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.     

Atomic hydrogen and muonium in alkali halides

Atomic hydrogen can be trapped at interstitial and substitutional cation and anion sites in alkali halides. The geometrical structure of these defects was established by electron nuclear double resonance (ENDOR). From the analysis of the ENDOR spectra also detailed information was obtained on the electronic structure. In this article the major experimental and theoretical results for atomic hydrogen in several alkali halides are briefly reviewed. Special emphasis is given to the isotope effects upon replacing hydrogen by deuterium. The nature of the dynamical hyperfine and superhyperfine interactions is discussed. Its magnitude to be expected for muonium is estimated. Recent results on muonium centres are discussed on the basis of the knowledge about the hydrogen centres.     

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.     

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.     

EPR and ENDOR Studies of Shallow Donors in SiC

Recent progress in the investigation of the electronic structure of the shallow nitrogen (N) and phosphorus (P) donors in 3C–, 4H– and 6H–SiC is reviewed with focus on the applications of magnetic resonance including electron paramagnetic resonance (EPR) and other pulsed methods such as electron spin echo, pulsed electron nuclear double resonance (ENDOR), electron spin-echo envelope modulation and two-dimensional EPR. EPR and ENDOR studies of the ²⁹Si and ¹³C hyperfine interactions of the shallow N donors and their spin localization in the lattice are discussed. The use of high-frequency EPR in combination with other pulsed magnetic resonance techniques for identification of low-temperature P-related centers in P-doped 3C–, 4H– and 6H–SiC and for determination of the valley–orbit splitting of the shallow N and P donors are presented and discussed.     

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.     

2D TRIPLE in orientationally disordered samples--a means to resolve and determine relative orientation of hyperfine tensors

The two-dimensional (2D) TRIPLE experiment provides correlations between electron-nuclear double resonance (ENDOR) frequencies that belong to the same electron-spin manifold, M(S), and therefore allows to assign ENDOR lines to their specific paramagnetic centers and M(S) manifolds. This, in turn, also provides the relative signs of the hyperfine couplings. So far this experiment has been applied only to single crystals, where the cross-peaks in the 2D spectrum are well resolved with regular shapes. Here we introduce the application of the 2D TRIPLE experiment to orientationally disordered systems, where it can resolve overlapping powder patterns. Moreover, analysis of the shape of the cross-peaks shows that it is highly dependent on the relative orientation of the hyperfine tensors of the two nuclei contributing to this particular peak. This is done initially through a series of simulations and then demonstrated experimentally at a high field (W-band, 95 GHz). The first example concerned the (1)H hyperfine tensors of the stable radical alpha,gamma-bisdiphenylene-beta-phenylallyl (BDPA) immobilized in a polystyrene matrix. Then, the experiment was applied to a more complex system, a frozen solution of Cu(II)-bis(2,2':6',2' terpyridine) complex. There, the 2D TRIPLE experiment was combined with the variable mixing time (VMT) ENDOR experiment, which determined the absolute sign of the hyperfine couplings involved, and orientation selective ENDOR experiments. Analysis of the three experiments gave the hyperfine tensors of a few coupled protons.     

Electron paramagnetic resonance and electron nuclear double resonance of the AsO4 4- centre in X-irradiated KH2AsO4

