  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.
