Orientation Dependence of Electron Spin Phase Memory Relaxation Times in Copper(II) and Vanadyl Complexes in Frozen Solution

Probing Bioinorganic Electron Spin Decoherence Mechanisms with an Fe2S2 Metalloprotein

Recent efforts have sought to develop paramagnetic molecular quantum bits (qubits) as a means to store and manipulate quantum information. Emerging structure-property relationships have shed light on electron spin decoherence mechanisms. While insights within molecular quantum information science have derived from synthetic systems, biomolecular platforms would allow for the study of decoherence phenomena in more complex chemical environments and further leverage molecular biology and protein engineering approaches. Here we have employed the exchange-coupled ST = 1/2 Fe2S2 active site of putidaredoxin, an electron transfer metalloprotein, as a platform for fundamental mechanistic studies of electron spin decoherence toward spin-based biological quantum sensing. At low temperatures, decoherence rates were anisotropic, reflecting a hyperfine-dominated decoherence mechanism, standing in contrast to the anisotropy of molecular systems observed previously. This mechanism provided a pathway for probing spatial effects on decoherence, such as protein vs solvent contributions. Furthermore, we demonstrated spatial sensitivity to single point mutations via site-directed mutagenesis and temporal sensitivity for monitoring solvent isotope exchange. Thus, this study demonstrates a step toward the design and construction of biomolecular quantum sensors.

Electron Paramagnetic Resonance, Electronic Ground State, and Electron Spin Relaxation of Seven Lanthanide Ions Bound to Lanmodulin and the Bioinspired Chelator, 3,4,3-LI(1,2-HOPO)

The electron paramagnetic resonance (EPR) spectra of lanthanide(III) ions besides Gd3+ , bound to small-molecule and protein chelators, are uncharacterized. Here, the EPR properties of 7 lanthanide(III) ions bound to the natural lanthanide-binding protein, lanmodulin (LanM), and the synthetic small-molecule chelator, 3,4,3-LI(1,2-HOPO) ("HOPO"), were systematically investigated. Echo-detected pulsed EPR spectra reveal intense signals from ions for which the normal continuous-wave first-derivative spectra are negligibly different from zero. Spectra of Kramers lanthanide ions Ce3+ , Nd3+ , Sm3+ , Er3+ , and Yb3+ , and non-Kramers Tb3+ and Tm3+ , bound to LanM are more similar to the ions in dilute aqueous:ethanol solution than to those coordinated with HOPO. Lanmodulins from two bacteria, with distinct metal-binding sites, had similar spectra for Tb3+ but different spectra for Nd3+ . Spin echo dephasing rates (1/Tm ) are faster for lanthanides than for most transition metals and limited detection of echoes to temperatures below ~6 to 12 K. Dephasing rates were environment dependent and decreased in the order water:ethanol>LanM>HOPO, which is attributed to decreasing librational motion. These results demonstrate that the EPR spectra and relaxation times of lanthanide(III) ions are sensitive to coordination environment, motivating wider application of these methods for characterization of both small-molecule and biomolecule interactions with lanthanides.

T1 Anisotropy Elucidates Spin Relaxation Mechanisms in an S = 1 Cr(IV) Optically Addressable Molecular Qubit

Paramagnetic molecules offer unique advantages for quantum information science owing to their spatial compactness, synthetic tunability, room-temperature quantum coherence, and potential for optical state initialization and readout. However, current optically addressable molecular qubits are hampered by rapid spin-lattice relaxation (T1) even at sub-liquid nitrogen temperatures. Here, we use temperature- and orientation-dependent pulsed electron paramagnetic resonance (EPR) to elucidate the negative sign of the ground state zero-field splitting (ZFS) and assign T1 anisotropy to specific types of motion in an optically addressable S = 1 Cr(o-tolyl)4 molecular qubit. The anisotropy displays a distinct sin2(2θ) functional form that is not observed in S = 1/2 Cu(acac)2 or other Cu(II)/V(IV) microwave addressable molecular qubits. The Cr(o-tolyl)4 T1 anisotropy is ascribed to couplings between electron spins and rotational motion in low-energy acoustic or pseudoacoustic phonons. Our findings suggest that rotational degrees of freedom should be suppressed to maximize the coherence temperature of optically addressable qubits.

