Simulating Suppression Effects in Pulsed ENDOR, and the ‘Hole in the Middle’ of Mims and Davies ENDOR Spectra

All pulsed electron-nuclear double resonance (ENDOR) techniques, and in particular the Mims and Davies sequences, suffer from detectability biases (‘blindspots’) that are directly correlated to the size of the hyperfine interactions of coupled nuclei. Our efforts at ENDOR ‘crystallography’ and ‘mechanism determination’ with these techniques have led our group to refine our simulations of pulsed ENDOR spectra to take into account these biases, and we here describe the process and illustrate it with several examples. We first focus on an issue whose major significance is not widely appreciated, the ‘hole in the middle’ of pulsed ENDOR spectra caused by the n = 0 suppression hole in Mims ENDOR and by the analogous A → 0 suppression in Davies ENDOR for I = ½ and for ²H (I = 1). We then discuss the general treatment of suppression effects for I = 1, illustrating it with a treatment of Mims suppression for ¹⁴N.     

Combining steady-state and dynamic methods for determining absolute signs of hyperfine interactions: pulsed ENDOR Saturation and Recovery (PESTRE)

The underlying causes of asymmetric intensities in Davies pulsed ENDOR spectra that are associated with the signs of the hyperfine interaction are reinvestigated. The intensity variations in these asymmetric ENDOR patterns are best described as shifts in an apparent baseline intensity that occurs dynamically following on-resonance ENDOR transitions. We have developed an extremely straightforward multi-sequence protocol that is capable of giving the sign of the hyperfine interaction by probing a single ENDOR transition, without reference to its partner transition. This technique, Pulsed ENDOR Saturation and Recovery (PESTRE) monitors dynamic shifts in the 'baseline' following measurements at a single RF frequency (single ENDOR peak), rather than observing anomalous ENDOR intensity differences between the two branches of an ENDOR response. These baseline shifts, referred to as dynamic reference levels (DRLs), can be directly tied to the electron-spin manifold from which that ENDOR transition arises. The application of this protocol is demonstrated on (57)Fe ENDOR of a 2Fe-2S ferredoxin. We use the (14)N ENDOR transitions of the S = 3/2[Fe(II)NO](2+) center of the non-heme iron enzyme, anthranilate dioxygenase (AntDO) to examine the details of the relaxation model using PESTRE.     

Non-Kramers ENDOR and ESEEM of the S = 2 Ferrous Ion of [Fe(II)EDTA]

We report here the first non-Kramers (NK) ESEEM and ENDOR study of a mononuclear NK center, presenting extensive parallel-mode ESEEM and ENDOR measurements on the S_t = 2 ferrous center of [Fe(II)ethylenediamine-N,N,N′,N′-tetraacetato]²⁻; [Fe(II)EDTA)]²⁻. The results disclose an anomalous equivalence of the experimental patterns produced by the two techniques. A simple theoretical treatment of the frequency-domain patterns expected for NK-ESEEM and NK-ENDOR rationalizes this correspondence and further suggests that the very observation of NK-ENDOR is the result of an unprecedentedly large hyperfine enhancement effect. The mixed nitrogen–carboxylato oxygen coordination of [Fe(II)EDTA]²⁻ models that of the protein-bound diiron centers, although with a higher coordination number. Analysis of the NK-ESEEM measurements yields the quadrupole parameters for the ¹⁴N ligands of [Fe(II)EDTA]²⁻, K = 1.16(1) MHz, 0 ≤ η ≤ 0.05, and the analysis indicates that the electronic zero-field splitting tetragonal axis lies along the N–N direction.     

