Resonance Offsets Research Articles

Double quantum coherence in pure nuclear quadrupole resonance spectroscopy

The results of a theoretical investigation on double quantum coherence in pure nuclear quadrupole resonance (NQR) for spin I = 5 2 with axial symmetry in a single crystal are presented. Using the tensor operator formalism it is shown that the creation and detection of double quantum coherence can be done by the application of a pulse scheme of the form (π/2) x (2ω Q)(π) x (ω Q)-τ-(π) x (2ω Q). The effect of resonance off-set on the double quantum coherence is also considered.

An analysis of fast imaging sequences with steady-state transverse magnetization refocusing.

Recently, several groups have proposed and demonstrated the use of rapid imaging methods, using short pulse repetition times and gradient-reversal echoes. Here, we analyze the behavior of the magnetization and the resulting image contrasts in such sequences for the case where the pulse repetition time TR is of the order of, or shorter than, the transverse relaxation time T2, and the transverse magnetization is not destroyed between phase-encoding cycles. Exact analytical expressions describing the signal evolution between the pulses are derived, taking into account the effects of resonance offsets and flip angles, and examining the influence of constant-phase or alternate-phase RF pulse trains. It is shown that for typical imaging sequences two distinct echo signals will develop between pulses, which may have a detrimental effect on image quality if they partially overlap within the sampling window. It is shown that artifact-free images can be obtained only if the two echo signals overlap precisely, which seems technically close to impossible to achieve, or if they are sufficiently separated in time to allow sampling of only one of the signals.

Three-spin effects in broadband decoupling

Current procedures for broadband decoupling in carbon-13 spectroscopy are slightly perturbed by a new phenomenon called the “three-spin effect.” It arises when there is a spin-spin coupling between two nonequivalent protons and introduces spurious splittings into the carbon-13 spectrum. These are normally too weak to be resolved, leaving a slight line-broadening effect. The three-spin effect is treated theoretically and shown to be a result of bilinear terms in the propagator equation, not compensated by the action of the decoupling sequence. The general case is too complicated to be treated analytically but numerical methods demonstrate that the magnitude of the effect is proportional to the value of the proton-proton coupling constant and the direct proton-carbon coupling constant but virtually independent of the small long-range proton-carbon coupling. The magnitude of the splitting is inversely proportional to the level at which the decoupler operates and is a complex function of the two proton resonance offsets. The effect vanishes if the two protons have the same chemical shift or if the distant proton lies outside the effective bandwidth of the decoupler. Splitting due to the three-spin effect is demonstrated experimentally for an extreme case where there is a large ( trans) proton-proton coupling and an unrealistically low decoupler level (750 Hz). The form of the spectrum is in excellent agreement with computer simulations which take into account the spatial inhomogeneity of the decoupler field.

Homonuclear Hartmann-Hahn effects in broadband decoupling

The technique of noise decoupling is gradually being replaced by new deterministic pulse sequences (I-4) for broadband heteronuclear decoupling, allowing very high resolution with minimal radiofrequency heating. For example, the WALTZ-16 sequence (3, 4) can be used to achieve decoupled carbon-l 3 linewidths of the order of 0.0 1 Hz provided that there is good control of the probe temperature to avoid broadening by temperature-dependent chemical shifts (5). WALTZ-16 has also been used to decouple carbon13 from protons (6), a particularly demanding application in view of the large chemical-shift range of the carbon13 nucleus. In applications where decoupling efficiency is of prime importance, for instance, in vivo carbon13 spectroscopy, where even kilowatt transmitters may only produce & fields of the order of I kHz at the region of interest, the GARP decoupling sequence (7) may prove to be useful; it has an effective decoupling bandwidth ABIB = k2.4. Although few applications require the very high resolution mentioned above, it is disconcerting to see two recent reports (8,5) of instances where WALTZ16 decoupling falls short of its expected performance with regard to the residual carbon-l 3 linewidth. For instance, certain ethyl groups (8) give unexpectedly large residual linewidths, even when other carbon13 resonances in the same molecule decouple as expected. As an example, Fig. 1 shows the carbon-13 spectrum of a mixture of alcohols; the ethyl resonances, and the methine carbon of isopropanol are particularly broad. This effect is relatively independent of the decoupler offset and becomes more pronounced as the decoupler power is decreased. Is all well with decoupling theory? HOHAHA! We believe that these “anomalous” linewidths are due to magnetization transfer between coupled protons through the homonuclear Hartmann-Hahn “HOHAHA” effect (9, 10). Modern decoupling sequences are based on the use of a composite 180” pulse (R) that provides good I spin inversion over a wide range of resonance offsets. This is combined with its phaseinverted counterpart R in a “magic cycle” R R l? 2 and any remaining imperfections are minimized by an expansion into a “supercycle” (I 1). This prescription assumes that the I-spin offset remains constant throughout the decoupling cycle (12). This will not be the case if there is transfer of I spin magnetization from one chemical site to another, a process which can occur when there is scalar coupling between I spins and magnetization transfer in the rotating reference frame-the homonuclear analogue of the classic Hartmann-Hahn experiment (9). There are well-documented instances of Hartmann-Hahn transfer in liquid-phase experiments (13, 14). The condition for efficient transfer is that the two sites have essentially equal precession frequencies in their respective rotating reference frames. For the heteronuclear case, this normally

Composite pulses without phase distortion

Composite pulses for broadband spin excitation over large ranges of radiofrequency field amplitudes and resonance offsets are presented. They are derived according to a previously presented method based on the Magnus expansion in the manner of coherent averaging theory. It is shown theoretically and in simulations that these composite pulses do not introduce a strong dependence of the NMR signal phase on the rf amplitude or resonance offset, overcoming a common problem of composite pulses derived by other means. Experimental demonstrations include the use of composite π pulses for refocusing transverse magnetization in spin-echo sequences and the use of composite π 2 pulses in a simple multiple-pulse experiment. Further applications are discussed.

