Spin dynamics in the modulation frame: application to homonuclear recoupling in magic angle spinning solid-state NMR.

We introduce a family of solid-state NMR pulse sequences that generalizes the concept of second averaging in the modulation frame and therefore provides a new approach to perform magic angle spinning dipolar recoupling experiments. Here, we focus on two particular recoupling mechanisms-cosine modulated rotary resonance (CMpRR) and cosine modulated recoupling with isotropic chemical shift reintroduction (COMICS). The first technique, CMpRR, is based on a cosine modulation of the rf phase and yields broadband double-quantum (DQ) (13)C recoupling using >70 kHz omega(1,C)/2pi rf field for the spinning frequency omega(r)/2=10-30 kHz and (1)H Larmor frequency omega(0,H)/2pi up to 900 MHz. Importantly, for p>or=5, CMpRR recouples efficiently in the absence of (1)H decoupling. Extension to lower p values (3.5<or=p<5) and higher spinning frequencies is possible using low power (1)H irradiation (<0.25 omega(r)/2pi). This phenomenon is explained through higher order cross terms including a homonuclear third spin assisted recoupling mechanism among protons. CMpRR mitigates the heating effects of simultaneous high power (13)C recoupling and (1)H decoupling. The second technique, COMICS, involves low power (13)C irradiation that induces simultaneous recoupling of the (13)C DQ dipolar and isotropic chemical shift terms. In contrast to CMpRR, where the DQ bandwidth (approximately 30 kHz at omega(0,H)/2pi=750 MHz) covers the entire (13)C spectral width, COMICS recoupling, through the reintroduction of the isotropic chemical shift, is selective with respect to the carrier frequency, having a typical bandwidth of approximately 100 Hz. This approach is intended as a general frequency selective method circumventing dipolar truncation (supplementary to R(2) experiments). These new gamma-encoded sequences with attenuated rf requirements extend the applicability of homonuclear recoupling techniques to new regimes--high spinning and Larmor frequencies--and therefore should be of major interest for high resolution biomolecular studies.