Application of Nutations to Studying the Exchange Processes by the Method of Nuclear Quadrupole Resonance Spectroscopy

A method of direct determining the discontinuous rotational reorientation angles from NQR exchange spectra based on recording of two-dimensional nutations of magnetization after the mixing period is suggested. The possible modification of the Jeener pulse sequence with independently varying duration of pulses for obtaining a 2D exchange nutation spectrum is described. Shapes of singularities in the 2D nutation spectrum of CCl₂- and CCl₃-group reorientations, which depend on the angle _S between C–Cl bonds and on the asymmetry parameter for nonequivalent positions of nuclei participating in the exchange are examined. The 2D exchange NQR nutation spectra of ³⁵Cl in powders prepared from C₂Cl₄ and C₂Cl₆ molecular crystals are modeled. The advantages and capabilities of the method are discussed.     

Determination of Reorientation Angles from Two-Dimensional Exchange Spectra of Powders in Radiospectroscopy

A method for transforming a 2D exchange spectrum into an orientation representation is proposed which is based on finding the reorientation probability as a function of angles. A procedure of evaluation and analysis of two-dimensional magnetic spectra of powders is described and a method for finding the asymmetry parameter from 2D exchange spectra is proposed. The capabilities of the method are illustrated for a model ³⁵Cl 2D nutation exchange NQR spectrum of chloral hydrate CCl₃CH(OH)₂ and an experimental ¹³C 2D exchange NMR spectrum of dimethylsulphone CH₃–SO₂–CH₃. The asymmetry parameter of the chemical shift tensor for this compound is determined.     

Relaxation effects in two-dimensional zero-field nutation NQR spectroscopy

The relaxation and off-resonance effects on the NQR (nuclear quadrupole resonance) nutation frequency and on the damping constant of the nutation spectrum for spinsI = 3/2 are considered. Using the solution of dynamic equations for nuclear magnetisation in the rotating frame, we obtained a general expression for determination of the asymmetry parameter η, which includes the relaxation time and frequency offset. Specific requirements for the RF (radio frequency) field allowing the presence of nutation and the sufficient resolution of nutation spectra are determined. It is shown that at low RF field it is necessary to take into account theT ₂ relaxation effect on the location of frequency singularities in the nutation spectrum. The values ofH ₁ andT ₂ must be exactly known in nutation NQR spectroscopy. The 2D NQR spin-echo separation technique was used for determination of transverse relaxation of individual spin packets in case of inhomogeneously broadened NQR lines, so that the asymmetry parameter could then be determined by the nutation experiment with consideration of relaxation effects and frequency offset. The theoretical results are confirmed experimentally for the narrow and inhomogeneously broadened 2D-nutation NQR spectra in several molecular compounds containing the³⁵Cl and⁷⁵As nuclei.     

Two-dimensional exchange nuclear quadrupole resonance spectroscopy of molecular crystals

A theoretical treatment of the 2D exchange NQR pulse sequence is presented and applied to the quantitative study of exchange processes in molecular crystals. It takes into account the off-resonance irradiation, which critically influences the spin dynamics. The response of a system of spins I = 3/2 in zero applied field, experiencing electric quadrupole couplings, to the three-pulse sequence is analysed. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. The mixing dynamics by exchange and the expected cross-peak intensities as a function of the frequency offset have been derived. The theory is illustrated by a study of the optimization procedure, which is of crucial importance for the detection of the cross- and diagonalpeaks in a 2D exchange spectrum. The systems investigated here were hexachloroethane and tetrachloroethylene, which show threefold and twofold reorientational jumps about the carbon-carbon axis, respectively.     

Off-Resonance Nutation NQR Spectra

Various methods for measuring multivariate nutation NQR spectra under off-resonance conditions are considered. A method is proposed which is based on optimum filtration. An experimental Cl-35 3D nutation NQR spectrum of chloral hydrate is reported for the first time.     

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.     

