Fourier synthesis techniques for NMR spectroscopy in inhomogeneous fields

This paper describes a method for synthesizing spin rotations with arbitrary space dependence on a sample of noninteracting spin 12 by using nonselective radio frequency pulses and pulsed field gradients. This method is used to map out spatial distribution of inhomogeneous B(0) field and to engineer a space dependent evolution of spins that cancels the space dependent phase spins acquire when precessing in an inhomogeneous magnetic field. The technique allows one to record high resolution spectra in inhomogeneous magnetic field by using only time varying linear gradients and rf fields and is expected to find applications in ex situ NMR.     

Applications of pi-photon-induced transparency in two-frequency pulse electron paramagnetic resonance experiments

An approach to pulse electron paramagnetic resonance (EPR) experiments which are based on two different resonance fields is introduced. Instead of using two microwave (mw) sources or a magnetic field jump, bichromatic pulses consisting of a transverse microwave field with frequency omega(mw) and a longitudinal radio frequency field with frequency omega(rf) are employed. Such bichromatic pulses excite a number of multiple photon transitions at frequencies omega(mw)+komega(rf) (k in Z). The pi-photon-induced transparency phenomenon is used to select the required transitions. This approach is used in the stimulated soft electron spin echo envelope modulation and the four-pulse double electron-electron resonance experiments. The results obtained using the bichromatic pulse approach are in agreement with those obtained with the standard pulse EPR techniques. It is shown that applying bichromatic pulses is straightforward and advantageous in several respects.     

Fourier decompositions and pulse sequence design algorithms for nuclear magnetic resonance in inhomogeneous fields

In this paper, we introduce algorithms based on Fourier synthesis for designing phase compensating rf pulse sequences for high-resolution nuclear magnetic resonance (NMR) spectroscopy in an inhomogeneous B0 field. We show that using radio frequency pulses and time varying linear gradients in three dimensions, it is possible to impart the transverse magnetization of spins phase, which is a desired function of the spatial (x,y,z) location. Such a sequence can be used to precompensate the phase that will be acquired by spins at different spatial locations due to inhomogeneous magnetic fields. With this precompensation, the chemical shift information of the spins can be reliably extracted and high resolution NMR spectrum can be obtained.     

On the Tuning of High‐Resolution NMR Probes

Three optimum conditions for the tuning of NMR probes are compared: the conventional tuning optimum, which is based on radio‐frequency pulse efficiency, the spin noise tuning optimum based on the line shape of the spin noise signal, and the newly introduced frequency shift tuning optimum, which minimizes the frequency pushing effect on strong signals. The latter results if the radiation damping feedback field is not in perfect quadrature to the precessing magnetization. According to the conventional RLC (resistor–inductor–capacitor) resonant circuit model, the optima should be identical, but significant deviations are found experimentally at low temperatures, in particular on cryogenically cooled probes. The existence of different optima with respect to frequency pushing and spin noise line shape has important consequences on the nonlinearity of spin dynamics at high polarization levels and the implementation of experiments on cold probes.     

Use of Nuclear Spin Noise Spectroscopy to Monitor Slow Magnetization Buildup at Millikelvin Temperatures

At ultralow temperatures, longitudinal nuclear magnetic relaxation times become exceedingly long and spectral lines are very broad. These facts pose particular challenges for the measurement of NMR spectra and spin relaxation phenomena. Nuclear spin noise spectroscopy is used to monitor proton spin polarization buildup to thermal equilibrium of a mixture of glycerol, water, and copper oxide nanoparticles at 17.5 mK in a static magnetic field of 2.5 T. Relaxation times determined in such a way are essentially free from perturbations caused by excitation radiofrequency pulses, radiation damping, and insufficient excitation bandwidth. The experimental spin‐lattice relaxation times determined on resonance by saturation recovery with spin noise detection are consistently longer than those determined by using pulse excitation. These longer values are in better accordance with the expected field dependence trend than those obtained by on‐resonance experiments with pulsed excitation.     

J-modulated ADEQUATE experiments using different kinds of refocusing pulses

Owing to the recent developments concerning residual dipolar couplings (RDCs), the interest in methods for the accurate determination of coupling constants is renascenting. We intended to use the J-modulated ADEQUATE experiment by K?vér et al. for the measurement of (13)C - (13)C coupling constants at natural abundance. The use of adiabatic composite chirp pulses instead of the conventional 180 degrees pulses, which compensate for the offset dependence of (13)C 180 degrees pulses, led to irregularities of the line shapes in the indirect dimension causing deviations of the extracted coupling constants. This behaviour was attributed to coupling evolution, during the time of the adiabatic pulse (2 ms), in the J-modulation spin echo. The replacement of this pulse by different kinds of refocusing pulses indicated that a pair of BIPs (broadband inversion pulses), which behave only partially adiabatic, leads to correct line shapes and coupling constants conserving the good sensitivity obtained with adiabatic pulses.     

