Field dependent isotropic shifts in solid state nuclear magnetic resonance: A Floquet treatment

The apparent field dependence observed for some isotropic shifts in high resolution solid state NMR is reinvestigated using the Floquet formalism. For 13C–1H systems, second order dipolar shifts are derived that largely agree with the experimental observations made by VanderHart and his theoretical treatment while resolving some difficulties in the use of a secular approximation to handle an inherently time-dependent problem. Additional second order terms are shown to give rise to both frequency shifts and line broadening which can be significant in some spin pairs. This line broadening is found to arise from a second order coupling of the rf field with the I–S dipolar interaction.