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 object of interest appears under several names depending on which perturbation you apply:
| Perturbation | Response object |
|---|---|
| Uniform electric field | Polarizability \( \alpha \) |
| Density fluctuation | Susceptibility \( \chi \) |
| Screened Coulomb interaction | Dielectric function \( \varepsilon \) |
| Constraint potential | \( \partial N / \partial \lambda \) |
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 motivating 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 matrix 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, then organizing the computation around response should make it cheaper: attenuate the operator, keep the dominant dielectric modes.
What is actually demonstrated
This is where honesty matters more than the pitch.
The low-rank half is demonstrated. PDEP's compression of the dielectric matrix works and is used in production paths — see RPA and GW. Keeping only the dominant eigenmodes removes the explicit sum over empty states that conventional RPA and GW require.
The real-space locality half remains a design premise, not a measured result. Several attempts to exploit it are implemented and measured negative:
- The AO-sparse Laplace SOS-MP2 variant's truncation radius tracks the molecular diameter instead of saturating — so it is not a reduced-scaling path.
- Local MP2 (amplitude-threshold) is implemented with localized virtuals and per-pair domain-local RI fits, but the J build is still dense-from-RI, so no scaling claim is made.
- RI-Laplace MP2 is dense; it serves as a correctness reference for the AO formulation, not as an O(N) path.
Those are reported as negative results rather than quietly omitted, because a locality claim that has not survived measurement is not a feature.
Why this framing is useful anyway
Even where the scaling payoff has not materialized, the response framing buys something concrete: it makes the error in one method diagnosable through another.
MP2's dispersion error is the clearest case. MP2 builds dispersion from an uncoupled polarizability, which over-polarizes — giving \( C_6 \) coefficients that are too large and overestimated π-stacking. That is not a mysterious failure of a wavefunction ansatz; it is a specific, identifiable defect in a response function, and it suggests a specific fix: attenuate the correlation operator so the over-polarizing long-range part is damped.
That is attenuated MP2, and it works for a reason the response picture predicts.