AICCM2026DEV-B (experimental)

aiccm2026dev-b is the independent AICCM implementation. It is deliberately separate from aiccm2026dev-a: the selectors, core mathematics, tests, examples, and handovers do not alias one another. Agreement between them is evidence; it is not built in.

The B stream defines a finite Born–von Karman translation group from a real-space lattice extension. Its full Gamma-centered character net is then derived exactly. It minimizes RHF/RKS or UHF/UKS energy over translation-commuting idempotent spin densities. Wigner–Seitz weights select only tied representatives of one translation class. They are not multiplied into an otherwise non-periodized three- or four-center tensor.

Run it

result = vq.run_periodic_job(
    system,
    basis,
    method="RKS",
    functional="pbe0",
    jk_method="aiccm2026dev-b",
    aiccm_lattice_extension=(2, 1, 1),
    aiccm_backend="ri",  # "four_center", "ri", or "rijcosx"
)

check = result.aiccm2026dev_b
print(result.energy)
print(check.density_idempotency_error, check.electron_count_error)

aiccm_wigner_seitz_shells=2 is the radius-style alternative. It produces five primitive translations in every active direction, from (-2) through (+2), and hence an odd cyclic extension of five. The legacy kpoints= tuple is retained as an exact alias, but it is not a second convergence parameter.

The direct SCF APIs are run_aiccm2026dev_b_rhf, run_aiccm2026dev_b_rks, run_aiccm2026dev_b_uhf, and run_aiccm2026dev_b_uks. Every invocation emits AICCM2026DevBExperimentalWarning.

Canonical RI-MP2 is available in 3D through run_aiccm2026dev_b_mp2(system, basis, lattice_extension). It uses B’s own RI-RHF orbitals and pair-resolved three-center tensors. It does not route through the older Gamma-supercell post-HF helper because that helper has a different finite HF energy. MP2 fails closed in 1D/2D until their long-range gauges are matched.

The same 3D B Hamiltonian is available through run_aiccm2026dev_b_dlpno_mp2, run_aiccm2026dev_b_dlpno_ccsd, and run_aiccm2026dev_b_dlpno_ccsd_t. These routes inverse-transform the pair-resolved RI factors to the complete real finite torus; they do not run a different Gamma-supercell SCF. The total finite-torus correlation energy is divided by the number of cyclic cells exactly once.

run_aiccm2026dev_b_ccsd and run_aiccm2026dev_b_ccsd_t select the canonical-occupied, complete-domain, zero-threshold limit explicitly. They use the same finite-torus contractions as the local route and are validation oracles, not a second Hamiltonian.

The default occupied localization is PBC-safe Pipek–Mezey. Molecular Boys localization is rejected. The B-only localise="wannier" and localise="iao" options feed the finite-torus localized occupieds into the same PAO/PNO pipeline. The Wannier spread is currently a projected circular AO-centre approximation; the IAO cross overlap is not yet periodized across the supercell boundary. PNO truncation is available, but pair-distance screening, finite occupied-coupling radii, and local auxiliary fitting fail closed until their domains use minimum-image periodic distances. Use localise="none", zero PNO/domain thresholds, all pairs, and complete occupied coupling to reach the canonical finite-torus validation limit. At that MP2 limit, the result exposes raw_local_e_corr_per_cell and the independent complete_space_correction_per_cell audit.

The unrestricted 3D counterparts are run_aiccm2026dev_b_ump2, run_aiccm2026dev_b_uccsd_t, run_aiccm2026dev_b_dlpno_ump2, and run_aiccm2026dev_b_dlpno_uccsd_t. Alpha and beta occupied projectors are localized independently. The full-domain UCCSD(T) implementation is the explicitly cost-capped O(N^6) correctness oracle from the DLPNO stack, not a claim of production reduced scaling. The truncated route uses PNO subspaces, but representative-only pair propagation remains disabled.

derive_aiccm2026dev_b_scf_properties reports electron and spin counts, Mulliken charge/spin populations, finite-net band gaps, idempotency, and spin contamination. Periodic cell dipoles, Berry-phase polarization, analytic response, and correlated properties without a relaxed correlated one-particle density fail closed.

Space-group analysis is opt in with symmetry_mode="diagnostic" on the direct APIs or aiccm_symmetry="diagnostic" on run_periodic_job. It attaches the spglib group, exact cluster-compatible subgroup, atom/cell maps, and irreducible k orbits without changing the SCF build. The integrals mode fails closed until general-k sewing matrices and shell-quartet scatter pass energy and Fock parity.

Electron-repulsion backends

Backend	Coulomb	Exact exchange	Current purpose
four_center	direct periodic four-center build	direct periodic four-center build	definition-level check
ri	pair-resolved periodic three-center fit	pair-resolved fitted exchange	scalable RI reference
rijcosx	same RI-J	chain-of-spheres exchange	faster HF and hybrid KS trial route

All three run for neutral restricted and unrestricted 1D, 2D, and 3D cells. The derived character net is Gamma-centered. RIJCOSX currently requires at least two cyclic cells. Post-HF remains 3D-only until the lower-dimensional long-range gauges are matched.

Dimensional Coulomb conventions

The finite translation-group identity is dimension independent. The Coulomb kernel is not. The current 3D four-center route uses the neutral Ewald J split and the Ewald exact-exchange finite-size correction. The 1D and 2D four-center routes use the native direct-truncated lower-dimensional gauge. The periodic RI routes use their own dimension-aware fitted metric.

Consequently, a lower-dimensional four-center energy and RI energy are not yet an absolute-energy parity pair. They solve finite Hamiltonians with different long-range conventions. Both routes run and satisfy their internal density invariants, but matched 1D wire and 2D slab Green functions remain an acceptance item. The code does not disguise this mismatch with damping or a fitted offset.

What is checked on every result

• Wigner–Seitz representative weights sum to one for every translation class.

• A restricted density obeys \(DSD=2D\); unrestricted spin densities obey \(D^\sigma S D^\sigma=D^\sigma\) independently.

• The weighted total and spin-resolved electron counts match the cell.

• The inverse Bloch transform has a negligible imaginary residual for the Gamma-centered character mesh.

These checks establish internal consistency, not thermodynamic-limit accuracy. Converge the cyclic lattice extension and compare against a matched reciprocal-space calculation before using a number quantitatively.

Separate examples and theory

• Worked B-stream tutorial

• B-only occupied localization

• B-only symmetry diagnostics

• examples/periodic/aiccm2026dev_b_demo.py

• examples/periodic/aiccm2026dev_b_mp2.py

• examples/periodic/aiccm2026dev_b_local_correlation.py

• examples/regression/benchmark_aiccm2026dev_b.py

• Complete B-stream fleet inputs

• Independent derivation

• Decisions and open questions

The comparative manuscript is the detailed theory record. It includes the historical ab-initio weighting, the Janetzko–Köster–Salahub deMon2k KS-ADFT construction, both 2026 development streams, and the reciprocal-space reference formulation.