diag(flapw/xps): stage-2a Madelung deficit attribution (report, no Coulomb-layer change)

[wladerer]

Stage 2a — diagnose the wrong-signed within-cell O1s core-level shift

Diagnosis only. No src/ changes — this adds reproducers + a findings doc
(experiments/autoapw/xps_madelung_stage2a.md) and stops short of a _weinert_multi
change, per the stage-2 guardrail. For review, not auto-merge.

What was asked vs what was found

The task premise was that the entire ~2 eV C0_ext deficit lives in
scf._weinert_multi (the interstitial Weinert reconstruction). Direct comparison of the
interstitial Coulomb potential against matched-basis Elk 11.0.2 shows the premise is only
partly right: the Weinert layer is the smaller cause.

Confirmed gap (both codes, same decomposition, matched basis)

O R_MT (Bohr)	gradwave dC0_ext	Elk dC0_ext	gap
1.00	+0.736	+2.903	2.17
1.40	+2.814	+4.794	1.98

In-sphere O charges match, so the analytic own-monopole term matches; the whole gap is in
v_hart's l=0 surface value. Elk's VCLIR is nearly flat (~+1.4 eV) across the interstitial;
gradwave's v_hart swings −3..−20 eV between the atoms — corrupted.

Two independent causes

1. Dominant (~1.3–1.45 eV): Ti sphere charge (a semicore choice, not Coulomb). At
   matched R_MT (1.70075 Bohr) gradwave's Ti holds ~0.8 e more than Elk (19.52 vs 18.67–18.75)
   because _CORE["Ti"] freezes the Ti 3s as localized core while Elk treats 3s as valence.
   A less-negative Ti weakens the near/far-O Madelung-field difference. Not fixable in
   _weinert_multi.
2. Secondary (~0.4–0.7 eV): unmasked interstitial density. gradwave feeds the full
   plane-wave density to _weinert_multi (+25..+32 e continuation inside the small Ti MT →
   a −27 e deficit pseudocharge, catastrophic cancellation); Elk masks ρ_I to the interstitial
   (rhoir = 0 in MTs, measured). Masking recovers part of the gap; the unmasked variant is
   grid-converged at the wrong value.

Scaling gradwave's Ti charge to Elk's with masking reproduces Elk (+4.82 vs +4.79 at
R 1.40), confirming the attribution.

Why nothing is merged

No single _weinert_multi change reaches the target (Elk +2.90/+4.79 + O1s sign flip), and
the masking prototype changes v_hart everywhere — hence the l=2 EFG lattice term — with
unverified EFG impact (and the naive real-space mask aliases). Per the guardrail, the Coulomb
layer is left untouched.

Follow-up levers (owner decision)

• Mask ρ_I inside _weinert_multi with a band-limited Θ_I and re-converge (does the SCF
  feedback also pull the Ti charge toward Elk's?), gated on an EFG (corundum V_zz, torture)
  re-validation.
• Treat Ti 3s as valence (the dominant lever) — a semicore change with its own EFG/core-level
  consequences; belongs in its own investigation.

Full numbers, mechanism, and reproduce commands in experiments/autoapw/xps_madelung_stage2a.md.

🤖 Generated with Claude Code

https://claude.ai/code/session_018j6BBnPtBSjkrnASSc52mT