Tunable Cr4+ Molecular Color Centers

The inherent atomistic precision of synthetic chemistry enables bottom-up structural control over quantum bits, or qubits, for quantum technologies. Tuning paramagnetic molecular qubits that feature optical-spin initialization and readout is a crucial step toward designing bespoke qubits for applications in quantum sensing, networking, and computing. Here, we demonstrate that the electronic structure that enables optical-spin initialization and readout for S = 1, Cr(aryl)₄, where aryl = 2,4-dimethylphenyl (1), o-tolyl (2), and 2,3-dimethylphenyl (3), is readily translated into Cr(alkyl)₄ compounds, where alkyl = 2,2,2-triphenylethyl (4), (trimethylsilyl)methyl (5), and cyclohexyl (6). The small ground state zero field splitting values (<5 GHz) for 1-6 allowed for coherent spin manipulation at X-band microwave frequency, enabling temperature-, concentration-, and orientation-dependent investigations of the spin dynamics. Electronic absorption and emission spectroscopy confirmed the desired electronic structures for 4-6, which exhibit photoluminescence from 897 to 923 nm, while theoretical calculations elucidated the varied bonding interactions of the aryl and alkyl Cr⁴⁺ compounds. The combined experimental and theoretical comparison of Cr(aryl)₄ and Cr(alkyl)₄ systems illustrates the impact of the ligand field on both the ground state spin structure and excited state manifold, laying the groundwork for the design of structurally precise optically addressable molecular qubits.

Spin-spin interaction and relaxation in two trityl-nitroxide diradicals

Trityl-nitroxides show substantial promise as polarizing agents in solid state dynamic nuclear polarization. To optimize performance it is important to understand the impact of spin-spin interactions on relaxation times of the diradicals. CW spectra and electron spin relaxation were measured for two trityl-nitroxides that differ in the substituents on the amide linker and have different strengths of the exchange interaction J. Analysis of the EPR spectra in terms of overlapping AB spin-spin splitting patterns explains the impact of J on various regions of the spectra. Even modest values of J are large relative to the separation between trityl and nitroxide resonances for some nitrogen nuclear spin state. Two conformations for each diradical were observed in CW spectra in fluid solution at X-band and Q-band. For one diradical J = 15 G (83%) and 5 G (17%) at 293 K, and J = 27 G (67%) and 3 G (33%) with interspin distances of 16 Å and 12 Å, respectively, at 80 K. For the second diradical the exchange interaction is stronger: the two conformations in fluid solution at 293 K had J = 113 G (67%) and 59 G (33%) and at 80 K the value of J was 43 G and there were two conformations with interspin distances of 13 and 11.5 Å. The observation of two conformations for each diradical, with different values of J, demonstrates the dependence of their exchange interactions on through-bond orbital interactions. X-band values of spin relaxation rates 1/T₁ and 1/T_m at 80 to 120 K for the trityl-nitroxides are similar to values for nitroxide mono-radicals, and faster than for trityl radicals. These observations show that even for a relatively small value of J, the nitroxide is very effective in enhancing the relaxation of the more slowly relaxing trityl.

Electron paramagnetic resonance of lanthanides

Many applications of lanthanides exploit their electron spin relaxation properties. Double electron-electron measurements of distances are possible because of the relatively long relaxation times of Gd³⁺. Relaxation enhancement measurements of distance are possible because of the much shorter relaxation times of other lanthanides. Magnetic resonance imaging contrast agents use the long relaxation time of the S-state Gd³⁺ ion, and NMR shift reagents use the fast relaxation of selected other lanthanides. Other than Gd³⁺ and the isoelectronic Eu²⁺ ion, spin relaxation of the lanthanides is so fast that their EPR spectra can be observed only in the liquid helium temperature range. In this chapter the EPR properties of each of the lanthanides is briefly summarized, with an emphasis on electron spin relaxation.

