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Validated against Quantum ESPRESSO

Reproduced CPU fp64 results from checked-in paired inputs.

12/12pass
Paired QE cases
CPU fp64 against Quantum ESPRESSO 7.6
1.4587meV/atom
Largest energy delta
Graphene; acceptance threshold is 2 meV/atom
3.23×10⁻⁵Ry/bohr
Largest derivative delta
Nonzero forces; stress max is 1.12×10⁻⁶ Ry/bohr³

Methodology

Each comparison uses the same pseudopotential file, the same cell parameters, and the same plane-wave cutoff on both KRONOS and Quantum ESPRESSO (QE) v7.x. Total energies are compared in Rydberg, with the per-atom delta reported in meV. Every case must converge and stay below 2 meV/atom. Cases declaring forces, stress, or magnetization also fail closed when that output is absent or outside its tolerance.

The matrix covers LDA, PBE, PBEsol, NLCC, metals, molecules, two-dimensional cells, nonzero forces, anisotropic stress, and constrained collinear magnetism. CPU fp64 is the reference path; no CUDA, HIP, or Metal result is represented here.

Quantum ESPRESSO reference values on this page were obtained by running QE 7.6 (pw.x) on the checked-in inputs under validation/cases/. The machine-readable runner and acceptance logic live in validation/run_qe_validation.py.

Total energy vs QE

SystemMethodKRONOS (Ry)QE (Ry)|Δ| (meV/atom)Stress ΔForce Δ
Si diamondLDA, Γ-only-14.518760-14.5187580.0120
Si diamondLDA, shifted 2×2×2-15.794496-15.7944960.0026
Si diamondPBE, shifted 2×2×2-15.748188-15.7481890.01131.17e-82.89e-19
Si displacedPBE forces and stress-15.746857-15.7468580.01131.27e-72.69e-5
Si shearedAnisotropic PBE stress-15.742847-15.7428490.01102.49e-73.23e-5
Si diamondPBEsol code parity
Matched PBE-generated PP isolates functional parity
-15.716677-15.7166790.01142.09e-81.45e-18
H₂OLDA molecule, nonzero forces-30.771863-30.7718630.00156.81e-6
Al FCCLDA metal, 4×4×4-4.173801-4.1738010.0002
MgOLDA NLCC solid-31.538025-31.5380250.00203.29e-80.00e+0
MgO displacedNLCC forces and stress-31.537723-31.5377220.00201.11e-76.68e-7
GrapheneLDA, 2D 4×4×1-21.708644-21.7088591.4587
Fe BCCLSDA, constrained 2 μB
Fixed-moment magnetic stress validation
-30.040390-30.0404300.54551.12e-6

Per-configuration error

Logarithmic scale. The dashed line at 2 meV/atom marks the Δ-test target for this validation matrix.

Reproduce these numbers

Every number on this page is produced by the paired runner and inputs under validation/. Quantum ESPRESSO 7.6 must be available as pw.x.

# Build
cmake -B build -S . && cmake --build build -j

# Run all paired KRONOS/QE cases
python3 validation/run_qe_validation.py --pw /path/to/qe-7.6/bin/pw.x

# Run CPU, force, and stress regressions
ctest --test-dir build -j2 --output-on-failure

Add new pairs as validation/cases/name.yaml and validation/cases/name.in, then declare required outputs in the runner.

Citations and references

KRONOS's reference comparison code is Quantum ESPRESSO (QE), a widely used open-source plane-wave DFT engine. If you use the numbers on this page in a publication, please cite both KRONOS (forthcoming, see /docs) and the QE primary references:

BibTeX for QE:

@article{Giannozzi2009,
  title = {QUANTUM ESPRESSO: a modular and open-source software project for
           quantum simulations of materials},
  author = {Giannozzi, P. and Baroni, S. and Bonini, N. and Calandra, M. and
            Car, R. and Cavazzoni, C. and Ceresoli, D. and Chiarotti, G. L. and
            Cococcioni, M. and Dabo, I. and others},
  journal = {Journal of Physics: Condensed Matter},
  volume = {21},
  number = {39},
  pages = {395502},
  year = {2009},
  publisher = {IOP Publishing},
  doi = {10.1088/0953-8984/21/39/395502}
}

@article{Giannozzi2017,
  title = {Advanced capabilities for materials modelling with Quantum ESPRESSO},
  author = {Giannozzi, P. and Andreussi, O. and Brumme, T. and others},
  journal = {Journal of Physics: Condensed Matter},
  volume = {29},
  number = {46},
  pages = {465901},
  year = {2017},
  publisher = {IOP Publishing},
  doi = {10.1088/1361-648X/aa8f79}
}

The pseudopotential Si.pz-vbc.UPF used throughout the Si comparisons ships with the QE distribution (PZ LDA, norm-conserving, Zval=4).