Fitting of deuterium quadrupole echo spectra with multiple motional models

Dynamic information is generally extracted from deuterium quadrupole echo spectra by matching a spectrum calculated for a particular motional model to the experimental spectrum. In this work, a set of computer programs has been written to facilitate fitting of calculated spectra to experimental spectra that represent from one to five motional models. The fitting program requires pre-calculated libraries of spectra for the models of interest, and accomplishes the fitting either by a systematic method or by simulated annealing. The systematic method is convenient for fitting with one or two motional models, but the simulated annealing method is faster for two or more models, if the libraries are made up of hundreds of spectra. The parameter Q, with the standard deviation of the spectral points estimated as the standard deviation of the baseline noise, provides a stringent measure of goodness of fit. Acceptable fits of experimental data as judged by this criterion have not been found, even in the case of ring flip motion in phenylalanine-d(5) in which the fit may be judged acceptable by eye. An example of fitting with isotropic and methyl rotation motional models of alanine-d(3), which have distinct spectral patterns, shows that it is possible to obtain reasonably accurate estimates of the relative amounts of deuterium representing the different models, even from poorly fitted spectra.     

Generalization of the lineshape useful in magnetic resonance spectroscopy

A new lineshape function is derived from the Tsallis distribution to describe electron paramagnetic resonance (EPR) spectra, and possibly nuclear magnetic resonance (NMR) spectra as well. This lineshape generalizes the Gaussian and Lorentzian lineshapes that are widely used in simulations. The main features of this lineshape function are presented: the normalization, moments, and first derivative. A number of experimental EPR spectra are compared with the results of simulations employing the new lineshape function. The results show that the new lineshape often provides a better approximation of the experimental spectrum. It is also shown that the new parameter of the lineshape function can be used to quantify the intermolecular spin-spin interactions.     

Spectral Intensity and Lineshape Measurements in the First Overtone Band of HF Using Tunable Diode Lasers

High-resolution absorption lineshapes for the P(3) and P(6) transitions of the first overtone (v = 2-0) band of HF at 296 K have been measured using a pair of distributed feedback diode lasers operating near 1.31 and 1.34 μm, respectively. Spectral line intensities and self-broadening parameters were determined by fitting the measured spectra with Voigt, Galatry, and Rautian lineshape models. Voigt profiles fit the low-pressure (<10 Torr) spectra of the P(3) transition reasonably well due to the relatively strong collisional broadening effect. Lineshape measurements of the P(6) transition (for pressures ranging from 5 to 60 Torr) show significant variation from the Voigt lineshape model due to velocity-changing collisions that effectively reduce the Doppler component of the spectral line. Lineshape models that include motional (Dicke) narrowing effects, Galatry (soft collision) and Rautian (hard collision) profiles yield significant improvements in the spectral lineshape fits compared with Voigt profiles. The collisional broadening coefficient (gamma) of the P(6) transition obtained from a Voigt fit is approximately 4% lower than those found with either Galatry or Rautian profile fits. The measured intensities and self-broadening coefficients are compared with values in the HITRAN database and previous measurements. Copyright 1999 Academic Press.     

Lineshapes of spin exchange broadened EPR spectra

An unexplained residual in the fits of theoretical and experimental spectra of exchange broadened nitroxide spin probes reported by Robinson et al. [J. Magn. Reson. 138 (1999) 199] is shown to be understood by inclusion of theoretically predicted lineshape changes into the fitting routine. These lineshape changes provide an additional estimate of the spin exchange frequency that is independent of linewidth methods.     

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.     

Determination of the asymmetry parameter of EFG tensor from moments of NQR nutation spectra in powders

A novel approach to determination of the asymmetry parameter of the EFG tensor from zero-field nutation NQR spectra of the spinI = 3/2 nuclei in powder samples is reported. The proposed theoretical treatment uses lineshape analysis of the nutation NQR spectra by the method of line moments. The analytical formulas for the lineshape of the powder nutation spectrum are given. It is shown that the asymmetry parameter can be determined from the second moment 〈ω²〉 and the frequency of only one singularity ω₂ of the nutation spectrum. It is also shown that the asymmetry parameter can be determined from the second and fourth spectrum moments alone. The method is successfully demonstrated for the simulated nutation NQR spectra of the spinI = 3/2 nuclei in powder samples.     

Comparative study of motions in dimethylsulfone by noise excitation and solid echo spectroscopy

2H NMR spectra of dimethylsulfone were measured with noise excitation and solid echo NMR spectroscopy in the temperature range from 125 to 355 K. Besides the known fact that broad NMR spectra can be measured with both methods, in comparable times it is shown that for noise excitation, the signal loss is negligible compared to echo spectroscopy in the regime when the correlation times of the motions are of the order of magnitude of the echo pulse spacing. For simulating the dynamic NMR spectra acquired with noise excitation, only the motional process must be taken into account and relaxation can be neglected. Furthermore, the problem of restricted acquisition bandwidth in noise NMR spectroscopy is discussed.     

Iterative lineshape analysis of quadrupolar echo spectra of a damped CD(3) quantum rotor: preliminary evidence of a novel mechanism of stochastic spin exchange

It is demonstrated that the wealth of information about damped quantum rotation of CD(3) groups, contained in quadrupolar echo spectra, can be fully explored in a broad temperature range using a method of iterative analysis of the spectral lineshapes. The recently reported lineshape equation which, apart from the quantum tunneling and the dissipative Alexander--Binsch terms, contains an additional dissipative term having no classical analog is shown to be capable of describing even subtle details of the spectra of a crystal of acetylsalicylic acid--CD(3) oriented specifically in the magnetic field. Preliminary evidence of the occurrence of this novel dissipative mechanism in the system studied is reported. The results obtained seem to suggest that there is no "classical limit" in the dissipative behavior of this system.     

