Diamond Γ-CCM / χ-CCM bond and band comparison

Status: experimental

Both routes this input runs (the four-centre Γ-line drivers run_ccm_rhf_scalable / run_ccm_rks and the χ-CCM drivers) is an experimental route. Every Γ-line SCF driver emits vibeqc.AICCM2026DevAExperimentalWarning and every χ-CCM driver emits vibeqc.AICCM2026DevBExperimentalWarning; the .system manifest records method_status = "experimental" for every AICCM job run through run_periodic_job(method="aiccm", variant=...). Its numbers are research output, not validated results, and it is not part of the release gate. The label vocabulary is defined in Methods: theory and status.

This experimental input compares two distinct CCM development approaches on primitive diamond:

• aiccm2026dev-a, the Γ-CCM development line in vibeqc.periodic.ccm: Γ-CCM is the neutral finite-torus construction (variants real-gamma and neutral-bloch); the script’s Γ side runs the four-center variant, the 2014 union-and-weight/Wigner-Seitz lineage kept in the same line.

• aiccm2026dev-b, χ-CCM[1], the finite-translation-group character stream in vibeqc.periodic.chi.

The script writes the two property bundles side by side and explicitly marks the Γ-CCM/χ-CCM approach comparison not-defined. It does not form energy, band, charge, or bond-order deltas. A matched exchange-q=0 label is necessary but not sufficient to prove a common finite Hamiltonian.

The input is:

python examples/periodic/aiccm2026dev_diamond_bonds_bands_compare.py \
  --route both \
  --basis sto-3g \
  --functional pbe \
  --backend four_center \
  --extension 2 2 2

It writes all files below output/aiccm-diamond-compare/ by default:

• diamond-aiccm2026dev-a-vs-b-summary.json, with energies per primitive cell, finite-net gaps, Mulliken charges, C-C Mayer bond orders, band metadata, and occupied-localization diagnostics.

• diamond-aiccm2026dev-a-rhf.qvf and diamond-aiccm2026dev-b-rhf.qvf, containing the primitive structure, the HF band path, and QVF bond connectivity.

• diamond-aiccm2026dev-a-rks.qvf and diamond-aiccm2026dev-b-rks.qvf, the matching KS-DFT band and bond archives.

• diamond-aiccm2026dev-a-rhf-localized.qvf and diamond-aiccm2026dev-b-rhf-localized.qvf, finite-supercell localized occupied orbitals for visualization.

• PNG band plots when matplotlib is installed.

The default is a route smoke calculation, not a publication benchmark or an approach comparison. Do not quote cross-approach differences from this output. The band path is obtained from each route’s converged finite-torus Fock blocks: it is exact at the folded character net and an interpolation between those points. Converge it with respect to --extension.

Optional local-PNO summary

Add --with-b-pno-mp2 to run the χ-CCM local-PNO MP2 pilot after the SCF steps:

python examples/periodic/aiccm2026dev_diamond_bonds_bands_compare.py \
  --route b \
  --backend ri \
  --extension 2 2 2 \
  --with-b-pno-mp2

This writes diamond-aiccm2026dev-b-dlpno-mp2.json with PAO rank, translation-pair reduction, and local-PNO MP2 energy data. Full correlated natural orbitals from a relaxed correlated one-particle density matrix are not implemented in this input and should not be inferred from the PNO summary.

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[1]

Γ-CCM and χ-CCM are distinct CCM approaches. Γ-CCM is the neutral finite-torus construction with two producers, variant="real-gamma" and variant="neutral-bloch" (ruling R1, 2026-08-21); the four-center variant is the 2014 union-and-weight/Wigner-Seitz lineage, a different construction kept in the same aiccm2026dev-a development line. χ-CCM uses the finite-translation-group character construction. They are compared at a declared common exchange-q=0 convention. Their distinction is not a choice of Coulomb kernels, and equality for a specified operator/route is evidence to establish, not a naming premise.