Where the methods come from

The method families in ferric are not an arbitrary selection. Each one works on the response function from a different direction. The definitions and parameters live on the method pages; this page is the map.

Attenuated MP2: removing the long-range part

MP2's dispersion comes from an uncoupled response, which over-polarizes for systems with low-lying, highly polarizable excitations (π-stacked aromatics are the classic case); it is not a general property of polarizable molecules. In small basis sets the resulting overbinding is partly cancelled by basis-set superposition error, which disguises it.

Attenuated MP2 replaces \( 1/r \) in the correlation energy with a short-range operator (erfc or terfc) and fits its range to interaction energies in a chosen basis. It removes the long-range correlation entirely rather than correcting it, so it has no asymptotic \( C_6 \), and its parameters are specific to the basis and protocol they were fitted in. MP2-V restores long-range dispersion with VV10; RS-MP2 + LR-RPA restores it with long-range RPA.

Goldey & Head-Gordon (JPCL 2012) introduced it in aug-cc-pVDZ; Goldey, Dutoi & Head-Gordon (PCCP 2013) introduced terfc in aug-cc-pVTZ; the dual-attenuated SCS variant is Goldey & Head-Gordon (JPCB 2014). Operators, parameters and fitting protocol: The MP2 family.

PDEP-RPA and GW: compressing the response

The dielectric matrix is built from the density–density response function. ferric forms the independent-particle response in the RI auxiliary basis by summing over occupied–virtual pairs, then works in the eigenbasis of the static dielectric matrix, dropping eigenpotentials that carry almost no screening. PDEP (projective dielectric eigenpotentials) is that compression. It is the demonstrated part of the low-rank premise; the empty-state sum that feeds it is still there. See RPA, GW and excited states.

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. It also yields charge-localized diabatic states whose electron-transfer couplings \( H_{ab} \) follow from non-orthogonal determinant overlaps. See Constrained DFT.

What this buys

Three families, 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 what has and has not been measured.