  A significant hurdle in developing high-performance semiconductor quantum
technologies utilizing deep defects is related to charge dynamics.
Unfortunately, progress in modeling their charge dynamics has been hindered
over recent decades due to the absence of appropriate multiscale models capable
of accurately representing the atomic properties of these defects and their
impact on device performance. Here, we present a semi-\textit{ab initio} method
for modeling the bound states of deep defects in semiconductor quantum
technologies, applied to the negatively charged nitrogen vacancy (NV$^-$)
center in diamond. We employ density functional theory calculations to
construct accurate potentials for an effective mass model, which allow us to
unveil the structure of the bound hole states. We develop a model to calculate
the nonradiative capture cross sections, which agrees with experiment within
one order of magnitude. Finally, we present our attempt at constructing the
photoionization spectrum of NV$^0\rightarrow$ NV$^-$ + bound hole, showing that
the electronic transitions of the bound holes can be distinguished from phonon
sidebands. This paper offers a practical and efficient solution to a
long-standing challenge in understanding the charge dynamics of deep defects.
