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 Starrett, private communication (unpublished)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.

The Wünsch Be panels contain three Otter results made from one IS-QOZ pair 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.

Thus the HNC–MD difference diagnoses the ionic closure without changing the average atom, ionization, screening density, or pair potential. 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

The downloadable script Ion-structure literature library exposes one switch:

USE_PRECOMPUTED_DATA = True

True verifies and loads checksummed Otter results. False runs the audited producer, including the Wünsch HNC/VMHNC and LAMMPS calculation, writes new files under benchmarks/outputs/ion_structure_library/gallery_recomputed, and plots those results. Accepted files are never overwritten automatically. Each run exports PNG and PDF figures.

The common single- and multi-species MD implementation is tools/otter_lammps_md.py. The benchmark producer benchmarks/runners/regenerate_ion_structure_library.py keeps all Wünsch particle counts, temperatures, time scales, sampling intervals, and MPI settings in its user-editable Python constants. A run preserves atoms.data, pair_potentials.table, in.otter_md, LAMMPS logs, RDF blocks, the trajectory, statistical results, and a checksummed JSON metadata record below benchmarks/outputs/ion_structure_library/recomputed/md_work. For mixtures the same tool requires every unordered pair potential and writes all partial \(g_{ij}(r)\) and \(S_{ij}(k)\) channels.

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.