  We present a molecular orbital candidate Ba$_{4}$TaMn$_{3}$O$_{12}$ with a
face-sharing octahedra trimer, by comparing it with a related compound
Ba$_{4}$NbMn$_{3}$O$_{12}$. The synthesis of the polycrystalline powder is
optimized by suppressing the secondary impurity phase via x-ray diffraction.
Magnetic susceptibility measurements on the optimized samples reveal a weak
magnetic hysteresis with magnetic transitions consistent with heat capacity
results. The effective magnetic moments from susceptibility indicate a strongly
coupled $S=2$ antiferromagnetic trimer at around room temperature, whereas the
estimated magnetic entropy from heat capacity suggests the localized $S=3/2$
timer. These results can be explainable by a partial molecular orbital state,
in which three $t_{2g}$ electrons are localized in each Mn ion and one $e_{g}$
electron is delocalized over two-end Mn ions of the trimer based on density
functional theory calculations. This unconventional 3$d$ orbital state is
comprehended as a consequence of competition between the hybrid interatomic
orbitals within the Mn trimer and the local moment formation by on-site Coulomb
correlations.
