A practical functional that obeys the flat-plane condition · revision history

Revision 2

Accepted · core change · record

Changes against revision 1:

Title
A practical functional that obeys the flat-plane condition
Plain
The exact energy changes in straight lines when a fraction of an electron is added or when spin is fractionally shared, and approximate functionals bend those lines. Bending one way spreads electrons out too much; bending the other way mistreats stretched bonds.
Precise · changed · core
Revision 1: Construct an exchange-correlation approximation, at cost no higher than a global hybrid, whose energy $E(N, S_z)$ is piecewise linear in fractional electron number N (no delocalization error) and constant in fractional spin at fixed N (no static correlation error), as tested on H2+ and H2 dissociation, fractional-charge atoms and the stretched-bond benchmark sets, while keeping main-group thermochemistry errors below 3 kcal/mol. An answer is such a functional, or a proof that no functional of a given class can satisfy both conditions.
Revision 2: Construct an exchange-correlation approximation, at cost no higher than a global hybrid, whose energy $E(N, S_z)$ is piecewise linear in fractional electron number N (no delocalization error) and constant in fractional spin at fixed N (no static correlation error), as tested on H2+ and $\mathrm{H_2}$ dissociation, fractional-charge atoms and the stretched-bond benchmark sets, while keeping main-group thermochemistry errors below 3 kcal/mol. An answer is such a functional, or a proof that no functional of a given class can satisfy both conditions.
Settled by
A functional passing fractional-charge, fractional-spin and standard thermochemistry benchmarks simultaneously, or a no-go theorem for a defined functional class.
Kind
well-posed
Answer type
identification
References
(empty)
Literature status
partially-resolved
Status note
In 2021 the DM21 learned functional, trained on fractional-charge and fractional-spin data, reduced both errors for small systems; no functional satisfies both conditions in general.
Posed since
(empty)

Decisions