engineering: integrate CASSCF orbital optimization into molecule registry (+80 mHa one-shot)

[thc1006]

TL;DR

N2 reference systems use HF (RHF) canonical orbitals by default. Switching to CASSCF-optimized orbitals lowers ground-state energy by ~80 mHa for the same active space, with no algorithmic change. Required for fair comparison against published SQD/NQS-SCI work that uses CASSCF orbitals.

Evidence

System	HF orbital best	CASSCF orbital best	Δ
N2-CAS(10,20) HCI gold	-109.21473	-109.30609	86 mHa
N2-CAS(10,20) HI-NQS-SQD	-109.21460	-109.29549	81 mHa

Source: nano4 historical bench_orbital_fair_163794.log (job 163794, 2026-04-13)

Why removed/missing

qvartools/molecules/registry.py builds Hamiltonians directly from PySCF SCF integrals — never invokes CASSCF orbital rotation. SCI baseline (-109.21034) shipped as reference is the HF-orbital SCI, not the gold standard.

Literature support

• JCTC 19:8 2023, "Complete Active Space Methods for NISQ Devices": "canonical orbital optimization is a key strategy for accuracy and noise resilience"
• Robledo-Moreno et al., Sci. Adv. 2025: IBM N2 SQD on 58 qubits used CASSCF orbitals (default in their workflow)
• Multiple multireference benchmarks confirm CASSCF orbitals mirror FCI dissociation curve closely

Proposal

Add orbital_basis: "rhf" | "casscf" field to MOLECULE_REGISTRY entries. When casscf:

1. Run PySCF CASSCF preprocessing (cache result) — typical wall ~7000s for CAS(10,20)
2. Use CASSCF MO coefficients to rotate one- and two-electron integrals
3. Build MolecularHamiltonian from rotated integrals

"n2-cas(10,20)": {
    "factory": _make_n2_cas_10_20,
    "orbital_basis": "casscf",   # NEW; default "rhf" for compat
    "casscf_cache_path": "~/.cache/qvartools/casscf/n2_cas_10_20.npz",
}

Impact

• Direct +80 mHa improvement on N2 benchmarks
• Required to compare with GTNN-SCI, ADAPT-QSCI, Robledo-Moreno SQD
• Without this, qvartools pipelines are systematically worse than published baselines by ~80 mHa

Effort: 1 week

• PySCF CASSCF wrapper + caching
• Integral rotation
• Registry field + factory updates
• Migration tests on H2/BeH2/NH3 (small) before scaling to 40Q