Otter 0.4.1 numerical validation
The example gallery and scientific benchmarks were recalculated with the 0.4.1 external-AA fixes. Recorded figures, tables and terminal output refer to these calculations. Numerical arrays, trajectories and restart files remain local outputs; documentation builds do not run the solvers.
Scope
The calculations cover the electronic, ionization and ion-structure examples listed in the gallery and benchmark catalogue. Carbon’s 100 eV density scan is calculated once by its benchmark; the example gallery shares its figure. AA radial grids, continuum controls and SCF settings use the project defaults. Schörner’s comparison explicitly selects LDA-PW92 and PBE through Libxc.
Electronic states are checked before ion-structure or MD calculations. The workflow retains its existing convergence, threshold-state, common chemical-potential and screening-charge checks. The ion-structure library also retains its native screening-charge integral check. These acceptance conditions were not relaxed for this recalculation.
Molecular dynamics
The MD comparisons include Wünsch Be, Johnson Al, Schörner Al and nine CH₂ states. They use the recalculated electronic potentials rather than an unverified overlay of new closures with older MD curves. Potential tables, run parameters and complete trajectories are checked before accepting a calculated state.
CH₂ uses 3072 ions and a fixed 0.01 fs timestep. Its equilibration and production durations remain \(50\omega_p^{-1}\) and \(500\omega_p^{-1}\). The two hottest cases restore the analytic Coulomb core below 0.3 Bohr and join the native QOZ potential by 0.5 Bohr; this numerical treatment is included in the interpretation of HNC–MD differences. The published C and CH DFT-MD timesteps provide reference scales, not a material-independent stability criterion [Bethkenhagen et al., 2020]. MD uses MPI; the recorded CH₂ runs use four physical CPU cores per trajectory.
Each trajectory is checked for completion, finite output and NVE energy drift. Structure factors are evaluated from periodic density modes, with an additional RDF-transform comparison for CH₂. Reported frame or block SEMs are sampling diagnostics; they do not include every autocorrelation, finite-size or discretization error. Global temperature stability alone does not establish convergence of every species or structural observable.
The table reports thermostat targets separately from actual NVE means. Final energy changes use the initial NVE total energy as their reference; this relative diagnostic depends on the potential-energy zero.
Te / target Ti (eV) |
Mean NVE Ti (eV) |
NVT / NVE steps |
Final energy change (%) |
MD + analysis (min) |
|---|---|---|---|---|
9 / 1.8 |
1.7948 |
13,330 / 133,302 |
+0.0000 |
37.22 |
9 / 4.5 |
4.4017 |
13,330 / 133,302 |
-0.0001 |
37.07 |
9 / 9 |
9.1091 |
13,330 / 133,302 |
-0.0002 |
37.66 |
29 / 5.8 |
5.7601 |
13,330 / 133,302 |
-0.0000 |
37.19 |
29 / 14.5 |
14.4021 |
13,330 / 133,302 |
-0.0003 |
37.86 |
29 / 29 |
27.9257 |
13,330 / 133,302 |
+0.0000 |
38.18 |
99 / 19.8 |
19.9520 |
13,330 / 133,302 |
+0.0000 |
38.13 |
99 / 49.5 |
49.3585 |
13,330 / 133,302 |
+0.0001 |
38.43 |
99 / 99 |
99.2829 |
13,330 / 133,302 |
-0.0202 |
38.44 |
Interpretation
The external solve now receives the full system’s evaluated final continuum energy cutoff and retains the common infinite-radius potential reference. Three consecutive QM SCF confirmations are required. These changes repair specific cutoff, potential-reference and stopping inconsistencies; they do not establish global electron-number convergence at every state.
In particular, tighter source-charge diagnostics still detect residual pseudoatom electron-number errors for some hot H and CH₂ states. Passing the established workflow checks must not be interpreted as satisfying an arbitrarily tighter charge budget.
Agreement with a literature curve tests the stated model at the listed conditions. It does not validate all elements, densities, temperatures or transport observables. The default Dirac model contains local exchange; correlation is present only when the selected XC model includes it.
See Benchmark data and provenance for reference-data provenance and the separation between calculation outputs and recorded presentation assets.