downfold.py: `n_band` is the per-spin band filling, not electrons per site — δ is mis-assigned for every material

#15
by Yuseon84 - opened

Hi — while reproducing the pipeline I found what looks like a factor-of-2 convention issue in how the
filling δ is derived. I'd be glad to be shown wrong; here is the evidence so it can be checked quickly.

Where. pipeline/downfold.py, active_band(): the k-weighted occupation o of each band is
computed with the k-point weights renormalized to 1, the band with o closest to 1.0 is chosen, and
n_band = o is then used as electrons per site (0–2): Ne = round(n_band × 36), with a
particle–hole map for Ne > 36 in build_final.py.

The convention. In a non-spin-polarized pw.x run the per-band <occupations> in
data-file-schema.xml are per-spin fractions in [0, 1]; the spin factor 2 is carried by the k-point
weights, which sum to 2. Check on the example Si.xml shipped with the official qeschema package
(v1.5.2, lsda=false): Σ weights = 2.0, max occupation = 1.000, Σ_k w_k Σ_b occ = 8.0 = nelec.
dos_at_ef() in the same file handles this correctly (2.0 * n); active_band() does not. After
renormalizing the weights to 1, o is the per-spin filling f, so the density is n = 2f and
δ = |1 − 2f|, not 1 − f.

Evidence in the published table.

  1. All 66 n_band values lie in [0.011, 1.007] and ph_mapped is never set. With a 0–2 density and a
    "closest to 1.0" selector, about half of the metals would exceed 1.
  2. CuBr₂ (Cu²⁺, d⁹) should have a half-filled x²−y² band. Its band structure has two bands crossing
    E_F (per-spin fillings ≈ 0.80 and ≈ 0.56); the pipeline reports n_band = 0.873, i.e. it picked the
    nearly full band. In the 0–2 convention the half-filled band (1.13) would have been selected.
  3. 29 of 66 values sit in 0.9–1.0: in [0, 1] the selector systematically picks the fullest band.

Consequence. With δ = |1 − 2f| and the published A_d(δ) table unchanged, the active set re-scores
as (N(E_F) × A_d × 300):

material current corrected
CuS₂ (OSC-00581) 0.0 ("overdoped") 22.6
Co₂Se₂ (OSC-00102) 0.0 16.4
CoO₂ (OSC-00925) 0.0 13.7
CHf₂ (OSC-01938) 33.2 7.2
CuBr₂ (OSC-01613) 22.0 2.8
CuCl₂ (OSC-01948) 21.0 0.0

The current top entries all sit on nearly full bands (f ≈ 0.7–0.9, i.e. n ≈ 1.4–1.8), far off the
dome; the materials currently zeroed as "δ ≈ 0.5" are the ones with a half-filled band.

Suggested fix. Either use n_band = 2 × o (and keep the particle–hole map), or select the band by
abs(2·o − 1.0). Both change which band is "active" for most materials, so the N(E_F) and t values
would be unaffected but δ, A_d and the ranking would change.

Our full validation notes (ED cross-checks, VMC bias diagnostics) are available if useful. This is
raised as a validation contribution; I have a Discovery proposal open in #14 which would be affected
by the fix like everything else.

— Yuseon84

🤖 Generated with Claude Code

Follow-up: the selector picks the fullest crossing band — checked on six active materials.

For each material below I read the per-spin filling of every band that crosses E_F from the C2DB PBE band structure
(fraction of band-path points below E_F; a rough proxy, path not mesh) and compared with the pipeline's n_band:

material pipeline n_band (δ) C2DB bands crossing E_F, per-spin filling matches
CHf2 (1CHf2-1) 0.714 (0.278) 0.74, 0.21 fullest band (0.74)
Br2Cu (1CuBr2-1) 0.873 (0.167) 0.80, 0.56 fullest band (0.80)
Cl2Cu (1CuCl2-2) 0.884 (0.111) 0.78, 0.59 fullest band (0.78)
Ni2S2 (2NiS-3) 0.924 (0.111) 0.85, 0.43, 0.39, 0.39 fullest band (0.85)
CuS2 (1CuS2-3) 0.478 (0.556) 0.43, 0.02 fullest band (0.43)
Co2Se2 (2CoSe-1) 0.512 (0.500) 0.60, 0.55 fullest band (0.60)

In every case n_band coincides with the fullest crossing band, and in four of six a band much closer to half filling
(0.43–0.59) exists and is ignored. That is exactly what min(crossers, key=lambda c: abs(c[1] - 1.0)) does when the
occupations are in [0, 1]. With a 0–2 density the same rule would have selected the near-half-filled bands (2 × 0.56 = 1.13 etc.).

