Dynamic frequency shift in the E.S.R. spectra of transition metal ions

The factors which determine the electron spin resonance lineshapes and shifts of transition metal complexes in solution are discussed. It is shown that for ions with S > ½ the dynamic frequency shift may have pronounced effects on the E.S.R. lineshapes, and experimental evidence for this effect in complexes of Cr³⁺, Fe³⁺ and Gd³⁺ is presented. A quantitative interpretation of these spectra in terms of a relaxation mechanism due to fluctuation of the quadratic zero field splitting interaction is given.     

Program for the analysis of pulse height spectra and the background from a proportional detector

A PC-Fortran program is presented for fitting of lineshapes and the analysis of pulse height spectra obtainable with proportional detectors. The common fitting and analysis of pulse height spectra by means of mixed Gaussian lineshapes is readily improved by using Voigt lineshapes. In addition, the background can be evaluated during the fitting process without the need of extra measurements. As an application of the program, a pulse height transmission spectrum accumulated with a static⁵⁷Co source and detected with an argon-metane proportional detector, was least squares fitted to an elaborated complex trial lineshape function containing two Voigt lines plus a straight line. The fitting straight line parametersa andb characterize quantitatively the background. The very good PC-fitting obtained shows that the fitting of experimental spectra with the more realistic Voigt lineshapes is no longer a formidable task and that it is possible to evaluate and subtract the background inherent to the experiment during the fitting process.     

Oxygen-17 cross-polarization nmr spectroscopy of inorganic solids

We have obtained ¹⁷O nuclear magnetic resonance spectra of a variety of ¹⁷O-labeled solids (Mg(OH)₂, Ca(OH)₂, boehmite (AlO(OH)), talc (Mg₃Si₄O₁₀(OH)₂), (C₆H₅)₃SiOH, and amorphous SiO₂) using high-field static and “magic-angle” sample spinning techniques, together with ¹H cross polarization and dipolar decoupling. Our results show that large cross-polarization enhancements can be obtained and that reliable second-order quadrupolar powder lineshapes can be observed under cross-polarization conditions. We have also investigated the dynamics of cross polarization for several samples, including measurements of cross-relaxation rates and ¹H and ¹⁷O rotating-frame spin-lattice relaxation times. We show that rapid ¹⁷O rotating-frame spin-lattice relaxation reduces the cross-polarization enhancement in some cases and that differences in cross-relaxation rates can be used to “edit” spectra by selectively enhancing protonated oxygen resonances (in general, hydroxide versus oxide ions, in inorganic solids). When applied to high surface area metal oxides such as amorphous silica, this selectivity enables the observation of resonances from surface hydroxyl groups that are difficult to detect by conventional ¹⁷O NMR. Overall, the cross-polarization approach appears to have considerable utility for aiding in the interpretation of ¹⁷O NMR spectra of complex inorganic solids.     

Fast and accurate characterization of biological membranes by EPR spectral simulations of nitroxides

A method by which it is possible to characterize the membranes of biological samples on the basis of the EPR spectral lineshape simulation of membrane-dissolved nitroxide spin probes is described. The presented simulation procedure allows the determination of the heterogeneous structure of biological membranes and fluidity characteristics of individual membrane domains. The method can deal with isotropic and anisotropic orientations of nitroxides introduced into the biological samples described by restricted fast motion with a correlation time between 0.01 and 10 ns. The linewidths of the Lorentzian lineshapes are calculated in a restricted fast-motion approximation. In the special case of samples with high concentrations of nitroxides or in the presence of paramagnetic ions, the lineshapes are calculated directly from the exchange-coupled Bloch equations. The parameters describing ordering, relaxation, polarity, and the portions of the individual spectral components are extracted by optimizing the simulated spectra to the experimental spectrum with either a Simplex or a Monte Carlo algorithm. To improve the algorithm's efficiency, a new way of characterizing the goodness of fits is introduced. The new criterion is based on the standard least-squares function, but with special weighting of the partial sums. Its benefits are confirmed with membrane spectral simulation. Two classes of examples-simulation and optimizations of synthetic spectra to evaluate the accuracy of the optimization algorithms and simulation and optimization of EPR spectra of nitroxides in liposome suspensions in the presence of a broadening agent and in human leukocytes are shown.     

