GPU backend gives incorrect energies at long range with small-σ atom types

[mlund]

Summary

The GPU backend produces non-zero energies at long separations where the reference backend correctly returns near-zero values. This occurs when the topology contains atom types with small σ values (e.g. σ=2 Å for coarse-grained titratable site beads alongside backbone beads with σ=4.5–6.78 Å).

Reproduction

# Generate coarse-grained topology (cif2top produces σ=2 titratable sites)
cif2top 4lzt.cif convert -o t.xyz --top topology.yaml

# GPU backend — energy does NOT decay to zero at long separations
duello scan --mol1 t.xyz --mol2 t.xyz --top topology.yaml \
  --rmin 24 --rmax 40 --dr 1.0 -r 1.0 --backend gpu

# Reference backend — correct behavior (smooth decay to zero)
duello scan --mol1 t.xyz --mol2 t.xyz --top topology.yaml \
  --rmin 24 --rmax 40 --dr 1.0 -r 1.0 --backend reference

Root cause

Tracked upstream in mlund/interatomic#7. The f32 spline coefficients lose precision for atom pairs with small σ, where the spline grid spans a wide range (r_min = σ×0.6 = 1.2 Å to cutoff = 20–50 Å) and coefficients near the steep LJ wall have large magnitudes.

Workaround

Use --backend reference for topologies with large σ mismatches between atom types.

Increasing grid size (--grid size=4000) or using --grid type=inversersq may also help but has not been verified.

Environment

• duello (latest git)
• interatomic 0.5.0
• macOS (Apple Silicon)
• Default grid settings (2000 points, PowerLaw2)