Electron spin lattice relaxation rates for S = 12 molecular species in glassy matrices or magnetically dilute solids at temperatures between 10 and 300 K

Detrimental Increase of Spin-Phonon Coupling in Molecular Qubits on Substrates

Molecular qubits are a promising platform for quantum information systems. Although single molecule and ensemble studies have assessed the performance of S = 1/2 molecules, it is understood that to function in devices, regular arrays of addressable qubits supported by a substrate are needed. The substrate imposes mechanical and electronic boundary conditions on the molecule; however, the impact of these effects on spin-lattice relaxation times is not well understood. Here we perform electronic structure calculations to assess the effects of a graphene (Cgr) substrate on the molecular qubit copper phthalocyanine (CuPc). We use a progressive Hessian approach to efficiently calculate and separate the substrate contributions. We also use a simple thermal model to predict the impact of these changes on the spin-phonon coupling from 0 to 200 K. Further analysis of the individual vibrational modes with and without Cgr shows that an overall increase in SPC between the vibrations modes of CuPc with the surface reduces the spin-lattice relaxation time T1. We explain these changes by examining how the substrate lifts symmetries of CuPc in the absorbed configuration. Our work shows that a surface can have a large unintentional impact on SPC and that ways to reduce this coupling need to be found to fully exploit arrays of molecular qubits in device architectures.

New series of mononuclear β-diketonate cerium(III) field induced single-molecule magnets

Five new β-diketonate Ce3+ mononuclear complexes, [Ce(Btfa)3(H2O)2] (1), [Ce(Btfa)3(phen)] (2), [Ce(Btfa)3(bipy)] (3), [Ce(Btfa)3(terpy)] (4) and [Ce(Btfa)3(bathophen)(DMF)] (5), where Btfa- = 4,4,4-trifluoro-1-phenyl-1,3-butanedionate, phen = 1,10-phenanthroline, bipy = 2,2'-bipyridyl, terpy = 2,2':6',2''-terpyridine and bathophen = 4,7-diphenyl-1,10-phenanthroline, have been synthesized and structurally characterized through X-ray diffraction of single crystals. The central Ce3+ atom displays a coordination number of 8 for 1, 2 and 3 and of 9 for 4 and 5. Under a 0 T external magnetic field, none of the given compounds exhibits single molecule magnet (SMM) behaviour. However, a small magnetic field, between 0.02 and 0.1 T, is enough for all the compounds to exhibit slow relaxation of the magnetization. A comprehensive magnetic analysis, with experimental magnetic data and ab initio calculations, was undertaken for all the complexes, and the study highlights the significance of the different spin relaxation mechanisms that must be considered for a Ce3+ lanthanide ion.

Magnetic Relaxations of Chromium Nitride Porphyrinato Complexes Driven by the Anisotropic g-Factor

Molecule-based magnetic materials are useful candidates as the spin qubit due to their long coherence time and high designability. The anisotropy of the g-values of the metal complexes can be utilized to access the individual spin of the metal complexes, making it possible to achieve the scalable molecular spin qubit. For this goal, it is important to evaluate the effect of g-value anisotropy on the magnetic relaxation behaviour. This study reports the slow magnetic relaxation behaviour of chromium nitride (CrN2+ ) porphyrinato complex (1), which is structurally and magnetically similar with the vanadyl (VO2+ ) porphyrinato complex (2) which is known as the excellent spin qubit. Detailed analyses for vibrational and dynamical magnetism of 1 and 2 revealed that g-value anisotropy accelerates magnetic relaxations greater than the internal magnetic field from nuclear spin does. These results provide a design criterion for construction of multiple spin qubit based on g-tensor engineering.

Improving the molecular spin qubit performance in zirconium MOF composites by mechanochemical dilution and fullerene encapsulation

Enlarging the quantum coherence times and gaining control over quantum effects in real systems are fundamental for developing quantum technologies. Molecular electron spin qubits are particularly promising candidates for realizing quantum information processing due to their modularity and tunability. Still, there is a constant search for tools to increase their quantum coherence times. Here we present how the mechanochemical introduction of active spin qubits in the form of 10% diluted copper(ii)-porphyrins in the diamagnetic PCN-223 and MOF-525 zirconium-MOF polymorph pair can be achieved. Furthermore, the encapsulation of fullerene during the MOF synthesis directs the process exclusively toward the rare PCN-223 framework with a controllable amount of fullerene in the framework channels. In addition to the templating role, the incorporation of fullerene increases the electron spin-lattice and phase-memory relaxation times, T1 and Tm. Besides decreasing the amount of nuclear spin-bearing solvent guests in the non-activated qubit frameworks, the observed improved relaxation times can be rationalized by modulating the phonon density of states upon fullerene encapsulation.

Single-electron spin resonance detection by microwave photon counting

Electron spin resonance spectroscopy is the method of choice for characterizing paramagnetic impurities, with applications ranging from chemistry to quantum computing^1,2, but it gives access only to ensemble-averaged quantities owing to its limited signal-to-noise ratio. Single-electron spin sensitivity has, however, been reached using spin-dependent photoluminescence^3-5, transport measurements^6-9 and scanning-probe techniques^10-12. These methods are system-specific or sensitive only in a small detection volume^13,14, so that practical single-spin detection remains an open challenge. Here, we demonstrate single-electron magnetic resonance by spin fluorescence detection¹⁵, using a microwave photon counter at millikelvin temperatures¹⁶. We detect individual paramagnetic erbium ions in a scheelite crystal coupled to a high-quality-factor planar superconducting resonator to enhance their radiative decay rate¹⁷, with a signal-to-noise ratio of 1.9 in one second integration time. The fluorescence signal shows anti-bunching, proving that it comes from individual emitters. Coherence times up to 3 ms are measured, limited by the spin radiative lifetime. The method has the potential to be applied to arbitrary paramagnetic species with long enough non-radiative relaxation times, and allows single-spin detection in a volume as large as the resonator magnetic mode volume (approximately 10 μm³ in the present experiment), orders of magnitude larger than other single-spin detection techniques. As such, it may find applications in magnetic resonance and quantum computing.

