  We use a method based on metadynamics to locate multiple low-energy
Unrestricted Hartree--Fock (UHF) self-consistent-field (SCF) solutions of two
model octahedral $d^1$ and $d^2$ transition-metal complexes,
$[\mathrm{MF}_6]^{3-} (\mathrm{M} = \mathrm{Ti}, \mathrm{V})$. By giving a
group-theoretical definition of symmetry breaking, we classify these solutions
in the framework of representation theory and observe that a number of them
break spin or spatial symmetry, if not both. These solutions seem unphysical at
first, but we show that they can be used as bases for Non-Orthogonal
Configuration Interaction (NOCI) to yield multi-determinantal wavefunctions
that have the right symmetry to be assigned to electronic terms. Furthermore,
by examining the natural orbitals and occupation numbers of these NOCI
wavefunctions, we gain insight into the amount of static correlation that they
incorporate. We then investigate the behaviors of the most low-lying UHF and
NOCI wavefunctions when the octahedral symmetry of the complexes is lowered and
deduce that the symmetry-broken UHF solutions must first have their symmetry
restored by NOCI before they can describe any vibronic stabilization effects
dictated by the Jahn--Teller theorem.
