We present highly robust, optimal control-based shaped pulses designed to replace all 90{deg} and 180{deg} hard pulses in a given pulse sequence for improved performance. Special attention was devoted to ensuring that the pulses can be simply substit
uted in a one-to-one fashion for the original hard pulses without any additional modification of the existing sequence. The set of four pulses for each nucleus therefore consists of 90{deg} and 180{deg} point-to-point (PP) and universal rotation (UR) pulses of identical duration. These 1 ms pulses provide uniform performance over resonance offsets of 20 kHz (1H) and 35 kHz (13C) and tolerate reasonably large radio frequency (RF) inhomogeneity/miscalibration of (+/-)15% (1H) and (+/-)10% (13C), making them especially suitable for NMR of small-to-medium-sized molecules (for which relaxation effects during the pulse are negligible) at an accessible and widely utilized spectrometer field strength of 600 MHz. The experimental performance of conventional hard-pulse sequences is shown to be greatly improved by incorporating the new pulses, each set referred to as the Fantastic Four (Fanta4).
Broadband inversion pulses that rotate all magnetization components 180 degrees about a given fixed axis are necessary for refocusing and mixing in high-resolution NMR spectroscopy. The relative merits of various methodologies for generating pulses s
uitable for broadband refocusing are considered. The de novo design of 180 degree universal rotation pulses using optimal control can provide improved performance compared to schemes which construct refocusing pulses as composites of existing pulses. The advantages of broadband universal rotation by optimized pulses (BURBOP) are most evident for pulse design that includes tolerance to RF inhomogeneity or miscalibration. We present new modifications of the optimal control algorithm that incorporate symmetry principles and relax conservative limits on peak RF pulse amplitude for short time periods that pose no threat to the probe. We apply them to generate a set of pulses suitable for widespread use in Carbon-13 spectroscopy on the majority of available probes.
