Summary
We ran the same energy-and-force calculation twice from scratch on the 45-atom ethanol–coronene system. The energies differed by 1.4 × 10⁻¹² hartree, and the largest difference among the 135 force components was 6.7 × 10⁻¹¹ hartree/bohr. The check passed. It does not, however, show that one software package is better than another.
Why check this at all
A geometry search follows forces. If the same input could give noticeably different forces on different runs, two searches from the same start could end in different places, and small effects such as the influence of water could be lost in the noise. Before relying on a calculation for comparisons, we wanted to know how far apart two identical runs land.
How the check was done
- Both runs used the same geometry, taken from the middle of the first geometry search at cycle 48.
- Each run started from scratch, with no information carried over from the other.
- The settings matched the geometry search: r2SCAN-3c, ORCA 6.1.1, and the same integration grid.
- The acceptance tolerances—|ΔE| ≤ 1 × 10⁻⁸ hartree and max|Δg| ≤ 1 × 10⁻⁷ hartree/bohr—were fixed before the runs and were not changed afterward.
This was the second such pair. The first, at the starting geometry and a different grid setting, had also passed.
Result
| Quantity | Difference between the two runs |
|---|---|
| Total energy | 1.4 × 10⁻¹² hartree |
| Largest force component | 6.7 × 10⁻¹¹ hartree/bohr |
| Force components outside tolerance | 0 of 135 |
For scale, the geometry search treats forces below 1 × 10⁻⁴ hartree/bohr as small enough to stop. The run-to-run difference is roughly 1.5 million times smaller than that threshold.
What the result does not show
- It does not rank the software. A second program, Psi4, was also repeatable at the same starting geometry. Its relative run-to-run difference there was smaller by a factor of about 302. Repeatability is therefore not a reason to prefer ORCA, and no final production program has been selected. The difference is consistent with different parallel calculation paths, but the saved records do not establish its cause.
- It says nothing about accuracy. Two runs can agree perfectly and still both differ from the physical value. Accuracy will be assessed separately against published reference data.
- Two numerical questions remain open. One concerns a difference between results from the two programs. The other concerns an earlier Psi4 configuration that was not repeatable. Both are tracked with their own closure conditions.
- It is not an external reproduction. The check was run within the project. Independent external review has not yet been carried out.
Change history
v1.0 ·
First publication.