  There is a high level of interest in black hole-neutron star binaries, not
only because their mergers may be detected by gravitational wave observatories
in the coming years, but also because of the possibility that they could
explain a class of short duration gamma-ray bursts. We study black hole-neutron
star mergers that occur with high eccentricity as may arise from dynamical
capture in dense stellar regions such as nuclear or globular clusters. We
perform general relativistic simulations of binaries with a range of impact
parameters, three different initial black hole spins (zero, aligned and
anti-aligned with the orbital angular momentum), and neutron stars with three
different equations of state. We find a rich diversity across these parameters
in the resulting gravitational wave signals and matter dynamics, which should
also be reflected in the consequent electromagnetic emission. Before tidal
disruption, the gravitational wave emission is significantly larger than
perturbative predictions suggest for periapsis distances close to effective
innermost stable separations, exhibiting features reflecting the zoom-whirl
dynamics of the orbit there. Guided by the simulations, we develop a simple
model for the change in orbital parameters of the binary during close
encounters. Depending upon the initial parameters of the system, we find that
mass transfer during non-merging close encounters can range from essentially
zero to a sizable fraction of the initial neutron star mass. The same holds for
the amount of material outside the black hole post-merger, and in some cases
roughly half of this material is estimated to be unbound. We also see that
non-merging close encounters generically excite large oscillations in the
neutron star that are qualitatively consistent with f-modes.
