  In search of a reliable methodology for the prediction of light absorption
and emission of Ce$^{3+}$-doped luminescent materials, 13 representative
materials are studied with first-principles and semiempirical approaches. In
the first-principles approach, that combines constrained density-functional
theory and $\Delta$SCF, the atomic positions are obtained for both ground and
excited states of the Ce$^{3+}$ ion. The structural information is fed into
Dorenbos' semiempirical model. Absorption and emission energies are calculated
with both methods and compared with experiment. The first-principles approach
matches experiment within 0.3 eV, with two exceptions at 0.5 eV. In contrast,
the semiempirical approach does not perform as well (usually more than 0.5 eV
error). The general applicability of the present first-principles scheme, with
an encouraging predictive power, opens a novel avenue for crystal site
engineering and high-throughput search for new phosphors and scintillators.
