Engineering spin Hamiltonians using multiple pulse sequences in solid state NMR spectroscopy.

Multiple pulse sequences are often used to manipulate spin Hamiltonians in solid-state nuclear magnetic resonance spectroscopy. In this paper, we analyze multiple pulse sequences using the well-known average Hamiltonian theory. We first expand the resulting average Hamiltonian into a reachable set of sub-Hamiltonians and then develop a general procedure using both flip-angle and phase of the applied pulses as control variables to select any of those sub-Hamiltonians. We use this method to analyze solid-echo based sequences and to design new proton-proton homonuclear decoupling sequences in static solids. It is found that this newly designed decoupling scheme, in the presence of finite pulse length, effectively suppresses the 1 H-1 H homonuclear dipolar interactions while establishes variable scaling factors on the heteronuclear dipolar interactions and chemical shift interactions, depending on the flip-angle of the applied pulses. When the pulse flip-angle is close to 54.7°, this sequence possesses a large scaling factor with relatively low average decoupling field. When the pulse flip-angle becomes ∼120°, the scaling factor is almost zero. A static 15 N-acetyl-valine crystal sample has been used as an example to confirm and validate the performance of this new decoupling scheme.