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We study two materials and clarify the mechanisms at play in stabilizing aninsulating state, and an impurity level in the bandgap using ab initiocalculations: Cu-doped Pb$_{10}$(PO$_4$)$_6$O ('LK-99') and V-doped SrTiO$_3$,both transition metal-doped insulators. In both cases, the electron degeneracyand crystal lattice symmetry are broken, leading to an insulating state, and amagnetically and orbitally polarized impurity state within the bulk gap,clearly separated from the doped material's valence and conduction bands.Doping slightly lowers the band gap of the bulk materials, with possibleapplications related to bandgap tuning (e.g. photocatalysis). We also resolvepreviously noticed inconsistencies between density functional theory resultsand experiment regarding doping site energetics, crystal structure, andtransparency in Cu-doped phosphate lead apatite 'LK-99'. Doping one of eachtype of site in the same unit cell ($20 \%$ doping) leads to two spin-polarizedimpurity bands in the material's gap. The local transition metal ion sites maybehave like color centers (or f-centers), possibly giving color at lowtemperatures to what we predict to be a transparent, insulating material in therecently synthesized LK-99 at low temperatures. The results shown here likelyexclude superconductivity by known mechanisms. We also note the potential ofthis type of doping to lead to altermagnetism - though the Cu-doped leadapatite does not seem particularly promising in this regard. Throughout thispaper, we also discuss tools that can be used to quickly understand the locald-orbital symmetry of the impurity, and the coupling between the crystalstructure and the impurity electronic order on the d-shell.

Coupled electron-crystal lattice symmetry reduction in insulating  materials with transition metal dopants: Cu-doped Pb$_{10}$(PO$_4$)$_6$O, and  Vanadium doped SrTiO$_3$