Observation of slow magnetic relaxation phenomena in spatially isolated π-radical ions

The use of molecular spins as quantum bits is fascinating because it offers a wide range of strategies through chemical modifications. In this regard, it is very interesting to search for organic radical ions that have small spin-orbit coupling values. On the other hand, the feature of the magnetic relaxation of π-organic radical ions is rarely exploited due to the difficulty of spin dilution, and π-stacking interaction. In this study, we focus on N,N',N''-tris(2,6-dimethylphenyl)benzenetriimide (BTI-xy), where three xylene moieties connected to the imide groups cover the π-plane of the BTI core. As a result, BTI-xy radical anions without π-stacking interaction were obtained. This led to the slow magnetization relaxation, which is reported for the first time in organic radicals. Furthermore, the relaxation times in a solution state revealed the importance of spin interaction.

Impact of Chlorine Substitution on Electron Spin Relaxation of a Trityl Radical

A perchlorotriarylmethyl tricarboxylic acid radical 99% enriched in ¹³C at the central carbon (¹³C₁-PTMTC) was characterized in phosphate buffered saline solution (pH = 7.2) (PBS) at ambient temperature. Samples immobilized in 1:1 PBS:glycerol or in 9:1 trehalose:sucrose were studied as a function of temperature. Isotope enrichment at C₁ creates a trityl that can be used to accurately measure microscopic viscosity. Understanding of the impact of the ¹³C hyperfine interaction on electron spin relaxation is important for application of this trityl in oximetry and distance measurements. The anisotropic ¹³C₁ hyperfine couplings (A_x = A_y = 24 ± 2 MHz, A_z = 200 ± 1 MHz) are larger than for the related ¹³C₁-perdeuterated Finland trityl (¹³C₁-dFT) and the g anisotropy (g_x = 2.0013, g_y = 2.0016, g_z = 2.0042) is slightly larger than for ¹³C₁-dFT. The tumbling correlation times (τ_R) for ¹³C₁-PTMTC are 0.20 ± 0.02 ns in PBS and 0.40 ± 0.05 ns in 3:1 PBS:glycerol, which are shorter than for ¹³C₁-dFT in the same solutions. T₁ for ¹³C₁-PTMTC is 3.5 ± 0.5 μs in PBS and 5.3 ± 0.4 μs in 3:1 PBS:glycerol, which are shorter than for ¹³C₁-dFT due to faster tumbling, larger anisotropy of the ¹³C₁ hyperfine, and about 30% larger contribution from the local mode. In immobilized samples T₁ for ¹³C₁-PTMTC is similar to that for ¹³C₁-dFT and other trityls without chlorine or ¹³C₁ substituents, indicating that the ¹³C₁ and Cl substituents on the phenyl rings have little impact on T₁. The temperature dependence of T₁ was modeled with contributions from the direct, Raman, and local mode processes. Broadening of CW linewidths of about 0.6 G in fluid solution and about 2 G in rigid lattice is attributed to unresolved ^35,37Cl hyperfine couplings.

Monitoring electron spin fluctuations with paramagnetic relaxation enhancement

The magnetic interactions between the spin of an unpaired electron and the surrounding nuclear spins can be exploited to gain structural information, to reduce nuclear relaxation times as well as to create nuclear hyperpolarization via dynamic nuclear polarization (DNP). A central aspect that determines how these interactions manifest from the point of view of NMR is the timescale of the fluctuations of the magnetic moment of the electron spins. These fluctuations, however, are elusive, particularly when electron relaxation times are short or interactions among electronic spins are strong. Here we map the fluctuations by analyzing the ratio between longitudinal and transverse nuclear relaxation times T₁/T₂, a quantity which depends uniquely on the rate of the electron fluctuations and the Larmor frequency of the involved nuclei. This analysis enables rationalizing the evolution of NMR lineshapes, signal quenching as well as DNP enhancements as a function of the concentration of the paramagnetic species and the temperature, demonstrated here for LiMg_1-xMn_xPO₄ and Fe(III) doped Li₄Ti₅O₁₂, respectively. For the latter, we observe a linear dependence of the DNP enhancement and the electron relaxation time within a temperature range between 100 and 300 K.

The Impact of Ligand Field Symmetry on Molecular Qubit Coherence

Developing quantum bits (qubits) exhibiting room temperature electron spin coherence is a key goal of molecular quantum information science. At high temperatures, coherence is often limited by electron spin relaxation, measured by T₁. Here we develop a simple and powerful model for predicting relative T₁ relaxation times in transition metal complexes from dynamic ligand field principles. By considering the excited state origins of ground state spin-phonon coupling, we derive group theory selection rules governing which vibrational symmetries can induce decoherence. Thermal weighting of the coupling terms produces surprisingly good predictions of experimental T₁ trends as a function of temperature and explains previously confounding features in spin-lattice relaxation data. We use this model to evaluate experimental relaxation rates across S = 1/2 transition metal qubit candidates with diverse structures, gaining new insights into the interplay between spin-phonon coupling and molecular symmetry. This methodology elucidates the specific vibrational modes giving rise to decoherence, providing insight into the origin of room temperature coherence in transition metal complexes. We discuss the outlook of symmetry-based modeling and design strategies for understanding molecular coherence.

Deconvolving Contributions to Decoherence in Molecular Electron Spin Qubits: A Dynamic Ligand Field Approach

In the past decade, transition metal complexes have gained momentum as electron spin-based quantum bit (qubit) candidates due to their synthetic tunability and long achievable coherence times. The decoherence of magnetic quantum states imposes a limit on the use of these qubits for quantum information technologies, such as quantum computing, sensing, and communication. With rapid recent development in the field of molecular quantum information science, a variety of chemical design principles for prolonging coherence in molecular transition metal qubits have been proposed. Here the spin-spin, motional, and spin-phonon regimes of decoherence are delineated, outlining design principles for each. It is shown how dynamic ligand field models can provide insights into the intramolecular vibrational contributions in the spin-phonon decoherence regime. This minireview aims to inform the development of molecular quantum technologies tailored for different environments and conditions.