Broadband inversion for MAS NMR with single-sideband-selective adiabatic pulses

We explain how and under which conditions it is possible to obtain an efficient inversion of an entire sideband family of several hundred kHz using low-power, sideband-selective adiabatic pulses, and we illustrate with some experimental results how this framework opens new avenues in solid-state NMR for manipulating spin systems with wide spinning-sideband (SSB) manifolds. This is achieved through the definition of the criteria of phase and amplitude modulation for designing an adiabatic inversion pulse for rotating solids. In turn, this is based on a framework for representing the Hamiltonian of the spin system in an NMR experiment under magic angle spinning (MAS). Following earlier ideas from Caravatti et al. [J. Magn. Reson. 55, 88 (1983)], the so-called "jolting frame" is used, which is the interaction frame of the anisotropic interaction giving rise to the SSB manifold. In the jolting frame, the shift modulation affecting the nuclear spin is removed, while the Hamiltonian corresponding to the RF field is frequency modulated and acquires a spinning-sideband pattern, specific for each crystallite orientation.     

Offset‐compensated and zero‐quantum suppressed ROESY provides accurate 1H–1H distances in small to medium‐sized molecules

A robust version of the off‐resonance ROESY pulse scheme is suggested for the measurement of proton–proton distances or slow chemical exchange in small to medium‐sized molecules. The method implements adiabatic ramps to establish a pair of opposite frequency off‐resonance spin lock fields – with optionally randomized duration – and adiabatic inversion pulses with simultaneous gradients for efficient zero‐quantum suppression. The amended pulse sequence yields pure absorption cross‐peaks and works safely for small to medium‐sized molecules. The applicability of the method has been demonstrated using small, rigid molecules (strychnine and codeine) and was also applied for a cyclic peptide and a small protein. We found that the pure phase cross‐peaks of the new ROESY version are beneficial for distance measurements. The one‐dimensional (selective) version of the new method is also powerful for measuring selected pair‐wise interactions and distance determination. Copyright © 2016 John Wiley & Sons, Ltd.     

Electron Spin Echo Study of Molecular Structure and Dynamics: New Approaches Based on Spontaneous Fluctuations of Magnetic Interactions

Modulation phenomena that take place during electron spin echo signal decay have long been used in structural studies of free radicals and their environment. These phenomena are based on coherent dynamic effects, arising from simultaneous excitation (by microwave pulses) of two or more transitions in the EPR spectrum. Recently, a new source of stimulated electron spin echo (ESE) modulation was discovered due to spontaneous changes in the magnetic parameters of radicals during the operation of the pulse sequence. For monoradicals, these changes are caused by intramolecular motions. For radical pairs, additional mechanisms are longitudinal relaxation of spin counterparts and transformations of the paramagnetic partners during chemical reactions. Promising applications of this phenomenon to structural studies of radicals and radical pairs in solids and to investigations of their mobility and chemical transformations are considered.     

Pivotal steps towards quantification of molecular diffusion coefficients by NMR.

Using nuclear magnetic resonance (NMR) spectroscopy with a pair of pulsed field gradients (PFGs), Stajeskal and Tanner successfully measured molecular diffusion coefficients in solution in 1965. This method has since been used extensively in various applications, especially after the PFG was implemented in commercial NMR probes. Due to the nonuniformity of the PFG and radio frequency (RF) fields, molecules distributed throughout the sample experience different PFG and RF fields and contribute unevenly to the measured diffusion coefficients, resulting in considerable errors in conventional NMR diffusion experiments. By selective excitation of a central sample region with an offset-independent adiabatic inversion pulse and a PFG, a uniform RF field can be assumed, and the PFG can be represented as a linear approximation. Under these conditions, the molecules diffuse as if they were all experiencing the same effective gradient g(e), leading to a Gaussian signal decay as a function of the PFG strength. Quantitative measurement of molecular diffusion coefficients is therefore made possible. From the diffusion coefficient of a 90 % H(2)O/10 % D(2)O sample, it is convenient to calibrate g(e) with a Java program. In a similar way the nonlinearity of the PFG can be corrected.     