Electron paramagnetic resonance studies of the AsO₄ ^4- centre in X-irradiated crystals of KH₂AsO₄ in the ferroelectric phase at 77 and 4·2 K are reported. The symmetry of the spin-hamiltonian has been found to be orthorhombic, and the g tensor and the A tensor describing the interaction of the unpaired electron with the arsenic nucleus (I = 3/2) have been obtained. Domain splitting has been observed in he spectra recorded in the ab plane of the crystal. By studying these spectra in the presence of an applied electric field, it has been possible to plot the hysteresis curve of ferroelectric KH₂AsO₄. Electron-nuclear double resonance (ENDOR) of protons surrounding the AsO₄ ^4- units has been studied at 4·2 K. Two sets of ENDOR lines have been found arising from the protons in the two equilibrium positions (labelled ‘ close ’ and ‘ far ’) along the hydrogen bonds linking the AsO₄ tetrahedra. The angular variation of the ENDOR lines from both ‘ close ’ and ‘ far ’ protons has been plotted in the crystal symmetry planes. The observed ENDOR frequencies have been fitted to those calculated from the numerical diagonalization of the Hamiltonian. The superhyperfine parameters for the ‘ close ’ and ‘ far ’ protons thus obtained are found to be quite anisotropic. The ENDOR results are shown to explain all details of the partially-resolved proton superhyperfine structure at room temperature as well as at low temperatures. An isotropic contact hyperfine coupling of -2·875 MHz of the unpaired electron to the proton in the ‘ far ’ position of the hydrogen bond has been determined, providing direct evidence for covalency in the hydrogen bonding in KH₂AsO₄ crystals.     

Linewidth Analysis of Spin Labels in Liquids: I. Theory and Data Analysis

We present a method of simulating the EPR spectra of spin labels in liquids using direct convolution of hyperfine splitting with Lorentzian linewidths. The aim is to simulate the experimental lineshape by considering all spectrometer characteristics as well as inhomogeneous and homogeneous linewidth effects. A major advance in this method is the correction for the broadening produced by Zeeman modulation commonly used to obtain EPR signals; this allows experimenters much more freedom to optimize their experimental conditions for the best signal-to-noise ratio. Microwave power broadening (saturation) effects on the EPR lines are significant even at very low observer levels. Successful simulation requires that all contributions from unresolved hyperfine splittings be explicitly included. Inhomogeneous broadening is dealt with by including all spins that interact with the electron (as a set of superhyperfine interactions); there is no "effective Gaussian" to substitute for the correct superhyperfine interactions. The effects of spin exchange on the linewidth and lineshape can be observed and must be taken into account in order to extract the fundamental linewidths.     

Proton ENDOR study of copper(II) bis(dithiocarbamate)

The proton hyperfine coupling tensors of the methylene protons in methyl-deuterated copper(II) bis(N,N-diethyldithiocarbamate) in a diamagnetic host crystal of the corresponding nickel complex have been measured by ENDOR spectroscopy. Two intermolecular and all four intramolecular proton coupling tensors could be determined. With the aid of spin densities, obtained from extended Hückel molecular orbital calculations, the anisotropic part of the tensors can be reproduced quantitatively, taking into account all two- and three-centre contributions. Comparison of the transition frequencies which are computed from the theoretical tensors with the experimental transitions enables the tracing of another five tensors which cannot be completely determined experimentally.     

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.     

Electrical detection of coherent nuclear spin oscillations in phosphorus-doped silicon using pulsed ENDOR

We demonstrate the electrical detection of pulsed X-band electron nuclear double resonance (ENDOR) in phosphorus-doped silicon at 5 K. A pulse sequence analogous to Davies ENDOR in conventional electron spin resonance is used to measure the nuclear spin transition frequencies of the (31)P nuclear spins, where the (31)P electron spins are detected electrically via spin-dependent transitions through Si/SiO(2) interface states, thus not relying on a polarization of the electron spin system. In addition, the electrical detection of coherent nuclear spin oscillations is shown, demonstrating the feasibility to electrically read out the spin states of possible nuclear spin qubits.     

