Joint work with Jacek Karwowski, Yvon Maday, Etienne Polack, and Andreas Savin.
The Hohenberg-Kohn theorem opened the path to density functional approximations. However, there is no clear prescription on how to construct them. Here, we try to open a new framework for designing approximations where density functionals were used.
The present work starts from the observation that the density functional approximations work well when they are used to correct a model system (the non-interacting Kohn-Sham system, or a more elaborate one).
As an alternative, this work explores two ways to correct the model errors:
i) extrapolating on a family of models, or
ii) exploiting a generalization of Kato's cusp condition.
For both variants, no density functional approximation is produced.
However, they both exploit an idea that is used to explain how density functional approximations work and how they are designed (the adiabatic connection).
In both cases the results are as good (or even better) than with density functional approximations - as long as the models are not too far from the target (from "ground truth"). In contrast to density functional theory, there is no restriction to the ground state, or to the property produced. However,
i) the method is more expensive than the Kohn-Sham method (costing as much as models that go beyond Kohn-Sham),
ii) numerical experience exists only for very small electronic systems.
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