Correspondence between spin-dynamic phases and pulse program phases of NMR spectrometers

Spin state selective experiments have become very useful tools in solution NMR spectroscopy, particularly in the context of TROSY line narrowing. However, the practical implementation of such pulse sequences is frequently complicated by unexpected instrument behavior. Furthermore, a literal theoretical analysis of sequences published with specific phase settings can fail to rationalize such experiments and can seemingly contradict experimental findings. In this communication, we develop a practical approach to this ostensible paradox. Spin-dynamic design, rationalization, and simulation of NMR pulse sequences, as well as their confident and reliable implementation across current spectrometer hardware platforms, require precise understanding of the underlying nutation axis conventions. While currently often approached empirically, we demonstrate with a simple but general pulse program how to uncover these correspondences a priori in the general case. From this, we deduce a correspondence table between the spin-dynamic phases used in NMR theory and simulation on the one hand and pulse program phases of current commercial spectrometers on the other. As a practical application of these results, we analyze implementations of the original (1)H-(15)N TROSY experiment and illustrate how steady-state magnetization can be predictably, rather than empirically, added to a desired component. We show why and under which circumstances a literal adoption of phases from published sequences can lead to incorrect results. We suggest that pulse sequences should be consistently given with spin-dynamically correct (physical) phases, rather than in spectrometer-specific (software) syntax.