A reaction-coordinate perspective of magnetic relaxation

Understanding and utilizing the dynamic quantum properties of metal ions is the frontier of many next generation technologies. One property in particular, magnetic relaxation, is a complicated physical phenomenon that is scarcely treated in undergraduate coursework. Consequently, principles of magnetic relaxation are nearly impenetrable to starting synthetic chemists, who ultimately design the molecules that fuel new discoveries. In this Tutorial Review, we describe a new paradigm for thinking of magnetic relaxation in metal complexes in terms of a simple reaction-coordinate diagram to facilitate access to the field. We cover the main mechanisms of both spin-lattice (T1) and spin-spin (T2) relaxation times within this conceptual framework and how molecular and environmental design affects these times. Ultimately, we show that many of the scientific methods used by inorganic chemists to study and manipulate reactivity are also useful for understanding and controlling magnetic relaxation. We also describe the cutting edge of magnetic relaxation within this paradigm.

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.

Metal-ligand covalency enables room temperature molecular qubit candidates

Metal–ligand covalency enables observation of coherent spin dynamics to room temperature in a series of vanadium(iv) and copper(ii) catechol complexes.

Harnessing synthetic chemistry to design electronic spin-based qubits, the smallest unit of a quantum information system, enables us to probe fundamental questions regarding spin relaxation dynamics. We sought to probe the influence of metal–ligand covalency on spin–lattice relaxation, which comprises the upper limit of coherence time. Specifically, we studied the impact of the first coordination sphere on spin–lattice relaxation through a series of four molecules featuring V–S, V–Se, Cu–S, and Cu–Se bonds, the Ph₄P⁺ salts of the complexes [V(C₆H₄S₂)₃]^2– (1), [Cu(C₆H₄S₂)₂]^2– (2), [V(C₆H₄Se₂)₃]^2– (3), and [Cu(C₆H₄Se₂)₂]^2– (4). The combined results of pulse electron paramagnetic resonance spectroscopy and ac magnetic susceptibility studies demonstrate the influence of greater M–L covalency, and consequently spin-delocalization onto the ligand, on elongating spin–lattice relaxation times. Notably, we observe the longest spin–lattice relaxation times in 2, and spin echos that survive until room temperature in both copper complexes (2 and 4).

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.

Electron paramagnetic resonance of a 10B-containing heterocyclic radical

Electron paramagnetic resonance measurements for a ¹⁰B-containing heterocyclic phenanthrenedione radical, (C₆F₅)₂B(O₂C₁₄H₈), were made at X-band in 9:1 toluene:dichloromethane from 10 to 293 K and in toluene from 180 to 293 K. In well-deoxygenated 0.1 mM toluene solution at room temperature hyperfine couplings to ¹⁰B, four pairs of protons and five pairs of fluorines contribute to a continuous wave spectrum with many resolved lines. Hyperfine couplings were adjusted to provide the best fit for spectra of the radical enriched in ¹⁰B and the analogous radical synthesized with ^10,11B in natural abundance, resulting in small refinements of the hyperfine coupling constants previously reported for the natural abundance sample. Electron spin relaxation rates at temperatures between 15 and 293 K were similar for samples containing ¹⁰B and natural isotope abundance. Analysis of electron spin echo envelope modulation and hyperfine correlation spectroscopy data at 80 K found A_xx = -7.5 ± 0.3, A_yy = -8.5 ± 0.3, and A_zz = -10.8 ± 0.3 MHz for ¹¹B, which indicates small spin density on the boron. The spin echo and hyperfine spectroscopy data for the ¹⁰B -containing radical are consistent with the factor of 2.99 smaller hyperfine values for ¹⁰B than for ¹¹B.

Overhauser effects in non-conducting solids at 1.2 K

Recently, it was observed that protons in non-conducting solids doped with 1,3-bisdiphenylene-2-phenylallyl (BDPA) or its sulfonated derivative (SA-BDPA) can be polarized through Overhauser effects via resonant microwave irradiation. These effects were present under magic angle spinning conditions in magnetic fields between 5 and 18.8 T and at temperatures near 100 K. This communication reports similar effects in static samples at 6.7 T and, more importantly, at temperatures as low as 1.2 K, in a different dynamic regime than in the previous study. Our results provide new information towards understanding the mechanism of the Overhauser effect in non-conducting solids. We discuss possible origins of the fluctuations that can give rise to an Overhauser effect at such low temperatures.

Measuring Spin⋅⋅⋅Spin Interactions between Heterospins in a Hybrid [2]Rotaxane

Use of molecular electron spins as qubits for quantum computing will depend on the ability to produce molecules with weak but measurable interactions between the qubits. Here we demonstrate use of pulsed EPR spectroscopy to measure the interaction between two inequivalent spins in a hybrid rotaxane molecule.

Electron spin relaxation of a boron-containing heterocyclic radical

Preparation of the stable boron-containing heterocyclic phenanthrenedione radical, (C₆F₅)₂B(O₂C₁₄H₈), by frustrated Lewis pair chemistry has been reported recently. Electron paramagnetic resonance measurements of this radical were made at X-band in toluene:dichloromethane (9:1) from 10 to 293K, in toluene from 180 to 293K and at Q-band at 80K. In well-deoxygenated 0.1mM toluene solution at room temperature hyperfine splittings from ¹¹B, four pairs of ¹H, and 5 pairs of ¹⁹F contribute to an EPR spectrum with many resolved lines. Observed hyperfine couplings were assigned based on DFT calculations and account for all of the fluorines and protons in the molecule. Rigid lattice g values are g_x=2.0053, g_y=2.0044, and g_z=2.0028. Near the melting point of the solvent 1/T_m is enhanced due to motional averaging of g and A anisotropy. Increasing motion above the melting point enhances 1/T₁ due to contributions from tumbling-dependent processes. The overall temperature dependence of 1/T₁ from 10 to 293K was modeled with the sum of contributions of a process that is linear in T, a Raman process, spin rotation, and modulation of g anisotropy by molecular tumbling. The EPR measurements are consistent with the description of this compound as a substituted aromatic radical, with relatively small spin density on the boron.

