Trityl-Aryl-Nitroxide Based Genuinely g-Engineered Biradicals, as

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A: Spectroscopy, Molecular Structure, and Quantum Chemistry

Trityl-Aryl-Nitroxide Based Genuinely g-Engineered Biradicals, as Studied by Dynamic Nuclear Polarization, Multi-Frequency ESR/ENDOR, Arbitrary Wave Generator Pulse Microwave Waveform Spectroscopy and Quantum Chemical Calculations Kazunobu Sato, Rei Hirao, Ivan Timofeev, Olesya A. Krumkacheva, Elena Zaytseva, Olga Yu. Rogozhnikova, Victor M. Tormyshev, Dmitry V. Trukhin, Elena G. Bagryanskaya, Torsten Gutmann, Vytautas Klimavicius, Gerd Buntkowsky, Kenji Sugisaki, Shigeaki Nakazawa, Hideto Matsuoka, Kazuo Toyota, Daisuke Shiomi, and Takeji Takui J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b07169 • Publication Date (Web): 02 Aug 2019 Downloaded from pubs.acs.org on August 6, 2019

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Trityl-Aryl-Nitroxide Based Genuinely g-Engineered Biradicals, as Studied by Dynamic Nuclear Polarization, Multi-Frequency ESR/ENDOR, Arbitrary Wave Generator Pulse Microwave Waveform Spectroscopy and Quantum Chemical Calculations Kazunobu Sato,1,* Rei Hirao,1 Ivan Timofeev,2,3,4 Olesya Krumkacheva,2,3,4 Elena Zaytseva,2,4 Olga Rogozhnikova,2,4 Victor M. Tormyshev,2,4 Dmitry Trukhin,2,4 Elena Bagryanskaya,2,4,* Torsten Gutmann,5,6 Vytautas Klimavicius,5 Gerd Buntkowsky,5 Kenji Sugisaki1, Shigeaki Nakazawa,1,# Hideto Matsuoka,1 Kazuo Toyota,1 Daisuke Shiomi1 and Takeji Takui1,7,* 1 Department

of Chemistry and Molecular Materials Science, Graduate School of Science, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan 2 N. N. Vorozhtsov Novosibirsk Institute of Organic Chemistry, Novosibirsk, 630090, Russia 3 International Tomography Center SB RAS, Institutskaya ЗА, Novosibirsk. 630090, Russia Novosibirsk State University, Novosibirsk, 630090, Russia Eduard-Zintl Institute for Inorganic and Physical Chemistry, Technische Universität Darmstadt, Alarich-Weiss-Str. 8, 64287 Darmstadt, Germany 6 Institute of Chemistry and Center for Interdisciplinary Nanostructure Science and Technology, Universität Kassel, Heinrich-Plett Straße 40, 34132 Kassel, Germany. 7 Research Support Department/University Research Administrator Center, University Administration Division, Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-ku, Osaka 558-8585, Japan 4 5

# Deceased on March 23, 2019. ABSTRACT: Trityl and nitroxide radicals are connected by -topologically controlled aryl linkers, generating genuinely gengineered biradicals. They serve as a typical model for biradicals in which the exchange (J) and hyperfine interactions compete with the g-difference electronic Zeeman interactions. The magnetic properties underlying the biradical spin Hamiltonian for solution, including J’s, have been determined by multi-frequency CW-ESR and 1H-ENDOR spectroscopy, and compared with those obtained by quantum chemical calculations. The experimental J-values were in good agreement with the quantum chemical calculations. The g-engineered biradicals have been tested as a prototype for AWG (Arbitrary Wave Generator) based spin manipulation techniques, which enable GRAPE (GRAdient Pulse Engineering) microwave control of spins in molecular magnetic resonance spectroscopy for use in molecular spin quantum computers, demonstrating efficient signal enhancement of specific weakened hyperfine signals. DNP effects of the biradicals for 400 MHz NMR signal enhancement have been examined, giving an efficiency factor of 30 for 1H and 27.8 for 13C nuclei. The marked DNP (dynamic nuclear polarization) results show the feasibility of these biradicals for hyperpolarization.

1. INTRODUCTION Stable radicals have played important roles toward understanding the electronic structures of open shell molecules in terms of quantum chemistry,1,2 as spin probes in biological systems, as building blocks in molecule-based magnetic materials3,4 for a long time, and in emerging heterospin exchange clusters with multi-paramagnetic centers.4 Their recent applications to marked dynamic nuclear polarization (DNP) effects in solid-state NMR spectroscopy5–16 and to building components of two-qubit molecular spin systems capable of CNOT gate operations of quantum computing in the

solid state17 have encouraged further development of radical chemistry in synthetic aspects. Among various stable radicals, nitroxide (NO) and trityl (Tr) radicals are the most typical ones. The magnetic properties of the former originate in the -spin delocalized NO site with an anisotropic g-tensor and sizable hyperfine tensor due to their N nucleus, and those of the latter in an isotropic g-tensor due to the C-centered unpaired electron and nearly vanishing proton hyperfine tensors, which are due to the particular features of triphenyl methyl structures hampering the -spin delocalization of the electron network.


