Analytical optimization of active bandwidth and quality factor for TOCSY experiments in NMR spectroscopy.

Active bandwidth and global quality factor are the two main metrics used to quantitatively compare the performance of TOCSY mixing sequences. Active bandwidth refers to the spectral region over which at least 50 % of the magnetization is transferred via a coupling. Global quality factor scores mixing sequences according to the worst-case transfer over a range of possible mixing times and chemical shifts. Both metrics reward high transfer efficiency away from the main diagonal of a two-dimensional spectrum. They can therefore be used to design mixing sequences that will function favorably in experiments. Here, we develop optimization methods tailored to these two metrics, including precise control of off-diagonal cross peak buildup rates. These methods produce square shaped transfer efficiency profiles, directly matching the desirable properties that the metrics are intended to measure. The optimization methods are analytical, rather than numerical. The two resultant shaped pulses have significantly higher active bandwidth and quality factor, respectively, than all other known sequences. They are therefore highly suitable for use in NMR spectroscopy. We include experimental verification of these improved waveforms on small molecule and protein samples.