A Davies/Hahn multi-sequence for studies of spin relaxation in pulsed ENDOR

We extend earlier studies of the effects of relaxation on the intensities of pulsed ENDOR signals by introducing a Davies/Hahn (D/H) pulsed ENDOR multi-sequence that corresponds to a series of Davies sequences with the preparation pulse 'turned off'. In this pulse train, the Hahn [pi/2, pi] detection pulse pair of sequence n-1 both generates the echo detected for that sequence and acts as the preparation portion of sequence n, in effect replacing the pi preparation pulse of the Davies sequence. We show both theoretically, through a master-equation approach, and with both (1)H(I=1/2) and (14)N(I=1) ENDOR experiments on the non-heme Fe enzymes, superoxide reductase (SOR) (S=1/2) and AntDO (S=3/2), that under conditions of high electron-spin polarization (high microwave frequency/low temperature) the D/H multi-sequence allows simplification of ENDOR spectra by suppression of nuclear transitions associated with the m(S)=+1/2 (alpha) manifold. As such suppression depends on the sign of A, it allows determination of this sign. The suppression as a function of the time between individual sequences is found to exhibit behaviors that can be classified into three regimes of the ratio of cross-relaxation to spin-lattice relaxation rates: strong cross-relaxation (X-case); comparable rates (XL); negligible cross relaxation (L). Interestingly, the ENDOR behavior of the S=1/2 SOR center indicates it is an L case, while the S=3/2 AntDO is an L case. Overall, the D/H protocol appears to be a robust and general tool for using relaxation effects to manipulate ENDOR spectra.     

Matrix Line in Pulsed Electron-Nuclear Double Resonance Spectra

The intense line in Mims and Davies electron-nuclear double resonance (ENDOR) spectra due to the hyperfine interactions of an unpaired electron with distant matrix nuclei is shown to originate from a simultaneous inversion of a large number of nuclear spins by a radiofrequency pulse. Theoretical expressions describing the matrix ENDOR effect are derived and verified experimentally.     

Determination of signs of hyperfine coupling constants for an S = ½ system through E.P.R., ENDOR and double ENDOR

A systematic method of obtaining relative signs of hyperfine coupling constants is described. It applies to systems consisting of (a) a set of one or more nuclei coupled fairly strongly to the electron spin, and possessing a two-fold (or higher) axis of symmetry, together with (b) a set of weakly coupled nuclei defining superhyperfine transitions. ENDOR measurements for several E.P.R. hyperfine transitions, with the field oriented along the symmetry axis, give relative signs of hyperfine components for this direction. Signs for the other directions can then be obtained through ENDOR measurements on a single hyperfine transition at various field orientations. Additional double ENDOR measurements may be necessary for very weakly coupled nuclei. This method can complement double ENDOR studies in favourable cases. It is illustrated by the determination of signs of coupling constants of protons and of ⁷⁵As in the AsO₄ ^4- radical in KH₂AsO₄.     

Spin dynamics in continuous wave and pulsed ENDOR spectroscopy of coals

ENDOR experiments on coals recorded using continuous wave (CW) and pulsed techniques appear to give qualitatively different spectra. A matrix proton signal dominates the ENDOR spectrum of coals recorded in the CW ENDOR experiment while both a matrix and local proton ENDOR signals with huperfine couplings of up to 20 MHz are observed in spectra recorded using pulsed excitation techniques. Analysis of these spectra lead to different implications for the structure of the molecules that host the unpaired electron. Using a combination of pulsed EPR (Electron Spin Echo, FID detected hole burning) and pulsed Electron Nuclear Multiple Resonance (Sub-level relaxation, hyperfine selective ENDOR, EPR sub-spectra) experiments, we investigate the electron and nuclear spin dynamics in order to reconcile the different signal amplitudes observed in the CW and pulsed ENDOR spectra. In the CW ENDOR experiment, the results of the FID detected hole burning experiments prove that the low ENDOR signal intensity can not be attributed to spectral diffusion mechanisms competing with ENDOR mechanisms. Instead, we find that an unfavorable ratio of the electron and nuclear spin relaxation rates results in small local ENDOR signals. The matrix line dominates the spectrum because of the large number of matrix protons. In the pulsed ENDOR experiment, the hyperfine contrast selectivity mechanism suppresses the intensity of the matrix ENDOR signal and enhances the amplitudes of the local ENDOR signals. In addition, the ENDOR signal is not a function of the ratio of the electron and nuclear relaxation rates.     