Understanding Covalent versus Spin-Orbit Coupling Contributions to Temperature-Dependent Electron Spin Relaxation in Cupric and Vanadyl Phthalocyanines

Recent interest in transition-metal complexes as potential quantum bits (qubits) has reinvigorated the investigation of fundamental contributions to electron spin relaxation in various ligand scaffolds. From quantum computers to chemical and biological sensors, interest in leveraging the quantum properties of these molecules has opened a discussion of the requirements to maintain coherence over a large temperature range, including near room temperature. Here we compare temperature-, magnetic field position-, and concentration-dependent electron spin relaxation in copper(II) phthalocyanine (CuPc) and vanadyl phthalocyanine (VOPc) doped into diamagnetic hosts. While VOPc demonstrates coherence up to room temperature, CuPc coherence times become rapidly T₁-limited with increasing temperature, despite featuring a more covalent ground-state wave function than VOPc. As rationalized by a ligand field model, this difference is ascribed to different spin-orbit coupling (SOC) constants for Cu(II) versus V(IV). The manifestation of SOC contributions to spin-phonon coupling and electron spin relaxation in different ligand fields is discussed, allowing for a further understanding of the competing roles of SOC and covalency in electron spin relaxation.

A concentrated array of copper porphyrin candidate qubits

Synthetic chemistry offers a pathway to realize atomically precise arrays of qubits, the smallest unit of a quantum information science system. We harnessed framework chemistry to create an array of qubit candidates, featuring one qubit every 13.6 Å, by synthesizing the new copper(ii) variant of the porphyrinic metal-organic framework PCN-224. We subjected the framework to pulse-electron paramagnetic resonance (EPR) measurements, establishing spin coherence at temperatures up to 80 K within a fully spin concentrated framework. Observation of Rabi oscillations further support the viability of the qubits within these arrays. To interrogate the spin dynamics of qubit arrays, we investigated spin-lattice relaxation, T 1, through a combination of pulse-EPR and alternating current (ac) magnetic susceptibility measurements. These data revealed distinct vibrational environments within the frameworks that contribute to spin dynamics. The aggregate results establish a pathway for a synthetic approach to create spatially precise networks of qubits.

Counterion influence on dynamic spin properties in a V(iv) complex

Using transition metal ions for spin-based applications, such as electron paramagnetic resonance imaging (EPRI) or quantum computation, requires a clear understanding of how local chemistry influences spin properties. Herein we report a series of four ionic complexes to provide the first systematic study of one aspect of local chemistry on the V(iv) spin - the counterion. To do so, the four complexes (Et3NH)2[V(C6H4O2)3] (1), (n-Bu3NH)2[V(C6H4O2)3] (2), (n-Hex3NH)2[V(C6H4O2)3] (3), and (n-Oct3NH)2[V(C6H4O2)3] (4) were probed by EPR spectroscopy in solid state and solution. Room temperature, solution X-band (ca. 9.8 GHz) continuous-wave electron paramagnetic resonance (CW-EPR) spectroscopy revealed an increasing linewidth with larger cations, likely a counterion-controlled tumbling in solution via ion pairing. In the solid state, variable-temperature (5-180 K) X-band (ca. 9.4 GHz) pulsed EPR studies of 1-4 in o-terphenyl glass demonstrated no effect on spin-lattice relaxation times (T 1), indicating little role for the counterion on this parameter. However, the phase memory time (T m) of 1 below 100 K is markedly smaller than those of 2-4. This result is counterintuitive, as 2-4 are relatively richer in 1H nuclear spin, hence, expected to have shorter T m. Thus, these data suggest an important role for counterion methyl groups on T m, and moreover provide the first instance of a lengthening T m with increasing nuclear spin quantity on a molecule.

Azaadamantyl nitroxide spin label: complexation with β-cyclodextrin and electron spin relaxation

An iodoacetamide azaadamantyl spin label was studied in fluid solution and in 9:1 trehalose:sucrose glass. In 9:1 toluene:CH₂Cl₂ solution at 293 K, the isotropic nitrogen hyperfine coupling is 19.2 G, T₁ is 0.37 µs and T₂ is 0.30-0.35 µs. Between about 80 and 150 K 1/T_m in 9:1 trehalose:sucrose is approximately independent of temperature demonstrating that the absence of methyl groups decreases 1/T_m relative to that which is observed in spin labels with methyl groups on the alpha carbons. Spin lattice relaxation rates between about 80 and 293 K in 9:1 trehalose:sucrose are similar to those observed for other nitroxide spin labels, consistent with the expectation that relaxation is dominated by Raman and local mode processes. Although complexation of the azaadamantyl spin label with β-cyclodextrin slows tumbling in aqueous solution by about a factor of 10, it has little impact on 1/T₁ or 1/T_m in 9:1 trehalose:sucrose between 80 and 293 K.

