  Measuring the photoluminescence of defects in crystals is a common
experimental technique for analysis and identification. However, current
theoretical simulations typically require the simulation of a large number of
atoms to eliminate finite size effects, which discourages computationally
expensive excited state methods. We show how to extract the room-temperature
photoluminescence spectra of defect centres in bulk from an
$\mathrm{\textit{ab-initio}}$ simulation of a defect in small clusters. The
finite size effect of small clusters manifests as strong coupling to low
frequency vibrational modes. We find that removing vibrations below a cutoff
frequency determined by constrained optimization returns the main features of
the solid state photoluminescence spectrum. This strategy is illustrated for an
NV$^{-}$ defect in diamond, presenting a connection between defects in solid
state and clusters; the first vibrationally resolved
$\mathrm{\textit{ab-initio}}$ photoluminescence spectrum of an NV$^{-}$ defect
in a nanodiamond; and an alternative technique for simulating photoluminescence
for solid state defects utilizing more accurate excited state methods.