Long Coherence Times in Nuclear Spin-Free Vanadyl Qubits

Quantum information processing (QIP) offers the potential to create new frontiers in fields ranging from quantum biology to cryptography. Two key figures of merit for electronic spin qubits, the smallest units of QIP, are the coherence time (T₂), the lifetime of the qubit, and the spin-lattice relaxation time (T₁), the thermally defined upper limit of T₂. To achieve QIP, processable qubits with long coherence times are required. Recent studies on (Ph₄P-d₂₀)₂[V(C₈S₈)₃], a vanadium-based qubit, demonstrate that millisecond T₂ times are achievable in transition metal complexes with nuclear spin-free environments. Applying these principles to vanadyl complexes offers a route to combine the previously established surface compatibility of the flatter vanadyl structures with a long T₂. Toward those ends, we investigated a series of four qubits, (Ph₄P)₂[VO(C₈S₈)₂] (1), (Ph₄P)₂[VO(β-C₃S₅)₂] (2), (Ph₄P)₂[VO(α-C₃S₅)₂] (3), and (Ph₄P)₂[VO(C₃S₄O)₂] (4), by pulsed electron paramagnetic resonance (EPR) spectroscopy and compared the performance of these species with our recently reported set of vanadium tris(dithiolene) complexes. Crucially we demonstrate that solutions of 1-4 in SO₂, a uniquely polar nuclear spin-free solvent, reveal T₂ values of up to 152(6) μs, comparable to the best molecular qubit candidates. Upon transitioning to vanadyl species from the tris(dithiolene) analogues, we observe a remarkable order of magnitude increase in T₁, attributed to stronger solute-solvent interactions with the polar vanadium-oxo moiety. Simultaneously, we detect a small decrease in T₂ for the vanadyl analogues relative to the tris(dithiolene) complexes. We attribute this decrease to the absence of one nuclear spin-free ligand, which served to shield the vanadium centers against solvent nuclear spins. Our results highlight new design principles for long T₁ and T₂ times by demonstrating the efficacy of ligand-based tuning of solute-solvent interactions.

Electron spin dynamics and spin-lattice relaxation of trityl radicals in frozen solutions

Electron spin-lattice relaxation of two trityl radicals, d24-OX063 and Finland trityl, were studied under conditions relevant to their use in dissolution dynamic nuclear polarization (DNP). The dependence of relaxation kinetics on temperature up to 100 K and on concentration up to 60 mM was obtained at X- and W-bands (0.35 and 3.5 Tesla, respectively). The relaxation is quite similar at both bands and for both trityl radicals. At concentrations typical for DNP, relaxation is mediated by excitation transfer and spin-diffusion to fast-relaxing centers identified as triads of trityl radicals that spontaneously form in the frozen samples. These centers relax by an Orbach-Aminov mechanism and determine the relaxation, saturation and electron spin dynamics during DNP.

Effect of H bond removal and changes in the position of the iron-sulphur head domain on the spin-lattice relaxation properties of the [2Fe-2S](2+) Rieske cluster in cytochrome bc(1)

Here, comparative electron spin–lattice relaxation studies of the 2Fe–2S iron–sulphur (Fe–S) cluster embedded in a large membrane protein complex – cytochrome bc₁ – are reported.

Here, comparative electron spin–lattice relaxation studies of the 2Fe–2S iron–sulphur (Fe–S) cluster embedded in a large membrane protein complex – cytochrome bc₁ – are reported. Structural modifications of the local environment alone (mutations S158A and Y160W removing specific H bonds between Fe–S and amino acid side chains) or in combination with changes in global protein conformation (mutations/inhibitors changing the position of the Fe–S binding domain within the protein complex) resulted in different redox potentials as well as g-, g-strain and the relaxation rates (T₁^–1) for the Fe–S cluster. The relaxation rates for T < 25 K were measured directly by inversion recovery, while for T > 60 K they were deduced from simulation of continuous wave EPR spectra of the cluster using a model that included anisotropy of Lorentzian broadening. In all cases, the relaxation rate involved contributions from direct, second-order Raman and Orbach processes, each dominating over different temperature ranges. The analysis of T₁^–1 (T) over the range 5–120 K yielded the values of the Orbach energy (E_Orb), Debye temperature θ_D and Raman process efficiency C_Ram for each variant of the protein. As the Orbach energy was generally higher for mutants S158A and Y160W, compared to wild-type protein (WT), it is suggested that H bond removal influences the geometry leading to increased strength of antiferromagnetic coupling between two Fe ions of the cluster. While θ_D was similar for all variants (∼107 K), the efficiency of the Raman process generally depends on the spin–orbit coupling that is lower for S158A and Y160W mutants, when compared to the WT. However, in several cases C_Ram did not only correlate with spin–orbit coupling but was also influenced by other factors – possibly the modification of protein rigidity and therefore the vibrational modes around the Fe–S cluster that change upon the movement of the iron–sulphur head domain.