Determination of mutual orientation of tensor interactions from two-dimensional nutation NQR-spectra of solids

Expressions for singularities of 2D correlation nutation NQR-spectra are obtained. A method is proposed for measuring orientation of two tensor interactions in powder specimens, which relies on specimen re-orientation in an rf-coil within the pulse period between the second and third pulses of a sequence of stimulated echo signal and detection of a 2D nutation NQR spectrum. Feasibilities of the method are discussed and simulated spectra for the case of nuclei with the spin I = 3/2 are reported. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 29–32, January, 2008.     

Recording 2-D Nutation NQR Spectra by Random Sampling Method

The method of random sampling was introduced for the first time in the nutation nuclear quadrupole resonance (NQR) spectroscopy where the nutation spectra show characteristic singularities in the form of shoulders. The analytic formulae for complex two-dimensional (2-D) nutation NQR spectra (I = 3/2) were obtained and the condition for resolving the spectral singularities for small values of an asymmetry parameter η was determined. Our results show that the method of random sampling of a nutation interferogram allows significant reduction of time required to perform a 2-D nutation experiment and does not worsen the spectral resolution.     

Influence of relaxation on the two-dimensional nutational nuclear-quadrupole-resonance spectra

The influence of relaxation and frequency detuning on the nutational frequency and the damping factor of a nutational interference pattern is analyzed. It is established that relaxation leads to decrease in nutational frequency, while detuning increases the nutation frequency. A relation is obtained between the relaxation times and the frequency detuning at which the influence of both factors cancels out. Conditions such that singularities of the nutational nuclear-quadrupole-resonance (NQR) spectrum (I=3/2) may be resolved are determined, and a formula for the asymmetry parameter ν is obtained, taking account of relaxation. Having determined the region of existence of nutation and established the conditions under which the singularities of the NQR spectrum of the powder (I=3/2) may be resolved, the asymmetry parameter may be reliably determined from the experimental nutational spectrum of the powder. Experimental nutational³⁵Cl NQR spectra are given for TiCl₄ and 2,4,6-trichloro-1,3,5-triazine. Kaliningrad State University, Baltiisk State Academy of the Russian Federation, Kaliningrad. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 41, No. 12, pp 66–71, December, 1998.     

自旋I=3/2核四极共振体系对梳状脉冲的响应

用密度矩阵理论和计算机模拟较详细地讨论了自旋I=3/2核四极共振(NQR)粉末体系对梳状脉冲的响应以及偏共振效应的影响.在偏共振强度(包括谱线的非均匀增宽)较小的条件下.由它获得的谱与二维章动谱是相似的.但是实验所需时间能够减少近两个数量级. 关键词：     

Transient NQR signals in the effective field of multipulse trains

This paper is a theoretical analysis of time-dependent nutation and echo signals in the effective field of multipulse trains in NQR. The results of experimental investigations of the same aspects were reported in earlier papers. The various features of dipole-dipole interactions in three-level quadrupole spin systems are discussed. It is shown that, in contrast to NMR, the dipole Hamiltonian in the interaction representation determined by the quadrupole Hamiltonian contains only three diagonal components of the dipole-dipole interaction tensor. On the other hand, the strong inhomogeneous broadening characteristic of NQR hinders exact measurement of these components by ordinary methods. The theoretical analysis suggests that the decay of the echo-signal envelope in the effective field of multipulse trains is determined solely by the dipole relaxation time, which serves as justification of a new experimental method used in measuring the characteristics of the dipole-dipole interaction tensor in spin systems with an inhomogeneously broadened spectrum. Zh. éksp. Teor. Fiz. 115, 1580–1592 (May 1999)     

Application of two-dimensional pulsed EPR nutation spectroscopy to a disordered system with largeg-anisotropy

Two-dimensional (2-D) pulsed electron paramagnetic resonance (EPR) nutation spectroscopy is applied to a disordered system with strongly anisotropicg-factors. The analysis and interpretation of a 2-D nutation spectrum is performed by theoretical calculations appropriate for ferric myoglobin cyanide in frozen solution. The observed and calculated 2-D spectra show broad signals which correspond to the principalg-values. The advantage of nutation spectroscopy is demonstrated by measuring theg _x=0.93 signal, which cannot be observed in a conventional field-swept spectrum due to largeg strain broadening. It is shown that the 2-D nutation experiment can be considered as a sort of an angle-selected method but a nutation spectrum gives a powder pattern even for magnetic field settings at extreme field values of an EPR spectrum. This is in contrast to angle-selected electron nuclear double resonance, which gives a single-crystal type spectrum. The advantage of sine Fourier transform (FT) over complex FT is demonstrated for data processing in the nutation domain. Problems of experimental and data-processing procedures are also discussed.     

