Note

Electronic and ionic states use default AA controls. Be HNC, VMHNC and MD share one IS-QOZ potential. See Otter 0.4.1 numerical validation.

Ion-structure literature library

This benchmark compares Otter with published and author-provided ion-structure curves for aluminium, beryllium, and carbon.

Material

State

Observable

Reference

Al

2.7 g cm-3, \(T_e=T_i=5\) eV

\(S_{ii}(k)\)

Fig. 3 of Gill et al. [2015]

Al

8.1 g cm-3, \(T_e=T_i=10\) eV

\(S_{ii}(k)\)

Fig. 1 of Clérouin et al. [2015]

Al

8.1 g cm-3, \(T_e=10\), \(T_i=2\) eV

\(S_{ii}(k)\)

Fig. 1 of Clérouin et al. [2015]

Be

5.544 g cm-3, \(T_e=T_i=13\) eV

\(g_{ii}(r)\), \(S_{ii}(k)\)

Figs. 1(c) and 2 of Wünsch et al. [2009]

C

20 g cm-3, \(T_e=T_i=50\) eV

\(g_{ii}(r)\)

    1. Starrett, private communication (unpublished)

Each panel states whether it is an equilibrium or two-temperature comparison. The two Clérouin panels include independent Otter KS and Thomas–Fermi average-atom calculations; both use the same QOZ/HNC settings.

Reproduction uses the default AA radial resolution and SCF tolerances, without element-specific precision overrides. The native screening-charge integral is checked before accepting a calculated state.

The Wünsch Be panels compare three methods using one IS-QOZ potential:

  • Otter-HNC uses the bridge-free hypernetted-chain closure.

  • Otter-VMHNC uses the variational Rosenfeld–Ashcroft hard-sphere bridge [Rosenfeld and Ashcroft, 1979, Faussurier, 2004].

  • Otter-MD is a 2048-ion LAMMPS [Thompson et al., 2022] calculation with the same tabulated potential. Shaded bands are twice the standard error across RDF blocks or saved-frame reciprocal-shell averages.

The accepted archive retains every periodic reciprocal shell. The plotted MD \(S_{ii}(k)\) starts at the second shell, \(k=0.5025\,\mathrm{\AA}^{-1}\): the cubic-box fundamental at \(0.3553\,\mathrm{\AA}^{-1}\) has only three independent half-space vectors and is therefore excluded from the curve as a direction-starved finite-size estimate. No smoothing or replacement value is applied.

The common potential allows closure comparisons with MD, subject to finite-size, tabulation and sampling errors. VMHNC is not IEMHNC: VMHNC uses a variational hard-sphere reference, whereas IEMHNC maps an OCP bridge to a YOCP state.

Units

The Gill, Clérouin, and Wünsch reciprocal-space coordinates are in \(\mathrm{\AA}^{-1}\); the Wünsch real-space coordinate is in \(\mathrm{\AA}\); and the Starrett carbon coordinate is in Bohr. The plotting script converts Otter coordinates to the reference unit without modifying the archived reference columns.

Reproduce the comparison

Run the downloadable source from Ion-structure literature library:

poetry run python benchmarks/examples/plot_ion_structure_library.py

The default calculates the electronic and ionic states, writes local results under benchmarks/outputs, and exports PNG and PDF figures. No precomputed Otter NPZ is needed. Literature reference data remain separate inputs.

The MD curves are also recalculated and require LAMMPS and MPI. Particle counts, timesteps, sampling intervals and CPU counts are in the input block.

Reference-data notice

The publication-derived and author-provided coordinates are not covered by Otter’s BSD software license. Their attributions, per-file checksums, units, and license status NOASSERTION are recorded in benchmarks/reference_data/ion_structure_library. Consult those records before redistributing the numerical values.