  The NV$^-$ color center in diamond has been extensively investigated for
quantum sensing, computation, and communication applications. Nonetheless,
charge-state decay from the NV$^-$ to its neutral counterpart the NV$^0$
detrimentally affects the robustness of the NV$^-$ center and remains to be
fully overcome. In this work, we provide an $ab~initio$ formalism for
accurately estimating the rate of charge-state decay of color centers in
wide-bandgap semiconductors. Our formalism employs density functional theory
calculations in the context of thermal equilibrium. We illustrate the method
using the transition of NV$^-$ to NV$^0$ in the presence of substitutional N
[see Z. Yuan $et~al$., PRR 2, 033263 (2020)].