Spin Noise Detection of Nuclear Hyperpolarization at 1.2 K

We report proton spin noise spectra of a hyperpolarized solid sample of commonly used “DNP (dynamic nuclear polarization) juice” containing TEMPOL (4‐hydroxy‐2,2,6,6‐tetramethylpiperidine N‐oxide) and irradiated by a microwave field at a temperature of 1.2 K in a magnetic field of 6.7 T. The line shapes of the spin noise power spectra are sensitive to the variation of the microwave irradiation frequency and change from dip to bump, when the electron Larmor frequency is crossed, which is shown to be in good accordance with theory by simulations. Small but significant deviations from these predictions are observed, which can be related to spin noise and radiation damping phenomena that have been reported in thermally polarized systems. The non‐linear dependence of the spin noise integral on nuclear polarization provides a means to monitor hyperpolarization semi‐quantitatively without any perturbation of the spin system by radio frequency irradiation.     

Signal irreproducibility in high-field solution magnetic resonance experiments caused by spin turbulence

Turbulent spin dynamics arising from the joint action of radiation damping and the distant dipolar field are shown to generate irreproducible measurements in popular high-field, gradient-based magnetic resonance (MR) experiments, undermining the prevailing assumption of essentially predictable observables in MR. Sizeable fluctuations in echo amplitudes are reported and numerically simulated for pulsed gradient spin echo and stimulated echo diffusion measurements. The underlying microscopic dynamical instability is characterized by analysis of the finite-time Lyapunov exponents. Perturbations to the modulated magnetization are shown to render magic-angle gradients ineffective in suppressing signal fluctuations. Alternative approaches are suggested for cancelling out the feedback interactions leading to spin turbulence.     

Optical Kerr effect spectroscopy using time-delayed pairs of pump pulses with orthogonal polarizations

We characterize in detail a recently introduced technique in which perpendicularly polarized pulses with controllable intensities and timing are used for the excitation step in optical Kerr effect spectroscopy. We examine the ratio of pump pulse intensities required to cancel the contribution of reorientational diffusion or of a Raman-active intramolecular vibration to the signal as a function of the delay time between excitation pulses. These results indicate that the signal can be described well as arising from the sum of independent third-order responses initiated by each pump pulse. This conclusion is further supported by using data obtained with a single pump pulse to model decays obtained with two pump pulses.     

Optimal control design of NMR and dynamic nuclear polarization experiments using monotonically convergent algorithms

Optimal control theory has recently been introduced to nuclear magnetic resonance (NMR) spectroscopy as a means to systematically design and optimize pulse sequences for liquid- and solid-state applications. This has so far primarily involved numerical optimization using gradient-based methods, which allow for the optimization of a large number of pulse sequence parameters in a concerted way to maximize the efficiency of transfer between given spin states or shape the nuclear spin Hamiltonian to a particular form, both within a given period of time. Using such tools, a variety of new pulse sequences with improved performance have been developed, and the NMR spin engineers have been challenged to consider alternative routes for analytical experiment design to meet similar performance. In addition, it has lead to increasing demands to the numerical procedures used in the optimization process in terms of computational speed and fast convergence. With the latter aspect in mind, here we introduce an alternative approach to numerical experiment design based on the Krotov formulation of optimal control theory. For practical reasons, the overall radio frequency power delivered to the sample should be minimized to facilitate experimental implementation and avoid excessive sample heating. The presented algorithm makes explicit use of this requirement and iteratively solves the stationary conditions making sure that the maximum of the objective is reached. It is shown that this method is faster per iteration and takes different paths within a control space than gradient-based methods. In the present work, the Krotov approach is demonstrated by the optimization of NMR and dynamic nuclear polarization experiments for various spin systems and using different constraints with respect to radio frequency and microwave power consumption.     

Defeating Radiation Damping and Magnetic Field Inhomogeneity with Spatially Encoded Noise

A simple NMR experiment capable of providing well resolved spectra under conditions where either radiation damping or static magnetic field inhomogeneity would broaden otherwise high‐resolution NMR spectra is introduced. The approach involves using a strong pulsed magnetic field gradient and a selective radio‐frequency pulse to encode a predetermined noise pattern into the spatial distribution of magnetization. Following readout in a much smaller field gradient, the noise sequence may be deconvolved from the acquired data and a high‐resolution spectrum is obtained, eliminating the effects of either radiation damping or the static field inhomogeneity. In the presence of field inhomogeneity a field map is also obtained from the same single transient. A quasi‐two‐dimensional version of the experiment eliminates the need for deconvolution and produces improved results with simplified processing, but without requiring a full two‐dimensional experiment. Example spectra are shown for both radiation damping and one‐dimensional field inhomogeneity with improvement in linewidths of more than a factor of 40.     