Single-Crystal Fe Q-Band ENDOR Study of the 4 Iron–4 Sulfur Cluster in its Reduced [4Fe–4S] State

⁵⁷Fe Q-band ENDOR has been used to study the [4Fe–4S]¹⁺ state created by γ irradiation of single crystals of the synthetic model compound [N(C₂H₅)₄]₂[Fe₄S₄(SCH₂C₆H₅)₄] enriched in ⁵⁷Fe. This compound is an excellent biomimetic model of the active sites of many 4 iron–4 sulfur proteins, enabling detailed and systematic studies of its oxidized [4Fe–4S]³⁺ and reduced [4Fe–4S]¹⁺ paramagnetic states. Taking advantage of the fact that Q-band ENDOR, in contrast with X-Band ENDOR, allows for a very good separation of the ⁵⁷Fe transitions from those of the protons, the complete hyperfine tensors of the four iron atoms for the [4Fe–4S]¹⁺ species has been measured with precision. For each iron atom, the electron orbital and electron spin isotropic contributions have been determined separately. Moreover, it is remarkable that two ⁵⁷Fe hyperfine tensors attributed to the ferrous pair of iron atoms are very different. In effect, one tensor presents a much larger anisotropic part and a much smaller isotropic part than those of the other. This difference has been interpreted in terms of a differential electron orbital hyperfine interaction among the two ferrous ions.     

The Electronic State of Flavoproteins: Investigations with Proton Electron–Nuclear Double Resonance

Electron–nuclear double resonance (ENDOR) spectroscopy provides useful information on hyperfine interactions between nuclear magnetic moments and the magnetic moment of an unpaired electron spin. Because the hyperfine coupling constant reacts quite sensitively to polarity changes in the direct vicinity of the nucleus under consideration, ENDOR spectroscopy can be favorably used for the detection of subtle protein–cofactor interactions. A number of pulsed ENDOR studies on flavoproteins have been published during the past few years; most of them were designed to characterize the flavin cofactor by means of its protonation state, or to detect individual protein–cofactor interactions. The aim of this study is to compare the pulsed ENDOR spectra from different flavoproteins in terms of variations of characteristic proton hyperfine values. The general concept is to observe limits of possible influences on the cofactor’s electronic state by surrounding amino acids. Furthermore, we compare ENDOR data obtained from in vivo experiments with in vitro data to emphasize the potential of the method for gaining molecular information in complex media.     

Rubidium and proton ENDOR on ion pairs in solution

The E.S.R. spectrum of the o-dimesitoylbenzene anion-alkali cation radical shows unusually large isotropic alkali hyperfine splitting constants. We report a solution ENDOR study of this radical in which both alkali (^85,87Rb) and proton ENDOR spectra were recorded. Both the alkali and proton intensities showed a strong dependence on the metal ion nuclear spin quantum number of the E.S.R. line being saturated. This dependence is attributed to strong flip-flop cross-relaxation induced by modulation of the isotropic alkali hyperfine splitting. The powder E.S.R. spectrum of the complex reveals a small anisotropy of the Rb hyperfine splitting tensor. This indicates a small metal non-s-contribution to the half-filled molecular orbital, which is consistent with the observed relaxation behaviour and the small g shift. The intensity variations in the alkali and proton ENDOR spectra were used to determine the relative signs of all hyperfine splitting constants, and the absolute signs of the hyperfine splitting constants are deduced from a model of the structure of the complex.     