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Hybrid biradical systems, which have different types of radical sites characteristic of non-equivalence in the electronic structure, have been recently introduced as potential polarization sources for high-field DNP in the solid-state by Mathies et al.18 and later applied by Wisser et al.19 and by some of us.20 The reason for the success of such hybrid radicals is their ability to decrease the DNP effect much slower with a static magnetic field, so unwanted depolarization effects are much less detrimental, as compared to di-nitroxides.21 In contrast to the classical monoradicals, in biradicals there are both exchange and dipolar couplings present, which can influence the efficacy of the DNP enhancement. In low-field DNP type experiments on single crystalline samples employing optical triplet states, it was found that the presence of the dipolar interaction, which causes a zero-field splitting of the electronic Zeeman levels, has a major influence on the amount of generated nuclear polarization.22-24 At the high magnetic field, however, neither the combined influence of these twointeractions on the DNP efficacy, nor the effect of the molecular flexibility of the radical on the DNP efficacy are fully understood yet. A recent model study on AMUPOL by Huber et al.25 showed that dipolar interactions may have an influence on the DNP efficacy of the radical. To further shed light into these questions it is necessary to provide reference DNP data on systems with well-characterized ESR parameters. Biradical systems composed of trityl and nitroxide can further afford a prototype of genuinely g-engineered biradical,26 in which differences in the g-value between the radical moieties competes with other magnetic interactions, including the exchange interaction in the presence of a conventional static magnetic field. Genuinely g-engineered synthetic biradicals (galvinoxyl-nitroxide mixed biradicals) appeared early in 1980 in a pioneering work by Kurreck, and coworkers,26 showing it feasible that 14N-ENDOR spectroscopy can determine the sign of the exchange interaction. But, since then, to our knowledge, theoretical and experimental analyses of further g-engineered biradicals have been less documented.27,28 The sign and magnitude of the exchange interaction J can be governed by a -topological aryl linker such as p-phenylene (Ph) or 2,7naphthenylene (Nf), as in the biradicals depicted in Figure 1. It should be noted that any sizable exchange interactions give rather simple electron magnetic resonance spectral features, resulting in electronic structures characterized by the spin multiplicity, 2S + 1 = 3 (or 1) and a hyperfine coupling constant at = (1/2)ai, where ai is the hyperfine coupling of the monoradical moieties. Interestingly, the topological symmetry of the electronic network in the aryl linker predicts the sign of the J value where dominant -spin polarization occurs.29 From an experimental viewpoint, the magnitude of the competing interactions is expected to be on the order of 10 MHz, and thus conventional X- and Q-band ESR spectroscopies can give key information on the competing interactions in g-engineered biradicals. We emphasize that exchange interactions whose magnitude falls in the order of a few up to 10 MHz cannot be accessed by temperature dependence ESR spectroscopy,30 but solution ENDOR spectroscopy affords possibilities even for such cases,26 despite the fact that electronic spin dipolar interactions in biradicals hamper efficient ENDOR measurements. On the other hand, from the theoretical side, the accuracy of sophisticated quantum chemical calculations for

O

O O

S S

O

S

S

S

NH

S

HN

N O

S

O N

S

S

S

S

HN

S

O

S

S

S

S S

O O

Tr-Ph-NO

S S

O S

S

S

NH

S

O

O

S

O O

Tr-Nf-NO

Figure 1. Molecular structures of Tr-Ph-NO and Tr-Nf-NO.

exchange interactions still remains within an error of the order of 10 MHz, as shown in this work. An AWG (Arbitrary Wave Generator) based ESR technique allows us to make versatile pulse-experimental designs using arbitrary MW (microwave waveform) pulses with desired excitation. Thus, it can afford a possibility for pulsed ESR experiments with precise quantum control of electronic spin systems, which is the focus of current subjects in emerging quantum technology for molecular spin qubits.17,31 A broadband chirp MW pulse has been introduced in pulsed ESR spectroscopy,32 and applied to Pulsed ELectron-electron Double Resonance (PELDOR or DEER) spectroscopy for pumping the second electron spin,33–35 enhancing the dipolar modulation depth as a double resonance effect. In this work, two typical g-engineered synthetic biradicals, Tr-Ph-NO and Tr-Nf-NO (Figure 1) newly designed by the topological symmetry argument are chosen and their magnetic properties fully identified, illustrating that these biradicals can serve as testing grounds for development in quantum spin manipulation techniques for molecular magnetic resonance spectroscopy, based on novel AWG pulse microwave technology. It is important to note that chirp and arbitrary waveform pulses were applied to make signal enhancements of spin transitions by changing the frequency sweep rate or excitation profiles, instead of the conventional rectangle pulse. In addition, marked DNP effects due to the biradicals were examined, showing the feasibility of these types of biradicals to produce efficient DNP hyperpolarization and delivering reference data for theoretical modelling of DNP efficacies. 2. METHODS CW ESR/ENDOR experiments. CW ESR experiments at Xband to exclude the possible existence of the diastereomers were performed using a commercial Bruker EMX spectrometer. Experimental CW ESR settings at room temperature were typically as follows: sweep width, 7 mT; microwave power, 0.015 mW; modulation carrier frequency, 100 kHz; modulation amplitude, 0.05 mT; time constant, 81.92 ms; sweep time, 83.89 s; number of points, 1024; number of scans, 4. The X-band ESR measurements were done for solutions of the biradicals in dry dichloromethane (concentration 0.3-0.5 mM). All the simulations of the experimental CW ESR spectra were performed using the EasySpin toolbox.36 Multi frequency CW ESR experiments were performed using Bruker ELEXSYS E500 and E600 spectrometers. Bruker ESP350 spectrometer was applied for CW ENDOR measurements. For the CW ENDOR measurements at X-band, toluene solutions of the biradicals were used to enhance the sensitivity.



