Coupled cluster

RI-based coupled cluster, validated against exact-integral and PySCF references.

What exists

  • RI-CCD — doubles only
  • RI-CCSD — singles and doubles
  • (T) — the perturbative triples correction

H2O/cc-pVDZ CCSD(T) matches PySCF to roughly 1e-6 Ha.

CLI coverage is partial

Only method.kind = "ccsd" is wired into the CLI — see examples/water-ccsd.toml. CCD and CCSD(T) are library/Python-only:

ccd    = ferric.run_ccd(mol, bs, aux)
ccsd_t = ferric.run_ccsd_t(mol, bs, aux)

LinLCCD

Linearized hole-hole ladder CCD, closed-shell only. Its main use here is as the correlation component of wB97X-L-V — a double hybrid that converges its own KS reference and then adds a short-range LinLCCD(hh) correction, rather than the MP2 correction a conventional double hybrid uses.

The [dft] lambda and omega keys override the published 0.6 / 0.1 Bohr⁻¹ values; omitting them gives the published parameters.

Implementation

All contractions route through einsum!, a macro that maps tensor contractions onto BLAS3 GEMMs. That matters for performance: the alternative — many small explicit loops — leaves most of the machine's throughput unused.

The permutation copies that feed those GEMMs are parallelized. This is less trivial than it sounds: for a strided permutation the copy can dominate the contraction it feeds — measured at 47% at nv=40 and 70% at nv=80, since it is memory-bandwidth-bound and gets relatively worse with size.

Those copies are bit-identical regardless of thread count. A permutation is pure data movement — every output element written exactly once — so unlike a reduction there is no summation order to perturb. That property is pinned by a test that has been verified to fail when deliberately broken.

Memory

The amplitude tensors dominate, and they grow as \( n_o^2 n_v^2 \) — or \( (2n_o)^2 (2n_v)^2 \) in the spin-orbital drivers. Memory budgets are enforced: an oversized job is refused with a breakdown naming the dominant term rather than being OOM-killed midway.

The DLPNO family additionally reads its own budget, which it previously ignored.