Anomalous Phases in Cavity-Free 240 GHz Pulsed ENDOR Spectra of 1.44 GeV Xe-Irradiated LiF

Paramagnetic centers generated by swift heavy ion irradiation of LiF crystals could be identified as electrons trapped at regular anion vacancy sites (F centers). Well-resolved electron-nuclear double resonance (ENDOR) spectra resulting from the hyperfine interaction with ⁷Li and ¹⁹F nuclei located in six different shells could be recorded. In order to preserve the millimeter-sized crystals, a cavity-free setup was used for the ENDOR experiments at an electronic Larmor frequency of 240 GHz. Apparently even under conditions of extremely high local energy loss in the ion track, the local density of persistent F centers is still sufficiently low to prevent distortions of the ionic crystal. The spread of hyperfine coupling constants was less than 5 %. Neither in electron paramagnetic resonance (EPR) nor in ENDOR spectra there was evidence for different types of paramagnetic centers. When performing ENDOR by applying the radiofrequency pulse directly after the 3-pulse Mims-type microwave sequence, an anomalous ENDOR effect was observed. The observed “positive” and “negative” ENDOR response can be attributed to efficient hole and anti-hole formation in the inhomogeneously broadened EPR spectrum and can be used to determine the sign of hyperfine coupling constants.     

Complete Determination of Nitrogen Quadrupole and Hyperfine Tensors in an Oxovanadium Complex by Simultaneous Fitting of Multifrequency ESEEM Powder Spectra

One-dimensional C- and X-band as well as two-dimensional X-band ESEEM experiments were performed on the complex oxobis(2-methylquinolin-8-olato) vanadium(IV) in frozen solution. A¹⁴N ESEEM simulation strategy based on initial first- and second-order perturbation analysis of peak positions in orientationally selected ESEEM spectra is presented. The constraint parameters extracted enable one to reduce the number of free fitting parameters for each nitrogen from 10 to 4. These are the α, β resp. the φ, θ Euler angles of the NQI and the HFI tensor defined in the coordinate system of the axialgtensor. The local symmetry of the complex allows one to reduce the number of free parameters to two angles only. Subsequently, a grid search in the remaining Euler space produced the starting parameters for the final fit of the¹⁴N hyperfine and quadrupole tensors. The anisotropic nitrogen hyperfine interaction tensor was found to be strongly nonaxial (0.06, 0.51, −0.57) MHz with the components significantly smaller than the isotropic hyperfine constant −6.18 MHz. In contrast, the quadrupole tensor withK= 0.58 MHz is close to axial (η = 0.13). These tensors share the principal axis normal to the ligand plane (as imposed by the local symmetry). The axes in the ligand plane are, however, rotated 50° with respect to each other. The orientation of the quadrupole tensor axes correlate within 10° with the orientation of the ligand plane following from the X-ray structure.     

Hyperfine coupling constants of NCO in ÃΣ by sub-Doppler spectroscopy

Molecular constants including ¹⁴N hyperfine coupling constants of the NCO radical in the òΣ⁺(000) state have been determined precisely by using the microwave-optical double resonance (MODR) and intermodulated fluorescence (IMF) techniques, where the band was pumped by a dye laser. The results are B = 12 056.559(41), D = 0.0045(16), γ = 22.06(17), b = 430.4(12), c = 80.3(28), and eQq = 2.6(36), all in MHz with one standard error in parentheses. It was found that, because the òΣ⁺ state closely approximates a coupling case (b_βS), MODR did not provide any precise value for the Fermi contact term, but this constant was determined accurately by combining the MODR spectrum with the IMF spectrum.     

Large Deviation Techniques Applied to Systems with Long-Range Interactions

We discuss a method to solve models with long-range interactions in the microcanonical and canonical ensemble. The method closely follows the one introduced by R.S. Ellis, Physica D 133:106 (1999), which uses large deviation techniques. We show how it can be adapted to obtain the solution of a large class of simple models, which can show ensemble inequivalence. The model Hamiltonian can have both discrete (Ising, Potts) and continuous (HMF, Free Electron Laser) state variables. This latter extension gives access to the comparison with dynamics and to the study of non-equilibrium effects. We treat both infinite range and slowly decreasing interactions and, in particular, we present the solution of the α-Ising model in one-dimension with 0 ⩽ α < 1.     

