Reproduced CPU fp64 results from checked-in paired inputs.
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.
| System | Method | KRONOS (Ry) | QE (Ry) | |Δ| (meV/atom) | Stress Δ | Force Δ |
|---|---|---|---|---|---|---|
| Si diamond | LDA, Γ-only | -14.518760 | -14.518758 | 0.0120 | — | — |
| Si diamond | LDA, shifted 2×2×2 | -15.794496 | -15.794496 | 0.0026 | — | — |
| Si diamond | PBE, shifted 2×2×2 | -15.748188 | -15.748189 | 0.0113 | 1.17e-8 | 2.89e-19 |
| Si displaced | PBE forces and stress | -15.746857 | -15.746858 | 0.0113 | 1.27e-7 | 2.69e-5 |
| Si sheared | Anisotropic PBE stress | -15.742847 | -15.742849 | 0.0110 | 2.49e-7 | 3.23e-5 |
| Si diamond | PBEsol code parity Matched PBE-generated PP isolates functional parity | -15.716677 | -15.716679 | 0.0114 | 2.09e-8 | 1.45e-18 |
| H₂O | LDA molecule, nonzero forces | -30.771863 | -30.771863 | 0.0015 | — | 6.81e-6 |
| Al FCC | LDA metal, 4×4×4 | -4.173801 | -4.173801 | 0.0002 | — | — |
| MgO | LDA NLCC solid | -31.538025 | -31.538025 | 0.0020 | 3.29e-8 | 0.00e+0 |
| MgO displaced | NLCC forces and stress | -31.537723 | -31.537722 | 0.0020 | 1.11e-7 | 6.68e-7 |
| Graphene | LDA, 2D 4×4×1 | -21.708644 | -21.708859 | 1.4587 | — | — |
| Fe BCC | LSDA, constrained 2 μB Fixed-moment magnetic stress validation | -30.040390 | -30.040430 | 0.5455 | 1.12e-6 | — |
Logarithmic scale. The dashed line at 2 meV/atom marks the Δ-test target for this validation matrix.
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-failureAdd new pairs as validation/cases/name.yaml and validation/cases/name.in, then declare required outputs in the runner.
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).