On the theory of mixing-frequency electron spin-echo envelope modulation spectroscopy

It has recently been stated that the parametrization of the time variables in the one-dimensional (1-D) mixing-frequency electron spin-echo envelope modulation (MIF-ESEEM) experiment is incorrect and hence the wrong frequencies for correlated nuclear transitions are predicted. This paper is a direct response to such a claim, its purpose being to show that the parametrization in 1- and 2-D MIF-ESEEM experiments possesses the same form as that used in other 4-pulse incrementation schemes and predicts the same correlation frequencies. We show that the parametrization represents a shearing transformation of the 2-D time-domain and relate the resulting frequency domain spectrum to the HYSCORE spectrum in terms of a skew-projection. It is emphasized that the parametrization of the time-domain variables may be chosen arbitrarily and affects neither the computation of the correct nuclear frequencies nor the resulting resolution. The usefulness or otherwise of the MIF parameters |ψ| > 1 is addressed, together with the validity of the original claims of the authors with respect to resolution enhancement in cases of purely homogeneous and inhomogeneous broadening. Numerical simulations are provided to illustrate the main points.     

Line-shifting method in electron spin echo envelope modulation (ESEEM) studies

A novel line-shifting method, which is called mixing-frequency electron spin echo envelope modulation (MIF-ESEEM) spectroscopy, is introduced and analysed. It is shown that the spectral resolution is enhanced, and thus the overlapping is removed with this new method. The application of this method to systems withS≥1 andI≥1 is also discussed.     

5- and 6-pulse electron spin echo envelope modulation (ESEEM) of multi-nuclear spin systems

In 3-pulse ESEEM and the original 4-pulse HYSCORE, nuclei with large modulation depth (k approximately 1) suppress spectral peaks from nuclei with weak modulations (k approximately 0). This cross suppression can impede the detection of the latter nuclei, which are often the ones of interest. We show that two extended pulse sequences, 5-pulse ESEEM and 6-pulse HYSCORE, can be used as experimental alternatives that suffer less strongly from the cross suppression and allow to recover signals of k approximately 0 nuclei in the presence of k approximately 1 nuclei. In the extended sequences, modulations from k approximately 0 nuclei are strongly enhanced. In addition, multi-quantum transitions are absent which simplifies the spectra. General analytical expressions for the modulation signals in these sequences are derived and discussed. Numerical simulations and experimental spectra that demonstrate the higher sensitivity of the extended pulse sequences are presented.     

Refocused primary echo: A zero dead time detection of the electron spin echo envelope modulation

We report on the two-dimensional (2D) implementation of the refocused primary electron spin echo envelope modulation (ESEEM) technique, its theory and experimental application to a model system and a system of biological interest. This technique is virtually free of dead time along one time coordinate. The ESEEM obtained by integration of the 2D time-domain data of the refocused primary ESEEM over one of the time coordinates shows the intensity of the sum combination harmonics proportional to k² for k 1 and proportional to k for k 1 (k is a usual notation for the modulation amplitude factor). This feature, in combination with the adjustment of k by means of variation of the operational frequency of the spectrometer, was found to be very useful for detection of protons with distributed hyperfine interaction parameters situated close to the electron spin.     

Determination of the deuterium content of deuterated betaine arsenate by electron spin echo envelope modulation

An alternative method for the determination of the deuterium content in the hydrogen bonds of ferroelectric/antiferroelectric deuterated betaine arsenate is presented. Carbon radicals formed by gamma irradiation of the betaine arsenate have been used as paramagnetic probes. The deuterium content in the hydrogen bonds has been determined by analyzing the modulation in the electron spin echo spectra of the carbon radical (CH₃)₃N+CHCOO^? which arises because of the dipolar interactions between the paramagnetic radical and the deuterium nuclei.     

