Rigorous expressions for eneries as explicit functionals of the exact electron density n_exact(r)

What is it about?

Building upon the line-integral reconstruction methodology for energy functionals introduced by van Leeuwen and Baerends [1], this work presents rigorous expressions for the kinetic energy functional T_s[nexact] of the Kohn-Sham (KS) system and the Hohenberg-Kohn (HK) universal functional F_HK[nexact], in which both quantities are formulated as explicit functionals of the exact electron density n_exact(r). These functionals are obtained via the inverse KS procedure[2,3], which serves as a key intermediate step in the derivation, thereby establishing their dependence on the electron density. Once the forms of T_s and F_HK are determined, further quantities such as the exchange-correlation energy functional E_xc[n_exact] can be systematically derived. To substantiate the proposed formalism, numerical demonstrations are carried out for one-dimensional model systems, including He and H2 molecules. Moreover, a variational formulation of the total electronic energy based on the line-integral approach is proposed. [1] R. van Leeuwen and E.J. Baerends, Phys. Rev. A 51, 170 (1995). [2] T. Kato, K. Nobusada, and S. Saito, J. Phys. Soc. Jpn. 89, 024301 (2020). [3] T. Kato and S. Saito, J. Chin. Chem. Soc. 70, 554 (2023).

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Why is it important?

This work presents rigorous expressions for the kinetic energy functional T_s[n_exact] of the Kohn-Sham (KS) system and the Hohenberg-Kohn (HK) universal functional F_HK[n_exact], in which both quantities are formulated as explicit functionals of the exact electron density n_exact(r).