Development and optimization of shaped NMR pulses for the study of coupled spin systems

Asymmetric amplitude modulated radio frequency pulses for narrow-band inversion of coupled and uncoupled spin systems in NMR are introduced. We also introduce a new parameterization for pulse shapes using cubic spline interpolation that reduces the number of parameters. The spin response is obtained using a full density matrix calculation and pulse shapes were optimized numerically using a simplex algorithm. Coupling is shown to interfere with the performance of shaped pulses designed to invert uncoupled spins prompting the design of pulses that invert a model system consisting of two dipolar coupled spins 1 2. Amplitude modulated shaped pulses optimized for coupled systems are found to be specific for coupling strength and spin topology.