Symmetry Reduction Implementation — Status & Handover

Last updated: 2026-05-23 | Phase: complete — all milestones shipped

Milestone Status

#	Milestone	Status
M1	symmetry=True primitive reduction	✅
M2	1e compute reduction (S, T)	✅
M2a	Wire M2 into 5 drivers	✅
M3	build_jk_gamma_molecular_limit_explicit	✅
M3b	build_jk_2e_real_space_explicit	✅
M3b	build_jk_pair_contributions (C++)	✅
M3b	compute_jk_gamma_reduced (Python)	✅ — origin-fixed cells only
M4	IBZ-native SCF (4 drivers)	✅
M5	symmetry_scf.py	✅
M5a	symmetry_stabilize in GDF	✅
SYM5	symmetrize_forces()	✅
—	Non-symmorphic support	✅ — diamond Fd-3m validated
SYM6	Character tables (Oh, Td, D4h, C6v)	✅

Known Limitations

1. M3b: origin-fixed cells only. compute_jk_gamma_reduced works for single-atom primitive cells (Mg, He) but not multi-atom cells (NaCl) — per-atom lattice shifts break cell-pair Wigner-D reconstruction. Verified: Mg J err 2.7e-15.

2. M2a: S/T template workaround. The GDF driver computes full S/T as a template when using the symmetry-reduced path, because pybind11’s LatticeMatrixSet has read-only nbf/cells/blocks. The ERI compute reduction is unaffected.

Module Map

Module	Purpose
symmetry_core.py	Wigner D-matrices (SYM1)
symmetry_ao.py	AO permutation matrices (SYM2a)
symmetry_lattice.py	Lattice-cell orbits (SYM2b)
symmetry_lattice_c.py	Atom-pair orbits (SYM2c)
symmetry_integrals.py	Storage-reduced 1e integrals (SYM3a)
symmetry_integrals_reduced.py	Compute-reduced 1e integrals (SYM3b)
symmetry_fock_reduced.py	Compute-reduced 2e Fock (M3b)
symmetry_scf.py	Group-averaging + force symmetrization (M5, SYM5)
symmetry_salc.py	Character tables + irrep projection (SYM6)
periodic_runner.py	symmetry/reduce_to_primitive/symmetry_reduce_fock kwargs
periodic_rhf_gdf.py	GDF driver with M2a/M5a/M3b integration
pbc_bipole*.py	BIPOLE drivers with M2a/M4 integration

C++ Changes

File	Addition
lattice_integrals.cpp	compute_1e_lattice_matrix_explicit + wrappers
periodic_fock.cpp	build_jk_gamma_molecular_limit_explicit, build_jk_2e_real_space_explicit, build_jk_pair_contributions
bindings.cpp	pybind11 for all above