Vector model of electron spin echo envelope modulation due to nuclear hyperfine and zeeman interactions

The transverse electron spin magnetization of a paramagnetic center with effective spinS=1/2 interacting with nonquadrupolar nuclei may be presented as a function of pairs of nuclei magnetization vectors which precess around the effective magnetic field directions. Each vector of the pair starts its precession perpendicular to both effective fields. The free induction decay (FID) signal is proportional to the scalar product of the vectors for nuclear spinI=1/2. The electron spin echo (ESE) signal can be described with two pairs of magnetization vectors. The ESE shape is not equal to two back-to-back FID signals except in the absence of ESE envelope modulation. A recursion relation is obtained which allows calculation of ESE signals for larger nuclear spins in the absence of nuclear quadrupole interaction. This relation can be used to calculate the time course of the ESE signal for arbitrary nuclear spins as a function of the nuclear magnetization vectors. While this formalism allows quantitative calculation of modulation from nuclei, it also provides a qualitative means of visualizing the modulation based on simple magnetization vectors.     

Pure absorption electron spin echo envelope modulation spectra by using the filter-diagonalization method for harmonic inversion

Harmonic inversion of electron spin echo envelope (ESEEM) time-domain signals by filter diagonalization is investigated as an alternative to Fourier transformation. It is demonstrated that this method features enhanced resolution compared to Fourier-transform magnitude spectra, since it can eliminate dispersive contributions to the line shape, even if no linear phase correction is possible. Furthermore, instrumental artifacts can be easily removed from the spectra if they are narrow either in time or frequency domain. This applies to echo crossings that are only incompletely eliminated by phase cycling and to spurious spectrometer frequencies, respectively. The method is computationally efficient and numerically stable and does not require extensive parameter adjustments or advance knowledge of the number of spectral lines. Experiments on gamma-irradiated methyl-alpha-d-glucopyranoside show that more information can be obtained from typical ESEEM time-domain signals by filter-diagonalization than by Fourier transformation.     

Electron spin echo envelope modulation (eseem) in CaF2:Gd3+K+

The energy levels of the nucleus of a K⁺ ion near a paramagnetic Gd³⁺ ion, both substituted in CaF₂, have been measured with the recently developed technique of electron spin echo envelope modulation, combined with an also recently developed microwave cavity, the loop-gap resonator. The results provide confirmation of the theory of lattice distortion around substituted ions.     

OPTESIM, a versatile toolbox for numerical simulation of electron spin echo envelope modulation (ESEEM) that features hybrid optimization and statistical assessment of parameters

Electron spin echo envelope modulation (ESEEM) is a technique of pulsed-electron paramagnetic resonance (EPR) spectroscopy. The analyis of ESEEM data to extract information about the nuclear and electronic structure of a disordered (powder) paramagnetic system requires accurate and efficient numerical simulations. A single coupled nucleus of known nuclear g value (g_N) and spin I = 1 can have up to eight adjustable parameters in the nuclear part of the spin Hamiltonian. We have developed OPTESIM, an ESEEM simulation toolbox, for automated numerical simulation of powder two- and three-pulse one-dimensional ESEEM for arbitrary number (N) and type (I, g_N) of coupled nuclei, and arbitrary mutual orientations of the hyperfine tensor principal axis systems for N > 1. OPTESIM is based in the Matlab environment, and includes the following features: (1) a fast algorithm for translation of the spin Hamiltonian into simulated ESEEM, (2) different optimization methods that can be hybridized to achieve an efficient coarse-to-fine grained search of the parameter space and convergence to a global minimum, (3) statistical analysis of the simulation parameters, which allows the identification of simultaneous confidence regions at specific confidence levels. OPTESIM also includes a geometry-preserving spherical averaging algorithm as default for N > 1, and global optimization over multiple experimental conditions, such as the dephasing time (τ) for three-pulse ESEEM, and external magnetic field values. Application examples for simulation of ¹⁴N coupling (N = 1, N = 2) in biological and chemical model paramagnets are included. Automated, optimized simulations by using OPTESIM lead to a convergence on dramatically shorter time scales, relative to manual simulations.     

Suppression of electron spin-echo envelope modulation peaks in double quantum coherence electron spin resonance

We show the use of the observer blind spots effect for the elimination of electron spin-echo envelope modulation (ESEEM) peaks in double quantum coherence (DQC) electron spin resonance (ESR). The suppression of ESEEM facilitates the routine and unambiguous extraction of distances from DQC-ESR spectra. This is also the first demonstration of this challenging methodology on commercial instrumentation.     

