FLOQUET DENSITY-MATRICES AND EFFECTIVE-HAMILTONIANS IN MAGIC-ANGLE-SPINNING NMR-SPECTROSCOPY

Magic-angle-spinning (MAS) NMR experiments can be described in terms of Floquet theory. In this publication the Floquet approach is formulated in terms of Floquet density matrices and Floquet evolution operators. Expressions for expectation values of observables are derived and the analogy between the spin density matrix and the Floquet density matrix is shown. In addition, effective Hamiltonians are derived for MAS experiments during which data are acquired synchronously with the spinning speed. The effective Hamiltonians of three MAS experiments are derived: the dipolar decay of homonuclear spin pairs at their rotational resonance, the DRAMA experiment on a pair of equivalent homonuclear spins, and the REDOR experiment on heteronuclear spin pairs. The influences of off-resonance values, chemical-shift anisotropies, and pulse imperfections are taken into account. In addition the xy-4 phase-cycling scheme for the π pulses in the REDOR experiment is discussed. © 1993 by Academic Press, Inc.