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---
license: bsd-3-clause
---

The MatQ dataset comprises near-equilibrium and out-of-equilibrium structures. 
The 6,652,874  near-equilibrium structures comprise Materials Project crystals subject to strains of ±2%,  ±4% and ±6% along 
all crystallographic directions. The out-of-equilibrium structures were  obtained from the OMat24 validation set of 1,025,361 structures. 
The DImensionalityReduced Encoded Clusters with sTratified (DIRECT) sampling approach47 was then used  to select 60,000 structures each
from the near-equilibrium and out-of-equilibrium sets that  comprehensively covers the configuration space with minimal overlap, 
significantly reducing  the computational cost of reference data generation.  

Spin-polarized static DFT calculations were then performed using the Vienna Ab initio Simulation Package (VASP). 
The generalized gradient approximation (GGA) PerdewBurke-Ernzerhof (PBE) functional was employed to describe 
exchange-correlation interactions. The input files were generated using the “MatPESStaticSet” input set implemented 
in the Python Materials Genomics (pymatgen) package,49 which has been carefully  benchmarked to ensure well-converged 
PES properties. The main parameters include a  plane-wave kinetic energy cutoff of 680 eV, a k-spacing of 0.35  ̊A−1, 
and an electronic convergence condition of 10−5 eV. DDEC6 charges were computed using chargemol (version:  09 26 2017)
from the DFT charge densities.  The final MatQ dataset contains 114,445 structures, after excluding unconverged DFT 
calculations and structures with extremely large force components (|Fx,y,z| > 50 eV  ̊A−1).