Helen Geen

Band-selective radiofrequency pulses

A theoretical treatment is given of the general problem of designing amplitude-modulated radiofrequency pulses that will excite a specified band of frequencies within a high-resolution NMR spectrum with uniform intensity and phase but with negligible excitation elsewhere. First a trial pulse envelope is defined in terms of a finite Fourier series and its frequency-domain profile calculated through the Bloch equations. The result is compared with the desired target profile to give a multidimensional error surface. The method of simulated annealing is then used to find the global minimum on this surface and the result refined by standard gradient-descent optimization. In this manner, a family of new shaped radio-frequency pulses, known as BURP (band-selective, uniform response, pure-phase) pulses, has been created. These are of two classes—pulses that excite or invert z magnetization and those that act as general-rotation πr/2 or π pulses irrespective of the initial condition of the nuclear magnetization. It was found convenient to design the latter class as amplitude-modulated time-symmetric pulses. Tables of Fourier coefficients and pulse-shape ordinates are given for practical implementation of BURP pulses, together with the calculated frequency-domain responses and experimental verifications. Examples of the application of band-selective pulses in conventional and multidimensional spectroscopy are given. Pure-phase pulses of this type should also find applications in magnetic resonance imaging where refocusing schemes are undesirable.

Solid-state proton multiple-quantum NMR spectroscopy with fast magic angle spinning

Abstract The feasibility of multiple-quantum NMR spectroscopy with high resolution for protons in solids is explored. A new multiple-quantum excitation sequence suitable for use with fast magic angle spinning is described, and its performance is compared to that of both static and slow-spinning multiple-quantum methods. Modified sequences with scale the rate of development of the multiple-quantum coherences are also demonstrated, and two-dimensional double-quantum spectra of adamantane and polycarbonate are presented.

Band-Selective Pulses without Phase Distortion. A Simulated Annealing Approach

The design of shaped pulses for selective excitation experiments has received much attention in the fields of both high-resolution NMR and magnetic resonance imaging. The simplest pulse shape is rectangular, but the excitation profile has an undesirable “sine function” shape with side lobes extending a considerable distance from resonance. Pulse shaping can improve the frequency-domain response by localizing the excitation to a selected region around resonance, the most popular time-domain shaping functions being the Gaussian ( 1), Hermite (2), and “sine” pulses (3, 4). Although these shaped pulses succeed in eliminating side-lobe responses, they have the disadvantage that the excited signals exhibit a large frequency-dependent phase shift. Several authors have addressed this important problem (5-7). Fourier theory (8) predicts that all symmetric, purely amplitude-modulated pulses give rise to a linear phase error. Gaussian, Hermite, and sine pulses fall into this category. In many simple experiments a linear phase error across the spectrum can be corrected by conventional software routines, but if the spectrum contains broad lines this introduces an undesirable “rolling baseline.” In magnetic resonance imaging, a linear phase error can be corrected by reversing the direction of the field gradient immediately after the selective pulse, and allowing a suitable delay during which the magnetization can refocus. Field gradient reversal is not an option in high-resolution NMR, but the same effect can be achieved by a hard 180” refocusing pulse followed by a period of free precession ( 9). These methods suffer from the disadvantage that the refocusing delay causes extra signal loss due to relaxation; in addition, the 180” pulse method aggravates phase errors due to homonuclear spin-spin coupling. We describe here the design of shaped pulses which minimize such phase distortions. The resulting magnetization trajectories can be said to possess a self-focusing property. All signals are then in the pure absorption mode, an important consideration for coherence transfer and other experiments. In magnetic resonance imaging, much attention has been given to the problem of designing a pulse with a rectangular frequency-domain excitation profile-the socalled “top-hat” response. Computer optimization methods have proved popular, leading to a variety of elaborate modulation schemes (10-12). For practical reasons

Band-selective excitation for multidimensional NMR spectroscopy

We have used this method to design radiofrequency pulse shapes which excite essentially pure absorption signals with a «top-hat» profile. That is to say, the absorption-mode signal is near unity over a prescribed range of frequencies ΔF and essentially zero elsewhere, except for two narrow transitional regions Δf wide on either side of the principal excitation. The dispersion-mode signal is kept small everywhere

Improved scalar shift correlation NMR spectroscopy in solids

New isotropic mixing sequences suitable for scalar correlation experiments in solids have been designed using symmetry principles similar to those employed in the construction of the C7 dipolar recoupling sequence. Compared with existing methods, the new isotropic mixing sequences are appropriate for use with faster MAS rates and show improved magnetization transfer efficiencies for carbon-13.

Two-dimensional MAS-NMR spectra which correlate fast and slow magic angle spinning sideband patterns

Abstract A new NMR experiment which allows a measurement of the chemical shift anisotropy (CSA) tensor under magic angle spinning (MAS) is described. This correlates a fast MAS spectrum in the ω 2 dimension with a sideband pattern in ω 1 in which the intensities mimic those for a sample spinning at a fraction of the rate ω r / N . This method is particularly useful for accurately measuring narrow shift anisotropies. Since the sidebands intensities in ω 1 are identical to those expected at ω r / N , standard methods can be used to extract the principal tensor components. The nature of the experiment is such that a minimal number of t 1 increments is required.

HETERONUCLEAR MAGNETIZATION-TRANSFER IN RAPIDLY SPINNING SOLIDS

Abstract A new multi-pulse sequence is presented for heteronuclear magnetization transfer in solid-state NMR spectroscopy by isotropic mixing in samples undergoing fast magic angle spinning (MAS) at speeds exceeding the breadth of the static spectrum. The sequence has been designed by considering the behaviour of the lowest-order contribution to the average Hamiltonian resulting from a series of short radio-frequency pulses applied at specific times relative to the sample rotation period, an approximation which proves reasonable for the systems studied here at MAS speeds of about 15 kHz. Experiments show that the sequence enables magnetization transfer from protons to carbon-13 by reintroducing a heteronuclear dipolar coupling interaction at spinning speeds where the efficiency of conventional Hartmann-Hahn cross polarization becomes significantly reduced.

Theoretical design of amplitude-modulated pulses for spin decoupling in nuclear magnetic resonance

The problem of low-power spin decoupling over a broad range of chemical shifts in liquid-state nuclear magnetic resonance (NMR) is addressed through the design of periodic amplitude-modulated irradiation schemes. A principal feature of these is the composition of each decoupling period which contains a single modulated pulse in place of a composite-pulse train of the kind used traditionally. To satisfy the theoretical criterion for decoupling, the pulse amplitude is shaped such that the propagator is made cyclic and broadband, meaning here that it equals the identity matrix over a frequency range which is broad compared to the root-mean-square (RMS) pulse amplitude. The method of design is based on the use of the Floquet formalism to provide insight into the influence of the modulation on the dynamics of the irradiated spin-. Modulation functions formed from simple Fourier series are derived in the first instance using perturbation theory to impose the required cyclicity on the propagator. Broader bandwidth solutions are then obtained by the addition of higher-order Fourier components. Finally, numerical refinement of a selected solution is shown to raise the decoupling quality to the standards acceptable in routine high-resolution NMR.