AWG based pulse-ESR experiments. Pulsed ESR experiments using the chirp and arbitrary waveform pulses were performed by using a customized pulse X-band ESR spectrometer based on a Bruker ESP380E equipped with new AWG’s. The whole instrument was operated by using Specman4EPR.37 For the quantum control of spin qubits by the GRAPE (GRAdient Pulse Engineering) pulse, we optimized the control pulses to implement a given unitary operation Utarget. In our approach, the total duration of an operation is prefixed at time T and then the modulation of the microwave magnetic field is designed for the resulting time evolution operator U(T) to be as close to Utarget as possible. The resemblance of U(T) to Utarget can be evaluated by the fidelity f defined as 1

† 𝑓 = 𝑁|𝑇𝑟[𝑈𝑡𝑎𝑟𝑔𝑒𝑡 𝑈(𝑡)]|

(1)

where N is the number of spin-1/2 particles. The fidelity f is by definition in the range of 0 ≤ 𝑓 ≤ 1; f equals 1 when U(T) is identical to Utarget including a global phase. When optimizing the GRAPE pulses, we have utilized the DYNAMO package, which is a toolbox on MATLAB software.38 For a given T and Utarget, it optimizes the amplitude B1(t) of Hctrl as a function of time, using the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method.39 In this method, which enables optimization of the GRAPE pulses, the time profile of B1(t) over [0,T] is optimized simultaneously for all time steps during the duration T. DNP experiments. Solutions (15 mM) of biradicals Tr-Ph-NO and Tr-Nf-NO in 1,1,2,2-tetrachloroethane (TCE) were prepared to analyze their 1H and 1H13C CP enhancement factors. DNP measurements were carried out on a Bruker Avance III 400 DNP spectrometer operating at resonance frequencies of 400.02 MHz and 100.59 MHz for 1H and 13C, respectively, using a 3.2 mm low temperature H/X/Y triple resonance probe. Liquid samples were packed into 3.2 mm sapphire rotors, which were sealed with silicone rubber plugs and closed with zirconia drive caps. Microwave waveforms at a frequency of 263 GHz were generated by a 9.4 T Bruker gyrotron system. All 1H MAS (magic angle spinning) and 1H13C CP MAS measurements with and without MW irradiation were performed using a MAS frequency of 8 kHz. The sample temperature was nominally 110 K without the MW irradiation and 120 K with the MW irradiation, and was stabilized by a Bruker BioSpin low temperature MAS cooling system. To determine optimum repetition delays (1.3·T1) for 1H MAS and 1H13C CP MAS measurements, 1H saturation recovery experiments with MW irradiation were performed for all samples by collecting 4 scans per 12 data points using variable delays from 0.01 s to 240 s. For 1H MAS experiments a sequence employing two 180° refocusing pulses with a delay of 0.1 μs was employed to eliminate the signal from the probe background. The 1H 90° excitation pulse was 2.3 µs and 16 scans were accumulated. 1H13C CP MAS NMR experiments were performed with 128 scans using a 2 ms 50–100% ramp on the 1H channel. All 13C spectra were referenced to tetramethylsilane (TMS) using an external 30% 15N–13C labelled glycine sample (O=C group at 176.5 ppm) in 20 mM TOTAPOL in glycerol-d8/D2O/H2O (6/3/1, w/w/w).

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Biradical spin Hamiltonian for solution ESR/ENDOR spectral simulation/analyses for systems with competing interactions. A general spin Hamiltonian for a biradical system is described by H = H1 + H2 + H12 (2) where + H𝑖 = β𝐒𝑖 ∙ 𝐠𝑖 ∙ 𝐁 ∑ ( ― 𝑔𝑛𝑗𝛽𝑛𝐈𝑗 ∙ 𝐁 + 𝐒𝑖 ∙ 𝐀𝑖𝑗 ∙ 𝐈𝑗 + 𝐈𝑗 ∙ 𝐐𝑗 ∙ 𝐈𝑗) 𝑗

(3) (4)

H𝑖𝑗 = 𝐒𝑖 ∙ 𝐓𝑖𝑗 ∙ 𝐒𝑗

Hi stands for the spin Hamiltonian of a monoradical site which consists of electronic Zeeman, nuclear Zeeman, hyperfine and nuclear quadrupole terms. H𝑖𝑗 is an interaction term between the two radical sites, which includes the spin dipolar interaction D and exchange interaction J. We assume that the nuclear quadrupole and spin dipolar interactions are vanishing in solution under ordinary conditions. As described in a later section (see the caption of Figure 2), the anisotropic properties of the spin Hamiltonian terms underlie the ESR spectra, so we keep the general form of the spin Hamiltonian (2) for biradicals under study. Importantly, the above Hamiltonian (2) is only valid for cases in which overlap between the wave functions of two radical moieties is negligible. Genuinely g-engineered biradicals, in which the g-difference electronic Zeeman term competes with other magnetic interactions, give salient spectral features,26 and only elaborate analyses can yield accurate experimental spin Hamiltonian parameters. Analytical expressions for ESR transitions for biradical systems have frequently been documented,26,40 and those for ENDOR spectroscopy are explicitly given in Supporting Information. The expressions are general and applicable to the cases of gengineered biradicals. Quantum chemical calculations. The molecular and electronic structures, and spin Hamiltonian parameters of TrPh-NO and Tr-Nf-NO were theoretically investigated by density functional theory (DFT) methods. The geometry optimizations were performed at the UB3LYP/6-31G* level for the lowest spin-triplet state. There are many local minimum conformers, such as the rotamers at the C–C and C–N bonds next to peptide bonds (CO–NH), so the optimizations were started from several different initial geometries: results for the most stable conformers are reported. Vibrational frequency calculations gave no imaginary frequencies at the optimized geometries. Cartesian coordinates, single point energies, and ⟨S2⟩ values are summarized in Supporting Information. The exchange coupling parameter J was calculated by using Yamaguchi's equation as given in equation (5).41 J

S2 S2

HS HS

 S2  S2

LS

 EBS  EHS 

(5)

