2022-04-27 15:00  P5A-1/Online

[Journal Club] The complete inverse Kohn-Sham problem: from the density to the energy

Herlik Wibowo

In 1964, P. Hohenberg and W. Kohn proposed two fundamental theorems, known as the Hohenberg-Kohn (HK) theorems, which became the foundation of density functional theory (DFT). The first theorem states that, for a quantum many-body system of interacting particles under an external potential, there is a one-to-one correspondence between the ground state density of the system and the external potential. The first theorem asserts the existence of the universal functional and that the ground state energy of the system can be expressed as an energy density functional (EDF). The second theorem guarantees that the EDF has its minimum value at the exact ground state density, and this value corresponds to the exact ground state energy. The main challenge of the DFT is that the HK theorems do not provide any clue on how to build an EDF. In the direct Kohn-Sham scheme to solve the DFT problem, a form of EDF is assumed, and the Kohn-Sham potential is derived from this EDF. The auxiliary single-particle orbitals with the same ground state density as the true interacting system are obtained by solving the Kohn-Sham equation with the corresponding Kohn-Sham potential. In this journal club, I will present a paper titled "The complete inverse Kohn-Sham problem: from the density to the energy" [arXiv:2110.11193]. As suggested by the name, the inverse Kohn-Sham problem refers to the construction of the EDF from the knowledge of the ground state density. I will discuss the method proposed by the authors to obtain the complete solution to the inverse Kohn-Sham (KS) problem.

arXiv:2110.11193