections linking D+• and A23+• are very similar to those linking D+• and A3+•, so that it is unlikely that S-T decoherence results from J modulation. Alternatively, the ENDOR data for A23+• and A3+• show that rapid electron hopping between the two equivalent acceptors within D+•-C-A23+• occurs on a time scale comparable to or faster than kST and kTS, which implies that spin decoherence of the RP having the dimeric acceptor should be faster than that of the RP having the monomeric acceptor. The observed decrease in kST(0)/kTS(0) for D+•-C-A23+• relative to D+•-C-A3+• is consistent with spin decoherence for the RP with the dimeric acceptor being more rapid than the intrinsic spin relaxation rate between the triplet sublevels. Applying a B = 25 mT magnetic field, which is in the high field limit for these RPs (Figure 9), yields kST(25)/kTS (25) = 1.5 ± 0.2 for D+•-C-A23+• and kST(25)/kTS(25) = 4.5 ± 0.6 for D+•-C-A3+• in CH3CN. Interestingly, the quasi-equilibrium for the RP with the dimeric acceptor begins to approach the statistical limit where kST/kTS =1, whereas that of the RP with the monomeric acceptor does not change. In the high field limit, only coherent mixing of S-T0 occurs, so that rapid S-T decoherence resulting from electron hopping between the two equivalent electron


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acceptors of D+•-C-A23+• results in population transfer to the T+1 and T-1 states and a decrease in kST(25)/kTS (25) as we have noted previously.18 In earlier work, we have shown that deuterating the solvent can significantly increase RP S-T coherence lifetimes.23 When CD3CN is substituted for CH3CN, the fluctuating contact and dipolar hyperfine fields experienced by the RP through collisions with the solvent are strongly diminished because the relative gyromagnetic ratios of H and D, gH/gD = 6.5, which has been discussed previously in connection with T2 relaxation in stable radicals.72,73 Since the values of kST(0)kTS (0) and kST(25)/kTS (25) measured in CD3CN are within experimental error of those measured in CH3CN (Table 2), the interaction of the RP electron spins with the H nuclear spins is not the rate-limiting decoherence process. Conclusions A cyclophane having two cofacial ExV2+ units is used as an electron acceptor in a structurally well-defined D-C-A24+ triad. ENDOR spectroscopy shows that one-electron reduction of the A24+ acceptor results in rapid electron hopping between its two cofacial ExV2+ units. The electron transfer and spin dynamics of D+•-C-A23+• were compared to the analogous D+•-C-A3+• RP having only one reducible ExV2+ unit. Transient optical absorption spectroscopy combined with TREPR and MFE measurements show that rapid electron hopping within A23+• increases the S-T decoherence rate in D+•-C-A23+• relative to A3+• in D+•-C-A3+•. These results show that limiting or eliminating electron movement amongst equivalent sites is important for designing novel molecular spin qubit assemblies with long coherence times for QIS applications.



Methods The full experimental details are provided in the Supporting Information (SI), which includes the synthesis and characterization of each compound. Electrochemistry. Differential pulse voltammetry (DPV) experiments were carried out using a CH Instruments Model 622 electrochemical workstation. All measurements were performed at room temperature under an argon atmosphere in dichloromethane containing 0.1 M tetra-n-butylammonium hexafluorophosphate (TBAPF6), which was recrystallized twice from ethanol prior to use. Spectroscopic grade DMF was dried and the dimethylamine impurities were removed using a column-based solvent purification system (Pure Process Technology). DPV traces were recorded with a conventional single-compartment three electrode cell under an argon atmosphere. All DPV experiments were performed using a glassy carbon working electrode (0.071 cm2). The electrode surface was polished routinely with 0.05 µm alumina-water slurry on a felt surface immediately before use. The counter electrode was a Pt coil and the reference electrode was an Ag/AgCl electrode. The ferrocene/ferrocenium redox couple (E1/2(Fc/Fc+) = +0.45 V vs. SCE in DMF) was used as an internal reference for all measurements. Steady-State Spectroscopy. UV/Vis/NIR absorption spectra were recorded using a UV-3600 Shimadzu spectrophotometer. Steady-state emission spectra were acquired using HORIBA Nanolog spectrofluorimeter equipped with an integrating sphere for absolute photoluminescence quantum yield determination. Computational Details. All calculations were performed at the cam-B3LYP/6-31G** level with


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the Q-Chem 4.3 package.74 Geometry optimizations were carried out without symmetry constraints. IQmol was employed to generate the molecular orbitals. Transient Absorption Spectroscopy. Femtosecond transient absorption experiments were performed using instruments described previously.75,76 The 414 nm, ~100 fs pump pulses were depolarized using a commercial depolarizer (DPU-25-A, Thorlabs, Inc.) to eliminate orientational dynamics contributions from the experiment. Spectra were collected on commercial spectrometers for each time window (customized Ultrafast Systems, LLC Helios and EOS spectrometers, for fsTA and nsTA, respectively). All samples had an optical density of ~1.0 at 414 nm in a 2 mm path length cell and were stirred or rastered to avoid localized heating or degradation effects. EPR Spectroscopy. Continuous-wave ENDOR spectroscopy was performed at X-band (9.5 GHz) fields with a Bruker Elexsys E680X/W spectrometer, fitted with the DICE ENDOR accessory, an EN801 resonator, and an ENI A-500 RF power amplifier. Samples were prepared in DMF at 0.5mM and monoreduced using cobaltocene as the chemical reductant, loaded into 1.4 mm I.D. quartz tubes and sealed with epoxy resin in an argon-filled glovebox. In the resonator the sample temperature held at 260K using a liquid nitrogen flow system. The spectra were collected with 31 mW of microwave power, 200-400 W of RF power and 100 kHz frequency modulation. A polynomial baseline correction was applied to the ENDOR spectra following integration.

For the TREPR measurements, the compounds were dissolved in toluene to achieve an



optical density of 0.5 in 2 mm cuvette at 416 nm (ca. 10–4 M). To dry quartz tubes (4.0 mm o.d. × 3.0 mm i.d.), 0.5 mL of this solution was loaded, degassed with three freeze-pump-thaw cycles, and flame-sealed under vacuum (

Covalent Radical Pairs as Spin Qubits: Influence of Rapid Electron

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