BS

Here, the high-spin (HS) state is calculated by conventional spin-unrestricted U-DFT for the spin-triplet state, and the broken-symmetry (BS) state is computed in which the initial guess is prepared by mixing HOMO and LUMO to make a single determinant corresponding to a linear combination of open shell singlet (S = 0, MS = 0) and triplet (S = 1, MS = 0) wave functions. The J value defined in eqn (5) corresponds to


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the energy difference between the triplet and singlet states. The geometry optimizations and calculations of the exchange coupling parameter J and hyperfine coupling constants were executed by utilizing Gaussian 09 (Revision B.01) program.42 The g and D tensor calculations described below were performed at the UB3LYP/6-31G* and UBLYP/6-31G* level, respectively, using ORCA (Version 4.0.0) software package.43 The D tensor consists of spin–spin dipolar (DSS) and spin–orbit (DSO) contributions. In organic molecules the DSS term dominantly contributes to the D tensor and the DSO term is generally small. In this work, only the DSS term is computed, by using natural orbitals generated from spin-unrestricted DFT calculations in conjunction with McWeeny–Mizuno equation.44,45 3. RESULTS AND DISCUSSION Synthesis of biradicals, Tr-Ph-NO and Tr-Nf-NO. The synthetic route for Tr-Ph-NO is shown in Scheme 1. Biradical Tr-Nf-NO was synthesized by an analogous route. The detailed procedure of synthesis for both biradicals is given in Supporting Information (SI).46–50 Salient features of the CW-ESR X-, Q- and W-band spectra of biradicals, Tr-Ph-NO and Tr-Nf-NO, at room temperature. The ESR spectra presented in SI Figures S2 and S3 can be phenomenologically simulated to suggest that both the samples of Tr-Ph-NO and Tr-Nf-NO were mixtures of free starting trityl and two diastereomers of Tr-Ph-NO or Tr-Nf-NO, instead of biradical spectra for one species. The exchange coupling parameters (|J|) appear to be less than 0.04 mT for both the diastereomers of Tr-Ph-NO or Tr-Nf-NO, as hyperfine coupling constants on methyl protons were successfully resolved. To exclude the existence of the diastereomers with different ESR spectra as giving rise to the presumed biradial spectra for Tr-Ph-NO and Tr-Nf-NO, we used DMSO anion for to reduction of nitroxide units selectively. The details of this experiment are described in Supporting Information. The ESR spectra (Fig. S4) obtained from the reductions are singlets which are typical of trityl monoradicals with g = 2.00297. We conclude that there are no diastereomer mixtures with different magnetic properties for Tr-Ph-NO and Tr-Nf-NO, and thus the salient features of the ESR spectra arise from a small exchange interaction occurring in each of the biradicals. To obtain the spin Hamiltonian parameters of Tr-Ph-NO and Tr-Nf-NO, their ESR spectra in solution at X-, Q- and WCO2H

CO2Su

CO2H

H2N

BocHN

BocHN I

III

II

NH2

IV

N O O

O

O

O NH

NH

V

S

N

N

O

O

S

O

H2N

BocHN

band were recorded and simulated using EasySpin software.36 Figures 2 and 3 show the experimental and simulated spectra of Tr-Ph-NO and Tr-Nf-No, respectively. Simulations were performed as follows: to describe the doublet-split spectra of the trityl and nitroxide radicals, the model is underlain by the biradical spin Hamiltonian (1) for a two-spin system S1 = S2 = ½ with the isotropic g-factors and with an isotropic nitrogen hyperfine term of on the NO site and with an exchange interaction between the electron spins. For the trityl radical site, following the theoretical assumptions as given in the biradical spin Hamiltonian (1), we used the g-factor obtained from the reduction experiments. Multi-frequency ESR experiments and the spectral simulations measured the exchange interaction |J| for Tr-Nf-NO as 6.37 MHz at X-band, 6.10 MHz at Q band, and 6.52 MHz at W-band. For Tr-Nf-NO, the |J| value was 3.65 MHz at X-band, 3.30 MHz at Q-band, 3.75 MHz at W-band. We note that these exchange couplings are comparable to the magnetic dipolar interaction between the radical sites calculated from DFT (D = −15.10 MHz for Tr-Ph-NO and D = −11.75

VI O

S

O S

S S

S S

O OH

S S

S VII

S

S S

S

N H

S

S S

S

S O

NH

O

S

S

N O VIII

O

S

S O

O

Scheme 1. Synthesis of biradical Tr-Ph-NO

Figure 2. Experimentally observed and simulated ESR spectra of Tr-Ph-NO in toluene solution at room temperature by multifrequency ESR spectroscopy; (a) X-band, (b) Q-band, and (c) Wband CW-ESR spectra. The exchange interactions |J| in the simulated spectra for Tr-Ph-NO are 6.37 MHz at X-band, 6.10 MHz at Q-band, and 6.52 MHz at W-band. Applied MW frequencies were 9.30728 GHz, 33.9176 GHz, and 93.85302 GHz for X-, Q-, and W-band, respectively. The hyperfine structures due to 13C nuclei of the trityl radical were observed in all the experimental spectra as tiny bumps around the trityl doublets, but the spectral simulations didn’t include any 13C hyperfine contributions. The complete spectral simulations required the contribution from anisotropic hyperfine terms, interpreting the observed anisotropic line broadening for the hyperfine splitting due to the nitrogen nuclei.



