Polarization transfer dynamics in Lee–Goldburg cross polarization nuclear magnetic resonance experiments on rotating solids

Abstract

This paper presents a theoretical description of continuous wave (CW) high frequency Lee–Goldburg cross polarization magic angle spinning (LG–CPMAS) nuclear magnetic resonance experiments. The full time-dependent LG–CPMAS Hamiltonian is replaced by its zero order time-independent Hamiltonian in the interaction representation. Carbon signal enhancements of LG–CPMAS experiments are calculated for spin systems consisting of six H1 nuclei coupled to one C13 nucleus. These simulations are based on Floquet theory calculations, explicitly taking into account the time dependence because of magic angle spinning, and calculations based on the zero-order Hamiltonian. The good agreement between these calculations justifies the use of the zero-order Hamiltonian. The time-dependent intensities of the cross peaks in heteronuclear C13–1H correlation spectra, extracted from 3D LG–CPMAS experiments on a natural abundant DL–alanine sample with increasing CP mixing times, are in good agreement with the theoretical intensities simulated by using the zero-order Hamiltonian. The approximated LG–CPMAS Hamiltonian can be used to obtain structural information about a proton coupled to a single carbon. The simulated intensities of the carbon signals of an isolated C13–1H group and a C13–1H group that is coupled to additional protons, measured by LG–CPMAS experiments with increasing CP mixing times, are compared. This study suggests that the buildup curve of each LG–CPMAS carbon signal and its Fourier transformed CP spectrum can be interpreted in terms of a single distance between the observed C13 and its nearest proton, if the additional protons are removed from this carbon by at least 1.2 times this distance.