Proof of the Density Variation Equation for Exact Density Functional Theory

What is it about?

We proved the existence of a rigorous variational equation for the energy functional that appears in DFT.

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Why is it important?

While the Levy-Lieb formulation excludes transition contributions implicitly via constrained minimization, our formulation renders this exclusion explicit and provides a concrete route to evaluate the functional. The result is obtained from the series of studies of: (1)"A Rigorous Expression of the Hohenberg-Kohn Universal Energy Functional Based on the Analysis of the Spatial Scaling Property of the Kohn-Sham Potential", T. Kato and S. Saito, J. Phys. Soc. Jpn. 94, 074303 (2025). (2)"Kohn-Sham potentials by an inverse Kohn-Sham equation and accuracy assessment by virial theorem ", T. Kato and S. Saito, J. Chin. Chem. Soc. 70, 554 (2023). (3)"Inverse Kohn-Sham Equations Derived from the Density Equation Theory", T. Kato, K. Nobusada, and S. Saito, J. Phys. Soc. Jpn. 89, 024301 (2020).