A general theoretical description of the influence of isotropic chemical shift in dipolar recoupling experiments for solid-state NMR.

We present a general theoretical description that allows us to describe the influence of isotropic chemical shift in homonuclear and heteronuclear dipolar recoupling experiments in magic-angle-spinning solid-state NMR. Through a transformation of the Hamiltonian into an interaction frame with the combined radio-frequency irradiation and the isotropic chemical shift, we determine an effective Hamiltonian to first order with respect to the relevant internal nuclear spin interactions. This unravels the essential resonance conditions for efficient dipolar recoupling. Furthermore, we propose how to handle situations where the resonance conditions are not exactly fulfilled. To verify the general theoretical description, we compare numerical simulations using a time-sliced time-dependent Hamiltonian with simulations using the calculated effective Hamiltonian for propagation. The comparisons are exemplified for the homonuclear dipolar recoupling experiments C721 and POST-C721.