Symmetry principles for the design of radiofrequency pulse sequences in the nuclear magnetic resonance of rotating solids

Some new symmetry theorems are presented which simplify the task of designing multiple-pulse radio-frequency pulse sequences in magic-angle-spinning solid-state NMR. The symmetry theorems apply to sequences denoted RN_n^ν, which consists of N repetitions of a pulse sequence element R, alternating in phase between the values ±πν/N. Each R element ideally rotates the spins by an angle π about the rotating frame x-axis. The entire RN_n^ν sequence is timed to span n rotational periods. Applications are presented for homonuclear double-quantum and zero-quantum recoupling, heteronuclear decoupling and heteronuclear recoupling.