Fluctuations of an exposed π-helix involved in lipoxygenase substrate recognition

The second helix in lipoxygenases adapts to permit substrate access to the active site, but details of this process are varied and poorly understood. We therefore examined the dynamics of helix 2 in solutions of spin-labeled soybean lipoxygenase-1 and spin relaxation at 60 K of the spin-labels by catalytic iron. Helix 2 in soybean lipoxygenase structures is surface-exposed and contains one turn of π-helix, centrally located. A site-directed spin-label scan of 18 of the 21 helix 2 residues, and electron paramagnetic resonance, showed that the π-helical segment became unusually mobile, on a nanosecond time scale, under conditions favoring substrate binding (pH 9 and lipid addition), while segments before and after had relatively unchanged dynamics. Backbone dynamics of residues in the π-helical segment appeared to be correlated, at pH 9. Samples also were frozen to examine the polarity and proticity of the local environments, the effect of the local environment on intrinsic relaxation, and dipolar relaxation by two symmetries of catalytic iron. The average hyperfine tensor component, Azz, of four π-helix residues decreased by 1.75 G, with an increase in pH from 7 to 9, while it remained unaffected for nearby buried residues. Power saturation data suggested the change in polarity specific to the π-helix altered the intrinsic relaxation rates. Different symmetries of iron contributed to distance-dependent magnetic relaxation. We interpret these data to mean that a π-helix in the second helix of plant lipoxygenases is highly dynamic and is the site where lipid chains penetrate to inner helices that outline the substrate pocket.

Molecular organization of cytochrome c2 near the binding domain of cytochrome bc1 studied by electron spin-lattice relaxation enhancement

Measurements of specific interactions between proteins are challenging. In redox systems, interactions involve surfaces near the attachment sites of cofactors engaged in interprotein electron transfer (ET). Here we analyzed binding of cytochrome c₂ to cytochrome bc₁ by measuring paramagnetic relaxation enhancement (PRE) of spin label (SL) attached to cytochrome c₂. PRE was exclusively induced by the iron atom of heme c₁ of cytochrome bc₁, which guaranteed that only the configurations with SL to heme c₁ distances up to ∼30 Å were detected. Changes in PRE were used to qualitatively and quantitatively characterize the binding. Our data suggest that at low ionic strength and under an excess of cytochrome c₂ over cytochrome bc₁, several cytochrome c₂ molecules gather near the binding domain forming a “cloud” of molecules. When the cytochrome bc₁ concentration increases, the cloud disperses to populate additional available binding domains. An increase in ionic strength weakens the attractive forces and the average distance between cytochrome c₂ and cytochrome bc₁ increases. The spatial arrangement of the protein complex at various ionic strengths is different. Above 150 mM NaCl the lifetime of the complexes becomes so short that they are undetectable. All together the results indicate that cytochrome c₂ molecules, over the range of salt concentration encompassing physiological ionic strength, do not form stable, long-lived complexes but rather constantly collide with the surface of cytochrome bc₁ and ET takes place coincidentally with one of these collisions.

Effect of electron spin dynamics on solid-state dynamic nuclear polarization performance

Optimum integral EPR saturation, determined by electron T_1e and electron spin flip-flop rate, maximizes solid-state DNP performance using nitroxide radicals.

Electron spin resonance studies of trityl OX063 at a concentration optimal for DNP

We have performed temperature-dependent electron spin resonance (ESR) measurements of the stable free radical trityl OX063, an efficient polarizing agent for dissolution dynamic nuclear polarization (DNP), at the optimum DNP concentration (15 mM). We have found that (i) when compared to the W-band electron spin-lattice relaxation rate T1e(-1) of other free radicals used in DNP at the same concentration, trityl OX063 has slower T1e(-1) than BDPA and 4-oxo-TEMPO. At T > 20 K, the T1e(-1)vs. T data of trityl OX063 appears to follow a power law dependence close to the Raman process prediction whereas at T < 10 K, electronic relaxation slows and approaches the direct process behaviour. (ii) Gd(3+) doping, a factor known to enhance DNP, of trityl OX063 samples measured at W-band resulted in monotonic increases of T1e(-1) especially at temperatures below 20-40 K while the ESR lineshapes remained essentially unchanged. (iii) The high frequency ESR spectrum can be fitted with an axial g-tensor with a slight g-anisotropy: g(x) = g(y) = 2.00319(3) and g(z) = 2.00258(3). Although the ESR linewidth D monotonically increases with field, the temperature-dependent T1e(-1) is almost unchanged as the ESR frequency is increased from 9.5 GHz to 95 GHz, but becomes faster at 240 GHz and 336 GHz. The ESR properties of trityl OX063 reported here may provide insights into the efficiency of DNP of low-γ nuclei performed at various magnetic fields, from 0.35 T to 12 T.

Effect of glassy modes on electron spin-lattice relaxation in solid ethanol

Electron spin-lattice relaxation (SLR) of TEMPO radical was measured in the crystalline and glassy states of deuterated ethanol in the temperature range 5-80K using X-band electron paramagnetic resonance (EPR). The measured SLR rates are higher in the glassy than in crystalline state and the excess SLR rate in glassy state is much lower than in ethanol. This result suggests that extra modes in glassy state, i.e. glassy modes, produce the excess SLR rate via the electron-nuclear dipolar (END) interaction between the electron spin of radical and the matrix protons or deuterons. Using the soft-potential model and assuming the END interaction between the electron spin and the matrix protons, the contributions to SLR rate of various mechanisms of glassy modes were theoretically analyzed. The evaluations of SLR rates in glassy ethanol indicate two main mechanisms of glassy modes: thermally activated relaxation of double-well systems and phonon-induced relaxation of quasi-harmonic local modes. The SLR rates induced by these mechanisms correlate well with the experimental data.

Electron and nuclear spin dynamics in the thermal mixing model of dynamic nuclear polarization

A novel mathematical treatment is proposed for computing the time evolution of dynamic nuclear polarization processes in the low temperature thermal mixing regime. Without assuming any a priori analytical form for the electron polarization, our approach provides a quantitative picture of the steady state that agrees with the well known Borghini prediction based on thermodynamic arguments, as long as the electrons-nuclei transition rates are fast compared to the other relevant time scales. Substantially different final polarization levels are achieved instead when the latter assumption is relaxed in the presence of a nuclear leakage term, even though very weak, suggesting a possible explanation for the deviation between the measured steady state polarizations and the Borghini prediction. The proposed methodology also allows us to calculate nuclear polarization and relaxation times, once the electrons/nuclei concentration ratio and the typical rates of the microscopic processes involving the two spin species are specified. Numerical results are shown to account for the manifold dynamic behaviours of typical DNP samples.