Electron spin resonance and electron spin echo modulation studies of Fe-containing mesoporous MCM-48 molecular sieves

Through electron spin resonance (ESR) and electron spin echo modulation (ESEM) studies, three Fe(III) species are found in liquid ion-exchanged Fe-MCM-48 and synthesized FeMCM-48. Species A with ESR parameters g^A = 4.30 with a line width of 160 G is observed in hydrated samples. This species is accompanied by a shoulder atg = 7.60 and is assigned to distorted tetrahedral Fe(III) likely located at framework defect sites. Species B is a broad peak centered at g^B = 2.00 and is assigned to distorted octahedral Fe(III) located at extraframework sites. This species is also observed in dehydrated samples. Species C is a very narrow isotropic signal at g^C = 4.30 with a line width of 30 G and is only observed in synthesized mesophase materials. It is consistent with rhombic Fe(III) with zero field parametersD andE corresponding toD/E =1/3 and is assigned to tetrahedral Fe(III) located at framework sites. Framework Fe(III) in FeMCM-48 is less accessible to ND₃ than is extraframework Fe(III) in Fe-MCM-48. On the basis of deuterium ESEM data, framework Fe(III) in synthesized FeMCM-48 directly coordinates to two D₂O or CH₃OD molecules and interacts more weakly with two more molecules. However, no deuterium ESEM is observed for extraframework Fe(III) in ion-exchanged Fe-MCM-48 with adsorbed D₂O or CH₃OD. It is also found that Fe(III) is incorporated into the framework of FeMCM-48 at an early stage of the formation of the MCM-48 mesostructure.     

Four pulse electron spin echo modulation studies of Cu(II) complexes in MCM-41 silica tube materials

The coordination geometry of Cu(II) complexes with water and ammonia has been studied by four pulse electron spin echo modulation spectroscopy in siliceous (L)Cu-MCM-41 and in aluminum-containing (L)Cu-AlMCM-41 where (L) denotes Cu(II) incorporation by liquid phase ionexchange. An analysis of the proton sum peaks in the echo modulation pattern of the water and ammonia ligands reveals significant differences in the Cu(II) coordination between MCM-41 and AlMCM-41. In the aluminum-containing material (L)Cu-AlMCM-41, Cu(II) coordinates to two molecules of water or ammonia and three framework oxygens in a square-based pyramidal coordination geometry. The base of the pyramid is formed by two adsorbate molecules together with two framework oxygens. A third framework oxygen is located at the apex of the pyramid. The cupric ion site is slightly shifted from the plane of the pyramid base towards the apex resulting in an off-plane position. In the siliceous material (L)Cu-MCM-41, [Cu(H₂O)₆]²⁺ and [Cu(NH₃)₄]²⁺ complexes are observed. The results of four pulse electron spin echo modulation experiments support a distorted octahedral coordination geometry for the [Cu(H₂O)₆]²⁺ complex in (L)Cu-MCM-41.     

Analysis of anisotropic hyperfine interaction distributions in two-dimensional four- and five-pulse electron spin echo envelope modulation spectra of protons in single crystals

The effect of the distribution of anisotropic hyperfine interaction on the cross peak line shape of protons in single crystal two-dimensional four-pulse electron spin echo envelope modulation spectra are discussed. The inclusion of an additional mixing pulse in the evolution period of the four-pulse sequence allows the simultaneous measurement of cross and sum peaks in a two-dimensional experiment. The sum peaks directly map the distribution of the anisotropic hyperfine interaction. As an experimental example the hyperfine interaction parameter distribution of protons localzed in hydrogen bonds of a mixed single crystal betaine phosphate/betaine phosphite is examined.     

Observation of potassium hyperfine interactions in x-irradiated KH2AsO4 through the method of electron spin echo envelope modulation

Hyperfine interaction frequencies of ¹H and ³⁹K nuclei near the AsO^4-₄ radical in X-ray irradiated KH₂AsO₄ (KDA) have been observed through the method of electron spin echo envelope modulation (ESEEM). This method enabled us to record nuclear hyperfine interaction (ENDOR-like) spectra around the ferroelectric phase transition of KDA for the first time. The ESEEM spectrum of ³⁹K exhibits a clear change when passing the ferroelectric phase transition temperature, but that of close protons does not. The result for close protons is in agreement with the symmetry breaking of the AsO^4-₄ site as observed via the EPR spectrum [5]. Finally, at 4.2 K the hyperfine interaction parameters of a ³⁹K nucleus near the AsO^4-₄ unit could be determined through the ESEEM method.     

