[wladerer]

What

Adds a new manual tutorial page, docs/manual/flapw-spectroscopy.md, covering the one big remaining manual coverage gap: the all-electron FLAPW engine (task: flapw) and the NMR/EFG/XPS spectroscopy subsystem (task: nmr).

The page

Three entry points, each with a minimal working YAML and api.run example built from the real *Params surface:

• task: flapw — all-electron muffin-tin SCF: Γ eigenvalues, convergence, and initial-state (XPS) core-level shifts.
• nmr.task=efg — all-electron FLAPW electric field gradient ($V_{zz}$, $\eta$, tensor) and quadrupolar coupling $C_Q$.
• nmr.task=shielding — the plane-wave/PAW + GIPAW magnetic-shielding production path: $\sigma$, chemical shift $\delta_\mathrm{iso}$, optional PAW EFG and powder-spectrum synthesis.

Each section documents the exact summary[...] keys returned, the shielding_level / efg / spectrum gates, and the flapw / nmr block keys with defaults.

Honest scope (as verified in the code)

• FLAPW is a dense $O(N^3)$ all-electron oracle for small cells and code-to-code validation — not a production large-cell engine.
• FLAPW absolute eigenvalues wander with the interstitial zero, so only splittings and within-cell shifts are physical (stated up front and repeated per section).
• The realistic-material property path is PAW+GIPAW, distinguished clearly from the FLAPW oracle throughout.
• Converged EFG magnitudes need the full potential (fullpot, Kerker, Newton polish, converged k); the smoke-tier defaults are for wiring, not physics.

Validation claims

All cited from committed tests: Ne/Ar $s$–$p$ splittings vs Elk 11.0.2 (test_flapw_scf.py), corundum ²⁷Al EFG vs Elk (~118 %, ±35 % band, test_flapw_efg_vs_elk.py), core-level shifts (test_flapw_core_levels.py), and GIPAW core-Lamb / diamagnetic-augmentation anchors (test_gipaw.py). No numbers invented.

Nav

Adds an All-electron and spectroscopy subsection to the Tutorials tree.

Checks

• make doc-refs — clean (all path references resolve).
• mkdocs build --strict — clean, exit 0.

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