Electron spin relaxation governed by Raman processes both for Cu²⁺ ions and carbonate radicals in KHCO₃ crystals: EPR and electron spin echo studies

EPR studies of Cu²⁺ and two free radicals formed by γ-radiation were performed for KHCO₃ single crystal at room temperature. From the rotational EPR results we concluded that Cu²⁺ is chelated by two carbonate molecules in a square planar configuration with spin-Hamiltonian parameters g(||)=2.2349 and A(||)=18.2 mT. Free radicals were identified as neutral HOCO· with unpaired electron localized on the carbon atom and a radical anion CO₃·⁻ with unpaired electron localized on two oxygen atoms. The hyperfine splitting of the EPR lines by an interaction with a single hydrogen atom of HOCO· was observed with isotropic coupling constants a₀=0.31 mT. Two differently oriented radical sites were identified in the crystal unit cell. Electron spin-lattice relaxation measured by electron spin echo methods shows that both Cu²⁺ and free radicals relax via two-phonon Raman processes with almost the same relaxation rate. The temperature dependence of the relaxation rate 1/T₁ is well described with the effective Debye temperature Θ(D)=175 K obtained from a fit to the Debye-type phonon spectrum. We calculated a more realistic Debye temperature value from available elastic constant values of the crystal as Θ(D)=246 K. This Θ(D)-value and the Debye phonon spectrum approximation give a much worse fit to the experimental results. Possible contributions from a local mode or an optical mode are considered and it is suggested that the real phonon spectrum should be used for the relaxation data interpretation. It is unusual that free radicals in KHCO₃ relax similarly to the well localized Cu²⁺ ions, which suggests a small destruction of the host crystal lattice by the ionizing irradiation allowing well coupling between radical and lattice dynamics.

Pulsed EPR characterization of encapsulated atomic hydrogen in octasilsesquioxane cages

Hydrogen atoms encapsulated in molecular cages are potential candidates for quantum computing applications. They provide the simplest two-spin system where the 1s electron spin, S = 1/2, is hyperfine-coupled to the proton nuclear spin, I = 1/2, with a large isotropic hyperfine coupling (A = 1420.40575 MHz for a free atom). While hydrogen atoms can be trapped in many matrices at cryogenic temperatures, it has been found that they are exceptionally stable in octasilsesquioxane cages even at room temperature [Sasamori et al., Science, 1994, 256, 1691]. Here we present a detailed spin-lattice and spin-spin relaxation study of atomic hydrogen encapsulated in Si(8)O(12)(OSiMe(2)H)(8) using X-band pulsed EPR spectroscopy. The spin-lattice relaxation times T(1) range between 1.2 s at 20 K and 41.8 μs at room temperature. The temperature dependence of the relaxation rate shows that for T < 60 K the spin-lattice relaxation is best described by a Raman process with a Debye temperature of θ(D) = 135 K, whereas for T > 100 K a thermally activated process with activation energy E(a) = 753 K (523 cm(-1)) prevails. The phase memory time T(M) = 13.9 μs remains practically constant between 200 and 300 K and is determined by nuclear spin diffusion. At lower temperatures T(M) decreases by an order of magnitude and exhibits two minima at T = 140 K and T = 60 K. The temperature dependence of T(M) between 20 and 200 K is attributed to dynamic processes that average inequivalent hyperfine couplings, e.g. rotation of the methyl groups of the cage organic substituents. The hyperfine couplings of the encapsulated proton and the cage (29)Si nuclei are obtained through numerical simulations of field-swept FID-detected EPR spectra and HYSCORE experiments, respectively. The results are discussed in terms of existing phenomenological models based on the spherical harmonic oscillator and compared to those of endohedral fullerenes.

Suppression of Raman electron spin relaxation of radicals in crystals. Comparison of Cu2+ and free radical relaxation in triglycine sulfate and Tutton salt single crystals

Electron spin-lattice relaxation was measured by the electron spin echo method in a broad temperature range above 4.2 K for Cu(2+) ions and free radicals produced by ionizing radiation in triglycine sulfate (TGS) and Tutton salt (NH4)(2)Zn(SO4)2 ⋅ 6H2O crystals. Localization of the paramagnetic centres in the crystal unit cells was determined from continuous wave electron paramagnetic resonance spectra. Various spin relaxation processes and mechanisms are outlined. Cu(2+) ions relax fast via two-phonon Raman processes in both crystals involving the whole phonon spectrum of the host lattice. This relaxation is slightly slower for TGS where Cu(2+) ions are in the interstitial position. The ordinary Raman processes do not contribute to the radical relaxation which relaxes via the local phonon mode. The local mode lies within the acoustic phonon band for radicals in TGS but within the optical phonon range in (NH4)(2)Zn(SO4)2 ⋅ 6H2O. In the latter the cross-relaxation was considered. A lack of phonons around the radical molecules suggested a local crystal amorphisation produced by x- or γ-rays.

Scanned-probe detection of electron spin resonance from a nitroxide spin probe

We report an approach that extends the applicability of ultrasensitive force-gradient detection of magnetic resonance to samples with spin-lattice relaxation times (T (1)) as short as a single cantilever period. To demonstrate the generality of the approach, which relies on detecting either cantilever frequency or phase, we used it to detect electron spin resonance from a T (1) = 1 ms nitroxide spin probe in a thin film at 4.2 K and 0.6 T. By using a custom-fabricated cantilever with a 4 microm-diameter nickel tip, we achieve a magnetic resonance sensitivity of 400 Bohr magnetons in a 1 Hz bandwidth. A theory is presented that quantitatively predicts both the lineshape and the magnitude of the observed cantilever frequency shift as a function of field and cantilever-sample separation. Good agreement was found between nitroxide T (1) 's measured mechanically and inductively, indicating that the cantilever magnet is not an appreciable source of spin-lattice relaxation here. We suggest that the new approach has a number of advantages that make it well suited to push magnetic resonance detection and imaging of nitroxide spin labels in an individual macromolecule to single-spin sensitivity.

