  Optically and magnetically active point defects in semiconductors are
interesting platforms for the development of solid-state quantum technologies.
Their optical properties are usually probed by measuring photoluminescence
spectra, which provide information on excitation energies and on the
interaction of electrons with lattice vibrations. We present a combined
computational and experimental study of photoluminescence spectra of defects in
diamond and SiC, aimed at assessing the validity of theoretical and numerical
approximations used in first principles calculations, including the use of the
Franck-Condon principle and the displaced harmonic oscillator approximation. We
focus on prototypical examples of solid-state qubits, the divacancy centers in
SiC and the nitrogen-vacancy in diamond, and we report computed
photoluminescence spectra as a function of temperature that are in very good
agreement with the measured ones. As expected we find that the use of hybrid
functionals leads to more accurate results than semilocal functionals.
Interestingly our calculations show that constrained density functional theory
(CDFT) and time-dependent hybrid DFT perform equally well in describing the
excited state potential energy surface of triplet states; our findings indicate
that CDFT, a relatively cheap computational approach, is sufficiently accurate
for the calculations of photoluminescence spectra of the defects studied here.
Finally, we find that only by correcting for finite-size effects and
extrapolating to the dilute limit, one can obtain a good agreement between
theory and experiment. Our results provide a detailed validation protocol of
first principles calculations of photoluminescence spectra, necessary both for
the interpretation of experiments and for robust predictions of the electronic
properties of point defects in semiconductors.