Schonland ambiguity in the electron nuclear double resonance analysis of hyperfine interactions: principles and practice

For the analysis of the angular dependence of electron paramagnetic resonance (EPR) spectra of low-symmetry centres with S=1/2 in three independent planes, it is well-established-but often overlooked-that an ambiguity may arise in the best-fit g<--> tensor result. We investigate here whether a corresponding ambiguity also arises when determining the hyperfine coupling (HFC) A<--> tensor for nuclei with I=1/2 from angular dependent electron nuclear double resonance (ENDOR) measurements. It is shown via a perturbation treatment that for each set of M(S) ENDOR branches two best-fit A<--> tensors can be derived, but in general only one unique solution simultaneously fits both. The ambiguity thus only arises when experimental data of only one M(S) multiplet are used in analysis or in certain limiting cases. It is important to realise that the ambiguity occurs in the ENDOR frequencies and therefore the other best-fit result for an ENDOR determined A<--> tensor depends on various details of the ENDOR experiment: the M(S) state of the fitted transitions, the microwave frequency (or static magnetic field) in the ENDOR measurements and the rotation planes in which data have been collected. The results are of particular importance in the identification of radicals based on comparison of theoretical predictions of HFCs with published literature data. A procedure for obtaining the other best-fit result for an ENDOR determined A<--> tensor is outlined.     

On the centrifugal distortion in the microwave spectra of O2 and SO

Stable radicals formed by room temperature X-irradiation of single crystals of acridine and phenazine have been identified and their structures determined by detailed ENDOR studies at 77 K. The E.S.R. spectra are of little assistance in the identification of these radicals. However, the high resolution of ENDOR has made it possible to study all the proton hyperfine interactions in detail. The radicals investigated in this study are formed as a result of the addition of atomic hydrogen to the nitrogen atom of the acridine and phenazine molecules. ENDOR lines of all the protons have been identified and analysed. Spin densities have been deduced from the proton hyperfine tensors. Although the unpaired electron is extensively delocalized throughout the molecule, there are large spin densities (0·475 and 0·584, respectively) on C₉ in acridine and the second nitrogen in phenazine. Excellent agreement has been obtained between the observed spin densities and those computed by INDO molecular orbital calculations. The design and construction of a simple rectangular ENDOR cavity operating in the TE₁₀₁ mode is described.     

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.     

Liquid-phase EPR, ENDOR, and TRIPLE resonance studies on corrole and isocorrole cation radicals

The “Contracted Porphyrins” corrole and the recently synthesized isocorrole (as octaethyl derivatives) represent novel porphyrinoid macrocycles of biochemical interest. The radical cations of the free-bases of both corrole and its isomer are studied by EPR, ENDOR, and TRIPLE resonance in liquid solution to measure isotropic hyperfine couplings including signs. They yield detailed information of the electronic structure of the radical cations. The experimental findings are compared with results of all-valence-electrons self-consistent field molecular orbital calculations (RHF-INDO/SP). The comparison shows that the free-bases of corrole and isocorrole undergo protonation when oxidized to cation radicals in CH₂Cl₂ solution. Excellent agreement of the measured and calculated spin density distributions is achieved for the protonated dication radicals, which exhibit the C₂ symmetry observed for the hyperfine structure. The analysis of the hyperfine data discriminates against NH tautomerism as the sole source for an effective C₂ symmetry of the macrocycle.     

Studies of EPR and ENDOR spectra of14N and15N label bis(2-hydroxyacetophenyl ketoxime)-63Cu(II) and-65Cu(II) complexes in disordered system

The EPR spectra of isotopic label bis(2-hydroxyacetophenyl ketoxime)-Cu(II) [N?Cu-HAP] complexes, such as¹⁴N?⁶³Cu-HAP,¹⁵N?⁶³Cu-HAP and¹⁴N?⁶⁵Cu-HAP in frozen THF solution below 77 K, and their ENDOR spectra in frozen DMSO/EtOH (5∶1) solution below 20 K were studied. The exact values of the components ofg-tensor, of hyperfine tensors of copper isotopes, and of superhyperfine interaction tensors of copper with nuclei of nitrogen isotopes and¹H nuclei, and of the¹⁴N nuclear quadrupolar moment coupling tensor were obtained. The bond parameters α, β, δ, γ and the corresponding energy levels of N?Cu-HAP complexes were calculated by using EPR and ENDOR data. It was shown that the unpaired, electron is delocalized not only to the nearest N atom but also to the H atom, of ligands, which is more far from the Cu ion.