  Mergers of black hole-neutron star (BHNS) binaries have now been observed by
GW detectors with the recent announcement of GW200105 and GW200115. Such
observations not only provide confirmation that these systems exist, but will
also give unique insights into the death of massive stars, the evolution of
binary systems and their possible association with gamma-ray bursts,
$r$-process enrichment and kilonovae. Here we perform binary population
synthesis of isolated BHNS systems in order to present their merger rate and
characteristics for ground-based GW observatories. We present the results for
420 different model permutations that explore key uncertainties in our
assumptions about massive binary star evolution (e.g. mass transfer,
common-envelope evolution, supernovae), and the metallicity-specific star
formation rate density, and characterize their relative impacts on our
predictions. We find intrinsic local BHNS merger rates spanning
$\mathcal{R}_{\rm{m}}^0 \approx 4$-$830\,\rm{Gpc}^{-3}\,\rm{yr}^{-1}$ for our
full range of assumptions. This encompasses the rate inferred from recent BHNS
GW detections, and would yield detection rates of $\mathcal{R}_{\rm{det}}
\approx 1$-$180\, \rm{yr}^{-1}$ for a GW network consisting of LIGO, Virgo and
KAGRA at design sensitivity. We find that the binary evolution and
metallicity-specific star formation rate density each impact the predicted
merger rates by order $\mathcal{O}(10)$. We also present predictions for the GW
detected BHNS merger properties and find that all 420 model variations predict
that $\lesssim 5\%$ of the BHNS mergers have BH masses $\gtrsim 18\,M_{\odot}$,
total masses $ \gtrsim 20\,M_{\odot}$, chirp masses $\gtrsim 5.5\,M_{\odot}$,
mass ratios $ \gtrsim 12$ or $\lesssim 2$. Moreover, we find that massive NSs
$\gtrsim 2\,M_{\odot}$ are expected to be commonly detected in BHNS mergers in
almost all our model variations.