Absorption Lineshapes in Two-Dimensional Electron Spin Resonance and the Effects of Slow Motions in Complex Fluids

A methodology for obtaining pure absorption two-dimensional electron spin resonance spectra is presented for the case of large inhomogeneous broadening and/or slow motions. For slow motions, the spectra consist of “complex Lorentzians” superimposed with complex weighting factors, presenting a challenge to obtaining absorption spectra. It is shown how absorption-type spectra can be recovered for the two-pulse COSY and SECSY experiments in such cases. For three-pulse 2D ELDOR experiments, absorption lineshapes can be obtained for the autopeaks, whereas the cross peaks would be of mixed-mode character, in general. However, for practical cases the dispersive components in the cross peaks will be relatively small. Theoretical and experimental absorption spectra are provided to illustrate the method and to show the improved resolution obtained from absorption lineshapes. In particular, the variation in linewidths across a SECSY spectrum, which is a key component in elucidating motional dynamics, is clearly rendered in the pure absorption mode. A convenient method for introducing the necessary phase corrections for the slow-motional spectra is also provided.     

Electroreflectance of strontium titanate

The room temperature electroreflectance (ER) measurements for cubic SiTiO₃ are reported with particular emphasis on experimental conditions important for consistent reproducible lineshapes. This study includes for the first time a determination of the position of zero band perturbation (flatband) by making use of the even field nature of the ER lineshapes. The ER spectra are dependent upon dc bias, indicating the importance of a knowledge of the flatband position. A Kramers-Kronig analysis is performed and the lineshapes are reported in terms of ΔR/R, Δε₁ and Δε₂. The results in terms of Δε₂ show that the strongest direct transition occurs near 3.8 eV. The weak structure in the 3.4 eV region is due to either indirect transitions or weak direct transitions. Our unpolarized flatband ER spectra give rise to structures which for (110) samples are resolved into contributions from [001] and [12̄10] polarized spectra. In addition to the large oscillations observed above the band gap, weaker oscillatory structure is observed in the range 1.5 to 2.8 eV in the polarized spectra of (110) faced samples. The oscillations for [11̄0] polarization are 180° out of phase with those for [001] polarization.     

Lineshapes of collision-induced absorption (CIA) and of collision-induced scattering (CIS) for monatomic gas mixtures of Ne-Ar

Quantum mechanical lineshapes of collision-induced absorption (CIA) at different temperatures and of collision-induced light scattering (CIS) at room temperature are computed for gaseous binary mixtures of neon with argon using theoretical induced dipole moment and pair-polarizability trace and anisotropy as input. Comparison with measured spectra of isotropic and anisotropic light scattering shows satisfactory agreement, for which the uncertainty in measurement of its spectral moments is seen to be large. Empirical models of the dipole moment and pair-polarizability trace and anisotropy which reproduce the experimental spectra and the first three spectral moments more closely than the fundamental theory are also given. Good agreement between computed and experinental lineshapes of both absorption and scattering is obtained when potential models constructed from the thermophysical, transport and spectroscopic properties are used.     

Calculation of MAS spectra influenced by slow molecular tumbling.

A numeric algorithm is proposed that is suitable to calculate spectral lineshapes influenced by isotropic and anisotropic tumbling under sample spinning conditions. It is based on the stochastic Liouville equation and a rotational diffusion process described by a stationary Markov operator. A corresponding FORTRAN program can be implemented on a regular personal computer. The calculations result in spectral lineshapes including a complete set of spinning sidebands. The sensitive time scale of the resulting lineshapes depends on the deviation of the sample spinning axis from the magic angle. An example is presented demonstrating the potential of off-magic-angle spinning as a tool to analyze slow tumbling motions.     

Modelling IR-spectra of single-phase polycrystalline materials with random orientation – Supplementations and refinements for optically uniaxial crystallites

The IR-reflectance spectra of a bulk sample of randomly oriented polycrystalline fresnoite (Ba₂TiSi₂O₈) are presented. The sample was prepared by Spark Plasma Sintering from a powder consisting of optically large crystallites. The spectra are of notable higher quality than those of conventionally prepared samples, especially those of the cross-polarization terms. The spectra were modelled by a 4 ×4-matrix-formalism [T. G. Mayerhöfer, J. Opt. A: Pure Appl. Opt. 4, 540 (2002)], which was refined for optically uniaxial crystals, resulting in a correct prediction of the relative peak-intensities of the cross-polarization terms. The modelling was carried out with two different orientational averaging schemes. The comparison between modelled and measured spectra revealed that the use of any weighing factor is unjustified in case of orientational averaging of the IR-optical properties of solids.     