Calculations of Multipulse Sequence in NQR of Spins

The general formalism of the interaction representation with respect to an operator which is its own inverse is developed and applied to pure NQR of spins I = . Under the assumption of no relaxation and no dipolar coupling, it is shown that the calculation of the response to pure NQR multipulse sequences can be performed with the same concepts used in high field NMR, such as coherence pathways. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. It takes into account the off-resonance irradiation as well as the angular dependence of the excitation and detection for every value of the electric field gradient asymmetry parameter. Particular attention is devoted to the powder average, which is performed via a probability function derived analytically for the first time, leading to a drastic reduction of simulation times. The theory is illustrated by the study of the optimization and excitation bandwidths of one- to three-pulse sequences and compared to experimental results on Chloranil. We show that the three-pulse “stimulated echo” sequence gives a more uniform excitation profile than the traditional two-pulse echo sequence for powder samples. Thus, the “stimulated echo” sequence could be useful to cover a large spectrum when the experiment duration, or the signal to noise ratio, are not critical parameters. Analytical expressions for the nutation spectra obtained by one or two-pulse sequences are also derived for the first time.     

Comparison of some resolution enhancement methods applied to35Cl-NQR nutation spectroscopy

The³⁵Cl nuclear quadrupole resonance spin echo nutation spectroscopy method was used to determine asymmetry parameters,η, of the electric field gradient tensor in cyanuric chloride, 1,3,5-trichloro-cyanuric acid and 1,3-dichloro-5,5-dimethylhydantoin. For comparison of advantages and drawbacks of some data processing methods we have tried integral transforms of nutation interferogram (pseudo-FID) data (Hankel and Hartley transforms) alternative to the Fourier transform. Another processing method, which provides a power spectrum estimated from time-domain data, is the maximum entropy method (MEM), and we applied the Burg algorithm version of it. We found that MEM gives the best enhancement of the nutation spectrum resolution and the signal-to-noise ratio, provided the number of autocorrelation coefficients is chosen for optimum performance of the Burg algorithm, otherwise estimated singularities in the nutation spectrum can be obscured by multiple spurious peaks or the spectrum resolution is low. In the Hankel transform with the first-order Bessel functions the improvement in resolution is achieved at the expense of the overall signal-to-noise ratio and for noisy experimental data this transform did not show reliable results. The Hartley transform gives a resolution better than the Fourier transform but worse than the two other methods. Unlike the Hankel transform after the Hartley transform the signal-to-noise ratio is not degraded. Theη parameter determined by MEM for cyanuric chloride was 18%, which is close to previously reported values. For 1,3,5-trichloro-cyanuric acidη = 20% and for the two chlorine sites in 1,3-dichloro-5,5-dimethylhydantoinη = 0 and 12% respectively. These values are in substantial agreement with the anticipated double bond character of N-Cl bonds in the two last compounds.     

14N pulsed nuclear quadrupole resonance. 1. Nutation experiments in the case of an axially symmetric electric field gradient tensor

An exact theory based on density matrix calculations is provided for assessing the nuclear quadrupole resonance (NQR) behaviour of a spin 1 (¹⁴N) subjected to a single radio-frequency pulse. It concerns a powder sample in zero magnetic field with the assumption of an axially symmetric electric field gradient tensor. Theoretical results, in terms of signal evolution as a function of the pulse length (nutation experiments), are checked against values of the radio-frequency field amplitude provided by NMR measurements performed with the same equipment. Good agreement between theory and experiment is obtained.     

