Effects of finite rf pulses and sample spinning speed in multiple-quantum magic-angle spinning (MQ-MAS) and multiple-quantum quadrupolar Carr-Purcell-Meiboom-Gill magic-angle spinning (MQ-QCPMG-MAS) nuclear magnetic resonance of half-integer quadrupolar nuclei

The multiple-quantum magic-angle spinning (MQ-MAS) solid-state nuclear magnetic resonance (NMR) experiment and a sensitivity-enhanced variant detecting the second-order quadrupolar powder pattern through a train of quadrupolar Carr-Purcell-Meiboom-Gill refocusing pulses (MQ-QCPMG-MAS) are analyzed with respect to the effects of finite radio frequency (rf) pulse irradiation and the MAS frequency. Taking these effects explicitly into account, it is possible to accurately determine optimum conditions for excitation of MQ coherences and reconversion of these into detectable single-quantum coherences as well as simulate the second-order quadrupolar lineshape necessary to extract accurate parameters for quadrupolar coupling interactions and isotropic chemical shifts. This accurate determination is of great importance for the exploitation of MQ-MAS and MQ-QCPMG-MAS NMR experiments for quantitative determination of site populations. The various effects are described analytically and demonstrated by numerical simulations and by Rb-87 MQ-MAS and MQ-QCPMG-MAS experiments on RbNO3.