  The classical scenario of terrestrial planet formation is characterized by a
phase of giant impacts among Moon-to-Mars mass planetary embryos. While the
classic model and its adaptations have produced adequate analogs of the outer
three terrestrial planets, Mercury's origin remains elusive. Mercury's
high-core mass fraction compared to the Earth's is particularly outstanding.
Among collisional hypotheses, this feature has been long interpreted as the
outcome of an energetic giant impact among two massive protoplanets. Here, we
revisit the classical scenario of terrestrial planet formation with focus on
the outcome of giant impacts. We have performed a large number of N-body
simulations considering different initial distributions of planetary embryos
and planetesimals. Our simulations tested the effects of different giant planet
configurations, from virtually circular to very eccentric configurations. We
compare the giant impacts produced in our simulations with those that are more
likely to account for the formation of Mercury and the Moon according to
smoothed hydrodynamic simulations. Impact events that could lead to Moon's
formation are observed in all our simulations with up to ~20% of all giant
impacts, consistent with the range of the expected Moon-forming event
conditions. On the other hand, Mercury-forming events via a single giant impact
are extremely rare, accounting for less than ~1% of all giant impacts. Our
results suggest that producing Mercury as a remnant of a single giant impact
that strips out the mantle of a differentiated planetary object with Earth-like
iron-silicate ratio is challenging and alternative scenarios may be required
(e.g. multiple collisions).
