Title: Symmetry-Based Singlet-Triplet Excitation in Solution Nuclear Magnetic Resonance

Abstract: Coupled pairs of spin-1/2 nuclei support one singlet state and three triplet states. In many circumstances the nuclear singlet order, defined as the difference between the singlet population and the mean of the triplet populations, is a long-lived state which persists for a relatively long time in solution. Various methods have been proposed for generating singlet order, starting from nuclear magnetization. This requires the stimulation of singlet-to-triplet transitions by modulated radiofrequency fields. We show that a recently described pulse sequence, known as PulsePol (Schwartz $\textit{et al.}$, Science Advances, $\textbf{4}$, eaat8978 (2018) and arXiv:1710.01508), is an efficient technique for converting magnetization into long-lived singlet order. We show that the operation of this pulse sequence may be understood by adapting the theory of symmetry-based recoupling sequences in magic-angle-spinning solid-state NMR. The concept of riffling allows PulsePol to be interpreted using the theory of symmetry-based pulse sequences, and explains its robustness. This theory is used to derive a range of new pulse sequences for performing singlet-triplet excitation and conversion in solution NMR. Schemes for further enhancing the robustness of the transformations are demonstrated.