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We present a new molecular orbital candidate Ba$_{4}$TaMn$_{3}$O$_{12}$ witha face-sharing octahedra trimer, by comparing it with a related compoundBa$_{4}$NbMn$_{3}$O$_{12}$. The synthesis of the polycrystalline powder isoptimized by suppressing the secondary impurity phase via X-ray diffraction.Magnetic susceptibility measurements on the best samples reveal the intrinsicmagnetic hysteresis with magnetic transitions consistent with heat capacityresults. The effective magnetic moments from susceptibility indicate a stronglycoupled $S=2$ antiferromagnetic trimer at around room temperature, whereas theestimated 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 densityfunctional theory calculations. This new 3$d$ orbital state is comprehended asa consequence of competition between the hybrid interatomic orbitals within theMn trimer and the local moment formation by on-site Coulomb correlations. Wefurther find the potential manipulation of the band gap in the 3$d$ trimermaterial platform in searching for the unconventional insulator-metaltransition.

Partial molecular orbitals in face-sharing 3$d$ manganese trimer: Comparative studies on Ba$_{4}$TaMn$_{3}$O$_{12}$ and Ba$_{4}$NbMn$_{3}$O$_{12}$