Figure 3. Experimentally observed (lower plots) and simulated ESR spectra of Tr-Nf-NO in toluene solution at room temperature by multi-frequency ESR spectroscopy; (a) X-band, (b) Q-band, and (c) W-band CW-ESR spectra. The exchange interactions |J| in the simulated spectra for Tr-Nf-NO are 3.65 MHz at X-band, 3.30 MHz at Q-band, and 3.75 MHz at W-band. Applied MW frequencies were 9.30827 GHz, 33.789 GHz, and 93.8466 GHz for X-, Q-, and W-band, respectively. The hyperfine structures due to 13C nuclei of the tityl radical were observed in all the experimental spectra as tiny bumps around the trityl doublets, but the spectral simulations did not include any 13C hyperfine contributions

MHz for Tr-Nf-NO). The magnetic parameters obtained from the W-band measurements are summarized in Table 1. We noticed that the experimental |J| values subtly depend on the temperature of the sample, and thus the values have an estimated uncertainty of a few tenths of MHz.

Table 1. Experimentally determined magnetic parameters of Tr-Ph-NO and Tr-Nf-NO. Sample

giso(trityl)

giso(NO)

aiso(NO) /MHz

Tr-PhNO

2.00297

2.00611

43.8

Tr-NfNO

2.00297

2.00614

43.8

|J| /MHz 6.37(X) 6.10(Q) 6.52(W) 3.65(X) 3.30(Q) 3.75(W)

Page 6 of 12

Signs of the exchange interactions as determined by X-band 1H-ENDOR spectroscopy in solution. For rationalized molecular design of topological aryl linker based biradicals, experimental determination of the signs of the exchange interactions is important. Only methyl protons were observed at room temperature in 1H ENDOR spectra for both Tr-Ph-NO (positive J is predicted) and Tr-Nf-NO (negative J predicted); 14N ENDOR signals were not observed. The 1H ENDOR spectra from the trityl radical site were analyzed by monitoring the strong doublet-split ESR lines of the biradicals, comparing the subtle ENDOR frequency shift for Tr-Ph-NO with that for TrNf-NO. We assumed that the electronic structure of the trityl radical moiety in both biradicals is very similar according to the ESR spectral analyses, and thus the hyperfine coupling constants (hfcc’s) of the methyl protons are similar for both. Many methyl protons having similar hfcc’s (< 1 MHz) gave rise to a pair of the broadened ENDOR lines due to the overlap of many ENDOR transitions at room temperature (see SI for the 1H ENDOR spectra). The broadening hampered an experimentally precise evaluation of the predicted small line shifts (order of 0.1 MHz in magnitude), which depend on the sign of the J value. A positive sign gives higher frequency shifts and a negative one lower frequency shifts. In the ENDOR line shift analyses, the hfcc’s of the protons are assumed to be positive. The experimental signs for the exchange interactions are consistent with the theoretical prediction and quantum chemical calculations. The general treatments and detailed analyses for I = 1/2 cases are given in Supporting Information. Molecular design/optimization of the biradicals and their electronic structures. The spin density distributions of Tr-PhNO and Tr-Nf-NO at their optimized geometries in the principal coordinate system of the g tensor are illustrated in Figure 4. Approximate spin–spin distances measured from the centroid of the N–O bond of the nitroxide radical to the central carbon atom of trityl radical are 17.88 Å and 19.09 Å for Tr-Ph-NO and TrNf-NO, respectively. At the UB3LYP/6-31G* level of calculation, unpaired electron density is mainly distributed on nitroxide and trityl radical moieties, and only small amount is delocalized onto the phenylene and naphthylene linkers. The calculated spin Hamiltonian parameters are summarized in Table 2. Current theoretical calculations predict positive and negative J values in Tr-Ph-NO and Tr-Nf-NO, respectively. The sign difference of the J value can be rationalized by considering topologically controlled -spin polarizations in the aromatic linkers.29,51 In the p-phenylene linker of Tr-Ph-NO, different sign spin densities occur at the bridge positions, while same sign spin densities occurs at the 2,7-naphthylene linking sites. Note that the |J| value is small and they are comparable in the magnitude to the SCF convergence threshold. The N–O bond of the nitroxide site is approximately on the xy-plane of Figure 4 and it is inclined about 45° from the x-axis in the principal coordinate system of the g tensor. The isotropic hyperfine coupling constants are less sensitive to the aryl linkers, and Tr-Ph-NO and Tr-Nf-NO give similar aiso values (Table 2), indicating that the electronic structure of the corresponding radical site of the biradical is similar.


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Table 2. Spin Hamiltonian parameters of Tr-Ph-NO and Tr-NfNO calculated at the UB3LYP/6-31G* level. Note that the energy difference between triplet and singlet states corresponds to J, not 2J. Positions

Tr-PhNO

Tr-NfNO

J/MHz

+37.99

−26.77

D/MHz

−15.10

−11.75

gx

2.0062

2.0059

gy

2.0064

2.0063

gz aiso(14N)/MHz

|aiso(1H)|/MHz (13C)/MHz

aiso

2.0029

2.0029

+19.69

+19.71

N (Nitroxide–Ar)

+0.05

+0.06

N (Trityl–Ar)

+0.19

+0.19

4Me (Nitroxide) a

+1.05

+1.06

Trityl center

+46.44

+48.72

3 Trityl -position a

−15.29

−15.36

6 Trityl

o-position a

+13.92

+13.78

6 Trityl

m-position a

−3.51

−3.13

3 Trityl p-position a

+5.60

+5.17

+6.05

+6.05

N (Nitroxide)

4Me a

(Nitroxide) a

Averaged values

Figure 4. Spin density plots and relationships between molecular structures and principal axes of g tensors of Tr-Ph-NO (top) and Tr-Nf-NO (bottom) at the UB3LYP/6-31G* optimized geometry. Isosurface value is set to be 0.004.

