  The local environment of a barium monofluoride (BaF) molecule embedded in a
neon matrix is studied theoretically. The energy of the BaF-Ne triatomic system
is calculated with a scalar relativistic Hamiltonian, using coupled-cluster
theory at the CCSD(T) level for $1625$ positions of the Ne atom relative to the
BaF molecule. The calculations are repeated with increasing basis sets (from
double to quintuple zeta), and are extrapolated to estimate the
complete-basis-set limit. Using the potential obtained from these calculations,
it is determined that substituting a BaF molecule for ten Ne atoms is favoured
compared to substitutions for other numbers of Ne atoms. The equilibrium
position and orientation of the BaF molecule and the displacement of its nearby
Ne neighbours are determined. The potential barriers that prevent the BaF
molecule from migrating and rotating are calculated. These barriers are
essential for the EDM$^3$ collaboration, which is using BaF molecules embedded
in a noble-gas solid to perform a precision measurement of the electron
electric dipole moment.