Determination of the electric field gradient asymmetry from 2D nutation NQR spectra of 75As nuclei in oriented samples of As2Se3 semiconductor

The method of two-dimensional nutation nuclear quadrupole resonance in time domain is used to study the chalcogenide semiconductor As(2)Se(3). In this system, the nuclear quadrupole resonance (NQR) resonance line width is as large as 10 MHz; therefore, the radiofrequency field produced by a pulsed NQR spectrometer can excite only a portion of the nuclear spins. The proposed method relies on polarizing the melted glass specimen in a strong magnetic field so that orientational disorder is partially removed. After hardening the sample is placed in a spectrometer r.f. coil in such a way that that the axes of sample polarization and r.f. coil coincide. We demonstrate the application of this method to determine eta in glassy As(2)Se(3).     

A New Method of Obtaining Structural Information from 2M Exchange NMR and NQR Spectra of Powders

A method of calculating the singularities of two-dimensional correlation spectra of powders and determining the structural parameters with the help of a computer program is described. The opportunities of the method are illustrated on examples of experimental 2M exchange ¹³ C NMR spectra of dimethylsulfone, 2M exchange ² H NMR spectrum of hexamethylbenzene, and model 2M exchange nutational NQR spectrum for spin I = 3/2. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 72–75, August, 2005.     

Calculations of multipulse sequence in NQR of spins 32

The general formalism of the interaction representation with respect to an operator which is its own inverse is developed and applied to pure NQR of spins I = 32. Under the assumption of no relaxation and no dipolar coupling, it is shown that the calculation of the response to pure NQR multipulse sequences can be performed with the same concepts used in high field NMR, such as coherence pathways. All the tools and mathematical expressions to predict the time evolution of the signal created by a pure NQR multipulse sequence are presented explicitly. It takes into account the off-resonance irradiation as well as the angular dependence of the excitation and detection for every value of the electric field gradient asymmetry parameter. Particular attention is devoted to the powder average, which is performed via a probability function derived analytically for the first time, leading to a drastic reduction of simulation times. The theory is illustrated by the study of the optimization and excitation bandwidths of one- to three-pulse sequences and compared to experimental results on Chloranil. We show that the three-pulse "stimulated echo" sequence gives a more uniform excitation profile than the traditional two-pulse echo sequence for powder samples. Thus, the "stimulated echo" sequence could be useful to cover a large spectrum when the experiment duration, or the signal to noise ratio, are not critical parameters. Analytical expressions for the nutation spectra obtained by one or two-pulse sequences are also derived for the first time.     

Two-dimensional on- and off-resonance nutation FFT/MEM NQR spectroscopy

The new two-dimensional nuclear quadrupole resonance experiments based on the principle of nutation spectroscopy, which can be used to determine the asymmetry parameter, and thus the full quadrupolar tensor of spin-3/2 nuclei at zero applied magnetic field are discussed. The problems of reconstructing 2D-nutation NQR spectra using conventional methods and the advantages of using implementation of the maximum entropy method (MEM) are analyzed. Use of the MEM in 2D-NQR spectroscopy can lead to sensitivity improvement, reduction of instrumental artifacts and truncation errors, shortened data acquisition times and automatic suppression of noise, while at the same time increasing the resolution. The possibilities of off-resonance irradiation in nutation experiments are demonstrated experimentally and theoretically. It is shown that the off-resonance nutation spectroscopy is a useful extension of the conventional on-resonance experiments thus facilitating the determination of asymmetry parameters in multiple spectrum. The methods have been successfully demonstrated for the³⁵Cl on-and off-resonance 2D-nutation spectra in polycrystalline 2,4,6-trichloro-1,3,5-triazine.     

Singularties of the shape of the nonresonance nutation spectra of NQR powders

The singularities of nutation NQR spectra for nuclei with spin J=1, 3/2 in the absence of resonance are considered for powders. It is shown that when determining the asymmetry parameter from the frequency characteristics of the nutation spectrum one must take into account the frequency shift of the spectrometer relative to exact resonance. Structural studies of single crystals by nutation spectroscopy are demonstrated to be feasible.Kaliningrad State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 66–72, June, 1995.