Analytical form of the exact exchange–correlation functional in Kohn–Sham DFT

Determine the analytical form of the exact exchange–correlation density functional in Kohn–Sham density functional theory that yields the exact exchange–correlation energy for a given electron density, in order to replace current approximate forms used in practical computational chemistry.

Background

Density functional theory (DFT) is widely used in computational chemistry due to its balance of accuracy and computational cost, but its reliability hinges on the exchange–correlation (xc) density functional. While the existence of an exact xc functional is theoretically guaranteed, practitioners rely on approximate, often semi-empirical functionals because the exact form is not available.

The paper emphasizes that although approximate xc functionals can be effective—often due to error compensation—they lack systematic improvability and complicate rigorous uncertainty quantification. Establishing the analytical form of the exact xc functional would resolve a foundational uncertainty in DFT and potentially improve both accuracy and reliability across chemical applications.

References

Although an exact xc functional can be shown to exist, its analytical form is not known and would probably also be too involved for efficient computational chemistry approaches.

— A New Paradigm for Computational Chemistry  (2604.01360 - Husistein et al., 1 Apr 2026) in Section 1 (Introduction), page 2