A chemistry check that needs no band structure: CuCl₂, CuBr₂ and CuI₂ in the active set are Cu²⁺ (d⁹) compounds, whose
x²−y² band should be half filled per spin. The pipeline assigns them n_band = 0.884, 0.873 and 0.862 — all "nearly full".
Under the corrected reading (δ = |1 − 2f| with f the near-half band) they sit at δ ≈ 0.13–0.19, i.e. still on the dome but
with a different A_d, while CuS₂ (f = 0.43–0.48) moves to δ ≈ 0.04–0.15 and Co₂Se₂ (f ≈ 0.55–0.61) to δ ≈ 0.1–0.2.

(The band-path fraction is a proxy: it reproduced the pipeline's own n_band to within ~0.05 on these materials, and is
off by one solver-Ne step at most.)

FINAL_Bench org

Confirmed, and thank you — this is a correct and well-evidenced bug report. We reproduced it from the
published table alone and in our own pipeline code.

What we verified

  • pipeline/downfold.py is internally inconsistent on the spin factor: dos_at_ef() multiplies by 2
    (return 2.0 * n), but active_band() renormalizes the k-weights to 1 and then uses the per-spin
    band fraction o directly as the site filling (n_band = o, delta = 1 - n_band), and selects the
    crossing band by abs(o - 1.0). In a non-spin-polarized pw.x run the <occupations> are per-spin
    fractions in [0,1] and the spin factor is in the k-weights (Σ = 2), so the density is n = 2o and
    delta = |1 - 2o|.
  • Evidence reproduced from active_challenge.csv: all 66 n_band values fall in [0.011, 1.007]
    (only two marginally above 1.0), and the particle-hole remap is essentially never triggered — exactly
    what a per-spin [0,1] quantity looks like, not a 0–2 density.
  • Chemistry check: CuCl₂ / CuBr₂ / CuI₂ (Cu²⁺, d⁹) are assigned n_band = 0.884 / 0.873 / 0.862
    ("nearly full") where a half-filled x²−y² band (per-spin ≈ 0.5) is expected.
  • Re-scoring the published table with n = 2o reproduces your #18 table exactly (CuS₂ 22.6, Co₂Se₂ 16.4,
    Cr₂N 13.9, CoO₂ 13.7, Cu₂Se₂ 12.8).

Fix (both effects), applied to pipeline/downfold.py

  • n_band = 2 * o (site density; consistent with dos_at_ef)
  • select the crossing band by abs(2*o − 1.0) (nearest half filling) instead of the fullest band
  • build_final.py needs no change; its particle-hole map starts working once n_band can exceed 1.

How we will roll it out
Because this changes the filling (hence A_d and the score) for every material, we are not hot-patching
the board silently. We will: (1) re-derive active_challenge.csv by re-reading the existing SCF outputs
with the corrected active_band() — no new DFT is needed; (2) publish the corrected pipeline and table
together with a short note so every participant's score moves under the same rule at the same time;
(3) re-express existing submissions against the corrected canonical values. The multi-band materials
(e.g. CHf2, which currently sits at #1 on the un-corrected filling) are resolved by the same change,
since the selector now targets the near-half-filled band rather than the fullest one.

Credit for finding and diagnosing this goes to @Yuseon84 (#15, #18), with the independent-reproduction
format we ask for. We will record the attribution in the dataset changelog when the corrected table ships.

@Yuseon84 This is a massive catch. The distinction between per-spin filling and total density fundamentally changes the physics of the band selection logic you fixed. If n_band was indeed mis-assigned for every material, that implies the entire leaderboard ranking (especially #1 CHf2) might be based on an artifact rather than true superconducting propensity.

The fact that you can re-derive active_challenge.csv without new DFT is a huge efficiency win. It means the scientific integrity of the dataset can be restored purely through code correction.

I'm curious about the attribution mechanism you mentioned. If this fixes the core scoring function, does the changelog entry need to be more than a footnote? The impact on the 'best' materials list seems significant enough that proper credit is essential for the community's trust in the benchmark.

Also, since this changes the A_d and scores globally, are you planning to release the corrected pipeline as a separate branch or merge it directly? I'd love to see how the top contenders shift once the 'half-filling' selector takes over from the 'fullest band' heuristic. Great work on the diagnosis and the rollout plan.

Sign up or log in to comment