Iterative schemes for broad-band and narrow-band population inversion in NMR

We derive iterative schemes for generating rf pulse sequences that invert nuclear spin populations over either broad or narrow ranges of resonance offsets and rf amplitudes. The schemes employ only phase shifting and concatenation operations. Iterative application of a scheme produces a series of pulse sequences with successive improvements in population inversion performance.

Multiphoton NMR spectroscopy on a spin system with I=1/2

Multiple quantum effects in double frequency (df) pulsed NMR experiments on multilevel spin systems are studied. In these experiments, the spin systems are irradiated by two rf fields, applied simultaneously. A general theoretical description of these experiments is presented using the theory of Shirley for time dependent Hamiltonians. Multiphoton resonance conditions are given and time independent fictitious spin-1/2 Hamiltonians are derived using his perturbation theory treatment. With these Hamiltonians, the evolution of the spin systems during df irradiation is approximated. The example of df NMR experiments on an I=1/2 spin system is discussed. High order perturbation theory is developed to describe the time evolution of this spin system at a three photon resonance. Accurate computer calculations are performed to examine this time evolution. Df NMR experiments are performed on the single 31P(I=1/2) transition of phosphoric acid to check the theoretical results. The three photon resonance condition for these measurements is studied as a function of the rf irradiation intensities and of the resonance offsets of the two frequency components of df irradiation fields. Special NMR pulse cycles are used to study the dependence of the phase of the coherence created by df pulses on the initial rf phases of the two frequency components. Spin-echo type of experiments are developed to detect the spiral motion of the magnetization vector of the I=1/2 spin system at the three-photon resonance.

Resonance Offset Effects in Multiple-Pulse NMR Experiments

The behavior of multiple-pulse NMR line narrowing experiments in solids as a function of the frequency offset from resonance is examined experimentally and theoretically. Resolution in the four-pulse, six-pulse, and phase-alternated tetrahedral angle experiments was found to increase on going off resonance. These results are explained using coherent averaging theory. The effective Hamiltonian which determines the width of the spectral line off resonance must be averaged over the motion caused by both the rf pulse Hamiltonian and the resonance offset Hamiltonian. It is assumed that the period of the motion caused by one of these two cyclic Hamiltonians is much shorter than the other so that the averages can be carried out sequentially rather than simultaneously. Two relaxation rates are evident in the four-pulse experiment on solids, corresponding to relaxation parallel and perpendicular to one of the body diagonals, e.g., the (111) direction, in the coordinate frame appropriate to that experiment. For solids containing a single magnetic nuclear species the two rates appear to be equal on resonance, but off resonance relaxation along the (111) direction is slower than relaxation perpendicular to it. This behavior is explained qualitatively by the fact that average Hamiltonians which do not in general commute with (Ix + Iy + Iz) do commute with this operator when they are further averaged over the motion caused by an offset from resonance. The effective heteronuclear dipole–dipole interaction Hamiltonian commutes with (Ix + Iy + Iz) both on and off resonance, which accounts for the difference in the two relaxation rates independent of resonance offset observed in solids containing more than one magnetic nuclear species.

On the dense phases of He 3 at very low temperatures : Louis Goldstein

Excitation of electron spins with monochromatic rectangular pulses is limited to bandwidths that are smaller than the spectral widths of most organic radicals and much smaller than the spectral widths of transition and rare earth metal ions. With frequency-swept pulses, bandwidths of up to 800 MHz have previously been attained for excitation and detection of spin packets at frequencies of about 9.6 GHz and bandwidths of up to 2.5 GHz in a polarization transfer experiment at frequencies of about 34 GHz. The remaining limitations, mainly due to resonator bandwidth and due to pulse length restrictions are discussed. Flip angles for state-space rotations on passage of a transition can generally be computed from the critical adiabaticity by the Landau-Zener-Stückelberg-Majorana expression. For hyperbolic secant pulses, the Demkov-Kunike model describes excitation for spin packets within and outside the sweep range. Well within the sweep range, the Bloch-Siegert phase shift is proportional to critical adiabaticity to a very good approximation. Because of the dependence of both flip angle and coherence phase on critical adiabaticity, it is advantageous to use pairs of amplitude and frequency modulation functions that provide such offset-independent adiabaticity. Compensation for the resonator response function should restore offset-independent adiabaticity. Whereas resonance offsets and Bloch-Siegert phase can be refocused at certain pulse length ratios, phase dispersion in coupled spin systems cannot generally be refocused. Based on the bandwidth limitations that arise from spin dynamics, requirements are derived for a spectrometer that achieves precise spin control over wide bands. The design of such a spectrometer and hardware characterization by EPR experiments are discussed.