  Reducing parameter spaces via exploiting symmetries has greatly accelerated
and increased the quality of electronic-structure calculations. Unfortunately,
many of the traditional methods fail when the global crystal symmetry is
broken, even when the distortion is only a slight perturbation (e.g.
Jahn-Teller like distortions). Here we introduce a flexible and generalizable
parametric relaxation scheme, and implement it in the all-electron code
FHI-aims. This approach utilizes parametric constraints to maintain symmetry at
any level. After demonstrating the method's ability to relax metastable
structures, we highlight its adaptability and performance over a test set of
359 materials, across thirteen lattice prototypes. Finally we show how these
constraints can reduce the number of steps needed to relax local lattice
distortions by an order of magnitude. The flexibility of these constraints
enables a significant acceleration of the high-throughput searches for novel
materials for numerous applications.
