  Point defects are a universal feature of crystalline materials. Their
identification is often addressed by combining experimental measurements with
theoretical models. The standard approach of simulating defects is, however,
prone to missing the ground state atomic configurations associated with
energy-lowering reconstructions from the idealised crystallographic
environment. Missed ground states compromise the accuracy of calculated
properties. To address this issue, we report an approach to efficiently
navigate the defect configurational landscape using targeted bond distortions
and rattling. Application of our workflow to a range of materials ($\rm CdTe$,
$\rm GaAs$, $\rm Sb_2S_3$, $\rm Sb_2Se_3$, $\rm CeO_2$, $\rm In_2O_3$, $\rm
ZnO$, anatase-$\rm TiO_2$) reveals symmetry breaking in each host crystal that
is not found via conventional local minimisation techniques. The point defect
distortions are classified by the associated physico-chemical factors. We
demonstrate the impact of these defect distortions on derived properties,
including formation energies, concentrations and charge transition levels. Our
work presents a step forward for quantitative modelling of imperfect solids.
