  LIGO's third observing run (O3) has reported several neutron star-black hole
(NSBH) merger candidates. From a theoretical point of view, NSBH mergers have
received less attention in the community than either binary black holes (BBHs),
or binary neutron stars (BNSs). Here we examine single-single (sin-sin)
gravitational wave (GW) captures in different types of star clusters --
galactic nuclei (GN), globular clusters (GC), and young stellar clusters (YSC)
-- and compare the merger rates from this channel to other proposed merger
channels in the literature. There are currently large uncertainties associated
with every merger channel, making a definitive conclusion about the origin of
NSBH mergers impossible. However, keeping these uncertainties in mind, we find
that sin-sin GW capture is unlikely to significantly contribute to the overall
NSBH merger rate. In general, it appears that isolated binary evolution in the
field or in clusters, and dynamically interacting binaries in triple
configurations, may result in a higher merger rate.