A pulsed EPR method to determine distances between paramagnetic centers with strong spectral anisotropy and radicals: the dead-time free RIDME sequence

Methods to determine distances between paramagnetic metal centers and radicals are scarce. This is unfortunate because paramagnetic metal centers are frequent in biological systems and so far have not been employed much as distance markers. Successful pulse sequences that directly target the dipolar interactions cannot be applied to paramagnetic metal centers with fast relaxation rates and large g-anisotropy, if no echos can be detected and the excitation bandwidth is not sufficient to cover a sufficiently large part of the spectrum. The RIDME method Kulik et al. (2002) [20] circumvents this problem by making use of the T(1)-induced spin-flip of the transition-metal ion. Designed to measure distance between such a fast relaxing metal center and a radical, it suffers from a dead time problem. We show that this is severe because the anisotropy of the metal center broadens the dipolar curves, which therefore, only can be analyzed if the full curve is known. Here, we introduce five-pulse RIDME (5p-RIDME) that is intrinsically dead-time free. Proper functioning of the sequence is demonstrated on a nitroxide biradical. The distance between a low-spin Fe(III) center and a spin label in spin-labeled cytochrome f shows the complete dipolar trace of a transition-metal ion center and a spin label, yielding the distance expected from the structure.

Measuring Ti(III)-carotenoid radical interspin distances in TiMCM-41 by pulsed EPR relaxation enhancement method

Interspin distances between the Ti(3+) ions and the carotenoid radicals produced inside TiMCM-41 pores by photoinduced electron transfer from 7'-apo-7'-(4-carboxyphenyl)-beta-carotene (coordinated to Ti(3+)), canthaxanthin (formed as a random distribution of isomers), and beta-ionone (model for a short-chain polyene) to Ti(3+) framework sites were determined using the pulsed EPR relaxation enhancement method. To estimate the electron transfer distances, the temperature dependence of relaxation rates was analyzed in both siliceous and metal-substituted siliceous materials. The phase memory times, T(M), of the carotenoid radicals were determined from the best fits of two-pulse ESEEM curves. The spin-lattice relaxation times, T(1), of the Ti(3+) ion were obtained from the inversion recovery experiment with echo detection on a logarithmic time scale in the temperature range of 10-150 K. The relaxation enhancement for the carotenoid radicals in TiMCM-41 as compared to that in MCM-41 is consistent with an interaction between the radical and the fast relaxing Ti(3+) ion. For canthaxanthin and beta-ionone, a dramatic effect on the carotenoid relaxation rate, 1/T(M), occurs at 125 and 40 K, respectively, whereas for carboxy-beta-carotene 1/T(M) increases monotonically with increasing temperature. The interspin distances for canthaxanthin and beta-ionone were estimated from the 1/T(M) - 1/T(M0) difference, which corresponds to the Ti(3+) contribution at the temperature where the maximum enhancement in the relaxation rate occurs. Determination of the interspin distances is based on calculations of the dipolar interaction, taking into consideration the unpaired spin density distribution along the 20-carbon polyene chain, which makes it possible to obtain a fit over a wider temperature interval. A distribution of the interspin distances between the carotenoid radical and the Ti(3+) ion was obtained with the best fit at approximately 10 A for canthaxanthin and beta-ionone and approximately 9 A for 7'-apo-7'-(4-carboxyphenyl)-beta-carotene with an estimated error of +/-3 A. The interspin distances do not depend on 1/T(M) - 1/T(M0) for carboxy-beta-carotene which shows no prominent peak in the relaxation rate over the temperature range measured.

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 Chlorine Substitution on Spin Lattice Relaxation of Triarylmethyl and 1,4-Benzosemiquinone Radicals in Glass-forming Solvents between 25 and 295 K

Spin-lattice relaxation rates measured by long-pulse saturation recovery in glassy solvents for chlorinated aromatic radicals: perchlorotriphenylmethyl radical, 2,5-dichloro-3,6-dihydroxy-1,4-benzosemiquinone, and tetrachloro-1,4-benzosemiquinone, were compared with relaxation rates for non-chlorinated analogs. The impact of the quadrupolar chlorines is small, and less than the effects of changing the rigidity of the glass. The temperature dependence of relaxation rates below the glass transition temperature could be modeled as the sum of contributions from the direct, Raman, and local mode processes.

Relaxation-based distance measurements between a nitroxide and a lanthanide spin label

Distance measurements by electron paramagnetic resonance techniques between labels attached to biomacromolecules provide structural information on systems that cannot be crystallized or are too large to be characterized by NMR methods. However, existing techniques are limited in their distance range and sensitivity. It is anticipated by theoretical considerations that these limits could be extended by measuring the enhancement of longitudinal relaxation of a nitroxide label due to a lanthanide complex label at cryogenic temperatures. The relaxivity of the dysprosium complex with the macrocyclic ligand DOTA can be determined without direct measurements of longitudinal relaxation rates of the lanthanide and without recourse to model compounds with well defined distance by analyzing the dependence of relaxation enhancement on either temperature or concentration in homogeneous glassy frozen solutions. Relaxivities determined by the two calibration techniques are in satisfying agreement with each other. Error sources for both techniques are examined. A distance of about 2.7 nm is measured in a model compound of the type nitroxide-spacer-lanthanide complex and is found in good agreement with the distance in a modeled structure. Theoretical considerations suggest that an increase of the upper distance limit requires measurements at lower fields and temperatures.

