Spin dynamics of polarization inversion spin exchange at the magic angle in multiple spin systems

Polarization inversion spin exchange at the magic angle (PISEMA) [J. Magn. Reson. A 109, 270 (1994)] is an important experiment in NMR structural characterization of membrane proteins in oriented lipid bilayers. This paper presents a theoretical and experimental study of the spin dynamics in PISEMA to investigate the line-narrowing mechanism. The study focuses on the effect of neighboring protons on the spin exchange of a strongly coupled spin pair. The spin exchange is solved analytically for simple spin systems and is numerically simulated for many-spin systems. The results show that the dipolar couplings from the neighboring protons of a strongly coupled spin pair perturb the spin exchange only in the second order, therefore it has little contribution to the linewidth of PISEMA spectra in comparison to the separated-local-field spectra. The effects from proton resonance offset and the mismatch of the Hartmann-Hahn condition are also discussed along with experimental results using model single-crystal samples.