Where the methods come from

The three method families in ferric are not an arbitrary selection. Each one attacks the response function from a different direction.

Attenuated MP2 — fixing a response error

MP2 correlation is built from an uncoupled polarizability. Uncoupled means the density fluctuation does not feel the field it creates: there is no self-consistency in the response. The result over-polarizes, which shows up as:

• \( C_6 \) dispersion coefficients that are too large
• overestimated π-stacking energies
• basis-set superposition error that partly cancels the overestimate, disguising the problem in small basis sets

Attenuating the correlation operator — replacing \( 1/r \) with \( \mathrm{erfc}(\omega r)/r \) or a terfc form — damps the long-range part where the uncoupled approximation is worst, with a single tunable parameter.

This is Goldey & Head-Gordon (JPCL 2012); the dual-attenuated SCS variant is Goldey, Dutoi & Head-Gordon (PCCP 2013). See The MP2 family.

PDEP-RPA and GW — compressing the response

The dielectric matrix is the density–density response function. Conventional RPA and GW evaluate it through an explicit sum over empty orbital states, which is expensive and converges slowly with basis size.

PDEP — projective dielectric eigenpotentials — builds a low-rank basis from the dominant eigenmodes of the dielectric matrix instead. Because the spectrum decays quickly, a modest number of modes captures the physics, and the sum over empty states disappears.

This is the part of the locality-and-low-rank claim that is actually demonstrated in this codebase. See RPA and GW.

Constrained DFT — reading the response

A cDFT constraint couples a Lagrange multiplier \( \lambda \) to a fragment-weighted density operator. The derivative \( \partial N / \partial \lambda \) — how much charge moves per unit constraint potential — is a susceptibility.

That makes cDFT a direct probe of the same object, and it yields charge-localized diabatic states whose electron-transfer couplings \( H_{ab} \) follow from non-orthogonal determinant overlaps.

See Constrained DFT.

What this buys

Three methods, one object. An error in the polarizability shows up as an error in dispersion, in screening, and in charge-transfer coupling — so a fix validated in one place has predictable consequences in the others.

That is the design bet. Whether it pays off in cost is still open (see Electronic response for the measured negatives); that it pays off in diagnosis is already clear.