AWG based spin manipulation in solution ESR spectroscopy and selective signal enhancement. The hybrid biradicals under study are candidates suitable for model compounds for initial stages of quantum control experiments on multi-spin systems, since the molecules under study were designed on g-tensor engineering, which gives rise to competing energy difference in the electronic Zeeman interaction, as comparable to other interactions including the exchange coupling between radical moieties of the hybrid biradical. In terms of the progress in pulsed microwave technology, it is only until recently that control of the phase difference between two microwave irradiation frequencies has been achieved by utilizing a TPPI (Time Proportional Phase Increment) technique.52,53 The first phase control experiment demonstrated that the phase control is essential to show the occurrence of the entanglement between spin qubits. The quantum control experiment on multi-spin systems, which is applicable to methodologically implementing quantum gates, needs AWG (Arbitrary Waveform Generator) technique which enable us to manipulate spins simultaneously by optimizing multi-frequencies, their amplitudes and phases. In this work, we have only focused on the implementation of GRAPE (GRAdient Pulse Engineering) pulses which can afford the selective excitation of ESR transitions in the molecular spin systems. In this work we attempt to design only an initial stage of quantum control experiments on multi-spin systems by utilizing GRAPE pulses, in which only the amplitudes of multifrequencies are modulated with the same phase. This is partly because we don’t have enough information on relaxation phenomena particularly relevant to the biradicals under study yet. We note that current AWG techniques allow us to introduce the phase modulation of multi-frequencies for microwave excitations. In view of such practical applications of microwave irradiation, only well-designed AWG techniques have the potential for the technical implementation, currently. Also, any progress in the microwave-based AWG techniques is a technical challenge in new ESR spectroscopy. An exchangecoupled g-engineered system such as the present hybrid

Figure 5. Echo-detected field-swept X-band ESR spectra of TrPh-NO (a) and Tr-Nf-NO (b) at 295 K. Microwave frequency was 9.58134 GHz. A rectangle pulse with tp = 500 ns was applied as a /2 pulse.



biradicals gives us a testing ground for manipulating electron spins by well-designed pulse ESR techniques. In the present systems, the electronic Zeeman interaction can be treated as a controllable parameter in quantum control experiments. For this purpose, Q- and W-band AWG experiments are underway. Figure 5(a) and (b) show the echo-detected field-swept Xband ESR spectra of Tr-Ph-NO and Tr-Nf-NO, respectively. Splitting due to the exchange interaction was observed between the trityl and nitroxide radical sites, consistent with the corresponding CW-ESR spectra. It was hard to detect the splitting in the 14N hyperfine transitions of Tr-Nf-NO because of the small exchange interaction. Complicated spectral patterns at the signal position of the trityl radical indicate insufficient selectivity of the weak MW rectangle pulse applied. When we apply the linear chirp pulse for the broadband excitation, the spin system is effectively excited due to the excitation profile of the pulse. In the case of the present exchange-coupled system between the trityl and NO radicals, the trityl radical site with small anisotropy is highly isolated from the surrounding environments, showing a narrow transition. On the other hand, the NO radical site with the anisotropic g and 14N-hyperfine tensors give broadened line

Figure 6. FT-ESR spectra of Tr-Ph-NO observed by various pulse excitations. (a) A theoretical spectrum calculated for the rectangle pulse. (b) A rectangle pulse with a pulse length of 12 ns. (c) A combination rectangle pulse of three MW frequencies with a pulse length of 600 ns. (d) A chirp pulse with pulse length of 400 ns. Frequency was swept from 𝑓 ― 80 MHz to 𝑓 + 80 MHz. (e) A GRAPE pulse given in Fig S14(a) with a pulse length of 200 ns. (f) A different GRAPE pulse given in Fig S14(b) with a pulse length of 200 ns. The microwave strength irradiated was 20 MHz. The microwave frequency 𝑓, and static magnetic field were set to the resonance condition for the transition of the trityl radical. Signal intensities are normalized.

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shapes due to dynamic effects like molecular tumbling. The difference of the line broadening effect between the sites enhances the relative intensity of the trityl radical transition. In order to increase the signal intensity from the nitroxide radical site in the FT-ESR scheme, we attempted the use of the arbitrary waveform technique. The observed FT-ESR spectra of Tr-Ph-NO using various excitation pulses are shown in Figure 6 (Fig. S11 for the results of the quadrature detection). Similar experimental results for Tr-Nf-NO with its smaller exchange interaction are summarized in SI Figure S12 (Fig. S13 for the results of the quadrature detection). A static magnetic field was set to the field position of the trityl radical transition. A simple theoretical FTESR spectrum of Tr-Ph-NO with 12.5 ns pulse for a /2 pulse is given in Figure 6(a), based on a rotating frame Hamiltonian. The pulse length corresponds to a microwave irradiation strength of 20 MHz. The MW strength was calibrated by measuring the electron spin transient nutation frequency. The deadtime of the resonator with the Q value of 100 was ca. 120 ns. The FT-ESR spectrum observed using a short rectangular (hard) pulse of Tp = 12 ns is given in Figure 6(b). Then, the bandwidth is expected to be 83 MHz. It was difficult to see transitions due to the NO radical site. In the CW-ESR spectra in Figure 2, the linewidth of an ESR transition assigned to the NO radical site is broader than that of an ESR spectrum to the trityl radical site. The broadening effect at the NO radical site is due to motional effects originating from anisotropy in both the g and hyperfine tensors. The motional broadening accelerates the spin-spin relaxation. We could not observe the NO radical transitions in the FT-ESR spectrum with the short pulse because of the insufficient excitation bandwidth in addition to both the motional effect. In order to improve the relative intensities, we applied various pulses with broader excitation bandwidths for exciting the NO radical transition. Application of a long rectangular (soft) pulse enables us to selectively excite an ESR transition. When applying the combination of three coherent microwave pulses with different frequencies ( = -30, 15, 58 MHz), the FT ESR spectrum shown in Figure 6(c) was obtained. The spectrum shows the ESR transitions due to the NO radical site, clearly indicating that the combination of the coherent MW pulses effectively excites the ESR transitions simultaneously. Another possibility for exciting the NO site is to use arbitrary waveform pulses as optimized for the excitation for the NO radical. In order to improve the relative intensities, nonlinearly modified chirp and optimized GRAPE pulses are applied to Tr-Ph-NO. A linear chirp pulse known as a broadband excitation pulse is shown in SI Figure S9(b). On the other hand, a nonlinear chirp pulse enables us to control the excitation strength by changing the sweeping rate. The sweeping rate is related to the excitation efficiency of electron spin on resonance. In the case of a slow sweeping rate, the electron spin is effectively excited. We have designed and applied the nonlinear chirp pulse with a sweeping rate being proportional to |𝑓 ― 𝑓0| as a pulse suitable for the NO transitions. The excitation profile is indicated in red in Figure S9(b). In the case of the |𝑓 ― 𝑓0| sweep, the sweeping rate of the chirp pulse is designed so as to be slow for the transition far from 𝑓0, and to be fast for the transition near 𝑓0. On the other 𝑛 hand, a different type of the chirp pulses such as |𝑓 ― 𝑓0| sweep (𝑛 ≥ 2) is applied as an adiabatic inversion pulse


