  We study from first principles two lanthanum silicate nitride compounds,
LaSi$_{3}$N$_{5}$ and La$_{3}$Si$_{6}$N$_{11}$, pristine as well as doped with
Ce$^{3+}$ ion, in view of explaining their different emission color, and
characterising the luminescent center. The electronic structures of the two
undoped hosts are similar, and do not give a hint to quantitatively describe
such difference. The $4f\rightarrow 5d$ neutral excitation of the Ce$^{3+}$
ions is simulated through a constrained density-functional theory method
coupled with a ${\Delta}$SCF analysis of total energies, yielding absorption
energies. Afterwards, atomic positions in the excited state are relaxed,
yielding the emission energies and Stokes shifts. Based on these results, the
luminescent centers in LaSi$_{3}$N$_{5}$:Ce and La$_{3}$Si$_{6}$N$_{11}$:Ce are
identified. The agreement with the experimental data for the computed
quantities is quite reasonable and explains the different color of the emitted
light. Also, the Stokes shifts are obtained within 20\% difference relative to
experimental data.