Automated Peak Picking and Peak Integration in Macromolecular NMR Spectra Using AUTOPSY

A new approach for automated peak picking of multidimensional protein NMR spectra with strong overlap is introduced, which makes use of the program AUTOPSY (automatedpeak picking for NMRspectroscopy). The main elements of this program are a novel function for local noise level calculation, the use of symmetry considerations, and the use of lineshapes extracted from well-separated peaks for resolving groups of strongly overlapping peaks. The algorithm generates peak lists with precise chemical shift and integral intensities, and a reliability measure for the recognition of each peak. The results of automated peak picking of NOESY spectra with AUTOPSY were tested in combination with the combined automated NOESY cross peak assignment and structure calculation routine NOAH implemented in the program DYANA. The quality of the resulting structures was found to be comparable with those from corresponding data obtained with manual peak picking.     

Unusual "AB" Spectra in High-Resolution Magic-Angle-Spinning NMR-Studies of Solids

Phosphorus-31CP-MAS spectra of Cd(NO₃)₂(PPh₃)₂ have been obtained as a function of spinning frequency. Although the two ³¹P nuclei are crystallographically equivalent and have the same isotropic chemical shifts in the solid state, they exhibit spinning-rate-dependent MAS spectra which have been analyzed to obtain the value of ²J(P, P). At high spinning rates, the spectra are analogous to "A₂" spectra in isotropic solutions, while at slower spinning rates, the spectra are more characteristic of strongly coupled "AB" solution spectra. The AB spectra are unusual in that δ_A = δ_B and J(A, B) is given by the splitting between the alternate peaks in the four-peak multiplet as opposed to the splitting between the outer and adjacent inner lines. This assignment was confirmed by a 2D CP-MAS J-resolved experiment. The unusual spinning-rate-dependent MAS lineshapes result from recoupling of the J interaction between the two crystallographically equivalent nuclei via anisotropic interactions, i.e., weak homonuclear dipolar coupling and differences in the orientation dependence of the chemical-shift tensors. Such spinning-rate-dependent MAS lineshapes are predicted to be a more frequent observation at higher applied magnetic fields.     

An adaptive line-by-line—statistical model for fast and accurate spectral simulations in low-pressure plasmas

An adaptive grid method is proposed for the simulation of low-pressure plasma radiation. The method relies on two complementary approaches which significantly reduce calculation times and the size of the obtained grids: Weak lines are calculated as a so-called “pseudo-continuum”, hence reducing the number of calculated lines, and a numerical algorithm has been developed for accurately calculating Voigt lineshapes using a minimum number of points. The method is fully user-parametric, allowing the choice of privileging calculation efficiency, or alternatively privileging the accuracy of the computed spectra. Sample radiative transfer calculations are presented, which show the efficiency of the method, also providing some guidelines on how to define lineshape calculation parameters, depending on the problem to be solved.     

Calculation of solid-state NMR lineshapes using contour analysis

Two new methods for calculating lineshapes in solid-state NMR spectra are described. The first method, which we refer to as semi-analytical, allows the rapid calculation of quadrupolar central-transition lineshapes in both static and magic-angle spinning cases. The second method, which is fully numerical, allows the calculation of lineshapes resulting from any combination of interactions, including quadrupolar, dipolar and chemical shift anisotropy, and is not restricted to cases in which the principal axis systems for the different interactions are aligned. Both methods are derived from consideration of the contour lines on a plot of the resonance frequency against the Euler angles, allowing the intensity of the lineshape to be calculated at each frequency. Consequently, highly accurate lineshapes can be calculated more rapidly than previously possible, since only orientations contributing to each specific frequency are considered. For our semi-analytical method, the intensity of each point in the lineshape can be directly calculated in tens of milliseconds on a standard PC. In contrast, established methods can take several hours to calculate the same lineshape.     

The refocused INADEQUATE MAS NMR experiment in multiple spin-systems: interpreting observed correlation peaks and optimising lineshapes

The robustness of the refocused INADEQUATE MAS NMR pulse sequence for probing through-bond connectivities has been demonstrated in a large range of solid-state applications. This pulse sequence nevertheless suffers from artifacts when applied to multispin systems, e.g. uniformly labeled (13)C solids, which distort the lineshapes and can potentially result in misleading correlation peaks. In this paper, we present a detailed account that combines product-operator analysis, numerical simulations and experiments of the behavior of a three-spin system during the refocused INADEQUATE pulse sequence. The origin of undesired anti-phase contributions to the spectral lineshapes are described, and we show that they do not interfere with the observation of long-range correlations (e.g. two-bond (13)C-(13)C correlations). The suppression of undesired contributions to the refocused INADEQUATE spectra is shown to require the removal of zero-quantum coherences within a z-filter. A method is proposed to eliminate zero-quantum coherences through dephasing by heteronuclear dipolar couplings, which leads to pure in-phase spectra.     