Page 9 of 12 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


because the transition near 𝑓0 is efficiently excited during the frequency sweep. The linear chirp pulse (𝑛 = 1) is usually applied for broadband excitation. The microwave irradiation strength was tuned to be 20 MHz. A sweeping range of the chirp pulse is from 𝑓𝑚𝑖𝑛 = 𝑓0 ―80 to 𝑓𝑚𝑎𝑥 = 𝑓0 +80 MHz. The GRAPE pulses were also implemented to perform the selective excitation of the ESR transitions in the hybrid biradicals. The GRAPE pulses were optimized under the typical experimental conditions for the strength of microwave irradiation. Particularly, we have focused on the polarization of each electron spin in the hybrid biradicals, and this has been the first attempt at achieving the selective excitation of biradical systems by utilizing microwave-based AWG technologies. The GRAPE pulses were designed to efficiently increase the spin polarization of the nitroxide radical. The GRAPE pulses were numerically optimized for a 2 pulse operation on the electron spin of the NO radical, attempting to enhance the signal intensities from the NO site. Typical optimized GRAPE pulses are given in SI Figures S14 and S15 together with the FT-ESR spectra simulated by the pulses. The observed FT-ESR spectra of Tr-Ph-NO using the chirp and GRAPE pulses are shown in Figure 6(d) – (f). In these spectra, the NO transitions due to the sublevels of |MI = +1⟩ and |MI = 0⟩ were relatively enhanced by the designed arbitrary waveform pulses, by comparison to the conventional FT-ESR spectrum in (b). On the other hand, it was tough to enhance the transitions due to the sublevel |MI = −1⟩. This transition is the most broadened line due to anisotropic molecular motion, accelerating the transverse relaxation time. The acceleration of relaxation makes observation difficult. The experimental FT-spectrum given in Fig. 6 (f) shows that the intensities of the ESR transitions due to the nitroxide moiety were relatively increased, indicating that there are possibilities to improve the spectrum by applying well-designed GRAPE pulses. However, the experimental results are not perfect. This work is the first attempt to demonstrate the usefulness of microwave-based AWG techniques for the selective excitation, and further optimization of the experimental conditions, which include the molecular optimization of a hybrid biradical, is required to improve the efficiency. These newly designed pulse ESR experiments illustrate that the arbitrary waveform technology utilizing the nonlinear chirp and GRAPE MW pulses is capable of making a selective excitation. The new AWG-based technology is relevant to the development of spin manipulation technologies applicable to the issues of quantum spin control. We emphasize that the shaped or modulated pulses obtained by the AWG techniques can be used to modify excitation profiles by MW pulses. The modification of the profile enables us to manipulate both electron and nuclear spins in molecular spin qubit systems. By comparison, conventional MW pulse experiments with a rectangle pulse associated with specific frequencies have intrinsic limitations to control the excitation profile in a desired manner, currently. DNP effects of the biradicals under study. The 1H and 1H13C CP DNP enhancement factors (ε) were estimated by calculating the ratio of absolute signal intensity (I) obtained with and without MW irradiation (equation 6). Errors for the enhancement factors (Δε) were estimated by multiplying ε by the cumulative noise to signal ratio of the spectra obtained with and without the MW irradiation (equation 7).

Table 3. DNP enhancements obtained for 15 mM of Tr-PhNO and 15 mM of Tr-Nf-NO dissolved in 1,1,2,2tetrachloroethane (TCE). To determine the 1H MAS and 1H– 13C CP MAS enhancement factors, the TCE signal was analyzed. See the text for the error estimation. Sample

Tr-Ph-NO in TCE 15 mM

Tr-Nf-NO in TCE 15 mM

ε(1H)

30.1 ± 0.1

19.8 ± 0.1

ε(13C CP)

28.7 ± 0.6

17.6 ± 0.4

1

H

13

C CP MAS

 = 28.7 ± 0.6

w ON

*

*

w OFF x 10

150

100 50 , ppm

0

Figure 7. 1H→13C CP MAS spectra obtained for 15 mM Tr-Ph-NO in TCE solution with and without the MW irradiation. Note: a spectrum without the MW irradiation is enlarged by factor of 10, peak at 4.6 ppm arises from the plug, spinning sidebands are indicated by asterisks.