ESR, ENDOR, and ESEEM investigations on UV-irradiated 2,4,6-tri-tert-butyl phenol crystals

Electron spin resonance (ESR), electron nuclear double resonance (ENDOR), and electron spin echo envelope modulation (ESEEM) measurements were carried out for UV-irradiated 2,4,6-tri-tert-butyl phenol in the polycrystalline state. The radical produced in the crystal was detected by ESR and identified to be the corresponding phenoxyl radical, which is well characterized in the chemical oxidations in solutions. ENDOR and ESEEM spectra were unambiguously analyzed in terms of the hyperfine coupling constants determined from well-resolved ESR in solutions. Radical pairs in the crystals were also ascertained, and together with the single-crystal study the analysis disclosed zero-field splitting parameters in the triplet states. ESEEM time decays gave relaxation timesT ₁ = 5.94 andT ₂ = 1.12 μs at room temperature. These appropriate values permit an easy detection of the spin echoes, and therefore this radical matrix can be used as a useful standard for pulsed ESR investigations.     

Electron nuclear quadruple resonance for assignment of overlapping spectra

Multiple resonance methods are important tools in EPR for revealing the network of hyperfine levels of free radicals and paramagnetic centers. The variations of electron nuclear double resonance (ENDOR) or electron spin-echo envelope modulation (ESEEM) techniques help to correlate nuclear frequencies with each other. These methods have limited utility when there is extensive overlap or suspected overlap in the EPR spectrum between different species or different orientations. In the ENDOR spectrum, overlap and second-order shifts of lines also leads to ambiguity in assignment and interpretation. A new electron nuclear multiple resonance method is presented here that is based on population transfer ENDOR. It is a quadruple resonance method that correlates ENDOR lines and reveals the network of hyperfine levels in samples with unoriented paramagnetic species and in samples with overlapping EPR or ENDOR lines.     

Improved SNR in linear reordered 2D bSSFP imaging using variable flip angles

This article presents a variable flip-angle approach for balanced steady-state free precession (bSSFP) imaging, which allows increases in signal-to-noise ratio (SNR) and contrast-to-noise ratio (CNR) while keeping specific absorption rate (SAR) constant or reduces SAR for given CNR and SNR. The gain in SNR is achieved by utilizing the higher signal in the transient phase. Flip-angle variation during the echo train is realized using a trigonometric function with M steps (ramp length). Variation is combined with a linear k-space reordering such that outer parts of k-space are sampled using a lower flip angle α_min, while the central part of k-space is acquired with a higher flip angle α_max. No additional preparation or dummy cycles are applied prior to data acquisition. Several variation schemes with different starting flip angles α_min and ramp length M are considered. For example, using α_min=1° and M=96, α_max can be set to 47° without exceeding SAR limits at 3 T and gaining up to 50% in SNR, while, conventionally, α=34° is the maximal possible flip angle. Resolution seems unaffected in volunteer imaging. In all cases, no transient artifacts due to flip-angle variation were observed. This article demonstrates the use of flip-angle variations in bSSFP to increase SNR and CNR while keeping SAR constant, which is especially important at higher field strengths. Flip-angle variation can also be combined with other methods such as parallel imaging techniques for further SAR reduction.     

Pulsed ENDOR Spectroscopy at Large Thermal Spin Polarizations and the Absolute Sign of the Hyperfine Interaction

It is shown that in pulsed Mims-type ENDOR experiments performed at 95 GHz and 1.2 K the sign of the ENDOR signal can be positive, corresponding to an increase of the stimulated echo intensity, as well as negative, corresponding to a decrease of the stimulated echo. The positive “anomalous” sign is not observed at conventional EPR frequencies. It is explained that the effect arises through spin–lattice relaxation in the situation of large thermal spin polarizations and that it allows the determination of the absolute sign of the hyperfine interaction.     

ENDOR investigation of tellurium doped GaP

The hyperfine interactions of⁶⁹Ga,⁷¹Ga and³¹P nuclei with donor electrons in tellurium doped GaP have been measured by means of electron nuclear double resonance (ENDOR). Three groups of neighbour nuclei have been identified. Values of |(r)|², r ^–3, and the electric field gradient at the sites of the neighbour nuclei have been determined, and compared with those from ENDOR measurements on sulphur doped GaP.