Optimization of identity operation in NMR spectroscopy via genetic algorithm: Application to the TEDOR experiment

Identity operation in the form of π pulses is widely used in NMR spectroscopy. For an isolated single spin system, a sequence of even number of π pulses performs an identity operation, leaving the spin state essentially unaltered. For multi-spin systems, trains of π pulses with appropriate phases and time delays modulate the spin Hamiltonian to perform operations such as decoupling and recoupling. However, experimental imperfections often jeopardize the outcome, leading to severe losses in sensitivity. Here, we demonstrate that a newly designed Genetic Algorithm (GA) is able to optimize a train of π pulses, resulting in a robust identity operation. As proof-of-concept, we optimized the recoupling sequence in the transferred-echo double-resonance (TEDOR) pulse sequence, a key experiment in biological magic angle spinning (MAS) solid-state NMR for measuring multiple carbon-nitrogen distances. The GA modified TEDOR (GMO-TEDOR) experiment with improved recoupling efficiency results in a net gain of sensitivity up to 28% as tested on a uniformly ¹³C, ¹⁵N labeled microcrystalline ubiquitin sample. The robust identity operation achieved via GA paves the way for the optimization of several other pulse sequences used for both solid- and liquid-state NMR used for decoupling, recoupling, and relaxation experiments.