  Recent discoveries of gravitational wave (GW) events most likely originating
from black hole (BH) + neutron star (NS) mergers reveal the existence of BH+NS
binaries. The formation of BH+NS binaries and their merger rates through
isolated binary evolution have been investigated extensively with population
synthesis simulations. A detailed stellar evolution modelings of the formation
of this population, however, is missing in the literature. In this work, we
perform the first complete 1D model of more than 30 BH+NS progenitor systems
which are calculated self-consistently until the iron core collapse with infall
velocity exceeds 1000 km s^-1. Focusing on the progenitors of BH- NS GW
sources, we apply the MESA code starting from a post-common envelope binary
with short orbital period (< 1 day) consisting of a BH and a zero-age
main-sequence helium star that experiences stable mass transfer. These NS
masses could be significantly larger depending on the exact mass cut during the
supernova explosion. These BH+NS systems are likely to merge and produce GW
events within a Hubble time. System C is a potential progenitor of a
GW200115-like event, while Systems A and B are possible candidates for a
GW200105-like event and may represent the final destiny of the X-ray binary
SS433.
