The
transition metal manganese is attractive for magnetism and
luminescence engineering due to the nontrivial interplay of charge,
spin, lattice, and orbital freedom degrees. Here, we report the manganese
site occupancy and valence states by taking experimental synthesis
conditions into consideration and the optical features of target intra-atomic
Mn2+, Mn3+, and Mn4+ in the framework
of density functional theory in a prototype spinel ZnGa2O4 host. The formation energy results show that Mn2+ dominates in tetrahedral ligands at the Zn2+ site
and Mn3+ and Mn4+ dominate in octahedral ligands
at the Ga3+ site under the corresponding different chemical
potential conditions, and the distortion of the local coordination
environment of Mn3+ in octahedral ligands due to the Jahn–Teller
effect is studied in detail. The excited-state equilibrium geometries
and energies are obtained via spin or orbital occupancy constraints,
which are further complemented by the Tanabe–Sugano diagram
to predict the energy spectra and to interpret the experimental results
on Mn2+, Mn4+, and Mn3+. In particular,
the competition of 5T2 and 1T2 excited states and the relaxation processes leading to near-infrared
luminescence of rarely reported Mn3+ are analyzed. First-principles
calculations complemented by the Tanabe–Sugano diagram analysis
may serve as an effective and predictive tool for exploring valence
states, energy structures, and luminescence of complexes containing
3d
n
transition-metal ions.