Synthesis and Electron Spin Relaxation of Tetracarboxylate Pyrroline Nitroxides

We report the design, synthesis, and electron spin relaxation properties of hydrophilic tetracarboxylate ester pyrroline nitroxides 1 and 2, which serve as models in the search for new spin labels for DEER distance measurement at room temperature. The nitroxides are designed to have the methyl groups further away from the N–O spin site to decrease the inequivalent couplings of the unpaired electron to the methyl protons that shorten T_m at T > 70 K in currently used labels. The key step in the synthesis of 1 and 2 is the reaction of the dianion of pyrrole-1,2,5-tricarboxylic acid tert-butyl ester dimethyl ester with electrophiles such as methyl chloroformate and methyl bromoacetate. Structures of 1 and 2 are confirmed by X-ray crystallography. Studies of electron spin relaxation rates in rigid trehalose/sucrose matrices reveal approximately temperature independent values of 1/T_m for 1 and 2 up to about 160 K and modest temperature dependence up to 295 K, demonstrating that increasing the distance between the nitroxide moiety and methyl groups is effective in lengthening T_m at T > 70 K.

Field-stepped direct detection electron paramagnetic resonance

The widest scan that had been demonstrated previously for rapid scan EPR was a 155G sinusoidal scan. As the scan width increases, the voltage requirement across the resonating capacitor and scan coils increases dramatically and the background signal induced by the rapidly changing field increases. An alternate approach is needed to achieve wider scans. A field-stepped direct detection EPR method that is based on rapid-scan technology is now reported, and scan widths up to 6200G have been demonstrated. A linear scan frequency of 5.12kHz was generated with the scan driver described previously. The field was stepped at intervals of 0.01 to 1G, depending on the linewidths in the spectra. At each field data for triangular scans with widths up to 11.5G were acquired. Data from the triangular scans were combined by matching DC offsets for overlapping regions of successive scans. This approach has the following advantages relative to CW, several of which are similar to the advantages of rapid scan. (i) In CW if the modulation amplitude is too large, the signal is broadened. In direct detection field modulation is not used. (ii) In CW the small modulation amplitude detects only a small fraction of the signal amplitude. In direct detection each scan detects a larger fraction of the signal, which improves the signal-to-noise ratio. (iii) If the scan rate is fast enough to cause rapid scan oscillations, the slow scan spectrum can be recovered by deconvolution after the combination of segments. (iv) The data are acquired with quadrature detection, which permits phase correction in the post processing. (v) In the direct detection method the signal typically is oversampled in the field direction. The number of points to be averaged, thereby improving the signal-to-noise ratio, is determined in post processing based on the desired field resolution. A degased lithium phthalocyanine sample was used to demonstrate that the linear deconvolution procedure can be employed with field-stepped direct detection EPR signals. Field-stepped direct detection EPR spectra were obtained for Cu(2+) doped in Ni(diethyldithiocarbamate)2, Cu(2+) doped in Zn tetratolylporphyrin, perdeuterated tempone in sucrose octaacetate, vanadyl ion doped in a parasubstituted Zn tetratolylporphyrin, Mn(2+) impurity in CaO, and an oriented crystal of Mn(2+) doped in Mg(acetylacetonate)2(H2O)2.

Electron spin relaxation rates for semiquinones between 25 and 295K in glass-forming solvents

