Application of Optimal Control Theory in Solid-State NMR. Time-Suspension Multiple-Pulse Sequences

Abstract

Optimal control theory (computer-aided design and optimization) is applied in a search for new time-suspension pulse sequences which scale both linear and bilinear spin interactions to zero. This computer-aided approach allows one to rapidly examine and assess the characteristics of different time-suspension pulse sequences. The objective of our search is to find a sequence which operates effectively at modest RF field strengths. The initial result of this search is a simple semiwindowless, four-pulse sequence. The basic structure of this sequence is similar to that of a semiwindowless WAHUHA sequence, but with different pulse tip angles and delays resulting from the requirements for maximum overall scaling of the homonuclear dipole-dipole and chemical-shift Hamiltonians. Theoretical results are presented on how this sequence behaves with regard to resonance offsets and spin system parameters (couplings and chemical shifts). The experimental line-narrowing performance of this sequence as a function of RF field strength and resonance offset is examined and its performance is compared to those of two other time-suspension pulse sequences as well as the theoretical predictions. At moderate RF field strengths and small resonance offsets, this new sequence is found to perform reasonably well, but line-narrowing performance improves at higher RF field strengths or large resonance offsets. The experimental results corroborate the theoretical expectations. Possible applications for the use of this sequence, in particular solid-state imaging, are discussed.