  The study of defect centers in silicon has been recently reinvigorated by
their potential applications in optical quantum information processing. A
number of silicon defect centers emit single photons in the telecommunication
$O$-band, making them promising building blocks for quantum networks between
computing nodes. The two-carbon G-center, self-interstitial W-center, and
spin-$1/2$ T-center are the most intensively studied silicon defect centers,
yet despite this, there is no consensus on the precise configurations of defect
atoms in these centers, and their electronic structures remain ambiguous. Here
we employ \textit{ab initio} density functional theory to characterize these
defect centers, providing insight into the relaxed structures, bandstructures,
and photoluminescence spectra, which are compared to experimental results.
Motivation is provided for how these properties are intimately related to the
localization of electronic states in the defect centers. In particular, we
present the calculation of the zero-field splitting for the excited triplet
state of the G-center defect as the structure is transformed from the
A-configuration to the B-configuration, showing a sudden increase in the
magnitude of the $D_{zz}$ component of the zero-field splitting tensor. By
performing projections onto the local orbital states of the defect, we analyze
this transition in terms of the symmetry and bonding character of the G-center
defect which sheds light on its potential application as a spin-photon
interface.
