Floquet-Magnus expansion for general N-coupled spins systems in magic-angle spinning nuclear magnetic resonance spectra

- Floquet theory.
- Floquet-Magnus expansion.
- Gamma-encoding effect.
- Gamma-symmetry.
- Magic-angle spinning.

In this paper we present a theoretical perturbative approach for describing the NMR spectrum of strongly dipolar-coupled spin systems under fast magic-angle spinning. Our treatment is based on two approaches: the Floquet approach and the Floquet-Magnus expansion. The Floquet approach is well known in the NMR community as a perturbative approach to get analytical approximations. Numerical procedures are based on step-by-step numerical integration of the corresponding differential equations. The Floquet-Magnus expansion is a perturbative approach of the Floquet theory. Furthermore, we address the “γ-encoding” effect using the Floquet-Magnus expansion approach. We show that the average over “γ” angle can be performed for any Hamiltonian with γ symmetry.