Universal Equations for Linear Adiabatic Pulses and Characterization of Partial Adiabaticity

Exploring the limits of broadband excitation and inversion: II. Rf-power optimized pulses

“…Because some of the published pulse shapes are amplitude-modulated, we obtained slightly different values for calculated durations and bandwidths when considering rf-power compared to the ones reported in [21]. The pulses used were the following ones: composite pulses taken from [5,7,8] for excitation and from [2,[5][6][7]14,45] for inversion; sech/ tanh and tanh/tan adiabatic pulses for several bandwidths as described in [46]; BIP [19] and BIBOP [21] inversion pulses, and finally, the pulse shape reported in [44]. As in [21], we numerically determined the maximum bandwidth for which the quality factor U reaches 0.98 for all pulses.…”

Sensitivity enhancement of NMR spectra of half-integer quadrupolar nuclei in the solid state via population transfer

“…For a thorough discussion of HS pulses, the reader is referred to Garwood and coworkers (34,35), Tesiram and Bendall (62), Warnking and Pike (63), and Rosenfeld and Zur (64). Because of its broad and selective excitation inversion profile, the HS pulse has become an invaluable tool as a magnetization inverter in liquid-state NMR applications (62). In contrast to DFS, HS pulses have a nonlinear frequency sweep over the pulse duration.…”

“…12 is the variation of the (a) amplitude, (b) rf phase, and (c) effective frequency of the HS pulse as a function of the total pulse width, T p . The amplitude and frequency of the HS pulse between time zero and T p are given by (33,35,(61)(62)(63) [20] and (61) [21] respectively, which corresponds to shifting the rf phase according to (61):…”

Matrix method for analysis of selective NMR pulses

“…Numerical simulations and experimental measurements under magicangle spinning conditions demonstrate that homonuclear dipolar recoupling can be achieved with adiabatic inversion pulses, obtaining reliable estimates of internuclear distances. In the case of inversion of spins, we have shown that there is a universal method for implementing such adiabatic pulses (31), and performance can be guaranteed provided the pulses chosen operate in the linear adiabatic range. In the case of spin-1/2 nuclei that are initially transverse or where scalar and dipolar couplings are concerned, simulations also need to take into account the evolution of the various single and multiple quantum states.…”

“…In reality, it is this intolerance to changes in RF max that has made the use of adiabatic pulses popular. In terms of tolerance to variation in the magnitude of magnetization states across a discrete spectral width (better known as the "selectivity of the pulse"), this definition incorporates offset-independent adiabaticity (30), because the spectral selectivity (or effective bandwidth, bw eff ) of any adiabatic pulse is related to the extent of the frequency sweep, bwdth, and the duration, T p (31).…”