Effects of laser linewidth on coherent antiStokes Raman spectroscopy

Expressions for the generated antiStokes spectral density in coherent antiStokes Raman spectroscopy (CARS) are obtained, which take into account the finite linewidths of laser sources and which may be used to analyse observed spectra. Lorentzian and gaussian laser lineshapes are taken as special cases, which enable further analytic results for single and multiline CARS spectra to be derived. Emphasis is placed on scanning and broadband (multiplex) CARS techniques, and the choice of laser sources discussed from the spectral point of view. As examples of multiline spectra an analytical account of a periodic spectrum is presented and temperature measurement from Q-branch spectra is treated.     

The single basis filter diagonalization method: a rapid multidimensional data processing scheme

A new way to apply the filter diagonalization method (FDM) that results in a large increase in the speed of calculation of multidimensional NMR spectra is presented. The speed increase is accompanied by slight differences in spectral lineshapes, although frequency estimates remain essentially identical. For contoured spectra, the method does not result in appreciable differences from the full FDM calculation. Optimal parameter sets for an FDM calculation can be estimated far more rapidly, which makes the FDM more straightforward to employ in practice. The performance of the method versus the full FDM was investigated for both model and experimental signals. The effect of noise on the method was also studied.     

High Spatial Resolution Multi-Site EPR Oximetry: The Use of a Convolution-Based Fitting Method

We describe a new method to enhance the spatial resolution of multi-site electron paramagnetic resonance (EPR) oximetry. The method is suitable for any shape (density distribution function) of a solid paramagnetic material implanted in tissue. It corrects distortions of lineshapes caused by the gradient and thus overcomes limitations of previous multi-site EPR oximetry methods that restricted the ratio of the particle size to the distance between sites. The new method is based on consecutive applications of magnetic field gradients with the same direction but with a different magnitude and uses a convolution-based fitting algorithm to derive Lorentzian EPR linewidths of each individual peak of the EPR spectrum. The method is applicable for any particulate EPR oxygen sensitive materials whose EPR spectra can be approximated by a Lorentzian function or a superposition of Lorentzian functions. By incorporating this model of the lineshape in the data processing, we are able to decrease significantly the number of parameters needed for the calculations and to recover the oxygen concentration, even from quite noisy spectra. We (i) describe our method and the data-processing algorithm, (ii) demonstrate our approach in model and in vivo experiments, and (iii) discuss the limitations.     

PRAWN: mixing sequences for selective heteronuclear J cross polarization

In this work, we present a family of pulse sequences for selective heteronuclear J cross-polarization (JCP), which we have developed especially for indirect 13C imaging using JCP, for example in the CYCLCROP environment. The sequences are straightforward to implement and operate reliably. Results of an average Hamiltonian analysis are given for the basic sequence, which we term PRAWN (pulsed rotating frame transfer sequence with windows). It is shown experimentally that the pulse sequence, which operates efficiently with low RF duty cycles down to a few percent, has a useful tolerance range to absolute Hartmann-Hahn mismatch and generates coherence transfer spectra in close correspondence with the JCP average Hamiltonian. Computer simulation of the performance of the basic sequence on a heteronuclear spin-(1/2) AX system is also presented. The mismatch compensation of PRAWN may be markedly enhanced further by issuing a pi pulse to each spin halfway through the basic PRAWN train and in phase quadrature to it. A simple analysis of this modified sequence, PRAWN-pi, is given under conditions of mismatch and off-resonance irradiation.     

Spin pair geometry revealed by high-field DEER in the presence of conformational distributions

Orientation selection on two nitroxide-labelled shape-persistent molecules is demonstrated by high-field pulsed electron-electron double resonance experiments at a frequency of 95 GHz with a commercial spectrometer. The experiments are performed with fixed observer and pump frequencies by variation of the magnetic field, so that the variation of both the dipolar frequencies and the modulation depths can be analyzed. By applying the deadtime-free four-pulse double electron-electron resonance (DEER) sequence, the lineshapes of the dipolar spectra are obtained. In the investigated linear biradical and equilateral triradical the nitroxide labels undergo restricted dynamics, so that their relative orientations are not fixed, but are correlated to some extent. In this situation, the general dependence of the dipolar spectra on the observer field can be satisfyingly modelled by simple geometrical models that involve only one rotational degree of freedom for the biradical and two rotational degrees of freedom for the triradical. A somewhat better agreement of the dipolar lineshapes for the biradical is obtained by simulations based on a molecular dynamics trajectory. For the triradical, small but significant deviations of the lineshape are observed with both models, indicating that the technique can reveal deficiencies in modelling of the conformational ensemble of a macromolecule.