  Point defects in semiconductors are attractive candidates for quantum
information science applications owing to their ability to act as spin-photon
interface or single-photon emitters. However, the coupling between the change
of dipole moment upon electronic excitation and stray electric fields in the
vicinity of the defect, an effect known as Stark shift, can cause significant
spectral diffusion in the emitted photons. In this work, using first principles
computations, we revisit the methodology to compute the Stark shift of point
defects up to the second order. The approach consists of applying an electric
field on a defect in a slab and monitoring the changes in the computed
zero-phonon line (i.e., difference in energy between the ground and excited
state) obtained from constraining the orbital occupations (constrained-DFT). We
study the Stark shift of the negatively charged nitrogen-vacancy (NV) center in
diamond using this slab approach. We discuss and compare two approaches to
ensure a negatively charged defect in a slab and we show that converged values
of the Stark shift measured by the change in dipole moment between the ground
and excited states ($\Delta \mu$) can be obtained. We obtain a Stark shift of
$\Delta \mu$=2.68D using the semi-local GGA-PBE functional and of $\Delta
\mu$=2.23D using the HSE hybrid-functional. The results of the slab
computations are significantly different than those obtained with Modern Theory
of Polarization ($\Delta \mu$=4.34D for GGA-PBE) indicating a potential issue
with the combination of constrained-DFT and Modern Theory of Polarization, at
least in certain codes.