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 enhancement measurements of interspin distances in human, porcine, and Rhodobacter electron transfer flavoprotein-ubiquinone oxidoreductase (ETF-QO)

Electron transfer flavoprotein-ubiquinone oxidoreductase (ETF-QO) is a membrane-bound electron transfer protein that links primary flavoprotein dehydrogenases with the main respiratory chain. Human, porcine, and Rhodobacter sphaeroides ETF-QO each contain a single [4Fe-4S](2+,1+) cluster and one equivalent of FAD, which are diamagnetic in the isolated enzyme and become paramagnetic on reduction with the enzymatic electron donor or with dithionite. The anionic flavin semiquinone can be reduced further to diamagnetic hydroquinone. The redox potentials for the three redox couples are so similar that it is not possible to poise the proteins in a state where both the [4Fe-4S](+) cluster and the flavoquinone are fully in the paramagnetic form. Inversion recovery was used to measure the electron spin-lattice relaxation rates for the [4Fe-4S](+) between 8 and 18K and for semiquinone between 25 and 65K. At higher temperatures the spin-lattice relaxation rates for the [4Fe-4S](+) were calculated from the temperature-dependent contributions to the continuous wave linewidths. Although mixtures of the redox states are present, it was possible to analyze the enhancement of the electron spin relaxation of the FAD semiquinone signal due to dipolar interaction with the more rapidly relaxing [4Fe-4S](+) and obtain point-dipole interspin distances of 18.6+/-1A for the three proteins. The point-dipole distances are within experimental uncertainty of the value calculated based on the crystal structure of porcine ETF-QO when spin delocalization is taken into account. The results demonstrate that electron spin relaxation enhancement can be used to measure distances in redox poised proteins even when several redox states are present.

Impact of mutations on the midpoint potential of the [4Fe-4S]+1,+2 cluster and on catalytic activity in electron transfer flavoprotein-ubiquinone oxidoreductase (ETF-QO)

Electron-transfer flavoprotein-ubiquinone oxidoreductase (ETF-QO) is an iron-sulfur flavoprotein that accepts electrons from electron-transfer flavoprotein (ETF) and reduces ubiquinone from the Q-pool. ETF-QO contains a single [4Fe-4S]2+,1+ cluster and one equivalent of FAD, which are diamagnetic in the isolated oxidized enzyme and can be reduced to paramagnetic forms by enzymatic donors or dithionite. Mutations were introduced by site-directed mutagenesis of amino acids in the vicinity of the iron-sulfur cluster of Rhodobacter sphaeroides ETF-QO. Y501 and T525 are equivalent to Y533 and T558 in the porcine ETF-QO. In the porcine protein, these residues are within hydrogen-bonding distance of the Sgamma of the cysteine ligands to the iron-sulfur cluster. Y501F, T525A, and Y501F/T525A substitutions were made to determine the effects on midpoint potential, activity, and EPR spectral properties of the cluster. The integrity of the mutated proteins was confirmed by optical spectra, EPR g-values, and spin-lattice relaxation rates, and the cluster to flavin point-dipole distance was determined by relaxation enhancement. Potentiometric titrations were monitored by changes in the CW EPR signals of the cluster and semiquinone. Single mutations decreased the midpoint potentials of the iron-sulfur cluster from +37 mV for wild type to -60 mV for Y501F and T525A and to -128 mV for Y501F/T525A. Lowering the midpoint potential resulted in a decrease in steady-state ubiquinone reductase activity and in ETF semiquinone disproportionation. The decrease in activity demonstrates that reduction of the iron-sulfur cluster is required for activity. There was no detectable effect of the mutations on the flavin midpoint potentials.

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.

Comparing continuous wave progressive saturation EPR and time domain saturation recovery EPR over the entire motional range of nitroxide spin labels

The measurement of spin-lattice relaxation rates from spin labels, such as nitroxides, in the presence and absence of spin relaxants provides information that is useful for determining biomolecular properties such as nucleic acid dynamics and the interaction of proteins with membranes. We compare X-band continuous wave (CW) and pulsed or time domain (TD) EPR methods for obtaining spin-lattice relaxation rates of spin labels across the entire range of rotational motion to which relaxation rates are sensitive. Model nitroxides and spin-labeled biological species are used to illustrate the potential complications that arise in extracting relaxation data under conditions typical to biological experiments. The effect of super hyperfine (SHF) structure is investigated for both CW and TD spectra. First and second harmonic absorption and dispersion CW spectra of the nitroxide spin label, TEMPOL, are all fit simultaneously to a model of SHF structure over a range of microwave amplitudes. The CW spectra are novel because all harmonics and microwave phases were acquired simultaneously using our homebuilt CW/TD spectrometer. The effect of the SHF structure on the pulsed free induction decay (FID) and pulsed saturation recovery spectrum is shown for both protonated and deuterated TEMPOL. We present novel pulsed saturation recovery measurements on biological molecules, including spin-lattice relaxation rates of spin-labeled proteins and spin-labeled double-stranded DNA. The impact of structure and dynamics on relaxation rates are discussed in the context of each of these examples. Collisional relaxation rates with oxygen and transition metal paramagnetic relaxants are extracted using both continuous wave and time domain methods. The extent of the errors inherent in the CW method and the advantages of pulsed methods for unambiguously measuring collisional relaxation rates are discussed. Spin-lattice relaxation rates, determined by both CW and pulsed methods, are used to determine the electrostatic potential on the surface of a protein.

Electron spin-relaxation via vibronic level of nickel (I) and nickel (III) cyanide complexes in NaCl single crystals

Electron spin-lattice relaxation rates for the low spin [Ni(CN)(4)](1-) and [Ni(CN)(4)](3-) complexes in NaCl host lattice were measured by the inversion recovery technique in the temperature range 7-50K. The data for both paramagnetic species fit very well to a relaxation process involving localized anharmonic vibration modes, also responsible for the g-tensor temperature dependence.