The strongly luminescent and highly oxygen-sensitive Tb(III) complex [{(MeMeArO)3tacn}TbIII(THF)] (denoted hereafter as [1Tb THF]) was studied with d. functional theory (DFT) and wavefunction-based ab initio electronic structure methods combined with Tb relativistic ab initio pseudopotentials. The optimized geometries as well as the calculated UV-vis absorption spectra at the DFT level agree well with the available exptl. data. The calculated vertical S0*/5D4 → S0*/7FJ (ligand/Tb3+ states) emission energies for J = 0-6 at the RSPT2//CASSCF level including spin-orbit corrections are 475, 511, 549, 583, 614, 638, and 644 nm, resp., and are lower by 15, 36, 39, 39, 39, 35, and 35 nm, resp., than the corresponding exptl. values. The luminescence quenching mechanism of [1Tb THF] in presence of O2 was investigated. RSPT2//CASSCF calculations for [1Tb THF]·O2 indicate that the S0*/7FJ (J = 0-6)/1O2 (1Δg or 1Σ+g) states (ligand/Tb3+/O2 states) are energetically more stable than the emission states S0*/5DJ (J = 0-4)/3O2 (3Σ-g). Therefore, after initial photo excitation of the ligand and subsequent energy transfer to the Tb3+ ion, the energy will be further transferred to O2 leading to the observed luminescence quenching of [1Tb THF] in air. A comparison is made to [1Sm THF]·O2 which shows a significantly smaller luminescence quantum yield and no oxygen quenching.