Electronic response

ferric is organized around electronic response: how the electron density reacts to a perturbation. Standard quantum-chemistry codes are usually organized around a hierarchy of wavefunction ansätze (HF → MP2 → CCSD → CCSD(T)). That is a perfectly good organizing principle. It is not the one used here.

The central object appears under several names depending on which coupling you look at:

Object	Definition	Where it appears in ferric
Density response \( \chi \)	\( \chi = \delta\rho / \delta v_{\text{ext}} \); \( \chi_0 \) is its independent-particle form	RPA, GW, MP2's dispersion
Dielectric matrix \( \varepsilon \)	\( \varepsilon = 1 - v\chi_0 \) (RPA), with \( v \) the Coulomb kernel	PDEP-RPA and GW screening
Polarizability \( \alpha \)	response of the dipole to a uniform field; \( \alpha(i\omega) \) gives \( C_6 \)	polarizabilities, dispersion coefficients
\( \partial N / \partial \lambda \)	charge moved per unit constraint potential	constrained DFT

These are the same physics viewed through different couplings. A code that computes one well should be able to compute the others, and errors in one should be diagnosable as errors in the others.

The claim

The premise behind the architecture is that response is:

Local in real space: a density fluctuation here does not much affect the density far away, so the response should be sparse in a localized basis.
Low-rank in its eigenspectrum: the dielectric matrix has a small number of dominant eigenmodes, so it can be compressed without losing the physics.

If both hold, organizing the computation around response should make it cheaper: attenuate the operator, keep the dominant dielectric modes.

What is actually demonstrated

Low rank: demonstrated, and narrower than it sounds. PDEP compresses the dielectric matrix to its dominant eigenpotentials in the RI auxiliary space, and that works in production paths; see RPA and GW. It does not remove the sum over empty states: ferric builds \( \chi_0 \) by summing over every occupied–virtual pair, and PDEP compresses what comes out of that sum.

Locality: one positive result, still without a speedup.

AO-sparse Laplace SOS-MP2. Restricting each localized orbital's pseudo-density to an AO domain works: the radius needed grows far more slowly than the molecule (chemical accuracy at 3 to 5 Bohr from ethane to dodecane, while radius/diameter falls from 0.52 to 0.17; within 0.05% at 4 Bohr on a 71-atom drug molecule). The tensor algebra is still dense, so no timing gain is claimed. This result is specific to that formulation and does not carry over to the other locality lanes below. The test sos_ao_sparse_truncation_radius_is_transferable_across_sizes pins the STO-3G butane/octane comparison (12 Bohr exact on both; octane worse at 3 Bohr). The C2-C12 sweep and the drug-molecule figure are measurements, not regression tests.
Local MP2 (amplitude threshold) has localized virtuals and per-pair domain-local RI fits. The integral-direct variant (rimp2 with [local] integral_direct = true) is measured at about N^1.24 (erfc) to N^1.4 (Coulomb) on alkanes C20–C48, three points in one basis, so the reading is provisional. Local MP2 without integral_direct still builds the global 3-index tensor and makes no scaling claim.
RI-Laplace MP2 is dense; it is the correctness reference for the AO formulation, not a reduced-scaling path.

The locality premise is therefore partly supported and not yet cashed in as cost. Measured limits are kept on Capabilities and validation.

Why this framing is useful anyway

Even where the scaling payoff has not arrived, the response framing makes the error in one method diagnosable through another.

MP2's dispersion is the clearest case. Its dispersion energy is built from an uncoupled (uncoupled Hartree–Fock) response, in which the density fluctuation does not feel the field it creates. For systems with low-lying, highly polarizable excitations, such as π-stacked and other π systems, that uncoupled response over-polarizes, and MP2 overbinds. This is documented in the literature that replaces MP2's uncoupled dispersion with a coupled one (Cybulski & Lytle 2007; Heßelmann 2008; Pitoňák & Heßelmann 2010). The size of that coupling correction varies from system to system, and ferric has no coupled-dispersion (MP2C-style) implementation of its own, so read this as the literature's diagnosis, not a ferric measurement.

Attenuated MP2 takes a blunter route: it removes the long-range correlation altogether and relies on a fitted short-range operator plus the basis-set error it is fitted in. That is why it has zero asymptotic \( C_6 \), why its parameters belong to one basis, and why MP2-V adds long-range dispersion back through VV10. RS-MP2 + LR-RPA puts the long-range part back through response instead. See The MP2 family.