Magnetic resonance lineshape in the presence of slow motion

The effect on the magnetic resonance lineshape of slow molecular motion is considered. The molecules are assumed to undergo diffusive jumps of angle ε described by the distribution function W(ε)=(N/τ) exp (λ cos ε), where τ is the mean lifetime between jumps and λ a parameter describing the width of the distribution. As λ is varied from zero to infinity this distribution describes diffusion models that change continuously from the strong collision limit to Brownian rotational diffusion. Magnetic resonance lineshapes are calculated by Freed's method using the asymptotic expansion technique, and results are presented for an axially symmetric (secular) Zeeman hamiltonian.

An exact expression for the magnetic resonance lineshape is derived in the strong collision limit for any secular hamiltonian and a few examples are presented. It is also shown how this technique can be used as a basis for lineshape calculations in the presence of moderately large jumps.     

Spectral parameters for quantitative mobility contrast in NMR imaging of solid polymers

Different procedures based on parameters of the wideline NMR absorption spectrum are presented to obtain localized molecular mobility contrast for imaging of solid polymers. For this purpose a ¹H-NMR imaging technique with magic sandwich echoes is used for acquiring localized wideline spectra. With samples composed of polystyrene and high impact strength polystyrene, and polycarbonate and low density polyethylene a spatial difference in NMR absorption spectrum lineshape and linewidth is displayed. Furthermore, the spatial distribution of rigid and mobile domains in a heterogeneous polymer can be derived from the NMR spectral components. It is demonstrated that a van Vleck moment analysis can be performed from spatially resolved magic echo decays. The second (M₂) and fourth (M₄) moments of the rigid components show considerable variation with the spatial composition of the investigated samples.     

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.     

A solid-state deuterium NMR study of internal rotation in p-nitroaniline

Deuterium quadrupole echo spectra have been obtained at 55.3 MHz and several temperatures between 26 and 133°C for samples of solid p-nitroaniline, deuterated either in the amino group or in the 2,6 positions of the aromatic ring. At all temperatures, the aromatic deuterons exhibit a simple rigid lattice powder pattern which is accurately simulated using a quadrupole coupling constant of 174 ± 1 kHz and asymmetry parameter 0.06 ± 0.02. Quadrupole echo spectra for the amino deuterons show features characteristic of 180° flips about the D-N-D bisector, and the activation energy for this motion is found to be 49 ± 6 kJ/mol, with a rate k = (5.2 ± 0.3) × 10⁵ s⁻¹ at 133°C. For the amino deuterons, the dependence of echo amplitude and spectral lineshape on pulse spacing includes contributions from heteronuclear dipolar coupling as well as from internal rotation. This makes the extraction of accurate rates difficult, unless the lineshape data are supplemented by independent information. The spin-lattice relaxation rate, which is dominated by the flipping motion at high temperature, is very useful in this regard.     

NMR lineshape equations for hindered methyl group: a comparison of the semi-classical and quantum mechanical models

The semiclassical and quantum mechanical NMR lineshape equations for a hindered methyl group are compared. In both the approaches, the stochastic dynamics can be interpreted in terms of a progressive symmetrization of the spin density matrix. However, the respective ways of achieving the same limiting symmetry can be remarkably different. From numerical lineshape simulations it is inferred that in the regime of intermediate exchange, where the conventional theory predicts occurrence of a single Lorentzian, the actual spectrum can have nontrivial features. This observation may open new perspectives in the search for nonclassical effects in the stochastic behavior of methyl groups in liquid-phase NMR.     

Lineshape analysis of photoreflectance spectra from InGaAs/GaAs quantum wells

The fundamental optical transitions in In_0.15Ga_0.85As/GaAs single symmetric quantum wells (QWs) are studied through photoreflectance (PR) measurements and their dependence on the well distance from the surface. A phase rotation of the lineshape of the PR signal is observed as was predicted in our previous works. PR spectra of several samples, measured at 77 K, are compared with results of PR lineshape calculations, and a fairly good agreement is found. The quantum-confined Stark effect is shown to be the dominant modulation mechanism in the QW. Pronounced interference effects make PR spectra from QWs sensitive to the cap layer thickness.     

Relaxation effects in resonance Raman spectra

A density-matrix theory of resonance scattering spectroscopy is presented to characterize the relaxation processes which may be studied in these spectra. The distinction between Resonance Raman and Fluorescence emerges clearly from this treatment. It is shown that novel properties of the rotational and vibrational relaxation may be obtained from the lineshape of the scattered light. A new effect is discovered in the Resonance Raman excitation profile which, in principle, could be used to study the relaxation rate between specific vibronic levels of an excited electronic state.     

头盔的声学性能测试与分析

本文设计了使用自相关函数以测试混响声衰变速度、自功率谱以测试插入损失的方法，用于头盔的回声与隔声效果分析．结果表明，这一方法物理概念明确，测试简单，可以定量地说明头盔的声学性能可能存在的问题，可望用于头盔的声学性能客观测试与分析方法的建立．