Recovery of broad hyperfine lines in electron spin-echo envelope modulation spectroscopy of disordered systems

A novel approach is proposed for the recording and processing of electron spin-echo envelope modulation spectra that is less sensitive to lineshape distortions of broad hyperfine lines. An unusually long pulse delay is employed in three-pulse stimulated-echo experiments. Observation is restricted to the so-called echo-modulation echo, and magnitude calculation is used to eliminate blind spots that distort conventional three-pulse echo-modulation spectra.     

The theory of nuclear orientation via electron spin locking (NOVEL)

Nuclear orientation via electron spin locking (NOVEL) is a technique to orient nuclear spins embedded in a solid. Like other methods of dynamic nuclear polarization (DNP) it employs a small amount of unpaired electron spins and uses a microwave field to transfer the polarization of these unpaired electron spins to the nuclear spins. Traditional DNP uses CW microwave fields, but NOVEL uses pulsed electron spin resonance (ESR) techniques: a 90 degree pulse–90 degree phase shift–locking pulse sequence is applied and during the locking pulse the polarization transfer is assured by satisfying the Hartmann–Hahn condition. The transfer is coherent and similar to coherence transfer between nuclear spins. However, NOVEL requires an extension of the existing theory to many, inequivalent nuclear spins and to arbitrary, i.e. high electron and nuclear spin polarization. In this paper both extensions are presented. The theory is applied to the system naphthalene doped with pentacene, where the proton spins are polarized using the photo-excited triplet states of the pentacene molecules and found to show excellent agreement with the experimentally observed evolution of the polarization transfer during the locking pulse.     

Nuclear spin echo model based on Floquet–Lyapunov theory

The method of nuclear spin-echo amplitude calculation based on the density matrix technique is improved. The Floquet–Lyapunov theorem for a system of the ordinary differential equations with coefficients periodically dependent on time is used to find the solution of the Schrödinger equation for the time-evolution operator which describes behavior of a nuclear spin in the presence of a radiofrequency pulsed magnetic field. NQR spin echo for the case of nuclear spin I?=?1 and NMR spin echo for I?=?1/2 are considered as the simplest illustrations of the approach. The appearance of multiple spin echoes is predicted in the case of strong radiofrequency field.     

Comparison of dual spin echo echo planar imaging (SE_EPI), turbo spin echo with fat suppression and conventional dual spin echo sequences for T(2)-weighted MR imaging of focal liver lesions

The performance of T(2)-weighted spin-echo version of echo planar imaging (SE_EPI), conventional spin echo (SE) and fat-suppressed turbo spin-echo (TSE_SPIR) sequences for the detection of focal liver lesions was evaluated. Twenty patients that were included in our study, had CT examinations prior to the MR study and were scheduled for surgery for removal of liver lesions. All patients had intraoperative sonographic examinations. Qualitative and quantitative analysis of the images was performed. Overall image quality of SE_EPI sequences was better than SE (p<0.001) and similar to TSE_SPIR sequences. There were fewer motion and ghost artifacts on SE_EPI and TSE_SPIR images compared to SE images (p<0.001). Susceptibility artifacts were statistically equivalent on SE_EPI and SE images (p<0.001) while chemical shift artifacts were equally observed on SE and SE_EPI sequences. Overall image quality of EPI-SE and TSE_SPIR sequences was better compared to SE sequences. There was no significant difference in the number of lesions detected by each of the three sequences. Quantitative analysis showed that liver/lesion contrast-to-noise ratio (CNR) and signal-to-noise ratio (SNR) of liver, lesion, spleen was higher on TSE_SPIR sequences (p<0.001) while SE_EPI and SE sequences showed non-significant differences (p>0.05). SE_EPI sequences of the liver resulted in fewer artifacts and shorter acquisition times than SE sequences. They provide a diagnostic performance similar to TSE_SPIR and better than that of SE sequences.