New DEFT sequences for the acquisition of one-dimensional carbon NMR spectra of small unlabelled molecules

The acquisition time and quality of 1D 13C{1H} spectra can be improved substantially by using a modified driven equilibrium Fourier transform (DEFT) sequence, which is specifically designed to compensate for the effects of B1 inhomogeneity, pulse miscalibration and frequency offsets. The new sequence, called uniform driven equilibrium Fourier transform (UDEFT), returns the carbon magnetization with a high accuracy along its equilibrium position after each transient is complete. Thus, the sequence allows the use of relaxation delays (RD), which are much shorter than the carbon T1 of the molecule, thereby speeding up the acquisition process of 1D 13C{1H} spectra. To achieve this level of performance, UDEFT employs a refocusing element constituted by a composite adiabatic carbon pulse surrounded by two 90 degrees carbon pulses whose phases are designed to compensate for 90 degrees pulse miscalibrations in an MLEV manner (90 degrees+x-tau(FID)-180+y(Adia)-tau-90 degrees+x-180 degrees+x(Adia)). A version of the UDEFT sequence allows recording 1D 13C{1H} spectra devoid of heteronuclear NOE by using a matched adiabatic 1H decoupling scheme where an even number of 180 degrees adiabatic pulses is applied during the UDEFT module. Spectra of a solution of 300 mM camphor that contains some carbon nuclei with very long T1 relaxation times (90 s and 78 s) were acquired with 128 scans in 10 min using a 5 s relaxation delay.     

Ultra high-resolution NMR: sustained induction decays of long-lived coherences

Long-lived coherences (LLCs) in homonuclear pairs of chemically inequivalent spins can be excited and sustained during protracted radio frequency irradiation periods that alternate with brief windows for signal observation. Fourier transformation of the sustained induction decays recorded in a single scan yields NMR spectra with line-widths in the range 10 < Δν < 100 mHz, even in moderately inhomogeneous magnetic fields. The resulting doublets, which are reminiscent of J-spectra, allow one to determine the sum of scalar and residual dipolar interactions in partly oriented media. The signal intensity can be boosted by several orders of magnitude by "dissolution" dynamic nuclear polarization (DNP).     

Adiabatic pulses in 1H-15N direct and long-range heteronuclear correlations

The application of adiabatic inversion pulses to the detection of (1)H-(15)N heteronuclear correlations is described. The pulse sequences studied were gHSQC, CRISIS-gHSQC, gHMBC and CRISIS-gHMBC. The poor inversion quality of rectangular 180 degrees X pulses can lead to a loss of signal at the peripheries of the spectrum. Replacing these pulses with adiabatic sweeps significantly improves sensitivity across the potentially large (15)N spectral window. Satellite spectrum profiles are shown to demonstrate the increase in sensitivity when employing adiabatic pulses on wide spectral widths. Additionally, the active pharmaceutical nizatidine was used as a model compound to demonstrate the improvements in the long-range correlation data.     

Time-optimal control of spin 1/2 particles in the presence of radiation damping and relaxation

We consider the time-optimal control of an ensemble of uncoupled spin 1/2 particles in the presence of relaxation and radiation damping effects, whose dynamics is governed by nonlinear equations generalizing the standard linear Bloch equations. For a single spin, the optimal control strategy can be fully characterized analytically. However, in order to take into account the inhomogeneity of the static magnetic field, an ensemble of isochromats at different frequencies must be considered. For this case, numerically optimized pulse sequences are computed and the dynamics under the corresponding optimal field is experimentally demonstrated using nuclear magnetic resonance techniques.     

Parahydrogen‐Induced Radio Amplification by Stimulated Emission of Radiation

Radio amplification by stimulated emission of radiation (RASER) was recently discovered in a low‐field NMR spectrometer incorporating a highly specialized radio‐frequency resonator, where a high degree of proton‐spin polarization was achieved by reversible parahydrogen exchange. RASER activity, which results from the coherent coupling between the nuclear spins and the inductive detector, can overcome the limits of frequency resolution in NMR. Here we show that this phenomenon is not limited to low magnetic fields or the use of resonators with high‐quality factors. We use a commercial bench‐top 1.4 T NMR spectrometer in conjunction with pairwise parahydrogen addition producing proton‐hyperpolarized molecules in the Earth's magnetic field (ALTADENA condition) or in a high magnetic field (PASADENA condition) to induce RASER without any radio‐frequency excitation pulses. The results demonstrate that RASER activity can be observed on virtually any NMR spectrometer and measures most of the important NMR parameters with high precision.