Electron spin lattice relaxation rates for five semiquinones (2,5-di-t-butyl-1,4-benzosemiquinone, 2,5-di-t-amyl-1,4-benzosemiquinone, 2,5-di-phenyl-1,4-benzosemiquinone, 2,6-di-t-butyl-1,4-benzosemiquinone, tetrahydroxy-1,4-benzosemiquione) were studied by long-pulse saturation recovery EPR in 1:4 glycerol:ethanol, 1:1 glycerol:ethanol, and triethanolamine between 25 and 295K. Although the dominant process changes with temperature, relaxation rates vary smoothly with temperature, even near the glass transition temperatures, and could be modeled as the sum of contributions that have the temperature dependence that is predicted for the direct, Raman, local mode and tumbling-dependent processes. At 85K, which is in a temperature range where the Raman process dominates, relaxation rates along the g(xx) (g approximately 2.006) and g(yy) (g approximately 2.005) axes are about 2.7-1.5 times faster than along the g(zz) axis (g=2.0023). In highly viscous triethanolamine, contributions from tumbling-dependent processes are negligible. At temperatures above 100K relaxation rates in triethanolamine are unchanged between X-band (9.5GHz) and Q-band (34GHz), so the process that dominates in this temperature interval was assigned as a local mode rather than a thermally activated process. Because the largest proton hyperfine couplings are only 2.2G, spin rotation makes a larger contribution than tumbling-dependent modulation of hyperfine anisotropy. Since g anisotropy is small, tumbling-dependent modulation of g anisotropy makes a smaller contribution than spin rotation at X-band. Although there was negligible impact of methyl rotation on T(1), rotation of t-butyl or t-amyl methyl groups enhances spin echo dephasing between 85 and 150K.

Impact of electron-electron spin interaction on electron spin relaxation of nitroxide diradicals and tetraradical in glassy solvents between 10 and 300 k

To determine the impact of electron-electron spin-spin interactions on electron spin relaxation rates, 1/T1 and 1/Tm were measured for nitroxide monoradical, diradical, and tetraradical derivatives of 1,3-alternate calix[4]arenes, for two pegylated high-spin nitroxide diradicals, and for an azine-linked nitroxide diradical. The synthesis and characterization by SQUID (superconducting quantum interference device) magnetometry of one of the high-spin diradicals, in which nitroxides are conformationally constrained to be coplanar with the m-phenylene unit, is reported. The interspin distances ranged from about 5-9 A, and the magnitude of the exchange interaction ranged from >150 to >0.1 K. 1/T1 and 1/Tm were measured by long-pulse saturation recovery, three-pulse inversion recovery, and two-pulse echo decay at X-band (9.5 GHz) and Q-band (35 GHz). For a diradical with interspin distance about 9 A, relaxation rates were only slightly faster than for a monoradical with analogous structure. For interspin distances of about 5-6 A, relaxation rates in glassy solvents up to 300 K increased in the order monoradical < diradical < tetraradical. Modulation of electron-electron interaction enhanced relaxation via the direct, Raman, and local mode processes. The largest differences in 1/T1 were observed below 10 K, where the direct process dominates. For the three diradicals with comparable magnitude of dipolar interaction, 1/Tm and 1/T1 were faster for the molecules with more flexible structures. Relaxation rates were faster in the less rigid low-polarity sucrose octaacetate glass than in the more rigid 4:1 toluene/chloroform or in hydrogen-bonded glycerol glasses, which highlights the impact of motion on relaxation.

Electron spin relaxation of copper(II) complexes in glassy solution between 10 and 120 K

The temperature dependence, between 10 and 120 K, of electron spin-lattice relaxation at X-band was analyzed for a series of eight pyrrolate-imine complexes and for ten other copper(II) complexes with varying ligands and geometry including copper-containing prion octarepeat domain and S100 type proteins. The geometry of the CuN4 coordination sphere for pyrrolate-imine complexes with R=H, methyl, n-butyl, diphenylmethyl, benzyl, 2-adamantyl, 1-adamantyl, and tert-butyl has been shown to range from planar to pseudo-tetrahedral. The fit to the recovery curves was better for a distribution of values of T1 than for a single time constant. Distributions of relaxation times may be characteristic of Cu(II) in glassy solution. Long-pulse saturation recovery and inversion recovery measurements were performed. The temperature dependence of spin-lattice relaxation rates was analyzed in terms of contributions from the direct process, the Raman process, and local modes. It was necessary to include more than one process to fit the experimental data. There was a small contribution from the direct process at low temperature. The Raman process was the dominant contribution to relaxation between about 20 and 60 K. Debye temperatures were between 80 and 120 K. For samples with similar Debye temperatures the coefficient of the Raman process tended to increase as gz increased, as expected if modulation of spin-orbit coupling is a major factor in relaxation rates. Above about 60 K local modes with energies in the range of 260-360 K (180-250 cm-1) dominated the relaxation. For molecules with similar geometry, relaxation rates were faster for more flexible molecules than for more rigid ones. Relaxation rates for the copper protein samples were similar to rates for small molecules with comparable coordination spheres. At each temperature studied the range of relaxation rates was less than an order of magnitude. The spread was smaller between 20 and 60 K where the Raman process dominates, than at higher temperatures where local modes dominate the relaxation. Spin echo dephasing time constants, Tm, were calculated from two-pulse spin echo decays. Near 10 K Tm was dominated by proton spins in the surroundings. As temperature was increased motion and spin-lattice relaxation made increasing contributions to Tm. Near 100 K spin-lattice relaxation dominated Tm.