𝐼𝜇𝑤𝑂𝑁

(6)

𝜀 = 𝐼𝜇𝑤𝑂𝐹𝐹, Δ𝜀 = 𝜀 ∙

(

noise𝜇𝑤𝑂𝑁 𝐼𝜇𝑤𝑂𝑁

+

noise𝜇𝑤𝑂𝐹𝐹 𝐼𝜇𝑤𝑂𝐹𝐹

).

(7)

After the synthesis and basic characterization, the two biradicals, Tr-Ph-NO and Tr-Nf-NO were utilized for DNP enhanced solid-state NMR experiments. The results obtained in 1,1,2,2-tetrachloroethane (TCE) solution are summarized in Table 3. The strongest 1H and 1H→13C CP enhancement factors are 30, which were obtained for the Tr-Ph-NO radical in TCE solution (Figure 7) while for the Tr-Nf-NO radicals factors up to 20 were obtained. These results impressively show the feasibility of these designed radicals to produce DNP hyperpolarization. Importantly, in these non-optimized radical solutions such enhancement factors were obtained as would reduce the measurement time of solid-state NMR experiments from several hundreds of days to one day. 4. CONCLUSIONS



Trityl (Tr) and nitroxide (NO) radicals are connected by topologically controlled aryl linkers, generating genuinely gengineered biradicals. The rationalized molecular design of the aryl linkers bridging between the two stable radicals was underlain by the topological symmetry nature of the electronic network of the aryl linkers, i.e., p-phenylene (Ph) and 2,7-naphthylene (Nf). Ph and Nf linkers, respectively give a positive and negative exchange interaction (J) between the Tr and NO radical moieties. They serve as prototypical models for biradicals in which the exchange J and hyperfine interactions compete with the g-difference electronic Zeeman interactions. The magnetic properties, including J’s, underlying the biradical spin Hamiltonian in solution have been determined by multifrequency CW-ESR (X-, Q- and W-band) and 1H ENDOR (Xband) spectroscopies, and compared with values obtained by quantum chemical calculations. The signs of the J-values are in good harmony with the quantum chemical calculations and with the topological expectations based on the molecular engineering. The g-engineered biradicals have been tested as prototypes for AWG (Arbitrary Waveform Generator) based spin manipulation techniques, using GRAPE (GRAdient Pulse Engineering) microwave pulse control of spins in molecular magnetic resonance spectroscopy, and demonstrating the efficient signal enhancement of selective and weakened hyperfine signals of particular radical sites that can occur in pulse ESR experiments. The DNP effects of the biradicals for NMR signal enhancement have been examined, giving efficiency factors of up to 30 even under non-optimized experimental conditions, which drastically reduces the measurement time by a factor of 900. These data can be employed to support theoretical studies of the DNP efficacy as a function of the EPR parameters and the flexibility of the molecular frame of the radical, which are however beyond the scope of the present manuscript. An exchange-coupled g-engineered system such as the present hybrid biradicals gives us a testing ground for manipulating electron spins by well-designed multi-pulse ESR techniques. In the present systems, the electronic Zeeman interaction can be treated as an additional controllable parameter in quantum control experiments. For this purpose, Qand W-band AWG experiments are underway.

ASSOCIATED CONTENT Supporting Information. The Supporting Information is available free of charge on the ACS Publications website. Cartesian atomic coordinates of biradicals optimized at the UB3LYP/6-31G* level, syntheses of biradicals, Tr-Ph-NO and TrNf-NO, DNP studies: Experimental data, and general treatments for CW ENDOR spectroscopy for exchange-coupled biradical systems are given in the Supporting Information.

AUTHOR INFORMATION Corresponding Authors * E-mail: [email protected] (K. Sa.), Phone: +81-6-66053072, [email protected] (E. B.), Phone: +73-83-3308850 (E. B.), [email protected] (T. T.). Phone: +81-6-66052605.

Page 10 of 12

Notes The authors declare no competing financial interest.

ACKNOWLEDGMENTS We thank Prof. Paul Lahti, University of Massachusetts Amherst for reading the manuscript and for helpful discussions. This work was supported by JSPS – RFBR grant (17-53-50043) , JSPS Grants-in-Aid for Scientific Research on Innovative Areas (Quantum Cybernetics), JSPS KAKENHI Scientific Research (B) (No. 23350011, 17H03012), JSPS KAKENHI Scientific Research (C) (No. 17K 05840, 18K03465), JSPS Grant-in-Aid for Challenging Exploratory Research (No. 25620063), Elements Science and Technology Project from MEXT, Japan. We thank to partial supports by the Core Research for Evolutionary Science and Technology (CREST) Program “Creation of Innovative Functions of Intelligent Materials on the Basis of the Element Strategy” of the Japan Science and Technology Agency (JST), and by FIRST Quantum Information Processing Project, Cabinet Office, Japan. We also acknowledge AOARD for support by AOARD Scientific Project on "Quantum Properties of Molecular Nanomagnets" (Award No. FA2386-13-1-4029, 4030, 4031) and AOARD Project on “Molecular Spins for Quantum Technologies” (Award No. FA2386-17-1-4040). V. K. thanks the Alexander von Humboldt Foundation (AvH) for a Research Fellowship for Postdoctoral Researchers. The Deutsche Forschungsgemeinschaft (DFG) under grant Bu 911/26-1 is gratefully acknowledged.

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Trityl-Aryl-Nitroxide Based Genuinely g-Engineered Biradicals, as

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