Johnson et al. 2025 two-temperature aluminium

This benchmark compares Otter ion-sphere (IS) QOZ pair distributions from ordinary HNC and Rosenfeld–Ashcroft VMHNC closures with Figure 2 of Johnson et al. [2025] at \(\rho=2.7\ {\rm g\,cm^{-3}}\), \(T_i=1\) eV, and \(T_e=1,3,10,30\) eV. The reference package contains the paper’s 2TTCP HNC+bridge, DFT-MD, and YOCP HNC+bridge curves for panels 2(a)–2(d).

Otter uses the pseudoatom construction of Starrett and Saumon [2014], Starrett and Saumon [2013], finite-temperature Lindhard response, and the jellium LFC of Chabrier [1990]. For every panel, HNC and VMHNC reuse the same converged IS electronic result and effective ion–ion potential. VMHNC uses the bridge-universality ansatz of Rosenfeld and Ashcroft [1979], the exact Percus–Yevick hard-sphere reference of Wertheim [1963], Thiele [1963], and the variational packing- fraction condition of Faussurier [2004]. Its packing fraction is not fitted to the DFT-MD curves. A same-potential classical MD calculation with LAMMPS [Thompson et al., 2022] is included in every panel to separate error in the integral-equation closure from error in the IS-QOZ pair potential.

Bridge and plasma-model terminology

The following models are different and must not be treated as synonyms:

  • HNC: the bridge function is set to zero, \(B(r)=0\).

  • Otter VMHNC: the unknown bridge is replaced by a Percus–Yevick hard- sphere reference bridge. A variational free-energy condition determines its packing fraction. This is the one-component Rosenfeld–Ashcroft model implemented by Otter; it does not use DFT-MD fitting data.

  • OCP: ions interact through the bare Coulomb potential \(Q^2/r\) in a uniform neutralizing background. Its state is specified by the coupling parameter \(\Gamma\). Iyetomi, Ogata, and Ichimaru extracted an OCP bridge from Monte Carlo data [Iyetomi et al., 1992].

  • YOCP: ions interact through the screened Yukawa potential \(Q^2\exp(-r/\lambda)/r\); its state additionally needs \(\kappa=a/\lambda\). This is not the same system as the OCP.

  • IEMHNC: the isomorph-based empirically modified HNC maps an OCP bridge to a YOCP bridge as \(B_{\rm YOCP}(r/a,\Gamma,\kappa)= B_{\rm OCP}(r/a,\Gamma_{\rm iso})\) [Tolias and Lucco Castello, 2019]. The OCP input is simulation-derived, unlike VMHNC’s variational hard-sphere reference.

  • Daughton YOCP bridge: an earlier empirical Yukawa mapping multiplies the OCP bridge by \(\exp(-\kappa^2/4)\) [Daughton et al., 2000]. Johnson et al. cite this model for the plotted YOCP curve; it is not IEMHNC.

  • Same-potential MD: no integral-equation bridge is assumed. Classical trajectories sample the equilibrium structure generated by the same Otter IS-QOZ pair potential. Agreement between a closure and this MD result tests the closure for that potential, not the accuracy of the potential relative to DFT-MD.

Johnson et al. label their 2TTCP result as HNC with bridge and cite the Rosenfeld–Ashcroft universality paper [Rosenfeld and Ashcroft, 1979]. Their article does not provide enough numerical detail to identify that published curve with Otter’s VMHNC implementation, so the benchmark keeps the labels separate. Their Figure 2 also contains an OCP curve and their own pair- potential MD (PPMD). The current digitized reference package contains only 2TTCP HNC+bridge, DFT-MD, and YOCP HNC+bridge; it does not relabel the YOCP data as OCP. The MD curve added here is newly calculated with Otter’s pair potential and is not Johnson’s PPMD data.

The previous panel-(d) diagnostic used a long-wavelength Yukawa fit to map Otter’s non-Yukawa QOZ potential onto an effective IEMHNC state. That result was close to same-potential MD, but the extra Yukawa fit means it is correctly described as an IEMHNC-inspired mapping, not a general production IEMHNC closure for an arbitrary QOZ potential.

Johnson et al. used PAW DFT-MD with 11 explicit electrons per Al atom and 64-atom cells at 1 eV and 32-atom cells at 3, 10, and 30 eV [Johnson et al., 2025].

Model-scope warning

At low electron temperature, a spherical pseudoatom/average-atom model cannot represent directional chemical bonding or transient molecular structure. A bridge function changes the classical ionic closure, but it cannot reconstruct electronic or chemical structure missing from the pseudoatom pair potential. Low-temperature disagreement with DFT-MD is therefore expected in chemically structured regimes and must not be interpreted as a bridge-only error.

Coordinate unit

The publication labels the horizontal axis as \(r\) in atomic units, so the archived coordinate and Otter radius are compared directly in Bohr. A source plotting file labelled the same values as ångström; the benchmark does not repeat that label or rescale the data.

Reproduce the comparison

The standalone script benchmarks/examples/plot_johnson_et_al_2025_two_temperature_al.py contains the thermodynamic inputs, Otter workflow calls, convergence checks, checksum validation, and plotting. Set

USE_PRECOMPUTED_DATA = True

to load checksummed results, or set it to False to run all four IS electronic calculations and then evaluate both ionic closures. New files are written under benchmarks/outputs/johnson_et_al_2025_two_temperature_al/gallery_recomputed and do not overwrite accepted results. Potential-strength continuation with the Newton–Krylov HNC backend is used when needed. HNC residuals, transform- closure diagnostics, and the VMHNC variational residual are recorded in the manifest. With RUN_SAME_POTENTIAL_MD = True, the same script also runs 2048-ion LAMMPS calculations using \(\Delta t=0.005\omega_p^{-1}\), \(50\omega_p^{-1}\) NVT equilibration, and \(500\omega_p^{-1}\) NVE production, following the dimensionless protocol reported by Johnson et al. LAMMPS and an MPI launcher must be available for this optional recomputation path.

Set USE_RECOMPUTED_CANDIDATES = True only to review a complete candidate set from that output directory. Candidate file hashes are checked, but this mode does not label or promote the results as accepted benchmark baselines.

The rendered comparison is available at Two-temperature aluminium: Johnson et al. (2025).

Reference-data notice

The project maintainer digitized the reference curves from Figure 2(a)–2(d). The files record article panels, units, method labels, and SHA-256 checksums. The article does not attach an open-data license to these point sets, so they are distributed with attribution and license status NOASSERTION and are not covered by Otter’s BSD software license. See the manifest under benchmarks/reference_data/johnson_et_al_2025_two_temperature_al before reuse.