Molecular dynamics of nitroxides in glasses as studied by multi-frequency EPR

Pulsed multi-frequency EPR was used to investigate orientational molecular motion of the nitroxide spin probe (Fremy's salt) in glycerol glass near the glass transition temperature. By measuring echo-detected EPR spectra at different pulse separation times at resonance frequencies of 3, 9.5, 95 and 180 GHz, we were able to discriminate between different relaxation mechanisms and characterize the timescale of molecular reorientations (10(-7)-10(-10) s). We found that near the glass transition temperature, the orientation-dependent transverse relaxation is dominated by fast reorientational fluctuations, which may be overlapped with fast modulations of the canonical g-matrix values. The data was interpreted using a new simulation program for the orientation-dependent transverse relaxation rate 1/T2 of nitroxides based on different models for the molecular motion. The validity of the different models was assessed by comparing least-square fits of the simulated relaxation behaviour to the experimental data.

Restricted orientational motion of nitroxides in molecular glasses: Direct estimation of the motional time scale basing on the comparative study of primary and stimulated electron spin echo decays

A comparative study of anisotropic relaxation in two-pulse primary and three-pulse stimulated electron spin echo decays provides a direct way to distinguish fast (correlation time tau(c)<10(-6) s) and slow (tau(c)>10(-6) s) motions. Anisotropic relaxation is detected as a difference of the decay rates for different resonance field positions in anisotropic electron paramagnetic resonance spectra. For fast motion anisotropic relaxation influences the primary echo decay and does not influence the stimulated echo decay. For slow motion it is seen in both two-pulse echo and three-pulse stimulated echo decays. For nitroxide spin probes dissolved in glassy glycerol only fast motion was found below 200 K. Increase of temperature above 200 K results in the appearance of slow motion. Its amplitude increases rapidly with temperature increase. While in glycerol glass slow motion appears above glass transition temperature T(g), in ethanol glass it is observable below T(g). The scenario of motional dynamics in glasses is proposed which involves the broadening of the correlation time distribution with increasing temperature.

Measurement of spin-lattice relaxation times in EPR with enhanced orientation selectivity

Two schemes for the measurement of orientation-dependent spin-lattice relaxation times are introduced, which combine the inversion-recovery experiment with electron-Zeeman-resolved or right-angle wiggling EPR. The principles of the experiments are outlined and their performance is illustrated by examples of application. With the electron Zeeman-resolved approach the relaxation times of two metal complexes with different g values are unraveled, whereas with right-angle wiggling the orientation-dependent relaxation behavior of a metal complex with large hyperfine anisotropy is analyzed.

Solvent and temperature dependence of spin echo dephasing for chromium(V) and vanadyl complexes in glassy solution

The solvent and temperature dependence of the rate constant for spin echo dephasing, 1/Tm, for 0.2 to 1.2 mM glassy solutions of chromyl bis(1-hydroxy-cyclohexanecarboxylic acid), CrO(HCA)-2; aquo vanadyl ion, VO2+ (aq), and vanadyl bis(trifluoroacetylacetonate), VO(tfac)2 were examined. At low temperatures where 1/T1 << 1/Tm, 1/Tm in 1:1 H2O:glycerol is dominated by solvent protons. At low temperature 1/Tm increases in the order 1:1 H2O:glycerol or 9:1 CF3CH2OH:ethyleneglycol (no methyl groups) < 9:1 i-PrOH:MeOH (hindered methyl groups) < 9:1 n-PrOH:MeOH (less hindered methyl groups). This solvent dependence of 1/Tm is similar to that observed for nitroxyl radicals, which indicates that the effect of solvent methyl groups on spin-echo dephasing at low temperature is quite general. At higher temperatures the echo dephasing is dominated by spin-lattice relaxation and is concentration dependent. As the glass softens, echo dephasing is dominated by the onset of molecular tumbling.