Optimal control based design of composite dipolar recoupling experiments by analogy to single-spin inversion pulses

It is demonstrated that a simple analogy between single-spin composite radiofrequency (rf) pulses and solid-state NMR dipolar recoupling may be exploited to reduce the operator space dimensionality in design of recoupling experiments by optimal control based algorithms. The use of single-spin calculations speeds up numerical optimizations by an order of magnitude and allows for fast development of high-sensitivity experiments with good compensation for experimental artifacts such as off-resonance effects and rf inhomogeneity. By optimization in terms of error-compensating composite rf pulses, the corresponding recoupling experiments intrinsically benefit from reduced powder-angle dependencies and thereby offer higher transfer efficiencies than commonly used γ-encoded recoupling experiments. We demonstrate 50% gain in sensitivity for a 2D NCO experiment on ¹³C,¹⁵N-labeled ubiquitin using composite recoupling experiments with 9-30 pulse elements.